Tuesday, January 1, 2008


Marine Engineering Design

Chapter 1 Basic Concepts

Chapter 2 Engine Matching and selection

Chapter 3 Matching of ships, propellers and engine

Chapter 4 Gear design

Chapter 5 Shafting system

Chapter 6 Vibration problems on shafting

Chapter 7 Bearings

Chapter 8 Propellers

Chapter 9 Vibration

Chapter 10 Reliability concept on marine engineering

Chapter 11 Weight-Based Designs

Chapter 12 Machinery Selection

Chapter 13 Cost Estimating

Chapter 1

Basic Concepts

1.1 Historical Perspective

In or about 1712, Thomas Newcomen, an enterprising blacksmith from Dartmoor, England, successfully developed a rudimentary steam en¬gine for pumping water out of mines. This engine con¬sisted essentially of a single-acting piston working in a vertical open-topped cylinder. The piston was packed with hemp since the state of the metal-working art was very primitive, and a tolerance of about one-sixteenth inch out of round or "the thickness of a thin sixpence" was about the best that could be expected. The piston was connected to one end of a rocker arm by a chain without a piston rod or guide. The differential working pressure was derived primarily from the vacuum that was created below the piston by water spray into the steam space at the end of the upstroke. The steam and water valves were worked by hand. Some 60 years later, radical improvements were made by James Watt, whose name is more frequently associated with the early development of the steam en¬gine. In the course of time, numerous other improvements followed, of which the most important was probably the double-acting inverted vertical engine, which proved to have so many advantages that it continues to have applica¬tions.

Accounts of the work of men such as Newcomen, Watt, and others in connection with the invention and develop¬ment of steam engines are truly exciting. Despite the earlier development of steam engines, their applica¬tion to the propulsion of ships was not seriously under¬taken until about 1784. Attempts s to adapt steam engines to ship propulsion were carried out almost simultaneously in America, Scotland, and France. At least seven reason¬ably practical steamboats were developed by 1807. In that year Robert Fulton inaugurated the first commercially successful use of steam marine propulsion in the small, paddle-wheel vessel Clermonf. The wooden-hulled Clermont operated up the Hudson River from New York to Albany, a distance of 150 miles, in about 32 hours.

Although paddle-wheel vessels were promptly adopted for river service, twelve years elapsed after the launching of the Clermont before the steamer Savannah made the first ocean voyage from America to Europe. Notable, how¬ever, is that even in this instance the machinery was not operated continuously during the outbound leg of the trip and the inbound leg was made under sail.

The introduction of the screw propeller in 1837 was a revolutionary development, but this development also did not immediately lead to the demise of sails or paddle wheels. As late as 1860 the speed of the best clippers still exceeded that of any steamship, and the greater part of the work at sea continued to be accomplished under sail. The Great Eastern was an exception. It was an iron-hulled vessel, almost 700 ft long and of 22,000 tons bur¬den, with both a screw propeller at the stern and two side paddle wheels, as well as sails arrayed on six masts. The sails, however, were little used.

By 1893, when the Society of Naval Architects and Ma¬rine Engineers was founded, a screw propeller, driven by a triple-expansion reciprocating steam engine, had be¬come the predominant means of propulsion for seagoing ships. Paddle wheels were still used on river and excursion steamers. Steam was almost universally produced by Scotch (fire-tube) boilers, and coal was the common fuel. The steam turbine and diesel engine were yet to debut.

The decade from 1893 to 1903 was a period rich in ma¬rine engineering development. The early reciprocating steam engine reached the point of development of the six-cylinder quadruple-expansion engines of 10,000 indicated horsepower supplied with steam at 200 psi by Scotch boil¬ers. The use of electric power generated by steam engine driven '''dynamos" at 100 to 112 volts was increasing rap¬idly. Watertube boilers, which would eventually replace the Scotch boiler on the seas, had become established in England, France, and the United States.

By the end of the 19th century, ship's propulsion plants had become sufficiently reliable to assure the delivery of cargo to any port in the world, but often at great cost to their crews. Mechanical ventilation had not been devel¬oped, and those who shoveled coal commonly developed black lung. Steam leaks were chronic, and in warmer cli¬mates the risk of heat exhaustion was accepted by those who worked in machinery spaces. Large, exposed recipro¬cating mechanisms endangered the life and limb of care¬less crew members; and, in time, members of the machin¬ery space crew became progressively deaf because of the exposure to excessive noise. The development by Sir Charles A. Parsons of the first successful application of the steam turbine to marine propulsion was another important milestone in marine engineering. This was accomplished aboard the Turbinia, a small vessel about the size of a torpedo boat. The rotative speed of the Turbinia's three series turbines was about 2000 rpm, and they were coupled directly to relatively primitive screw propellers in a triple-shaft arrangement. Parsons had been dismayed on his earliest trials to dis¬cover that his first propellers "bored a hole in the water," developing disappointingly low driving thrust, a phenome¬non now recognized as cavitation. After further develop¬mental work, however, this new prime mover was success¬fully adapted to the requirements of marine propulsion.

In what must certainly be considered one of the earliest efforts at model tank testing of propellers, Parsons inves¬tigated the subject of cavitation and succeeded in rede¬signing his propellers. Three per shaft were ultimately employed and in 1897, at a naval review of the British fleet at Spithead, England, the Turbinia astounded the British admirals by steaming past smoothly at a speed of 34 knots, belching smoke like an angry bull tossing dust. Lord Kelvin described this development as "the greatest advance made in steam engine practice since the time of James Watt".

Before 1893, there were a number of attempts to de¬velop internal-combustion engines that involved fuels ranging from gunpowder to gas. One of these was of a radically different type, in which the combustion air charge was compressed to a pressure and temperature above the ignition point of the fuel. This engine was pat¬ented in 1892 by Dr. Rudolf Diesel, a German engineer. Serious difficulties had to be overcome with the diesel engine, and development proceeded slowly. Not until fif¬teen to sixteen years later was a successful commercial diesel engine of 25 hp produced. .Once this had been achieved, however, progress became rapid. In a few years many firms in Continental Europe were actively building diesel engines with as much as 500 hp per cylinder, and experimental engines developing 2000 hp per cylinder were under test.

The challenge to the coal-fired, low-pressure reciprocat¬ing steam engine came from the steam turbine and the diesel engine at about the same time, at the turn of the century. World War I caused a greater emphasis to be placed on marine engineering developments for military applications, while in the merchant marine arena the mass production of proven designs was emphasized. However, advances in the design of steam turbines and diesel engine were made. These developments continued after the war, and were spurred or by the constraints of the Washington Treaty, by the rapid development of diesels for railroad use and for submarine propulsion, and by the realization that there would be a growing requirement for merchant ships of standard design. The advantages of oil as fuel, became increasingly apparent. The use of oil reduced crew requirements and made fuel storage and handling an easier task. During the same period, the supe¬rior economy and performance of steam turbines and die¬sel engines, when compared with reciprocating steam en¬gines, became recognized. These trends in ship propulsion continued during World War II, and by the end of the war new applications of reciprocating steam engines for propulsion applications were rare.

The next major development in marine engineering his¬tory began a few years after World War II. Under the direction of Admiral Hyman G, Rickover, the submarine Nautilus, the world's first nuclear-powered ship, put to sea on January 17,1955 and transmitted the historic mes¬sage "underway on nuclear power." Nuclear propulsion enabled the Nautilus to establish many records, including distance, speed, time traveled submerged, and passage under the geographic North Pole, which she achieved in 1958. The Nautilus's pressurized-water reactor devel¬oped about 15,000 hp and was highly successful.

Nuclear propulsion revolutionized the design of subma¬rines by allowing them to remain underwater for extended periods of time. For surface ships, however, nuclear pro¬pulsion has received mixed reviews. The U.S. Navy has successfully used nuclear propulsion for aircraft carriers, starting with the Enterprise in 1962. Nuclear propulsion provides aircraft carriers with an unlimited range and the ability to carry more aviation fuel and weapons than conventionally powered carriers. Nuclear propulsion has also been used for cruisers; however, when compared with gas-turbine propulsion, the advantages provided—with an increased range being the most significant—are not offset by the higher acquisition cost.

Exploratory applications of nuclear propulsion for com¬mercial ships by the United States in 1959 (Savannah), Germany in 1968 (Otto Hahri), and Japan in 1974 (Mutsu) failed to establish commercial opportunities for nuclear propulsion. Nuclear propulsion was, however, proven to be advantageous by the Russian icebreaker Lenin in I960, and other nuclear-powered icebreakers have subse¬quently been built.

The historical developments noted in the foregoing, as well as many others, were magnificent concepts and achievements, especially when viewed against the tech¬nologies and materials available at the time. No effort has been made here to include the full roster of great names and pioneering events in marine engineering. However, additional material concerning the early days in marine engineering, which conveys an indication of the ingenuity of the early practitioners.

1.2 Marine Engineering Defined

The concept that motivated the majority of the early advances in marine engineering was quite simple, namely, to develop a system to overcome the vagaries of the wind and the inadequacy of muscle power in the propulsion of ships. In the early history of marine engineering, the concepts formed and the decisions made, although frequently ingenious, were of sufficiently narrow scope that a single individual could become intimately familiar with all facets of the undertak¬ing. The success of the early developments depended to a large extent upon intuitive perception and upon chance.

However, the accumulation of advances that have been made subsequently have caused the field of marine engi¬neering to become highly sophisticated.
From a functional point of view, a ship is a most complex vehicle which must be reliably self-sustaining in its ele¬ment for extended periods of time. A ship is perhaps the most multipurpose of vehicles, having more built-in func¬tions than does any other vehicle type. As a part of a transportation or military system, the ship contains a greater variety of components than any other vehicle.

The design of a ship's mechanical, electrical, and structural systems is further complicated by the fact that they must be compatible with the marine environment. Ship-board design constraints include space and weight limitations, which can be particularly severe in the case of weight- and space-sensitive vessels such as submarines, and high-impact shock, which, is a major design consideration for naval combatants. In addition, other constraints imposed by the marine environment range from hostile pitch and roll conditions resulting from violent seas, to the corrosive nature of seawater and its atmosphere. A comprehensive description of the marine environment, as it influences the design of shipboard systems.

Marine engineering is, therefore, not as simply catego¬rized as, for example, civil, mechanical, electrical, or chemical engineering. It is an integrated engineering effort comprising parts of many engineering disciplines directed to the development and design of systems of transport, warfare, exploration, and natural resource extraction that have only one thing in common, namely, that they operate in, or upon the surface of a body of water.

The division of responsibilities between naval architects and marine engineers is seldom sharp, and it differs from one activity to another. In any event, each needs some familiarity with the disciplines typically used by the other. Marine engineers are, in general, principally responsible for the engineering systems, including the main propulsion plant, the powering and mechanical aspects of ship functions such as steering, anchoring, cargo handling, weapon systems, heating, ventilation, air conditioning, electrical power generation and distribution, and interior and exterior communications.

Naval architects are, in general, primarily concerned with the hydrodynamic and hull form characteristics of the ship, the structural design of the hull, the maneuver¬ ability characteristics of the vehicle, and its ability to survive and endure in the marine environment. Naval architects, assisted in appropriate areas by marine engineers, are responsible for the overall exterior and interior arrangement of the ship. In addition, naval architects generally are charged with the responsibility for the overall aesthetics of the design, including the interior decorations and the pleasing quality of the architecture.

Some aspects of the design of marine vehicles are diffi¬cult to assign as the exclusive province of a naval architect or a marine engineer. The design of propellers or propulsors is one of these, being in the minds of some a hydrody¬namic device in the domain of a naval architect, and in the minds of others an energy conversion device, similar to pumps, and thus in the domain of a marine engineer. Hull vibration, excited by the propeller or by the main propul¬sion plant, is another such area. The development of the most effective means of achieving a desired ship's speed also requires trade-offs between naval architects and ma¬rine engineers, with due regard for the vessel's intended use. Noise reduction, shock hardening, and the dynamic response of structures or machinery in general are usu¬ally the joint responsibility of both a naval architect and a marine engineer. Cargo handling, cargo pumping sys¬tems, environmental control, habitability, hotel services, and numerous other such aspects of ship design involve joint responsibilities and require close interaction between naval architects and marine engineers.

The traditional distinctions between naval architecture and marine engineering have been replaced by broader concepts of systems engineering and analysis. The multi-disciplined nature of marine engineering and naval archi¬tecture has caused their definitions to evolve continuously and to assume new dimensions.

1.3 Marine Vehicle Applications and Limitations

The ranges of feasible characteristics for marine vehicles de¬pend upon their intended use. Some of the characteristics are based upon economic comparisons with alternative modes of transportation, whereas others are derived from the laws of physics. Marine vehicles are primarily used in the following ways:

(a) As a link in a transportation system. In this application, the payload, speed, turnaround time, and number of vessels involved in the trade are the primary variables. These factors must be considered principally in relation to initial and operating costs.

(b) As a mobile naval base. Seaborne bases for war¬fare systems are included in this group. In this instance, the design of the ship is subordinated to the military sys¬tem and weapon requirements, except for inescapable es¬sentials such as seaworthiness and habitability. Payload and speed in this case are generally defined in terms relat¬ing to military effectiveness and the successful accom¬plishment of the mission.

(c) As a special-purpose vehicle or platform. There remain many diversified craft which have little in common beyond the fundamentals of naval architecture and ma¬rine engineering, and are, therefore, difficult to catego¬rize. Oceangoing tugs, salvage vessels, oceanographic re¬search ships, submersibles, offshore vessels, dredging vessels, yachts, ferryboats, towboats, pushers, barges, hydrofoil craft, and surface-effect ships are examples of such craft.

Often, depending upon the application, payload and speed may be the predominant considerations in the selec¬tion of the type of vehicle employed and may either favor or rule out some types of marine vehicles. Figure 1.1 is a comparison of alternative means of transportation and shows the feasible ranges of speed for various types of vehicles.

In general, size restrictions are less stringent for ships than with the alternative modes of transportation. Geo¬metrically similar ships of different scales float at the same proportionate draft since both the amount of water displaced (the buoyancy or displacement) and the weight of the ship tend to vary as the cube of the scale.

In general, displacement ships are less weight sensitive than the alternative modes of transportation. Fixed-wing aircraft, hydrofoil craft, planning boats, and surface-effect vehicles in general are weight sensitive and size limited. Such craft derive their support while in motion from lift¬ing surfaces of various types; consequently, when geo¬metrically similar but larger versions of a prototype are considered, the weight of the craft, including its payload, increases approximately as the cube of the scale ratio while the area of the lifting surface increases only as the square of the scale. As a result, the pressure loading on the lifting surface increases directly with the scale.

As may be evident from Fig. 1.1, the displacement type of vessel, while generally unlimited in size, has very definite limitations with regard to the speed at which it can be efficiently driven. The speed limitations for ships are most appropriately expressed in terms of the so-called speed-length ratio.

Fig.1.1 Specific power versus speed for various vehicles

The most spectacular growth in the size of ships has been in tankers. Many tankers built in the early 1950's were in the cargo deadweight range of 20,000 to 30,000 tons, and they were appropriately called supertankers be¬cause they were twice the size of the T-2 tankers of World War II vintage. However, these "supertankers" have been eclipsed by later generations of tankers that are yet another order of magnitude larger in size. Some of the larger tankers became feasible when the natural limita¬tions imposed by harbor depths were avoided by the use of pipelines to offshore unloading terminals.

Chapter 2

Engine Matching and selection

2.1 Margins

Generally, diesel engines are so matched to their loads that normal operation in service is at some high fraction of rated output, typically in the range of 80% to 90% of the maximum continuous rating (MCR), at a speed slightly below rated rpm. This region of operation usually coincides with the best range of spe¬cific fuel consumption. Anticipated component lives and service recommendations for inspection, maintenance, renewal, and overhaul intervals are based upon operation in this range. The difference between the power at MCR and the power level established for normal operation: (which is sometimes called the continuous service power is the engine margin.

Figure 2.1 shows the speed-power curves for a ship. The curves can be projected at the design stage by methods described in Chapter 1. The power absorbed by the propeller is less than the brake power because of transmission and losses and attached loads. The average service condition curve reflects the fact that more power will required for a given ship speed to be achieved in service on trials, as described in Chapter 1. The allowance service conditions, which is applied to the power estimate for the trial condition, is called the service margin, and is applied in addition to the engine margin. The total margin is the difference between the installed power (or MCR) and the power required to achieve service speed on trials with the hull and propeller clean and smooth, and is equal to the sum of the engine margin and the service margin.

In practice, many operators will accept the use of the power reserve that is incorporated in the engine margin to meet required service speeds as the hull performance deteriorates. In fact, the division between engine margin; service margin is not consistently defined, since the continuous service power is arbitrarily determined. The only important consideration is that the total margin be adequate.

1.2 Relation Between Ship Speed and Engine Performance

The relation of the rpm of a fixed-pitch propeller to the ship speed at a particular draft and trim is illustrated in Fig.2.1 In service, as the hull and propeller roughen and drag increases, the rpm required at any given ship speed rises slightly (the slip increases).

The average service speed is indicated in Fig.2.1 If an were matched to run at 100% of rated rpm at the required service speed under trial conditions, it can be that to maintain the required service speed the engine would necessarily exceed its rated rpm increasingly thereafter, as the hull and propeller roughen. Consequently, propulsion engines must be matched to their pro¬pellers so that the ship speed achieved at 100% rpm under trial conditions (the trial speed) exceeds the required service speed.

An engine is normally limited in its power output by constraints on thermal over-load that are most conveniently expressed as an MEP limit. The MEP, like the torque, is proportional to the power developed divided by the rpm. Since the service speed is below the trial speed, it is normally the MEP limit that will be reached first as the hull and propeller performance deteriorate in service. Thus an engine can be forced into a condition of excessive torque MEP without exceeding rated power.

1.3 Required Engine Rating
The engine rating is generally determined so that, in the trial condition of the hull and propeller, at loaded draft and trim, the power required rive the propeller, allowing for transmission and shafting losses and any attached auxiliaries, will be between 80% and 90% of the MCR, at rated rpm. This allowance will usually result in adequate margins. Engines are often selected so that the power required under rated rpm at trial conditions is even less than 80% to 90% of the MCR, if:

Fig.2.1 Speed-power curves

—the ship must maintain rigorous schedules;
—the long-term effects of increased hull and propeller roughness are expected to be large;
—the ship is expected to be drydocked infrequently;
—a large allowance for adverse weather conditions is appropriate; or if
—the intended trade will take the ship for extended stays into warm, seawater ports or anchorages, where increased hull fouling is likely.
When the rating is determined so that the power ab¬sorbed at rated rpm under trial conditions is less than the MCR, higher average power outputs can be utilized in service as the hull and propeller roughen, without exces¬sive torque (as reflected in high MEP and cylinder exhaust temperatures), enabling higher ship speeds to be achieved. However, more power must be installed, and so acquisition cost and plant weight will be higher. As a further consequence, in single-screw, single-engine instal¬lations, even if the ship can be ballasted down to loaded draft on trials, it may not be feasible to achieve MCR without overspeeding the engine.

1.4 Engine Selection

Once the required engine rating has been established, other factors that affect the selec¬tion of engines for a particular application must be consid¬ered. Among these are the engine operating profile, the plant weight, the machinery space volume and configura¬tion, fuel quality and consumption, acquisition cost, reliability, maintenance requirements, and present and future parts cost and availability. Trade-offs are usually necessary. A requirement for low weight or minimum machinery volume may be achieved at the expense of high fuel consumption or high maintenance requirements. It is imperative that the engine be considered within the physi¬cal and operating context of the whole installation; selec¬tion of propulsion engines of light weight or low specific fuel consumption, for example, may not result in the lightest or most cost-effective power plant.

Fig.2.2Alternative arrangements for a 7500 bkW plant, with approximate dimensions
The operating profile of an engine assesses the time spent in various operating modes. All important mode must be considered, and periods of sustained idle or low-load operation must be included as well as those at high loads. For propulsion engines, operating modes may include conditions of deep and light draft, clean and fouled hull, calm and heavy weather, cruising and high ship speed, towing or icebreaking and running free, and operation with and without attached auxiliaries. The plant sign and engine selection will be affected if the profile includes frequent or extended periods of maneuvering or astern running.

In selecting propulsion engines, consideration must given to whether a single engine of the low-speed, direct-coupled type is most suitable, or if requirements are better met by one or more medium- or high-speed engine driving the propeller through gearing or electric drive. The decision may be dictated by the available space. Using geared engines as an example, Fig. 2.2 illustrates the flexibility that can be achieved. With an electric drive, there is even greater flexibility.

If low-speed operation is required for substantial periods of time, a multiple-engine installation should be considered is provided in matching the number of engines in service to the output required at different ship speed. Unneeded engines can be in a standby capacity and quickly started when required. With a controllable-propeller installation, additional flexibility is provided in matching the number of engines in service to the ship speed, since the propeller thrust can be controlled by adjusting the propeller pitch, thereby enabling the engine rpm to be maintained within practical limits. When two identical engines are connected to drive a fixed-pitch propeller, however, single-engine operation may be limited or not possible in some cases, as illustrated in Fig.2.3, be¬cause one engine, run alone, would be insufficient or over¬loaded. Alternative arrangements for this particular appli¬cation, to permit the number of engines to be matched to ship speed with greater flexibility, include two larger engines, one larger engine (which alone can provide a wider range of low-speed operation) with a smaller engine, a two-speed transmission, or a larger number of smaller engines.

Fig.2.3 Speed-power curves for two engines geared to a single fixed-pitch propeller
Chapter 3

Matching of ships, propellers and engine

3.1 Matching of ships and propellers

Such items in relation to certain operating condition of a propeller as thrust T, advance speed Vi, slips, and propeller revolution N will be given in functional re¬lation each other, when it is fitted to a ship or hull of given configuration.

Therefore, for instance, if the resistance condition of the ship would differ from the value expected at the de¬sign stage, actual operating condition would also become different from those values anticipated, which might result in unefficient propulsion or even in the trouble with engines due to over-torque or over-revolution. What is meant in "matching of ships and propellers" is to clarify such problems.

As shown in equations (1),
T = KT. ρD4. N2

where K is thrust coefficient determined for a given propeller as the function of s according to the result of behind test. The relation T - N is therefore given in a group of lines of N2, whose parameter is s as shown in Fig. 3.1. While advance speed V1 is as follows:

V1= NH (1-s)

which is also shown in the same figure, with a group of straight lines. A is supposed to be the design point,

where we assume s=s0 represented with notation 0. Other value of s is accordingly expressed with the value s-s0.

Fig. 3.1
By means of these two kinds of relation, propeller thrust T may be expressed along advance speed V~i , taking slip s-s0 for parameter as shown in Fig.3.2, where lines of constant revolution N may also be shown.

The necessary thrust TI for propulsion of a ship having resistance R may be given as the function of ship speed V, if we know augment of resistance a as afore-mentioned,

T1= (1+a). R

Therefore, T1 may also be expressed with advance speed V1 instead of ship speed V, if we know the wake fraction between these two kinds of speed. As the requirement of thrust at specified ship speed shall be satisfied with propeller thrust under anticipated condition of opera¬tion, curve T1 shall pass point A, when it is expressed along V, as shown in Fig.3.2. This is the case of what we call "correct matching of ships and propellers, and a ship will obtain specified speed under specified pro¬peller revolution developing expected thrust.

Fig. 3.2

If we increase revolution of propeller by putting a little more .fuel in the engine, thrust will increase by (∂T/∂N) V1= const, ie along ordinate V1in the direction of B, while will give surplus of thrust necessary for ship acceleration, and ship speed will increase, consequently required thrust will also in¬crease along curve T1 towards C. You may notice that ∆TB-A > ∆T C-A , therefore, we have to reduce the amount of fuel in order to keep propeller revolution at C, otherwise it will go over C with the increase of ship speed until it reach D, with higher revolution and higher ship speed.

As is shown herewith, thrust increment against propeller3T revolution under constant advance speed V1(∂T/∂N) V1= const. is larger than( (∂T1/∂N)) along ship's resistance character¬istics, the thrust variation and consequently torque variation acting on a propeller under varying revolution will become larger when the ship runs with less variation in her speed.

In case when ship's resistance characteristics are dif¬ferent from what is expected, operating condition of propeller will be given as the crossing point of the line of characteristics and that of the propeller; for example, under same revolution of propeller, thrust and slip of propeller will increase when ship resistance increases, as is the case with deeper draft, wind and waves, or uncleaned condition of ship's bottom, etc. It will be often the case that propeller revolution cannot be raised as designed, otherwise torque of the engine, would be over the limit due to the excessive requirement of propeller thrust. Designed ship speed consequently cannot be reached.

3.2 Thrust Vs Torque

Therefore, it is essential to know what is the most reasonable condition of the ship during service, to which the propeller shall be matched, in respect of draft and loading condition, cleanness of ship's bottom, as well as effect of wind and tide along navi¬gation routs. It is also important that certain range of allowance shall be considered around design point in such respects as engine revolution, engine torque, efficiency etc.

3.3 Heavy Vs light propellers.

Such propeller which requires more torque of propulsion machinery when fitted on board, than expected at the design stage, under the same engine revolution, is call¬ed "heavy" and if in opposite condition, it is called "light".

These cases are relatively the same as ship's resistance characteristics are in off-design relating against pro¬peller characteristics adopted, consequently resulting in following; propeller revolution will be limited lower because of torque limit of engine, when propeller is "heavy", while engine torque will not reach to its maxi¬mum value even at the maximum allowable engine speed.

In either case, the engine cannot develop its full power and consequently designed ship speed cannot be obtained.

3.4 Sea margin

Engine shaft horsepower (engine out-put) as well as en¬gine (propeller) revolution required in relation with ship speed are given as the result of behind test on model basin, as shown for example in Fig.3.3. It will specify loading condition or draft of ship, but dis¬regarding all other items, as clean bottom and calm sea.

Therefore in actual condition, there has been experienced 12 ~ 30% (sometimes even 50%) increase in engine out-put to keep the same ship speed, due to these effects beside that of the loading condition or draft of the ship. Consequently engine revolution shall be increased a few percent. Such difference in engine out-put required to keep same ship speed is called commonly as "Sea-Margin". This amount will naturally vary with navigation routes hull design, seasons of year, or the days after dry-docking, and will be assumed as statistical result of long experience of actual services. In Fig.3.3, some actual data are given for 10,000 DW cargo liners.


3.5 Matching of engines and ships

When the torque-revolution characteristics required for given hull and propeller condition are put on the per¬formance characteristics of the selected engine, there be often the case that the design point of these two characteristics will not coincide each other and that the engine power may be not fully utilized, (see Fig. 3.4)

Especially in case of turbocharged diesels, deviation of required characteristics from the designed point will affect considerably the available power limit comparing to non-charged engines, as shown in Fig. 3.4.

Such deviation from designed condition may be inevitable to some extent, owing to the variation in loaded condi¬tion of vessels, fouling of ship's bottom, not to say of sea condition, even though initial matching might be correct. Therefore, as we have mentioned, this must have been covered within the allowable margin of engine in both respects of power as well as engine revolution. It is important to know such inevitable range of devia¬tion beforehand, when we are going to decide the engine rating.

Fig. 3.4

Minimum speed required for maneuvering ships will not be affected even when sea-going speed of ships increases and consequently the ratio of sea-going speed against minimum speed will become larger. Required working range of propulsion machinery will, therefore, become wider in respect of power, not to say of resolution.

This requirement is not easily satisfied in case of diesel engines, especially with turbocharged type, as the torque ratio between maximum and minimum value will be 2nd power of the ratio of corresponding speed. Consequently it necessitates precision work on fuel injection system as well as special care on securing necessary air amount under such lower level of exhaust energy.

3.6 Selection of load on engines - Engine rating

Hating means the allowable limit of capacity in use, indicated on apparatus in most cases. For instance, in case of electrical machineries, rating is classified as continuous or only for limited duration etc. accord¬ing to their way of application. There are not only „ the indication of allowable limit on such items as capacity, current, voltage frequency, power factor etc., but the methods to approve it has also been established so that least ambiguity may exist.

In case of marine engines, however the definition on rating of several kind has been publicly adopted, but it is entirely trusted to the makers, how they will apply these rating to their product,, as there is no public rules other than the requirement of classifi¬cation societies.

Kinds of rating commonly used among marine engineering are MER, (most economical rating) MCR (maximum con¬tinuous rating), and over-load rating, which is excep¬tionally applied for limited duration of e.g. 15 min. or 1 hour.
Especially in JIS for marine application, there is definition on the following nomination; "normal" power is the output of engine corresponding to sea-speed of the ship, while power of "maximum continuous output" shall be the base of strength calculation as well as the nominal expression of the power of engine. Besides, power at overload, and astern power (MCR at astern run¬ning) are also mentioned.

Whatever nomination it may be, the load to which marine engine shall be subjected is continuous, and not all of decreasing, but of increasing tendency. In case of any type of marine engines, the capacity rating or the maximum available limit should be expressed with MCR, which shall be desirably selected as "normal power" for the ship in concern.

It should not be understood, thought it had been the case sometimes, that the "normal power" would be selected as 80~90% of MCR.

This practice would result in either over-nomination of the engine power, so that the engine may not develop "MCR" continuously as it should be, or otherwise, unnecessary surplus in capacity of the engine power, which is quite different character from what we have mentioned as "Sea Margin".

Chapter 4

Gear design

4.1 Determination of Approximate Size of Gears

While the detail design of a reduction gear requires a high degree of skill, it is fairly easy to establish approximate dimensions of a reduction gear. As an example, consider a double- reduction gear which is to be designed to meet the following requirements:

Shaft horsepower .......................25,000 hp at 108 rpm
HP turbine ..................................12,500 hp at 6100 rpm
LP turbine..................................12,500 hp at 4100 rpm
First reduction K-f actor............. K1 = 140
Second reduction K-f actor.........K2 = 110

conventional arrangement has been selected and suitable dimensions for the pitch diameters and face widths are to be computed.

The HP and LP turbines develop equal horsepower; I however, the HP turbine turns faster than the LP turbine. As a result, the HP side will require a larger gear reduction and will control the size of the second reduction elements; therefore, it will be computed first. The overall reduction ratio of the HP side is 6100 to 108. As a first approximation, the ratio of the second reduction can be taken as the square root of the overall ratio minus 1.0. (For a locked-train gear, 3.0 would be added to the square boot of the overall ratio.) The second reduction ratio then becomes

and the first reduction ratio is

The loading per inch of face per inch of pitch diameter for the first reduction can now be computed:

= 125.5 lb/in.-in.

The next step is to equate two expressions for the tan¬gential tooth load as follows,

solving for d12Fe1 :


Generally, the most economical reduction gear is one where the pinion diameter is as small as possible with relation to its working face. However, as will be seen later, the face width-to-diameter ratio cannot be too high if excessive deflections are to be avoided. Ratios of 2.0 to 2.25 represent good practice and 2.25 is selected. With this stipulation, the computations may proceed:


and the first reduction pinion diameter is


with an effective face width of


The first reduction gear is next computed as


Similar calculations can now be made for the second reduction:




Again selecting Fe2 = 2.25 d2, the second reduction pinion diameter becomes


with an effective face width of

and a second reduction gear diameter of


The LP first reduction can be proportioned in the same manner, but it is desirable to design the arrangement such that the second reduction pinions on both the HP and LP sides are identical. Since the first reduction gear speed on the LP side must be the same as that on the HP side (704 rpm), the first LP reduction ratio will be:

Proceeding as before



Selecting Fel = 2.25 d1




It may be desirable to use the same first reduction gear on the LP side as used on the HP side. In this case,

Fe1 = 21.8 in

D1 = 84.1 in



This LP first reduction is larger than it would be if it were designed to the maximum permissible AT-factor, but this may be offset by the economy of using the same part for both first reduction gears.

The pitch diameters as determined in the foregoing must now be laid out to determine if centerline positions and other arrangement considerations are acceptable. The optimum gear arrangement may require adjusting the choice of ratios between the first and second reductions and the choice of face width-to-diameter ratios.

With the approximate diameters and face widths as determined in the foregoing, the designer will next check to determine that bending and torsional deflections are acceptable. Formulas for these deflections are developed in the following section. A lower L/D ratio may be se¬lected if these deflections are too high, with the diameters and face widths adjusted accordingly.

Tooth pitch is then selected to provide the best balance between bending stress, scoring factor, and noise. The best compromise in this regard is generally the finest pitch permitted by the bending stress or unit loading lim¬its. This will result in an acceptable bending stress, mini¬mum scoring factor, and minimum noise level.

Tooth pitch, addendum, addendum, pressure angle, etc., and tooth proportions, are made to suit the standards for which the manufacturer has tooling. These standards are in small enough increments that no significant compro¬mise is involved. The numbers of teeth are chosen to pro¬vide "hunting tooth" combinations between mating pin¬ions and gears, and diameters or helix angles are adjusted to the precise values determined by the numbers of teeth. A hunting tooth combination is one in which the numbers of pinion and gear teeth have no common prime factor. This means that each tooth will mesh with every tooth of the mating element and thus avoid any wear or tooth spacing pattern that can give rise to a sub-harmonic of the tooth meshing frequency.

As noted previously, the design of gears is based on the tooth pressure being uniformly distributed across the entire face width. Many factors adversely affect this tooth pressure distribution and must be taken into account. Among these factors are torsional and bending deflec¬tions of the pinion, accuracy of manufacture, deflections due to centrifugal force, strains due to temperature varia¬tions, and casing distortions due to temperature differ¬ences and hull deflections. Two of these factors, torsional and bending deflections of the pinion, are important in proportioning gear elements and, fortunately, are readily evaluated.

4.2 Torsional Pinion Deflection

When subjected to a uniform tooth pressure, a pinion will deflect torsionally as shown in Fig. 4.1. The teeth will separate from the mating gear teeth by the distance y. However, since the pinion is always free to shift endwise to balance the load between the two helices, the separation

Fig.4.1 Pinion deflection

after this axial shaft will be yl on the helix next to the coupling and y2 on the helix away from the coupling. The torsional deflection in the space between the helices has no effect on the separation. The separations will then be

yl = tooth separation at driving end, in.
y2 = tooth separation opposite from driving end, in
where d0 = diameter of pinion bore, c=1.0 for a solid pinion
J = tooth loading, lb/in.-in.
Fe = effective face width of pinion, in.
d — pitch diameter of pinion, in.

These equations are based on a uniform distribution of tooth pressure, endwise freedom to equalize the load between both helices, an effective diameter for torsion equal to the pitch diameter, and a shear modulus for steel equal to 12.0 x106 psi.
4.3 Bending Pinion Deflection

In addition to torsional pinion deflections, the tooth loading will cause the pinion to deflect due to bending stress as shown in Fig. 4.1 The pinion can be assumed to be uniformly loaded, and by using the deflection equation for a simply supported, uni¬formly loaded beam, the tooth separation due to bending is found to be

where f is the tooth separation due to deflection and F the distance between ends of bearings, both in inches. The remaining terms are as defined previously.

This expression is based on a uniform distribution of tooth pressure, the tooth pressure acting over the distance between the ends of the bearings, the effective diameter for bending equal to the pinion pitch diameter including the space between helices, the pinion simply supported at the inner ends of the bearings, and the modulus of elastic¬ity for steel equal to 30.0 x 106 psi.

A generally accepted value for the allowable deflection due to torsion and bending is 0.001 in. However, other effects can add to these calculated values. The total effect can be observed by tooth contact patterns under full-load operation, estimated from experience on similar gears, or estimated by analysis. The sum may exceed 0.001, but the gearing can be made perfectly satisfactory by machining corrections into the helix angles so that the tooth contact will be uniform under full-load operating conditions. When this is done, the cold light-torque contact pattern will not be uniform. But since the direction and amount of the helix angle corrections are known, the light-torque contact pattern will be a good indication of the contact pattern under operating conditions.

Such a light-torque contact check will be made at the factory to confirm the correct machining and assembly of the unit, and the check will be repeated in the ship installation to confirm that the factory alignment has been duplicated. These contact checks can be made by observ¬ing the transfer of a marking compound such as Prussian Blue, or light layout lacquer, from one element to the other. Uniform transfer of compound over the full face width will indicate uniform face contact under light loads. While satisfactory contact checks can be made with very light torques, they can be made with greater reliability with higher torques. When light loads are not sufficient to bring about uniform contact, a quantitative measure of face contact can be made by gaging the opening between meshing teeth with feeler gages graduated in 0.0001-in. steps.

Despite the care which may be taken in factory and installation tests, the final quality of tooth contact must be judged after full-power operation in the ship. For this observation, the teeth of each pinion or gear may be coated in a band extending across each face with copper by the application of a weak acid copper sulfate solution, or with a thin coat of layout lacquer.

4.4 Other Deflections

There are other deflections that can act to affect the uniformity of tooth contact across the tooth faces. The gear housing structure will deflect under the forces applied to the bearings and may deflect to misalign the teeth; an example would be the case in which the support of one pinion bearing is more flexible than the support of the bearing at the opposite end of the pinion.

Gear casings are also subject to thermal strains and these can affect tooth alignment. For instance, the casing support structure for the bearings in the middle of a dou¬ble-reduction gear housing may be at a higher tempera¬ture than the structure that supports the end bearings.

The rotating elements are also subject to elastic and thermal deformations. Gear rims that are attached to their hubs by a series of thin plates or cone members are de¬formed by the action of centrifugal forces. The design must be such that these deflections do not have a signifi¬cant effect on the tooth portion.

Thermal strains can also be important, particularly with wide face widths. If a pinion is allowed to reach a tempera¬ture higher than its mating gear wheel, the uniformity of tooth contact across the faces of both helices will be affected.

4.5 Gear Alignment and Installation

An important source of misalignment in the second reduction mesh can be due to the difference in the magnitude of the forward and after slow-speed gear bearing reactions. Figure 4.2 is a typical bearing reaction diagram for a double-reduction gear. It may be seen that the gear bearing reactions con¬sist of one or more components due to the torque loadings and a component due to the static weight of the pinion or gear supported. With the exception of the slow-speed gear bearing reactions, none are affected by external influ¬ences. However, such is far from the case with the slow-speed gear bearings. When the static loads imposed on the forward and after slow-speed gear bearings are differ¬ent in magnitude, as opposed to being equal as shown in Fig. 4.2, the- resultant reactions will not be in the same direction. This will cause the forward and after gear bear¬ing journals to ride in different positions within their bear¬ing clearances. The slow-speed pinions are not subjected to a similar influence; therefore, there results a crossed-axis condition between the slow-speed pinions and gear.

The foundations of slow-speed gear bearings and line shaft bearings are completely dissimilar. Slow-speed gear bearings are located very close to the lube oil sump tank and, therefore, their foundations become very warm when at operating temperature, causing an attendant thermal rise in the position of the slow-speed bearings. On the other hand, little heat is generated in line shaft bearings, and they operate at a temperature little above the ambi¬ent. This being the case, it is unavoidable that the line shafting have an influence on the slow-speed gear bearing reactions when the plant goes from a cold to the operating condition. When going from a cold to the operating condi¬tion, the slow-speed gear bearings will rise about 15 to 30 mils higher than the line shaft bearings.

Prior to the late 1950's, misalignments due to this source were generally disregarded and the slow-speed gear shaft was aligned concentric to the line shafting. It is easily shown that the forward slow-speed gear bearing on many of the older ships carried no static load when in the operating condition. It is speculated that the disregard of this factor led to a number of their problems.

The successful operation and reliability of main reduc¬tion gears are not only the responsibility of the gear de¬signer, but also the naval architect and shipbuilder. Fac¬tors influencing the gear-mesh loading and distribution of load are affected by the design and manufacturing accuracy, foundation deflections, line shaft alignment and flexibility, and installation accuracy. These factors, along with system design responsibilities, alignment tech¬niques, installation procedures, and operational verifica¬tion of uniform gear tooth loading, are reviewed in SNAME T&R Bulletin 3-43, which was prepared by the M-16 Panel.

Fig.4.2 Typical reduction gear bearing reduction diagram

The achievement of an acceptable gear-mesh load distri¬bution, particularly in the slow-speed gear mesh, is a key factor towards reliable service, and compensation for the elastic and thermal deflections of the pinions and gears is the essential first step.

Reduction gear problems have also been encountered due to hull flexibility, excessive lineshaft stiffness, and improper alignment; therefore, as the design matures, continuous communications between the manufacturer, the architect, and the shipbuilder are important to ensure a satisfactory installation. Conducting alignment studies and establishing proper installation and alignment procedures are of vital importance in this regard.

Finally, the verification of gear tooth contact and the uniformity of load across the face widths are essential the achievement of high reliability and low risk of tooth wear. Brake tooth contact checking is used as an indicator of proper alignment. The verification of tooth contact and uniformity of load can be performed by using strain gages, coatings such as silver or copper, or either red or blue dykem. The "reading" of dykem and coatings requires experience and can be interpreted incorrectly by untrained personnel. Experienced personnel can judge proper tooth contacts; however, changes due to environmental conditions are difficult to detect. Strain gaging has been successfully applied to large reduction gears and is a reliable procedure for accurately determining the uniformity of load. Using frequency modulated telemetry, gear tooth strain can be monitored and quantified under all operating conditions, thus recording the influences of the external and internal factors that affect gear reliability.

4.6 Critical Speeds

Pinion and gears, designed as they are for stiffness to resist tooth forces, have lateral critical speeds that are well above any operating speed. They will run free of vibration with normal procedures for balancing. With both gas turbine or steam turbine prime movers, balance is a particularly important consid¬eration with the first-reduction pinion. It rotates at tur¬bine speed, and must be given the same high degree of dynamic balance as the turbine.

Coupling shafts connecting the turbine to the pinion are important elements in determining the lateral critical speeds of the turbine rotor-coupling-pinion assembly and must be considered when evaluating turbine critical speeds.

The combination of the propeller, shafting, gears, and prime mover forms a system, which can vibrate torsion-ally in response to the impulses from the propeller blades. With the very early gear designs, manufacturing irregu¬larities in the gear teeth occasionally were a source of serious torsional vibration; however, the precision with which modern gears are manufactured has eliminated this as a source of torsional vibration. With gas or steam tur¬bine-driven gears, the first three modes of torsional vibra¬tion warrant careful analysis. In the first mode of tor¬sional vibration with a geared-turbine drive, the angular vibratory motion is greatest at the propeller, but the vibra¬tory torque is a maximum at the reduction gear. This mode generally occurs within the operating range, being well down in the operating range with arrangements hav¬ing long shafts but relatively high in the operating range and potentially dangerous with very short shafting ar¬rangements.

The first mode of torsional vibration must be evaluated to ensure that the vibratory torque in the gear train, when added to the torque transmitted under steady power con¬ditions, will not be deleterious to the reduction gearing.

The inertia and elastic factors of the turbines and gears have no significant effect on the first critical speed; it is controlled by the inertia of the propeller and entrained water, the stiffness of the shafting, and the number of propeller blades.

The second mode of torsional vibration is one in which the two turbine branches vibrate in opposition and it may occur in the operating range. When this is the case, vibra¬tory torques must be evaluated as for the first critical. However, by employing a so-called "nodal drive" arrange¬ment, it is possible to render the second mode incapable of excitation. In a nodal drive arrangement, the two turbine branches are tuned by adjusting the dimensions of the quill shafts, such that they have identical frequencies with the slow-speed gear, shafting, and propeller considered nodal points. As a result, all motion in the second mode is in the turbine branches, and propeller excitation cannot excite this mode since the propeller is on a node.

The third mode of torsional vibration, in which the slow-speed gear is an antinode, may be of concern. It is usually well above the operating range, but when an unusually large number of propeller blades are used, it may be of importance.

A description of the modes of torsional vibration and a procedure for calculating the natural frequencies and amplitudes are included in later chapter.
Main propulsion systems using diesel engines as prime movers require extensive torsional evaluations to ensure satisfactory operation. Diesel engines have many excita¬tion orders. Four-stroke engines produce excitation orders of 1/2, 1, 11/2, 2, 21/2, etc. Two-stroke engines produce exci¬tation orders of 1, 2, 3, etc. It is not uncommon to analyze the propulsion system for as many as twelve orders.

Nearly all diesel propulsion systems require a torsional flexible coupling with proper stiffness and damping char¬acteristics to minimize torsional vibrations in reduction gears and power takeoff drives for generators. The selec¬tion of these couplings is very important for normal opera¬tion as well as for misfiring conditions.

Chapter 5

Shafting system

5.1 General.

A main propulsion shafting system con¬sists of the equipment necessary to convert the rotative power output of the main propulsion engines into thrust horsepower that is used to propel the ship. The propeller is included as an element of the shafting system, as is the means to transmit the propeller thrust to the ship structure. In the following pages, the design of a main propulsion shafting system is reviewed from the perspective of a shipbuilder undertaking the task of preparing a detailed design. It will, however, be assumed that the propeller hydrodynamic design has been developed; the hydrodynamic design of propellers and other propulsion devices is thoroughly covered by Van Manen and Oossanen in Principles of Naval Architecture and, therefore, will not be repeated here. Although the fundamentals outlined in the following sections apply to all types of propulsors and prime movers, the discussion has been directed primarily towards an arrangement with a fixed-pitch propeller and geared, turbine-driven, propulsion ma¬chinery; however, where the selection of a diesel prime mover has an influence upon the shafting design consider¬ations or procedures, those instances are discussed. This was necessary in order to avoid unduly confusing the discussion with details.

Due to the nonuniform wake field in which a ship's propeller operates, the propeller is a source of potentially dangerous vibratory excitations. The shafting system it¬self, which is inherently flexible, is extremely vulnerable to these vibratory excitations; consequently, an analysis of the dynamic characteristics of a shafting system is an integral aspect of the design process and is discussed in this chapter.

5.2 Shafting System Description.

The main propulsion shafting system must accomplish a number of objectives that are vital to the ship's operation. These objectives are: (a) transmit the power output from the main engines to the propulsor; (b) support the propulsor; (c) transmit the thrust developed by the propulsor to the ship's hull; (d) safely withstand transient operating loads (e.g., high¬-speed maneuvers, quick reversals); (e) be free of deleteri¬ous modes of vibration; (f) provide reliable operation throughout the operating range; and (g) be a low mainte¬nance system.

Figure 5.1 is a shafting arrangement typical of those found on multi-shaft ships and single-shaft ships having transom sterns. The distinguishing characteristic of this arrangement is that the shafting must be extended out¬board for a considerable distance in order to provide ade¬quate clearance between the propeller and the hull. One or more strut bearings are required to support the outboard shafting.

A shafting arrangement typical of single-screw mer¬chant ships is shown in Fig. 5.2. The arrangement illus¬trated corresponds to the so-called Mariner or clear-water stern design (there being no lower rudder support); how¬ever, the shafting arrangements of most merchant ships are very similar. The major difference between the shaft¬ing arrangements of various merchant ships is the loca¬tion of the main engines. When the main engines are lo¬cated well aft, such as on tankers, there may be as few as one or even no inboard line shaft bearings. When the main engines are located farther forward, which is pre¬dominantly the case for naval ships, a considerable length of inboard shafting may be required to accommodate the ship arrangement.

The shafting located inside the ship is termed line shaft¬ing. The outboard sections of shafting (wet shafting) are designated differently depending upon their location. The section to which the propeller is secured is the propeller shaft or tail shaft. The section passing through the stern tube is the stern tube shaft unless the propeller is sup¬ported by it (as is the case with many merchant ships), in which case it is designated as the propeller shaft or tail shaft. If there is a section of shafting between the propel¬ler and stern tube shafts, it would be referred to as an intermediate outboard shaft.

Shafting sections are connected by means of bolted flange couplings. The coupling flanges are normally forged integrally with the shafting section; however, when required by the arrangement (e.g., stern tube shafts which require flanges on both ends and also require corro¬sion-resistant sleeves to be fitted to the shaft in way of bearings), a removable coupling, sometimes referred to as a muff coupling, is used.

Bearings are used to support the shafting in essentially a straight line between the main propulsion engine and the desired location of the propeller. Bearings inside the ship are known by several names, with line shaft bearings, steady bearings, and spring bearings being the most popu¬lar in that order. Bearings which support outboard sec¬tions of shafting are called stern tube bearings if they are located in the stern tube and strut bearings when located in struts. Outboard bearings may be lubricated by either seawater or oil; seals having a very high reliability are required in the event the latter is used. Alternatively, the necessity for a muff coupling can be avoided by welding in place, onto the shaft, halves of a split sleeve that are made of a corrosion-resistant material; but in this case, the stern tube bore, with the bearing bushings removed, must be large enough to pass an integral flange.

In order to control flooding, in the event of a casualty, watertight bulkheads are installed within the ship. Stuff¬ing boxes are installed where the shafting passes through these bulkheads. A seal, which is more substantial than a bulkhead stuffing box, is installed where the shafting penetrates the watertight boundary of the hull.

The propeller thrust is transmitted to the hull by means of a main thrust bearing. When the main engine drives the propeller through reduction gears, the main thrust bearing may be located either forward or aft of the slow-speed gear. If located forward, the thrust collar is detach¬able from the gear shaft so as to permit the installation of the slow-speed gear on the shaft and, secondarily, to permit replacement of the thrust collar if ever required. If located aft, the collar is forged integrally with either the slow-speed gear shaft or a subsequent section of shafting. Since one purpose of the main thrust bearing is to limit movement of the slow-speed gear, the main thrust bearing is usually installed close to the gear. The installation of the thrust bearing close to the gear also facilitates ar¬rangements to lubricate the thrust bearing, as an oil line can readily be run from the gear to the thrust bearing with the oil returned by a gravity drain.

Direct-drive diesel ships have the thrust bearing aft of the engine, either attached directly to the engine crank¬shaft or located farther aft independent of the engine.

5.3 Design Sequence.

The design of a shafting sys¬tem is, by necessity, an iterative process because the vari¬ous system design parameters are, to some extent, mutu¬ally dependent. The iterative design process usually followed is illustrated in Fig. 5.3.
As indicated by Fig. 5.3, the first step in the design of a shafting system is to state the performance requirements, that is, the type of propulsive system, number of shafts, type of service, and the like. Next, the design criteria to be employed must be fixed. That is, one of the various classification society rules could be followed; the type of stern tube bearings may be selected (i.e., oil lubricated or water lubricated); hollow shafting may be ruled out, and so on. In establishing the design criteria, it must be recog¬nized that the shafting interfaces with the propulsor, the main engines, and the ship system as a whole.

After the design criteria are established and the general ship arrangement is available, an approximate shafting arrangement can be developed. This entails at least tenta¬tively locating the main engine, propeller, and shaft bear¬ings with due regard given to arrangement restrictions, clearances required, shaft rake, construction restraints, and overhaul and maintenance requirements.

Fig.5.3 Shafting system design sequence

Before the design can progress further, the shafting diameters, corresponding to the preliminary arrange¬ment, must be computed along with the length of shafting sections, flange dimensions, and preliminary propeller data. Preliminary shafting system alignment calculations can be initiated, and the changes in bearing loads due to the thermal expansion of the shaft bearing foundations, particularly those in the way of the main engines, can be investigated to ensure satisfactory bearing performance under all operating conditions. In addition, when the ar¬rangement includes water-lubricated outboard bearings that are designed to accommodate weardown, it must be ascertained that the weardown of these bearings will have no adverse effects. With these data the bearing reactions under the full range of operation conditions can be deter¬mined and the bearing dimensions and loadings can be checked. At this point, it will generally be desirable to adjust the bearing arrangement tentatively selected so as to obtain more equal bearing reactions or to alter the number of bearings.

There are three basic types of vibration that can occur in a main propulsion shafting system: torsional, longitudi¬nal, and whirling vibration, it is essential that a preliminary vibration analysis of the shafting system be made in the early design stages because the shafting vibration characteristics are largely established by the ship parame¬ters that are fixed at that time. Specifically, the shape of the hull afterbody, type of propeller, propeller aperture clearances, number of propeller blades, length of shaft¬ing, shaft material, position of the main thrust bearing, rigidity of main thrust bearing foundation, type and con¬figuration of prime mover, spacing of the aftermost bear¬ings, and type of aftermost bearings largely establish the dynamic characteristics of a shafting system. The subse¬quent development of design details has a relatively sec¬ondary effect as compared with these major parameters. In addition, an analysis of the system's response to shock loadings is required for naval combatant ships. An analy¬sis of the dynamic characteristics of a shafting system can be one of the more complex aspects of the design process.

Once the arrangement, component sizes, and dynamic characteristics have been shown to comply with the design criteria, design details are developed. This entails the de¬velopment of detailed designs for flange fillets, flange bolts, propeller attachment, sleeves, and the like.

Section 2

Arrangement Considerations

5.2.1 Main Engine Location.

The location of the main engine output flange and the propeller location are essen¬tial information in establishing the shafting arrangement. The fore-and-aft position of the main engine is generally established during the preliminary design stages after studying the ship arrangement, ship light-draft trim, and shafting system.

To minimize the use of prime shipboard space for the propulsion plant, the main machinery is located as far aft as practicable. For ships that are driven through reduction gears, the limiting factor is usually the breadth of the ship in way of the reduction gears, provided that the resulting light-load trim of the ship is satisfactory. With vessels that have provisions for ballast, the light-load draft of the ship can be adjusted by taking on ballast, and the main machinery is usually confined to the stern of the ship. This arrangement requires a short run of shafting, and the number of line shaft bearings required is minimal. On the other hand, other types of vessels such as warships and dry-cargo ships have a limited ability to adjust their operating draft and trim by taking on ballast; therefore, to provide satisfactory light-load draft conditions in these cases, it is necessary to locate the main engines (and the associated weight) well forward of the stern.

Normally a main engine with a reduction gear will be set as close to the innerbottom as the configuration of the main machinery will permit to reduce shaft rake. It is possible, and it is the usual case, to have limited projec¬tions of the main machinery (e.g., the slow-speed gear lube oil sump) below the innerbottom when such projections do not excessively weaken the innerbottom.

Projections into the innerbottom structure are gener¬ally not required with direct-drive diesel installations, be¬cause the distance from the crankshaft to the engine base is very much less than the radius of the slow-speed gear in a reduction gear arrangement.

Fig. 5.4 Propeller aperture clearances
The main engine location in the athwartship direction is on the ship centerline of single-screw ships. On multiscrew ships the engines are set off the ship center-line approximately the same distance as the propellers, but the shaft centerlines usually do not parallel the center-line of the ship. The location of the engine in the athwartship direction is controlled by the propeller loca¬tion, main engine details, and the machinery room ar¬rangement requirements.

5.2.2 Propeller Location.

The location of the propeller is determined by the propeller diameter, the acceptable clearance between the propeller and the baseline of the ship, and the acceptable clearances between the propeller and the hull in the plane of the propeller. Although the propeller diameter selected should theoretically be the one corresponding to optimum efficiency for the propeller-ship system, in practice the optimum propeller diameter is usually larger than can be accommodated. As a result, the propeller diameter selected is a compromise.

In locating the propeller in the aperture of a single-screw ship, a clearance of 6 to 12 in. is normally provided between the propeller tip and the baseline with clearwater sterns or to the rudder shoe with a closed stern (Fig. 5.4). With high-speed ships, which are generally characterized by shallow draft and multiple screws, propellers are often permitted to project below the baseline in order to provide adequate clearance between the propeller and the hull. This is satisfactory provided maximum draft limitations for service routes or dry-docking are not exceeded.
One of the most effective means of ensuring a satisfac¬tory level of vibration aboard ship is to provide adequate clearances between the propeller and the hull surface. For this reason, the subject of propeller clearances is one of overriding importance. Generally speaking, the greater the clearances, the better the performance from a vibra¬tion standpoint.

Three types of vibratory forces are generated by the propeller: (a) alternating pressure forces on the hull due to the alternating hydrodynamic pressure fields caused by the propeller blades; (b) alternating propeller-shaft bearing forces, which are primarily caused by wake irreg¬ularities; and (c) alternating forces transmitted through¬out the shafting system, which are primarily caused by wake irregularities. If the frequency of the exciting force should coincide with one of the hull or shafting system natural frequencies, very objectionable vibration can oc¬cur. An analysis of the forces generated by the propeller is given by W.S.Vorus which includes numerous references to papers and studies that deal with ship vibratory forces and dynamic behavior.

When establishing propeller clearances, the perform¬ance experience gained during the operation of similar ships should be taken into consideration. Of course, differ¬ences between the important parameters of the ships un¬der comparison must be assessed. Important parameters to consider are the unit thrust loading on the propeller blades, the number of propeller blades, the amount of propeller skew, the length of the ship, and the closing angle of the waterplane forward of the propeller.

Figure 5.4, which may be used as guidance in assessing aperture clearances, shows the range of experience which has been obtained in connection with large single-screw ships. When the propeller is supported by a strut bearing, i.e., multiscrew and transom-stern vessels, two clearance dimensions warrant careful study. These dimensions and the range of experience with them are shown in Fig. 5.5.

Fig.5.5 Clearances of a propeller supported by a strut bearing

5.2.3 Shaft Rake.

In order to provide latitude when lo¬cating the propeller and the main engine, it is usually necessary to rake the shaft centerline. The shaft is gener¬ally raked downward going aft as this permits the main engines to be located higher in the ship. In multi-screw ships the shaft is generally raked in both the vertical and horizontal planes, usually downward and outboard going aft.

Large rakes should be avoided since a reduction in the propulsive efficiency is associated with rake. The intro¬duction of rake incurs a reduction in the propulsion effi¬ciency equal to

e = (1 – cosθ cosφ) 100 (1)

where θ is the shaft vertical rake angle and φ is the athwartship rake angle, both of which are measured rela¬tive to the ship centerline. It is rare for θφ to exceed 3.75 deg or φ to exceed 2.5 deg. From rake alone the reduction in propulsion efficiency will normally not exceed 0.3%. Aside from the efficiency penalty, there is no objection to moderate amounts of rake.

5.2.4 Shaft Withdrawal.

Occasionally shafting sec¬tions, particularly those outboard, must be withdrawn to be inspected or repaired. Consequently, provisions for re¬moving shaft sections from the ship must be considered when developing a shafting arrangement.

On single-screw ships with shafting arrangements simi¬lar to Fig. 5.2, the propeller shaft is almost without excep¬tion withdrawn inboard for inspection. If repairs are nec¬essary, the shaft is removed from the ship by cutting a hole in the side of the ship and passing the shaft through it. This technique would be used for removing line shaft sections as well.

With shafts having struts as shown in Fig. 5.1, a check must be made to ensure that the propeller shaft can be withdrawn from the strut after the propeller is removed. Withdrawal can be accomplished by removing the bearing bushings so that the shaft can be inclined sufficiently to allow its forward end to clear the ship's structure, the mating shaft flange, etc. This consideration can govern the length of the propeller shaft and the size of the strut barrel. Figure 5.1 shows the removal position of the propel¬ler shaft.

Removal of the stern tube shaft, which must have flanges on both ends, requires a decision regarding the type of flanges to be provided on the shaft. If the shaft is manufactured with integral flanges on both ends, the stern tube barrel and bearing bushings must be sized to pass the flange diameter. Since it is desirable to pass the shaft outboard, sufficient clearance should be provided to incline the shaft such that it will clear outboard struts, etc. In order to use smaller stern tubes and bearing bush¬ings, the stern tube shaft can be manufactured with a removable flange coupling on the forward end. Prior to unshipping the shaft, the removal coupling is detached so that it is not necessary to disturb the stern tube bearings.

Section 3

Shafting Loads

5.3.1 Design Considerations.

In general, the dimen¬sions of shafting are predicated on the basis of strength requirements; however, it is occasionally necessary to modify an otherwise satisfactory shafting system design due to vibration considerations. Shafting diameters usu¬ally have only a minor impact on the longitudinal vibration characteristics, due to the fact that both the stiffness and the weight of the shafting change proportionately; but the whirling and torsional modes of vibration are sensitive to shaft diameters.

Propulsion shafting is subjected to a variety of steady and alternating loads, which induce torsional shear, axial thrust, and bending stresses in the shafting. In addition, there are radial compressive stresses between the shaft¬ing and mating elements (such as between the propeller and shaft) which, when coupled with axial strains from bending stress, are very important from a fatigue stand¬point.

The steady loads represent average conditions and can be estimated with a degree of certainty as they are di¬rectly derived from the main engine torque and the propel¬ler thrust. On the other hand, vibratory loads do not lend themselves to a precise evaluation and are difficult to treat in an absolute sense.

5.3.2 Propeller-Induced Loads.

Aside from the alternat¬ing bending stress due to the weight of the propeller, the circumferentially nonuniform velocity of the water inflow to the propeller (wake) generates one of the most impor¬tant sources of the alternating loads in the shafting sys¬tem. It is, however, important to distinguish between the importance of the circumferential nonuniformity of water inflow at a particular propeller radius and the nonunifor¬mity of the average flow at one radius as compared with another. While the former leads to vibratory propeller forces, the latter does not.

A propeller blade section working in a constant velocity field at a particular radius has a steady flow and force pattern. The average axial velocity at each radius can be different without causing alternating loads. In such a case the propeller design can be adjusted for radial variations in the inflow velocity to achieve optimum performance. However, a propeller can only be designed to satisfy aver¬age conditions at each radius.

A variation in the inflow water velocity at a particular radius results in a change in the angle of attack of the propeller blade section as the propeller makes one revolu¬tion, thereby creating alternating propeller forces. Figure 5.6 is an example of the axial, VA, and tangential, VT, inflow velocities in the plane of the propeller for a single-screw ship. The tangential velocity component is symmetric on both sides of the vertical centerline of single-screw ships and is generally upward. The symmetry of the tangential velocity component would tend to suggest that its effect is uniform, bit such is not the case. For a propeller blade rotating clockwise looking forward, the tangential veloc¬ity component effectively reduces the angle of attack of the blade sections as they pass up the port side (reducing thrust) and increases the angle of attack of the blade sections as they pass down the starboard side (increasing thrust).

Fig. 5.6 flow of water in plane of propeller

Figure 5.7 illustrates the variable propeller loads that result from nonuniform axial and tangential wake velocities. Also, another very important fact is that the tangential velocity components shift the center of propel¬ler thrust to,the starboard side of the propeller centerline of a propeller turning clockwise on a single-screw ship. This off-center thrust gives rise to a bending moment which is imposed upon the propeller shaft.

Fig. 5.7 Typical variation in advance angle of a blade section during one revolution

Analyses can be made to predict the magnitude of the alternating components of torque and thrust, including the eccentricity of the resultant thrust relative to the shaft centerline. An approximation of these alternating components, which is sufficiently accurate for most appli¬cations, can be obtained by using a quasi-steady analysis approach. A quasi-steady analysis is readily comprehensi¬ble and is conducted by making an instantaneous examina¬tion of the flow velocities relative to the propeller blades at discrete angular positions of a propeller blade. The inflow velocities are regarded as constant (quasi-steady) at each blade position. By using the open-water character¬istics (KT-KQ-J diagram) of the propeller, the thrust and torque can be determined per blade, summed, and plotted as shown in Fig. 5.8.

Fig. 5.8 Typical single-screw propeller alternating thrust, torque, and bending moments resulting from nonuniform water inflow velocities

Since the slowest axial inflow velocity (highest wake) of single-screw ships is generally in the region above the propeller centerline, the greatest thrust tends to be devel¬oped when the propeller blade is in the upper part of its orbit. The effect of the tangential inflow velocity is to shift the resultant thrust to the starboard side because the propeller blades develop greater thrust moving against the tangential velocity, as discussed in the forego¬ing. It is noted that as the shape of the stern sections change from a V to a U shape, the resultant thrust center tends to move down because the inflow velocities over the bottom region of the propeller disk become more nearly equal to those in the upper region. The position of the resultant thrust is also sensitive to the ship's draft. For instance, when a cargo ship operates lightly loaded with the propeller blades breaking the water surface, the cen¬ter of thrust obviously shifts lower in the propeller disk.

Figure 5.8 shows that a single-screw ship with a four- or six-bladed propeller (that is, an even number of blades) has larger torque and axial thrust variations than one with a five-bladed propeller. However, the thrust eccentricity (propeller shaft bending moment) is shown to be much greater for the five-bladed propeller than for the four-or six-bladed propeller. For a single-screw ship having a propeller with an even number of blades, the fluctuating forces of two opposite blades give rise to a larger total thrust and torque amplitude because opposite blades si¬multaneously pass through the blow water velocities at the top and bottom of the propeller disk. The transverse force and bending moment developed by one blade tend to be compensated by similar loads on the opposite blade.

For propellers having an odd number of blades, the blades pass the upper and lower high-wake regions alter¬nately. The total thrust and torque variations are there¬fore smaller as compared with a propeller having an even number of blades. However, due to the alternate loading of the propeller blades, the transverse forces and bending moments do not cancel. Therefore, larger bending mo¬ments occur with propellers having an odd number of blades. Propellers have been designed with a large amount of skew, in the order of 70 deg, as a means of reducing the alternating propeller thrust and torque loads.

The nonuniform character of the water inflow to the propeller can be resolved into Fourier components with the propeller rotational frequency (shaft frequency) as the fundamental. Since it may be assumed that linear¬ity exists between inflow velocity variations and propeller blade force variations, the Fourier components of the in¬flow velocity are also the Fourier components of force of a single blade making one revolution. Only those harmon¬ics of loading that are integral multiples of blade number (kZ) contribute to the unsteady thrust and torque, and only those harmonics of loading adjacent to multiples of blade frequency (kZ ± 1) contribute to the unsteady trans¬verse forces and bending moments. All other harmon¬ics cancel when summed over the blades. The selection of the number of blades can be based on the relative strengths of the harmonics in the inflow water velocity to the propeller to minimize the alternating thrust and torque and bending moments.

Variable propeller forces, in addition to those resulting from a nonuniform water inflow, are generated as a result of the proximity of the hull to the propeller. Hull surface forces generated by the propeller are of the utmost impor¬tance when evaluating hull vibrations.

5.3.3 Torsional Loads.

The mean torsional load on the shafting, which results in the average torsional stress, is calculated from the output of the main engine. If the full-power shaft horsepower output, H, of the main engine is developed at N rpm, then the steady torsional load, Q, on the shafting is
in.-lb (2)
In the design of naval shafting systems, it is common practice to increase the torque calculated with equation (2) by 20 percent. The increase in design torque is an allowance in recognition of the additional torque devel¬oped during high-speed maneuvers, rough-water opera¬tions, foul-hull conditions, etc. During turns, the ship speed decreases, which results in a reduction in the propel¬ler speed of advance; therefore, if there is no reduction in shaft horsepower, there is an increase in the shaft torque. Similarly, as the hull becomes foul, the ship speed reduces and full-power torque is developed at a lower rpm.
While high-speed maneuvers are a design criterion for naval ships, such torque increases are normally not con¬sidered in merchant practice because merchant ships do not engage in extensive high-speed maneuvers. Also, the torque increase, which is relatively small, due to hull foul¬ing is accepted as a reduction in the factor of safety in merchant practice.

The torque increases measured during trials of single-screw and multi-screw ships in high-speed turns are given in Table 1. The torque ratio shown is the peak torque value observed during steering maneuvers divided by the torque at the start of the tests.

Table 1 Ratio of shaft torque measured during high-speed maneuvers to normal torque

Although alternating torsional loads can be generated by other sources, the propeller is the only one of practical importance except in direct-drive diesel propulsion plants, where the cyclic engine torque may be significant. Shafting sys¬tems are carefully designed to avoid torsional resonant frequencies at full power; therefore, alternating torsional loads are not considered to be amplified by resonance. The range of the magnitude of the forced torsional alternating loads is given in Table 2. It will be noted that the variable torque can be of a significant magnitude even without magnification.

Table 2 Propeller variable torque excitation factors

5.3.4 Thrust Loads.

The magnitude of the mean propel¬ler thrust load on the shafting system is equal to the towed resistance of the ship, corrected by the interaction effect between the propeller and hull as the propeller pushes the ship. This interaction effect is known as the thrust deduction. The value of the design thrust can be obtained from powering calculations or from model basin tests conducted for the ship. For preliminary design purposes the propeller thrust can be estimated as

T = propeller thrust on shaft, lb
V = ship speed at maximum power, knots
R = hull resistance at V, lb
E = hull effective horsepower at V, hp
H = maximum shaft horsepower, hp
t = thrust deduction fraction
PC = propulsive coefficient
The value of t ranges from about 0.16 to 0.23 for single-screw ships that range from fine to full lines, respectively. Twin-screw ships have t values ranging from about 0.1 to 0.2, with the smaller value corresponding to ships with struts, and the larger value applying to ships with bossings. PC values of 0.73 for single-screw ships and 0.68 for multi-screw ships are average values and are normally found to be suitable for preliminary estimates.

In the design of submarines, another component of shaft load may become of sufficient magnitude to warrant explicit consideration. The shaft axial load resulting from submergence is equal to the submergence pressure times the shaft area in way of the hull-penetration shaft seal. The axial load is equal to:

Ts = 0.35 SD2s (4)

Table 3 Propeller variable thrust excitation factors

Ts = submergence-pressure shaft load, lb
S = submergence design test depth, ft
Ds = shaft sealing diameter, in.
The predominant alternating thrust load generated by the propeller occurs at propeller blade-rate frequency as a consequence of the nonuniform inflow water velocity to the propeller. The magnitude of the variable thrust loads is dependent upon the number of propeller blades. For single-screw ships, an even num¬ber of blades will result in greater alternating thrust loads than an odd number. For prelimi¬nary estimates, the magnitude of the alternating thrust as a percentage of mean thrust can be taken from Table 3.

Insofar as the strength of the shafting is concerned, neither the mean nor the alternating thrust loads are ma¬jor design considerations. With merchant ships, the mean compressive stress is 1000 to 1500 psi; even in highly stressed shafts in naval ships the mean compressive stress seldom reaches 2500 psi. Torsional shear stresses are of predominant importance; and since the stresses due to thrust do not combine additively with the torsional stresses, the importance of the thrust stress is reduced even further.

5.3.5 Bending Loads.

Loads which cause bending stresses to occur in the shafting are the result of gravity, shock, off-center thrust loads, and whirling shaft vibra¬tion. With the exception of once-per-revolution whirling vibration, all are alternating loads relative to a point on the shaft and occur at either shaft rotative frequency or once, or twice, the propeller blade frequency.

The weight of the shafting itself, which is a gravity load, is normally of minor importance with regard to in¬board shafting unless there are unusual weight concen¬trations, such as a shaft locking device or brake drum, a pitch-control mechanism for a controllable-pitch propeller, or an exceptionally long span between bearings. When the shaft spans between bearings are essentially equal, and neglecting the weight of flanges, the maximum static bending moment occurring at the shaft bearings as a re¬sult of shaft weight can be determined approximately as


M = bending moment at bearing, in.-lb
L = span between bearings, in.
w = weight per unit length of shafting, lb/in.

If the spans between bearings are not approximately equal, such a simple approach cannot be used; instead, a continually supported beam analytical technique must be used. The customary practice is to use a continuous-beam analytical procedure to calculate the bending moments at all critical shaft locations.

Gravity loads on the outboard shafting tend to be of major importance due to the large concentrated weight of the propeller. The long length of the bearings used outboard complicate an accurate definition of the bearing reaction resultant location. The assumed locations of the bearing reaction resultants are very important as they are direct determinants of the bending moments calcu¬lated. An accepted practice is to assume the reaction to be at the center of all bearings except the bearing just forward of the propeller. Because of the large weight of the propeller, the propeller shaft has a significant slope at this bearing; therefore, the resultant bearing reaction tends to be in the after region of the bearing. Water-lubricated bearings have L/D ratios of about 4 for this bearing, and the resultant reaction is usually assumed to be one shaft diameter forward of the aft bearing face. Oil-lubricated bearings have L/D ratios that range from about 1 to 2, and inspections of the shaft contact in these bearings indicate that hard contact is confined to the after region of the bearing for a length approximately equal to the diameter of the shaft. The accepted practice is to as¬sume that the resultant bearing reaction in oil-lubricated bearings is located one-half shaft diameter from the after bearing face.

Generally the most significant shaft bending moment is due to the overhung weight of the propeller. The maxi¬mum static propeller shaft bending moment is computed as

Mp = Wp Lp (6)
Mp = propeller overhung moment in propeller shaft, in.-lb
Wp = weight of propeller assembly in water, includ¬ing shafting, abaft the aftermost bearing re¬action resultant, lb
Lp = distance from CG of propeller assembly to aftermost bearing reaction resultant, in.

Equation (6) is the moment at the bearing reaction point assuming that the reaction is a point support rather than a distributed reaction over a region of the shaft. The point-support assumption is justified in that the exact load dis¬tribution on the bearing is unknown and the moment cal¬culated in this manner is somewhat in excess of the actual value, which could be determined if the distribution of the bearing reaction was known.

There are a number of influences in addition to the gravity moment of the propeller that can have a signifi¬cant impact on the propeller shaft bending stress. These are eccentricity of thrust, water depth, sea conditions, and ship maneuvers. Under the general guidance of SNAME Panel M-8, the propeller shafts of a total of five ships have been instrumented to measure the bending stresses under actual operating conditions. Table 4 summarizes the characteristics of the ships tested. The tests were conducted to show the significance of the ship loading, sea conditions, ship maneuvers, and thrust eccentricity.

Eccentricity of the propeller thrust produces a signifi¬cant propeller shaft bending moment. With the possible exception of submarines, the propeller resultant thrust is eccentric from the propeller shaft centerline under almost all operating conditions and is usually in the upper star¬board quadrant of single-screw ships. Therefore, it does not combine directly with the propeller gravity moment. Light-draft operating conditions and "U" shaped stern sections tend to bring the thrust and gravity moments closer together and make them more additive. Table 4 gives the thrust eccentricity factor, C/D, determined from full-scale test data for heavy-displacement, calm-sea con¬ditions. The thrust eccentricity, C, shown in Table 4 is the resultant of the eccentric thrust and the gravity compo¬nents.

Table 4 Ships instrumented to determine tail shaft bending stresses

Full-scale tests on the Jamestown permit an evalu¬ation of the influence of ship loading, sea conditions, and maneuvers. These factors are summarized in Table 5. The factors presented in Table 5 are the ratios of the bending stresses for the various conditions described to the bend¬ing stresses under full-load, deep-water, calm-seas, and straight-ahead operations. The extrapolated results from the Observation Island tests generally support the factors in Table 5. It should be noted that maneuvers such as crash-backs rarely occur, and that shafting need not be designed to withstand stresses three times the normal value on a continuing basis.

Table 5 Increase in propeller shaft bending stresses due to various effects

The shock loadings that must be considered in the de¬sign of shafting for naval combatant ships are akin to the gravity loading and are frequently determined by multi¬plying the gravity force loads by a "shock" factor; how¬ever, more sophisticated methods are available for de¬termining the shock loads through the application of dynamic analysis techniques.

Misalignment in shafting systems can produce very sig¬nificant bending loads and this factor is probably responsi¬ble for the majority of inboard shafting failures. The sensitivity of the shafting to misalignment should be reviewed with particular attention given to water-lubri¬cated stern tube and strut bearings, which are subject to weardown in service. The sensitivity of the shafting to misalignment can be assessed by calculating the shafting bearing reactions and moments with the shafting in various misaligned conditions. These calculations are very easily made by using the bearing reaction influence num¬bers, which are discussed in Section 5.4.4.

Lateral or whirling vibration of the shafting does not cause stress reversals, but it can result in increased bend¬ing loads in the shafting. However, since the shafting system is designed to avoid whirling critical in the upper operating range, bending loads from shaft whirling vibration are not considered when designing the shafting.

5.3.6 Radial Loads.

Radial loads in shafting are caused by driving the propeller onto the shaft taper, shrink-fit-ting sleeves on the shafting, and shrink-fitting removable-flange couplings. The radial compressive stresses re¬sulting from these loads are normally of insignificant magnitude and are not considered in determining the shaft factor of safety. However, these radial loads can be of importance in that they can give rise to fretting corro¬sion when coupled with bending loads or alternating torsional loads that cause minute relative movement of the mating surfaces. Fretting corrosion can be controlled by limiting the relative motion and by cold-rolling the mating shafting surface. Cold-rolling of shafting surfaces is dis¬cussed in Section 5.4.7.
Another consideration is that if a radial load is applied abruptly, a stress concentration can occur. Therefore, the ends of shrunk-on hubs, liners, etc. should be designed with stress-relief grooves to minimize sudden changes in radial compression loads caused by shrink or press fits.

Section 4

Shafting Design

5.4.1 Shaft Materials.

With the exception of naval ves¬sels and merchant vessels of very high power, mild steel is used for both inboard and outboard shafting. In the case of high-powered ships, the inboard shafting may be made of high-strength steel; however, high-strength steel is not recommended for outboard applications. Because of the seawater environment, as well as the fretting corro¬sion conditions that exist at shaft sleeves and the propeller interface, the fatigue limit of high-strength steel is not reliably greater than that of mild steel, nor is the endur¬ance limit in a fretting corrosion condition better than that of mild steel.

Considerations in the selection of shafting materials are: fatigue characteristics, weldability, the nil-ductility temperature, and the energy absorption capability. An array of chemistry and physical property standards has been established for marine shafting materials that pro¬vides a range from which shafting materials can be se¬lected.

5.4.2 Computation of Shaft Diameters.

Shafting for merchant vessels is required to meet the minimum stan¬dards set by the classification society which classes the vessel. Classification societies use rather simple formulas to compute the minimum shaft diameters. These formulas normally contain coefficients which are changed from time to time in recognition of experience or advancements in technology. The American Bureau of Shipping (ABS) formula for propulsion shafting is of the following form

D = required shaft diameter, in.
K = shaft design factor, which is dependent upon de¬sign details and ranges from: 0.95 to
1.2 for line shafts, 1.15 to 1.18 for stern tube shafts, and 1.22 to 1.29 for propeller
H = rated shaft horsepower
R = rated rpm
U = ultimate tensile strength of shaft material, not to exceed 60,000 psi for propeller shafts or 116,000 psi for other shafts

It may be noted that equation (7) does not explicitly recognize bending loads and dynamic loads; nevertheless, equation (7) does provide a sound basis for the establish¬ment of shafting diameters. This is because the predomi¬nant torsional shear stress in line shafting is properly considered and an appropriate allowance has been made for propeller bending loads and dynamic loads. The level of torsional shear stress, Ss, corresponding to equation (7) can be determined by observing that


By substituting equation (7) into equation (8) and setting U = 60,000 psi for mild-steel shafting, it is seen that


When K = 1, as for straight sections of line shafting for diesel-driven ships, the mean torsional shear stress would be 7226 psi. The minimum tensile yield stress of mild steel is 30,000 psi; consequently, it is seen that adequate margin is provided for secondary influences that may appear to be neglected.

The shaft design factor, K, specified for a propeller shaft that has a keyless propeller attachment and oil-lubricated stern tube bearings is 1.22, which means that the propeller shaft diameter is required to be 22% larger than the corresponding straight section of line shafting that is sized with K = 1. The 22% increase in diameter is based upon analytical and empirical data and is in recogni¬tion of influences such as the propeller shaft bending load due to the overhung propeller weight and dynamic propeller loads.

Equation (7) includes allowances for the shafting loads associated with conventional ship designs; however, no provisions are made for navigation in ice. The ABS Rules acknowledge the substantial loads that ice navigation can impose upon a ship, and the design criteria for the shafting system is one of the specific aspects of a ship that is required to be strengthened for navigation in ice. There are several classes of ice strengthening, which cor¬respond to different types of operating regions, ice condi¬tions, and vessel service.

In no case can a designer accept classification society design criteria without question, particularly when ap¬plied to unusual designs. Classification society rules are largely established on the basis of successful experience; consequently, a designer must analyze a particular design from the perspective of conventional practice and compen¬sate for the effects of influencing factors not appropri¬ately considered.

Prudence requires that the propeller shaft diameter specified for a particular application be increased by a small margin (0.25 to 0.5 in.) above the minimum diameter required by the classification society rules. This margin can be used to remove a small amount of surface metal in the event that the shaft becomes superficially damaged then being handled or during service without infringing upon the classification society minimum requirements. If no margin is provided, a small damaged area could neces¬sitate weld repairing the damaged area or perhaps scrap¬ping an expensive shaft.

The formulas included in the ABS Rules for the estab¬lishment of minimum shafting diameters do not preclude the use of other analytical design procedures. The ABS Rules include a provision which states that, as an alterna¬tive to the use of the formulas, shafting with a minimum safety factor of 2.0, based on a detailed fatigue analysis, will be specially considered.

A service life comparison of 15 oversized propeller shafts, which have section moduli that are 74% greater than required by ABS, with 15 shafts of normal size, which have section moduli that are 11.5% greater than required. The comparison showed that the mean expected service life of the oversized shafts was; less than that of the shafts of normal size. Although the statistical sample was small, the study clearly showed that propeller shaft problems are not necessarily solved by simply making the shaft larger.

The approach used to establish the size of naval shaft¬ing is considerably different from that used with mer¬chant shafting. An effort is made to assess all significant shafting loads in each particular case, although some loads are by necessity handled in an approximate manner. For example, in order to allow for the effects of off-center thrust and abnormal loadings due to rough weather and the like, the propeller shaft, bending stress due to the static weight of the propeller is multiplied by a factor of 3 for single-screw ships and 2 for multiple-screw ships.

An additional difference between merchant and naval procedures is the criteria of acceptance. In naval practice, dual criteria are used. Factors of safety are specified for all shafting and, in addition, a specific bending stress limit is specified for the propeller shaft. The reason for the latter requirement is that fatigue tests conducted on mod¬els of propeller shaft assemblies and crankpins showed that alternating bending stress levels in excess of 6000 psi in surface rolled (cold-rolled) shafts result in fatigue cracks after 84 million stress reversals. Therefore, normal operating bending stresses in excess of this stress level are not prudent design criteria. Furthermore, the endurance limit of a propeller shaft assembly can be essentially independent of the fatigue limit of the material in air. If seawater contacts the steel shaft, no endurance limit exists; and it is only a matter of time before cracks occur that are followed by ultimate failure.

5.4.3 Bearing Locations.

Bearing locations have been determined by an array of criteria. It was once thought that providing two bearings per shafting span was desir¬able because that arrangement facilitated shafting instal¬lation and alignment. Also, bearing locations were often based upon intuitive judgment. With design criteria such as these, problems due to unloading of bearings, excessive rates of weardown, shaft whirling, and gearing misalign¬ment were not rare. Problems were frequently related to the system having too many bearings. In order to better understand the optimum locations for bearings, designers began analyzing shafting as a continuous beam. The de¬velopment and general dissemination of computer pro¬grams specifically applicable to shafting system analysis made it feasible to routinely conduct in-depth studies to optimize shafting systems as well as diagnose recurring problem areas.

Factors to be considered in determining the number and location of shaft bearings are:
(a) Ship's fixed structure and arrangement.
(b) Equality of line shaft bearing reactions.
(c) Bearing unit loads and L/D ratios.
(d) Shafting flexibility.
(e) Lateral vibration natural frequencies (shaft whirl).

The ship's fixed structure such as bulkheads and stan¬chions will usually require compromises in the shafting arrangement. Also, provisions for maintenance and over¬haul must be considered before final bearing locations are set.

From a cost and interchangeability standpoint, all line shaft bearings should be identical. Therefore, the bear¬ings should be spaced such that the bearing reactions are approximately equal. If this is done, the total number of bearings in the run of shafting is set by the total shaft weight, the permissible design unit load, and the accept¬able L/D limits. The number, R, of line shaft bearings required to support a run of shafting can be tentatively determined as follows:

W = total weight of shafting to be supported (note that gear and stern tube bearings may carry some line shaft weight)
p = design bearing pressure based on projected area (maximum permissible pressure less 5 to 10 psi to allow for variations)
D = shaft diameter in way of journal (normal prac¬tice is to increase the shaft diameter 1/8 to 1/4 in. in way of bearings)
L/D = bearing length/diameter ratio

After tentatively selecting the number of bearings and spacing them approximately equally, a detailed analysis of the bearing loads under all normal operating conditions is made (see Section 5.4.4). Particular care must be taken during the selection of the aftermost and forwardmost line shaft bearing locations to ensure that adequate shaft¬ing flexibility is provided; these bearings are subjected to a varying alignment in service. The conditions of primary importance are the cold start-up condition, the hot op¬erating condition, and the bearing weardown and mis¬alignment conditions. A major consideration in this analy¬sis is the influence of the shafting on the reduction gear bearing loads or diesel engine bearing loads resulting from the thermal change in the position of these bearings when going from the cold to the hot operating condition. Criteria for the alignment of the propulsion unit to the shafting are developed on the basis of this analysis.

Weardown of water-lubricated outboard bearings al¬ters the loads on the aftermost line shaft bearings. The loads on the aftermost bearings must be analyzed for all operational conditions of weardown to ensure satisfactory performance. A major concern is the possibility of a bear¬ing becoming unloaded. The effects of weardown are dis¬cussed further in the following sections.

The conclusion reached was that for shafting arrangements having one or more line shaft bearings the minimum span ratio (i.e., ratio of bearing center distance to shaft diame¬ter) should be 14 for shafts with diameters in the range of 10 to 16 in. and 12 for shaft diameters of 16 to 30 in. The maximum span ratio could be in the range of 20 to 22 but the final determination must be based on strength, shaft slope at the bearings, and vibration characteristics.

5.4.4 Shafting System Calculation Output.

In the course of preparing a shafting arrangement, alignment studies are conducted to determine the effects of bearing wear-down and the effects of changes in the heights of the gear and steady bearings resulting from thermal expansion. The alignment studies are based upon a computer model that is developed from shafting arrangements such as illustrated by Figs. 5.1 and 5.2. The model incorporates the location of all concentrated weights, changes in shaft di¬mensions, and locations of bearings. The effect of buoy¬ancy on the weight of the propeller and wet shafting is considered. Specialized computer programs that are based on continuous-beam analysis methods are generally used to calculate the data required to conduct shafting analyses.

The important output from shafting computer calcula¬tions includes the following specific data:
(a) Line-in-line reactions.
(b) Slope of shafting at discrete points.
(c) Deflection of shafting at discrete points.
(d) Moments in shafting at discrete points.
(e) Lateral natural frequency of shafting.
(f) Bearing reaction influence numbers.

The shafting line-in-line bearing reactions are the reac¬tions with all bearings aligned concentrically, and are il¬lustrated by the first row of Table 6 for the shafting arrangement shown in Fig. 5.1. The significance of the shaft slopes, shaft deflections, shaft moments, and lateral natu¬ral frequency of the shafting is apparent; however, the importance of bearing reaction influence numbers may not be as evident. Table 7 is a tabulation of the bearing reaction influence numbers for the same shafting ar¬rangement. The numbers given in Table 7 represent the change in the magnitude of the bearing reaction of the various bearings as a result of raising any bearing one mil. Through the application of these influence numbers, which reflect the shafting system flexibility, it is possible to investigate the influence of shafting misalignment caused by thermal expansion, weardown, and other such effects. Alignment requirements are developed on the ba¬sis of the bearing reaction influence numbers. Also, the principles employed with the hydraulic jack method of measuring bearing reactions (see Section 5.4.12) originate with the bearing reaction influence numbers.

Table 6 Tabulation of bearing reactions for shafting arrangement shown in Fig 5.1

Table 7 Bearing reaction influence numbers for shafting arrangement shown in Fig. 5.1

There are many instances where bearing reaction influ¬ence numbers provide the basis for essential analytical capabilities; however, such data often are not available when they are needed. As an alternative to generating bearing reaction influence number data from specialized shafting analysis computer programs, it should be noted that the same data can be derived from any of the general¬ized finite-element analysis procedures. This is accom¬plished by creating a beam model that incorporates all bearing locations and all significant changes in shaft ge¬ometry. Successive calculations are then made to deter¬mine the effect upon all bearing reactions that results from each of the bearing positions being individually dis¬placed one mil vertically. To produce a complete table of bearing reaction influence numbers, a calculation must be made for each bearing in the shafting system. To simplify the calculations, the vertical stiffnesses of the bearing housings and foundations are generally assumed to be infinitely rigid relative to the flexibility of the shafting in way of the bearings. This is generally a permissible assumption; however, unusual arrangements, such as a rubber-mounted outboard bearing, may require that the flexibility of the bearing support be considered.

5.4.5 Shaft Alignment.

The alignment of all main pro¬pulsion shafting, including that for turbine-gear, diesel-gear, and direct-drive diesel prime movers, is carried out following essentially the same steps. There are some unique differences in the criteria for satisfactory alignments, which primarily concern the presence of a reduction gear; however, in all ships both the outboard bearings; and the line shaft bearings must be loaded within accept able limits, the shafting must be manufactured without excessive eccentricity, and the athwartship alignment of the shafting must ensure that there will be no objectionable side loads on bearings.

a. Shaft alignment to reduction gears.

The ship structure that supports propulsion reduction gears is com¬monly designed to serve as the main lubricating oil sump; consequently, when the lubricating oil warms to operating temperature, the containing structure expands. When the propulsion plant goes from the cold to the operating condi¬tion, the slow-speed gear bearings typically rise in the range of 15 to 30 mils relative to the line shaft bearings. This rise can significantly alter the reactions of the slow-speed gear bearings and the forward line shaft bearings. Of particular concern is the fact that the static load on the forward slow-speed gear bearing decreases while that on the after bearing increases. As can be seen from the typical reduction gear bearing reaction diagram, this causes the slow-speed gear to assume a crossed-axis position relative to the slow-speed pinions, which are not similarly affected. As a result, the tooth load tends to be more heavy on one end of each helix. loads on the slow-speed gear bearings. No standard procedure has been established for the determination of the allowable difference between the slow-speed gear bearing reactions and outlines some of the complexities that must be taken into consideration. One possible complication is a nonparallel rise of the gear bearings due to temperature differences in way of the forward and after slow-speed gear bearings.

The flexibility factor, which has also been less appropri¬ately called the allowable setting error, is conveniently used as an index of shafting flexibility in way of the reduction gear. The flexibility factor, FF, is defined as the allowable difference in the static vertical gear bearing loads divided by the difference between the bearing reac¬tion influence number of the forward slow-speed gear bearing on itself and the after slow-speed gear bearing on itself. Therefore, the flexibility factor is determined as follows:


ΔR= allowable difference between the two slow-speed gear bearing static reactions, lb
I11 = reaction influence number of forward slow-speed gear bearing on itself, lb/in.
I22 = reaction influence number of aft slow-speed gear bearing on itself, lb/in.

The flexibility factor represents the total of the permis¬sible error in estimating the thermal rise of the slow-speed gear bearings relative to the line shaft bearings and the permissible error in setting the gear to the line shafting without exceeding the maximum allowable difference in the static slow-speed gear bearing reactions. An absolute minimum acceptable value for the flexibility factor has been recognized to be 0,010 in.

If the flexibility of the shafting meets the flexibility factor criterion, the analysis proceeds to an investigation of the gear-to-shaft alignment. Beginning with the line-in-line reactions, that is, the bearing reactions with all bearings concentric, the estimated thermal rise of the gear bearings relative to the line shaft bearings when going from the cold to the operating temperature is used to establish alignment data that will provide approxi¬mately equal slow-speed gear bearing static reactions when in the operating condition. It must additionally be ascertained that the line shaft bearing reactions are satis¬factory under all operating conditions.

The installation of the shafting system is usually begun by positioning the line shafting on the theoretical shafting centerline (the line-in-line position), as established by con¬struction reference marks on the hull structure. The bear¬ings that support the outboard shafting are also installed relative to this theoretical reference line, but not necessar¬ily concentric with it, as required to satisfy the results of the alignment analysis. One convenient method that has been used to align the line shafting requires the shafting sections to be supported on temporary bearings such that the centers of the flanges are concentric with the shaft centerline through the support points and the flange faces are perpendicular to that centerline; while this cannot be done with absolute precision, sufficient accuracy can gen¬erally be obtained by supporting the shafting sections at approximately the 2/9 points from each end. When this is done, the flange drops and gaps are measured directly at the flanges with no corrections required. Drop is the vertical distance between the centers of adjacent flanges, and gap is the difference in opening between the top and bottom of the two flanges (nonparallelism of the flange faces). A correction usually must be made to the drop and gap measured at the stern tube shaft flange since it is impracticable to support the stern tube (or propeller) shaft such that the forward stern tube shaft flange is concentric and perpendicular to the theoretical shaft centerline. Consequently, the alignment of the stern tube shaft to the aftermost section of line shafting must include a correc¬tion for the slope and deflection of the forward stern tube flange when the stern tube shaft is supported in the as-aligned condition.

With the line shafting installed in the line-in-line condi¬tion, the positions of the slow-speed gear bearings relative to the centerline of the line shaft bearings are readily determined from the drop and gap of the slow-speed gear shaft flange relative to the line shaft flange; this is de¬rived geometrically. Based on these geometrical data, the bearing reaction influence numbers can be used to plot the bearing loads for various alignment conditions. Such a plot is shown in Fig. 5.9. Figure 5.9 is an informative means of illustrating the effects that the thermal rise of the slow-speed gear bearings and alignment errors have upon bearing loads.

Table 6 shows the cold alignment bearing reactions with an alignment corresponding to point A on Fig. 5.9. The hot reactions listed in Table 6 are the estimated bearing reactions after the gear has reached operating tempera¬ture; this is point B on Fig. 5.9.

The alignment of the athwartship direction should be such that no significant forces are imposed on the slow-speed gear bearings in the horizontal plane.

The initial bearing reactions are often measured with the shafting coupled-up in the line-in-line condition except for the outboard bearings and the slow-speed gear bear¬ings, which are positioned in compliance with the theoreti¬cal alignment calculations. The initially measured bearing reactions are then used to establish the bearing height changes that are required to optimize the bearing loads. After adjusting the bearing heights, the bearing reactions are measured again to confirm that the bearing reactions in the cold condition are within established criteria. As a subsequent confirmation, it may also be advantageous to measure the bearing reactions during dock trials or sea trials when the shafting system is in the hot operating condition.

Fig.5.9 Gear-to-shaft alignment analysis

The bearing reaction influence numbers also provide a means to study the effects of circumstances such as bear¬ing movements resulting from hull deflections, bearing weardown, and the like. An analysis of bearing reactions with the stern tube and strut bearings worn down is given in Table 6.

b. Shaft alignment to a slow-speed diesel.

The pro¬cedure used to align propulsion shafting to a direct-drive diesel engine is basically the same as that used for the alignment to reduction gears; however, there are signifi¬cant differences in the procedural details. The principal considerations are to ensure that the crankshaft stresses resulting from shafting loads are not excessive and to ensure that the shafting and engine bearing loads are within acceptable limits.

The distance between the engine foundation and the crankshaft bearings is relatively small when compared with the height of the heated structure below a slow-speed gear shaft; consequently, the thermal rise of the crankshaft when going from the cold to the hot operating condition is similarly small and more accurately predict¬able than is the thermal rise of reduction gear bearings. The engine manufacturer normally provides an estimate of the thermal rise of the engine crankshaft centerline resulting from the engine going from the cold to the hot operating condition.

The procedure begins by aligning the outboard shafting in accordance with the theoretical alignment calculations, installing the inboard shafting in the line-and-line position, and positioning the diesel engine to obtain engine bearing loads as determined by the shafting alignment calculation output. With these initial alignment conditions and with the engine output flange and the shafting flanges made up, the line shaft bearing reactions should be measured, as well as the aftermost engine bearing reaction, if acces¬sible, to establish the as-installed baseline. The as-in¬stalled bearing reaction baseline is then used to establish any changes to the bearing heights that are required to ensure satisfactory bearing loads. After adjusting the bearing heights, as predicated by the measured bearing reactions and the theoretical bearing influence numbers, the bearing reactions should be measured again to con¬firm that the cold bearing reactions satisfy the established criteria. The bearing reactions may also be measured with the engine at the operating temperature if there is any reason for concern relative to the effects that reaching operating temperature may have on shaft alignment.

Before operating the diesel engine, the stress variation in the crankshaft, as it rotates, should be measured with the shafting made up to the engine and the engine bolted down to its foundation. This can be accomplished by mea¬suring the variation in the axial deflections of the crank shaft throws as the crankshaft is rotated. Generally, the technical manual for the engine describes the procedure to be used to measure the throw deflections and establishes the bounds for acceptable deflection readings. If the crankshaft deflection measurements taken exceed the deflection limits established by the engine manufacturer, the underlying cause must be determined. Some of the factors that can influence the amount of crankshaft deflection are: loads imposed on the crankshaft by the shafting, engine casing distortion caused by foundation bolting loads, and improperly set or wiped crankshaft bearings.

When the shafting system bearing reactions are con¬firmed to be satisfactory and the crankshaft throw axial deflections, and hence stresses, are found to be within acceptable limits, a satisfactory shafting alignment is as¬sured.

5.4.6 Propeller-to-Shaft Interface.

Design details of the propeller-to-shaft interface are a critical aspect of a shaft¬ing system development. Propeller shaft failures in way of the propeller were not rare up through the 1960's and into the 1970's. However, the advances in design technol¬ogy (e.g., stress relief grooves at the forward end of the propeller and the aft end of the liner, shortened and spooned keyways, slotted keys, and improved sealing methods) significantly improved the reliability of propel¬ler shafts and increased their service lives. Also, improve¬ments in inspection technology have provided the means to detect incipient cracks and thus have greatly reduced the loss of propellers at sea.
The naval type of propeller-to-shaft interface is consistent with merchant practice and both have comparable service histories.

The propeller keyway introduces a stress concentration in the propeller shaft and weakens the shaft even though the keyway may have generous fillet radii and the for¬ward end of the key may have slots to relieve the key load at the forward end. To avoid the stress concentrations associated with propeller keys and to minimize the vagar¬ies associated with fitting the propeller on the shaft taper by brute-force hammering, propeller nuts have been de¬veloped that incorporate annular pistons, which are moti¬vated by hydraulic oil or grease. A "hydraulic" nut pro¬vides the means to apply a large force of a known magnitude to the propeller, thereby pushing it onto the shaft taper such that the frictional force between the propeller and shaft is sufficiently large to transmit all torsional and thrust loads, and no propeller key is re¬quired. The operating principles of a "hydraulic" nut are illustrated by Fig. 5.10. In effect, the device is seen to be a hydraulic ram that is built into the propeller nut. The tire, which is pressurized to about 15,000 psi, develops a large axial force under controlled conditions. A pneumatic-hy¬draulic pressure intensifier is used to produce the high hydraulic-oil pressure.


Fig. 5.10 Hydraulic propeller nut

The first, step in fitting a propeller to a shaft, with any procedure, is to ensure that there is uniform contact between the propeller and shaft over 60% of the mating surface. The propeller is then pushed firmly up on the taper, and the hydraulic nut is put in place and used to advance the propeller a specified amount that is depen¬dent upon the ambient temperature. The temperature cor¬rection is required because of the difference in thermal expansion between the material of the propeller and that of the shaft.

Keyless propeller designs rely entirely upon the friction between the propeller and shaft to withstand the propeller torsional and thrust loads, with the torsional loads gener¬ally the larger. For a dry, greaseless, installation, the coefficient of friction between the propeller and shaft may vary from a low of 0.13 to a high of approximately 0.18, being influenced by factors such as the materials and the quality of the fit-up. However, the effective coefficient of friction has been found to be about 0.15. To provide adequate service margins, the frictional loads that can be transmitted must be 2.8 times the loads corresponding to ahead operations. Loads experienced during astern opera¬tions are generally smaller than for ahead operations, but this should be confirmed to be the case. The amount of propeller advance required to achieve the desired fric¬tional load-carrying capability is readily calculated and is used to establish propeller installation criteria.

The hydraulic nut is also used to withdraw, or "jump," the propeller from the propeller shaft, as indicated by Fig. 5.10. The hydraulic oil pressure required to remove the propeller is 30 to 50% of that required to install the propeller, with the difference being the effect of shaft taper. The shaft taper used with keyless propellers ranges from 1:12 to 1: 20, with lower tapers becoming more common.

Some earlier hydraulic nut designs entailed the use of oil pressure to expand the propeller hub while it was forced onto the taper. By expanding the propeller hub, a reduced force was required of the hydraulic nut to ad¬vance the propeller hub up the taper; and theoretically, an expanded propeller hub could be withdrawn without the use of a hydraulic nut. Some earlier designs involved the use of cast-iron sleeves, which were installed between the shaft taper and propeller hub. However, as the design of hydraulic nuts has matured, these complexities of the earlier designs have been found to be unwarranted.

5.4.7 Cold Rolling.

Rotating shafts that are subjected to bending stresses in way of shrunk-on or tightly fitting mating components can result in fretting corrosion. Fret¬ting corrosion occurs where there are minute amounts of relative motion between two tightly fitting materials, which causes the surface material to tear, thereby intro¬ducing a stress riser in the shaft, with the progressive ultimate consequence of a shaft failure.

Fretting corrosion was first recognized as the cause of railway car axle failures where hubs were shrunk onto the the axles. Cold-rolling the axles in the shrink-fit area was accomplished to introduce compressive stresses in the shaft surface; these compressive stresses were found to alleviate the problems experienced with railway car axles.

Conditions conducive to fretting corrosion also exist at the ends of sleeves and at the forward end of propeller hubs in marine shafting configurations; and the develop¬ment of fretting fatigue cracks in the surface of the pro¬peller shaft at the forward end of the propeller hub and under the after end of the propeller shaft sleeve, where bending stresses are normally the highest, is one of the most common modes of propeller shaft failure. The intro¬duction of compressive stresses into a material by cold rolling the surface will not eliminate the occurrence of fatigue cracks that are caused by fretting corrosion; how¬ever, the compressive stresses will retard the formation of minute cracks by fretting corrosion and will significantly reduce the propagation rate of cracks that form. When tested and applied to marine shafting systems, cold rolling also proved to be effective in extending the life of marine shafting systems
Propeller shafts are commonly cold rolled for a distance forward and aft of the shaft taper, where the propeller hub mates, and in way of the ends of shaft liners. Residual compressive stresses are introduced into the shaft to a depth of about 0.5 in.

5.4.8 Protection from Seawater.

Except in the case of designs in which all bearings are of the oil-lubricated type, outboard shafting is provided with sleeves that are shrunk on the shafting in way of bearings, stuffing boxes, and fairings. Shaft sleeves are made of bronze or other materi¬als, which are resistant to attack by seawater.

Ships having a single short section of outboard shafting may employ a single continuous sleeve. Where continuous sleeves are not used and the steel shafting would other¬wise be exposed to seawater, those areas of the steel shaft are normally protected by applying a rubber or plastic compound directly to the shafting surface. The ade¬quacy of both rubber and plastic protective coverings for outboard shafting has not been uniformly good, and on occasion the protection offered to outboard couplings by such coverings has been particularly unsatisfactory. In applying these shaft coverings, good quality control and proper practices are essential for good results. Shaft cleanliness (bright clean steel) at covering installation is essential for the covering to bond properly, and bonding can be further improved by grit blasting the shaft to roughen its surface. Rotating coupling covers (fairwaters), which clamp onto and rotate with the shaft, thereby eliminating the violent erosive flow of water around cou¬pling bolts, have been used to avoid the erosive effect of the water.

A reliable static sealing arrangement at the propeller, which prevents seawater from contacting the propeller shaft, is of the utmost importance. A propeller-shaft as¬sembly in which seawater is allowed to contact the shaft will result in the shaft not having an endurance limit, and therefore, it is only a matter of cycle accumulation before a failure occurs. Typical designs of propeller-hub sealing arrangements, which are necessary with systems utilizing water-lubricated outboard bearings.

5.4.9 Shaft Couplings.

Except in instances where spe¬cial considerations preclude their use, shafting sections are connected by means of integrally forged couplings as illustrated by Fig. 5.11. Although the design of virtually all integral shaft couplings is similar, the details of shaft coupling designs vary. For example, despite individual preferences, no specific number of coupling bolts has been established as optimum, and the proportions of flange dimensions and flange fillet radii may vary from one de¬sign to the next.

The headed bolt design shown by the upper half of Fig. 5.11 is commonly used to connect shaft sections. The diameter of the bolt is given a taper of about 1/8 in. per foot and the mated bolt holes are reamed at assembly to ensure a metal-to-metal fit. The headless bolt illustrated by the lower half of Fig. 5.11 is an alternate design. The taper of headless bolts is increased to about 3/4 in. per foot for bolt diameters less than 3 in. and 1 in. per foot for larger bolts to provide an additional capability to transmit axial loads. The spot-faced surfaces on the coupling flanges, on which the coupling nuts land, must be perpen¬dicular to the axes of the coupling bolts; otherwise, galling can occur at local areas of hard contact.

Flange coupling bolts, such as illustrated by Fig. 5.11 are commonly installed by hammering custom-designed wrenches until the installing mechanic is satisfied with the "ring" of the hammer. Extensive experience confirms that satisfactory service can be obtained using this proce¬dure; although it entails the disadvantages of having to rely upon the experience of the mechanic, subjects the bolt mating surfaces to damage, and possesses no means of confirming the amount of preload achieved.

Fig.5.11 Shaft bolting designs

Fig. 5.12 Hydraulically preloaded bolt design
Figure 5.12 is an illustration of a hydraulically preloaded bolt that may be appropriate for use in some cases to avoid bolt mating-surface damage when the connection is broken and to provide a means of confirming the amount of bolt preload achieved. With this type of bolt, a hydraulic pressure of about 25,000 psi is used to elongate the bolt, with a simultaneous known decrease in bolt diameter. A hydraulic shutoff valve maintains the bolt in the elongated condition until it is in place. After installation, the hydrau¬lic power head is removed, and a depth gage is used to measure the length of the hole in the bolt and, conse¬quently, the preload achieved in the installed bolt. The bolts are easily removed by reversing the process. There are numerous appropriate applications for bolts of this type.

Couplings with removable flanges are required in some instances; for example, those cases where a liner (that is not designed as halves which are welded in place) is to be installed on a shaft that requires a bolted flange on each end. Figure 5.13 illustrates a typical removable-flange cou¬pling and shows the means provided to transmit both thrust and torque. Both torque and thrust are normally transmitted by friction between the shrunk-on muff and the shaft. The keys are a backup for the transmission of torque, and the split collar is a backup for the transmission of thrust.

Removal shaft couplings have also been used that are mounted in place by hydraulic pressure to both expand the coupling hub and advance the hub up a tapered liner, which is installed on the shaft. Torque and thrust are transmitted between the coupling hub and shaft solely by friction.

Some shafting arrangements are designed such that it is necessary to remove the forward flange of a stern tube shaft in order to withdraw the shaft aft; this is undesirable when particular types of coupling designs are used be¬cause it is difficult to remove the flange without damag¬ing the flange-shaft interface. An arrangement sometimes preferred is one in which the outside diameters of the stern tube bearing bushings are made sufficiently large so that they can be removed to permit the stem tube shaft to be withdrawn aft with the forward flange in place. Figure 7.8 illustrates a strut bearing with a remov¬able bushing that permits the shaft to be withdrawn with the forward flange in place.

Fig.5.13 Removable-flange coupling
5.4.10 Shaft Axial Movements.

The axial movement of the shafting relative to elements that are fixed to the hull must be considered to establish proper clearances between the propeller hub and stern frame structure and between bearing housings and rotating elements within the bearings that are secured to the shaft (oil slingers, oil disks, etc.). Several factors can contribute to the move¬ment of the shaft relative to hull structure; these are:

1. Thrust bearing clearances. Axial clearances between the thrust collar and shoes permit a corresponding fore-and-aft movement of the entire shafting system.
2. Propeller thrust. The propeller thrust results in a small axial deflection of the shafting and thrust bearing.
3. Submergence pressure. For surface ships the sub¬mergence pressure is a minor consideration; however, for submarines the effects of the submergence pressure, both in terms of shaft axial loading and hull compression, are important.
4. Hull hogging and sagging. Hull bending loads strain the hull; however, the shafting is not similarly affected. This factor is conveniently assessed by assuming an ex¬treme-fiber hull bending stress and the location of the neutral axis of the hull in bending; the stress, and corres¬ponding hull strain, at the shaft centerline is then deter¬mined by interpolation.
5. Temperature differences. The shafting can be at a warmer temperature (70-80º F) relative to that of the hull structure (in the vicinity of 30º F), and the difference in thermal expansion results in relative movement.

The foregoing factors would generally not reach maxi¬mum values simultaneously, but they are prudently con¬sidered to do so. Typical axial movements of the propeller (the point at which movement is a maximum) relative to the hull range from 0.5 in., for tankers with very short shafts, to 2 in., for ships with long shafts.

5.4.11 Shafting Balance.

Solid shafting is inherently balanced, but hollow shafting requires attention in this regard. The balance of hollow shafting is accomplished during the machining operation by shifting lathe centers prior to the final machining cuts. The amount of static unbalance in a shaft can be determined by either a static or dynamic balancing technique.

After the rough machining cuts have been made, a shafting section can be statically balanced by removing the shaft section from the lathe, placing it on rails, noting the equilibrium position of the shaft section, shifting the lathe centers to compensate for the unbalance, and then taking additional machining cuts on the shaft section to effect a static balance. Good practice dictates that adjoin¬ing shafting sections be installed such that the residual static unbalances, as determined by a check on the rails after final machining, tend to offset.

Although shafting sections have occasionally been spec¬ified to be dynamically balanced (shaft sections rotated in a balancing machine to determine both static and dynamic unbalance), there are conflicting schools of thought re¬garding the necessity of a dynamic balance. The need for dynamic balancing is influenced by the maximum rotating speed of the shafting. It has been argued that the toler¬ances customarily imposed on the manufacture of shaft¬ing sections in conjunction with good shop practice pre¬clude objectionable shafting dynamic unbalance.

5.4.12 Shafting Eccentricity.

Propulsion shafting can become eccentric for a number of reasons, with accidents being the most common, particularly those while under¬way that involve the propeller. Shafting eccentricity, it¬self, is not of practical significance provided that neither the shaft balance nor the bearing reactions are adversely affected, and provided that the balance of masses, such as a propeller, attached to the shafting is not adversely affected. The eccentricity of shafting sections can be mea¬sured before the shafting is installed, and variations in bearing reactions resulting from shaft eccentricity can be determined by an alignment check.

In general, shaft eccentricity of an objectionable magni¬tude cannot be corrected by machining without reducing the shaft diameter below acceptable dimensions; there¬fore, an eccentric shaft must be straightened to be usable. Three methods have been used to straighten propulsion shafting: peening, flame heating (hot-spot method), and selective cold rolling. Peening involves hammering a local linear shaft surface area on the inside of the eccentric bend sufficiently hard to exceed the yield strength of the shaft material and thereby introduce residual compressive stresses in the peened area. Peening is more effective on smaller shafts. The mechanics of peening entails many vagaries; however, peening can often be done with the shaft installed.

With the flame heating or hot spotting method, a nar¬row linear shaft surface area on the outside of the eccen¬tric bend is heated. As the local surface area heats, the metal expands and the metal yield point decreases. The objective is to heat a local area such that the restraint of the cooler surrounding metal causes the metal in the heated area to exceed the material yield strength at the elevated temperature; consequently, when cooled, resid¬ual tensile stresses are introduced in the shaft. Flame heating requires experience to accomplish satisfactorily as there is a risk of adversely affecting the metallurgy of the material; however, flame heating can often be accom¬plished in place.

The selective cold rolling method is the most controlled and reliable means of straightening shaft sections; how ever, the cold rolling procedure generally requires the shaft section to be placed in a lathe. Selective cold rolling is accomplished by cold rolling the entire shaft circumfer¬ence in way of the bend, but with a much heavier imposed load on the inside of the bend. Higher residual compressive stresses are, therefore, introduced on the inside of the bend, which tend to straighten the shaft.

5.4.13 Determination of Shaft Alignment.

There are ba¬sically three ways that the alignment of a completely in¬stalled shafting system can be checked. One, which is akin to the drop-and-gap method of alignment at initial installation, is to remove the bolts from select couplings and compare the relative positions of mating flanges with calculated values. Although the circumstances sometimes require this method to be used, it is the least preferred method because of the numerous opportunities for erratic readings. A second method, which is both easier to accom¬plish and more directly meaningful, is to measure the loads being carried by the bearings with either a cali¬brated hydraulic jack .or a hydraulic jack in conjunction with a load cell. The hydraulic jack is used to lift the shaft off of a bearing, and the load carried by the jack is then related to the bearing reaction. A third method is to install strain gages on the shafting at strategic positions and determine the bearing reactions by utilizing the measured strain (shaft moments) to make the shafting a determinate system.

a. Hydraulic jack method.

When using the cali¬brated hydraulic jack or hydraulic jack and a load cell method, the actual bearing load is determined by placing a hydraulic jack as close to the bearing housing as possible (bearing foundations are often designed with an extension to provide a jack foundation as illustrated by Fig. 5.14). A dial indicator is located on the shaft immediately above the jack so as to measure vertical movement of the shaft. Where possible, the anchor point for the dial indicator should be independent of the bearing housing because the shifting loads on the bearing foundation can cause the bearing housing to tilt, which would introduce confusing readings. Before recording any readings, the position of the shaft in the bearing clearance should be checked to ensure that the shaft is in the bottom of the bearing and is centered athwartship. The shaft should be lifted at least once to ensure that it can be lifted 20 to 30 mils without coming into contact with the upper half of the bearing; this preliminary jacking also tends to reduce hysteresis in the shaft and erratic readings. For short shaft spans, a dial indicator should also be installed on the shaft at adja¬cent bearings so that any rise of the shaft at these bear¬ings can be noted, because in stiff shafting arrangements it is possible to also lift the shaft off a bearing adjacent to the one being measured.

Fig.5.14 Hydraulic jack method for measuring bearing reactions

With the dial indicators and jack in place, the shaft is raised and lowered in increments, noting the jack load corresponding to each increment of shaft rise. These data are plotted as shown in Fig. 5.15. The data points conform to two basic slopes. The slope of the lift-versus-load line as the load is transferred to the jack from the bearing represents the spring constant of the bearing shell, bear¬ing housing, and the like. When the shaft lifts clear of the bearing, an abrupt change in the slope of the data points occurs. The second slope corresponds to the bearing reac¬tion influence number for the bearing.

Due to the friction in the shafting and load-measuring system, the data points when raising the shaft do not coincide with those obtained when lowering the shaft; the characteristic pattern is the equivalent of a hysteresis loop. The deflection-versus-load plot indicates a higher jack load for a given shaft lift when raising the shaft than when lowering it. When using a calibrated hydraulic jack, the hysteresis in the load versus shaft-deflection relation¬ship tends to be larger than when a load cell is used. This is caused by the friction in the hydraulic jack (primarily seals). Load cells located such that they are subject to the force developed by the jack and can provide a direct readout in pounds with an accuracy of 0.5%.Calibrated hydraulic jacks are inherently less accurate than load cells; however, their accuracy is adequate for most pur¬poses.

Experience indicates that the true relationship between the jack load and shaft lift is approximately midway be¬tween the lines determined when raising and lowering the shaft as indicated by Fig. 5.15. However, in cases where the increasing and decreasing load lines are significantly different, the increasing load line should be favored. With an effective mean line established that represents the true relationship between the measured load and shaft lift, the load that would be on the jack at zero shaft lift and with the bearing removed is determined by extrapolating the mean line downward to zero shaft lift. If the jack and bearing are close together, the load as determined may also be considered to be the load on the bearing if the jack were removed (or the bearing load being sought).

Fig.5.15 Bearing reaction determined by hydraulic jack

Under favorable jacking conditions (with no binding of the shaft in the bearing due to athwartship misalignment, interference with stuffing boxes, etc.), experience shows that the accuracy of the bearing reactions determined is usually within 10% of the actual value. However, the influence numbers obtained by jacking may not be as accurate. When the bearings being jacked are located to¬wards the middle of the shaft and span lengths are fairly equal, jack influence numbers are generally within 30% of the calculated influence numbers. For bearings located near the ends of the shaft, the influence numbers obtained by jacking may disagree with the calculated values by 50% or more.

Both the load and influence number errors are due to inaccuracies that are inherent in the jacking procedure; e.g., the jack not being located at the bearing center, the load center in adjacent bearings shifting as the shaft is raised, and hysteresis in the shafting system and load-measuring system. Consequently, when a bearing is to be realigned, the distance that the bearing should be raised or lowered is more appropriately based on the calculated influence numbers rather than on the influence numbers determined by jacking.

When jacking bearings that are very close together or in cases where the jack must be located some distance from the bearing, a correction factor must be applied to the jack load measured to obtain an accurate assessment of the bearing reactions. The correction factor is as follows:

where Ibb is the influence of bearing on bearing and Ijb the influence of the jack on the bearing. The influence numbers used to calculate the correction factor are deter¬mined by including both the jack and the bearing being jacked as support points in the shafting system calcula¬tions. To be theoretically accurate, this correction factor should be used for every bearing that is jacked; however, only in the aforementioned two cases is it a factor of significance.
Table 6 contains a tabulation of the measured bearing reactions for the shafting system in Fig. 5.1 and illustrates typical jacking results. The oil in the reduction gear was heated to operating temperature and circulated; there¬fore, the measured reactions should be correlated with the hot reactions.

The hydraulic jack procedure can also be used to detect bent shafts in that the bearing reactions can be deter¬mined with the shaft rotated in 90-deg increments. If the bearing reaction changes significantly with shaft position, a bent shaft can be suspected. This technique is often appropriately used when analyzing a shaft that is sus¬pected of being bent. However, the uniform tightness of flange coupling bolts should be confirmed before conclud¬ing that a section of shafting is bent.

b. Strain-gage method.

The alignment of an in¬stalled and complete shafting system can also be deter¬mined by measuring the strain in the shaft at strategic positions. A shafting system with N bearing supports is N-2 degrees statically indeterminate, and N-2 additional data points are required to determine the shaft alignment. Referring to the shafting arrangement illustrated by Fig. 5.2, which has 7 bearings, an additional 5 data points must be known for the shafting alignment to be determinate. By installing strain gages at the break points indicated on the free-body diagram of Fig. 5.16, the moments in the shafting at these points can be measured, and the mo¬ments measured can be used to calculate the bearing reac¬tions. The equations that can be used to relate the bearing reactions to the measured bending moments are outlined in Table 8.

In Fig. 5.16 there is a free section, which does not contain a shaft bearing. This section is inherently determinate and the unknown shear forces can be calculated. A free section can be used between any two bearings to act as the start¬ing point in either direction for the determination of the shaft bearing reactions. When the free section is located adjacent to a two-bearing stern tube arrangement such as Fig. 5.16, a value for the unknown shear is established and only the two bearing reactions are unknown. This permits the determination of both bearing reactions, and establishes a known shear force on the forward end of the free section, which permits the remaining bearing reactions in the shafting system to be quantified.

Fig. 5.16 Free-body diagram of shafting arrangement

Rn= Bearing reaction
Ln= Distance from shaft forward end
Xi= Distance to strain-gage location
Mi= Moment in shaft, positive
Vi= Shear in shaft, positive
P = Propeller weight
G= Gear weight
U(X)= Shaft weight per unit length

If the propeller shaft in Fig. 5.16 had only one bearing support, i.e., if bearing 6 were not there, the free section would not be necessary because, with the knowledge of Me, the aftermost free-body shaft section is determinate and the aftermost bearing reaction and the shear force at e can be determined.

Three bearings with inaccessible connecting shafting (e.g., a double stern tube and strut bearing arrangement, or the shafting arrangement shown by Fig. 5.1 with a sec¬ond stern tube bearing added) cannot be analyzed using the strain gage method alone. For a double stern tube/ i strut bearing configuration, bearing reactions forward of a free section can be determined since the free section provides the needed shear force at its forward end. How¬ever, to determine the values of the three aftermost bear¬ing reactions, one of the bearings, such as the forward stern tube bearing, would have to be weighed. By knowing the load on the forward stern tube bearing and by includ¬ing a free section of shafting in the free-body diagram, the outboard shaft section becomes determinate since only the strut bearing and aft stern tube bearing reactions are unknowns.

Once the free-body sections are established for a given shafting arrangement, which defines the strain-gage loca¬tions, the equations for determining the bearing reactions are obtained by setting ΣM and ΣF equal to zero for each free-body section. When the specific geometry for a shaft system is incorporated into the equations, the integrals reduce to constants with the only variables being the bear¬ing reactions, the moments to be measured, and shear forces at the locations.

Advantages associated with the strain-gage method of determining shaft alignment are as follows:
• Both horizontal and vertical alignment can be checked simultaneously.
• Strain-gage readings can be taken at sea because of the ease with which the reading can be obtained, and there is no need for jack or dial indicator support structure.
• Once the gages are installed, a complete set of strain readings can generally be taken in less than an hour.
• Reactions of bearings that are inaccessible for jack¬ing can be determined accurately.

The last two items are the most important advantages associated with the strain-gage method. However, the strain-gage method requires more calculations to interpret the test data and requires a more complex measurement technique.
Chapter 6

Vibration problems on shafting

As one of the particular problems on marine engineering, we may take vibration problems on shafting at first. The fundamental approach to these problems will give us good basis of engineer¬ing judgment when we would be involved in the troubles of this nature, which is rather frequent cases in practice.

Shafting is subjected to torque and thrust acting as external forces, beside weight and some constraint in bearing under running condition. These forces and moments induced are mostly of varying nature while shafting is consisting typically mass and spring systems in various aspects, therefore it has natural¬ly been fertile field for vibration studies to grow.

As we may easily assume the natural frequency of a simple model of a mass with elastic shaft as shown in Fig. 6.1,

Fig. 6.1

Natural frequencies of bonding as well as torsional vibration are given respectively by following equations;

we get

In most cases of vibration on shafting, we must be careful for lower frequency impulse against bending, while higher frequency impulse against torsion.

It may also be noted that natural frequency is dimensionally inversely proportional to , namely if ship size becomes doubled, the natural frequency of the geometrically similar shafting will decrease to Ca 70%. It would be the reason why such primitive vibration troubles as had been solved already and have never been experienced for years, happened occasionally on board large vessels, that their natural frequency might have become lower enough to come across harmful impulse of lower order under normal working revolution of engine.
Hereafter, basic knowledge will be mentioned.
6.1 Torsional vibration

i) It is normal method when treating torsional vibration, that the system is supposed to be a reasonable model consisting of springs and masses, which would have the same vibration characteristics in this respect. Namely the masses of equivalent rotative moment of inertia, and equivalent length of shaft with certain size, which would give the same distorsion under the same moment.

Example; - geared shaft
Consider J2 as fixed, and moment M acting on J1. Turning angle between J2-Z2 is φ2, and correspondingly Z1, turns by angleφ1, and further, turning angle between E1-J1 isφ3.

Fig. 6.2

Then, (gear ratio)

Total angle of turning φ between J2 - J1 is

If spring constant C is defined as the moment which gives unit turning angle as , we get for shaft J1-Z1, and J2-Z2, , .

Thus equivalent shaft shall have spring constant C given by above equation.

On the other hand, if we consider the inertia effect of J2 on shaft at A, it will be regarded as the equival¬ent moment of inertia J with the turning angle α; namely


C is given for the solid shaft as follows:

ii) Any model consisting of spring and masses has its own modes of free vibration particular to its system, such as with 1 node, 2 nodes, 3 nodes etc., having respec¬tive natural frequencies.

Mode and respective frequency calculation is carried out by computer, when input data of springs and masses of the system are given, with the aid of the program prepared for the purpose.

As example by Halzer's-method will be given as follows:-

Fig. 6.3
Assuming angular frequency w,
mass 1; amplitude (β1= 1)
moment of inertia
angle of torsion of shaft

mass 2; amplitude
moment of inertia (max)

moment of shaft
moment of shaft
angle of torsion of shaft

mass 3; amplitude

Calculation process is continued until the last mass P and if w is correctly assumed,

It may be noted that in free vibration, all the masses in a system vibrate in the same phase, namely their amplitudes reach their own maximum of minimum value at the same instant. The relative amplitude of each mass is determined under free vibration with particular mode and respective natural frequency, but the absolute amount of amplitude has of course nothing to do with the mode no frequency.

Various examples of mode are shown in Fig. 6.3

iii) Forced Vibration

As is usually the case, free vibration will be damped by energy absorption due to deformation cycle after cycle, and there is left only vibration forced period¬ically with the frequency of external impulse working upon the system. When the vibration is in stational state, the work done by external force must be consum¬ed by the damping work in every cycle. The relation between four vibrating vectors, such as moment of inertia Iw2φ0, damping moment kwφ0, spring moment Cφ0 and external moment Mo are shown in Fig. 6.4, as rotating vectors with angular velocity w, which corresponds to the angular frequency of external moment M. φ0 gives the vector of vibration ampli¬tude. When vibration is in steady state, all of these four vectors must be balanced. Work done by Mo per cycle is expressed with A and

As in the case of multi-cylinder engine, where Mi works on each mass having amplitude φi , with given phase differences each other, total sum of works done by each of Mi on each cylinder per cycle will be ex¬pressed with vector summation of ΠMiφi , multiplied by sin θ, where θ is given by the phase angle of the former resultant vector Π∑Miφi to φ0.

It may be noted that we assume in case of forced vibration also, the amplitude φi at each mass is in the same phase withφ0, while external moment Mi has its own phase differences each other corresponding to the firing order of respective cylinder.

Fig. 6.4

As the work done by external moment in total becomes maximum, when sin =1, =Π/2 there hold such relations as follows;

where is the magnitude of the sum of vectors and equation shows that the work is equivalent to the work of damping per cycle.

At the same time, vector balance gives


The condition may be summarized as follows;
1. This is the condition that frequency of exciting forces (moments) w coincides with natural frequency of the system v.

2. At that time, vibration amplitude φ0 reaches its maximum value,1/ρ times of the value of static deformation under the same external forces, ρ is often called damping coefficient. If damping is small, ρ becomes extraordinally large and would result in the cause of troubles due to vibration.
3. Vibration amplitude is 90° late in phase from resultant work vector of external forces.

iv) Miscellaneous remarks;

Such external forces or moments for diesel engine, which will play a part of exciting impulse for torsional vibration in shafting are mostly the harmonics included in engine torque due to cylinder gas pressure.

These harmonics are of frequencies of multiples of engine revolution (for 2 cycle) or multiples of half revolution of engine (for 4 cycle) , having the magnitude of 70 - 200% of mean torque for lower order, and for higher order, the magnitude is rather small and constant, independent on engine load. Beside gas torque as mentioned, inertia moments due to reciprocat¬ing mass will also work as impulse, and in this case, 1st, 2nd and 3rd order may be sufficient.

In case of steam turbine, there is no variation in torque but, as we have mentioned, impulse will occa¬sionally come from propeller torque, having the frequencies of NE, and 2 NE, where E is number of blades.

Damping effect is quantitatively difficult to analyse, consisting of energy absorption mostly by friction in cylinder and bearings, by pumping work in bearings, and hysterisis losses in shafting etc. As a whole, damping coefficient is 0.02 - 0.05 in actual data.

Propeller will give hydraulic damping and may be work¬ed out by torque characteristics of given propeller as



If Q is given in the form , damping k will be given

where Q is mean torque of propeller corresponding to Ω, mean angular velocity of the propeller at given revolution N.

It may be noted that either impulse or damping will become effective, when they are working on the masses close to the loop of vibration mode in question.

As most of the impulses have their own period or fre¬quency of excitation, often expressed with the order n, multiple number of engine revolution, we may define the critical number of revolution Nc when certain impulse becomes in resonance with natural frequency
Ne of given mode of vibration.

n Nc = Ne

There may be many cases of critical revolution, as is shown in Fig. 6.5.

Fig. 6.5

However those which is out of working range of revolution are of no importance, and furthermore, only the dangerous one should be con¬sidered, where resultant work vector will considerably be large. This value will be estimated in the combination of vibration mode and firing order of each cylinder, not to say of the order of impulse in question.

6.2 Axial vibration of shafting

i) Shafting of steam turbine ship is regarded as a system consisted of two large masses with springs, supported elastically at the position of thrust collar, as shown in Fig. 6.6, in view of axial vibration frequently observed on board. It has been often accompanied by the secondary vibration of upper structure of hull, eg., ship's bridge or funnel vibrating fore and aft transversely, and claimed uncomfortable.

Fig. 6.6
The mechanism has been cleared up in the following way; Due to the axial vibration induced in the shafting by the thrust variation of propeller, thrust block will vibrate fore and aft in the direction of shaft, thus exciting lateral vibration of the particular structure of ship in resonance condition.

Approximate analysis has proved that the above assump¬tion holds good with the result of measurement. Equation of motion may be expressed on each mass as follows: -

where kij is spring constant between masses (mi and mj) in relation to axial displacement x, and C45 is spring constant for the relative angular displacement between M4 and M5.

I4 is moment of inertia of M4. All other notation is self-explanatory in Fig. 6.6.

Following table shows an example of a large tanker

Weight of
propeller 47.1 ton
shafting 37.8
Total 84.9


86.6 kg/sec2 /cm

thrust shaft 3.0
shaft 32


35.8 ?

2nd wheel 39.7
2nd pinion 10


50.7 ?
thrust bearing
effect of hull structure
spring constant
? m4
6.0 estimated
10x106 ?
5.36xl06 kg/cm
487xl06 ?
3.85xl06 ?
1.95xl06 ?

critical revolution Nc = 83, order 12
frequency 85 x 12 = 995 /min (Wc=103/sec)
x1= x2 =0.036cm measured
force 1 - 2 = 11 ton (calculated)

As is noted in above example, the stiffness of thrust bearing will play an important role on this kind of shaft vibration, which would induce trouble of hull vibration. The stiffness is consisted of that of oil film on thrust bearing, deformation of thrust bearing, but mostly influenced by the bending stiffness of double bottom, where thrust bearing is placed. In this ex¬ample, it is represented by k40, and the value calculat¬ed on basis of measured data.

Attention may be noted to the fact that longitudinal stiffness is considerably weakened by the cut in double bottom due to large diameter of bull gear. Resonance impulse of vibration is 2 time of number of propeller blades.

ii) In case of diesel engine, axial vibration has been often observed and sometimes associated with torsional vibra¬tion.

Crankshaft is regarded as a spring in axial direction with the mass distributed uniformly along its length and its natural frequency may be easily estimated.

In case of simple bar, fixed at one end, frequency V is given in the following equation.

where A is section, M is total mass of bar,

Fig. 6.7

We may apply this equation also for crankshaft, with the following notation: -

A= cross sectional area of shaft cm2

M= total mass of crankshaft kg-sec2 /cm

L = equivalent length

n = number of cylinder

l = reduced length per 1 cylinder, cm
Namely the length of crankshaft having A cm2 cross-section, which will give the same axial displacement as the actual crankshaft gives under the same load. We may assume it with calculation or roughly Ca 20 times of cylinder distance for preliminary check purpose.


= Cylinder distance

G=830,000 kg/cm2

where l, means displacement due to bending of pin and webs owing to moment P.R, l3 that of shear in webs, and l4 is assumed as the effect of constraint on journal to neighbouring cylinders.

Mode of vibration on board will be varying, mostly affected by the stiffness of bearing, as well as the excitation with the resonance occurs.

Fig. 6.9

Propeller thrust variation will often give the mode (a) and (b) while when inherent impulse of engine becomes effective, it will vibrate indifferent to the propeller as shown in (a).

Torsional vibration itself may become an excitation of axial vibration as its one cycle corresponds to two cycle of the latter, and it has been the case when their natural frequencies are closely in such proportion.

Vibration troubles on shafting due to this kind of vibration have been of miner importance when compared with that of torsional vibration.

But for large bored engine, we should be also careful on this problem, as its natural frequency becomes lower and resonance may well be anticipated within working range of revolution.

6.3 Lateral (transverse) vibration on shafting

A- quill shaft
B- bearings for bull gear
C- axial clearance for thrust movement

Centre line of shafting statically forms a deflection curve under its weight supported by several bearings, as we have mentioned before. When shafting vibrates transversely, we may consider the cyclic displacement of shaft center (x,y) around the deflected (centre line in a plane perpendicular to the axis of shafting. (direction Z)

In most cases, bearings are not supposed to be movable, but in some cases, it becomes necessary to take into con¬sideration the effect of elasticity of bearing support, namely the vibratory displacement of shafting at bearings corresponding to their elastic characteristics.

Fundamental mode is as follows;

Fig. 6.10

when displacement due to gravity is given in followings with δst,

δst= mg/k

natural angular frequency wn is therefore given in the followings;

or number of frequency fn per minute is given

where δst in cm.

It may be noted that increase in deflection amount will make natural frequency lower. This is the reason why such problem as lateral vibration has become occasionally the subject of technical interest in case of mammoth tankers as well as large container ships or car ferries, where absolute amount of δst becomes inevitably large because of constructional reasons.
Exact calculation of natural frequency for bending vibra¬tion will be carried out, assuming shafting as an elastic continuous beam under gravitation, supported by given condition. Several calculation programs are available, like the case of torsional vibration.

The excitation impulse for this kind of vibration in most cases is the moment due to eccentric thrust on propeller shaft, with the frequency of NZ or 2 NZ. Occasionally torsional vibration of one node mode would give the influence in resonance.

There may be also considered theoretically the effect of whirling, namely self-excitation as is commonly, the case of lateral vibration of high speed shaft as turbines, especially when the large size propeller is used. But the case has proved very rare in practice.

Although in most cases, there would be little possibility of dangerous operation in resonance with lateral vibration of propeller shaft, we have still experienced the vibra¬tion troubles in stern tube bearings as well as oil seals in stern tubes.

In some case, even a propeller was suspected of unbalance, due to uncomfortable vibration around stern part.

The most of such vibration seems that the ship's stern is vibrating laterally while rotating shaft is kept in posi¬tion, as ship structure will loose its stiffness reversely proportional to , while propeller shaft will increase its stiffness (in proportion to Ln ), as its strength is required by power transmitted. The problem of such interaction between engine and hull will be discussed in later chapter.

6.4 Vibration problems of interaction between hull and engine

The problems of balancing in multi-cylinder reciprocating engines have been one of the decisive importance on crankshaft arrangement, as such unbalance forces or moments would be the cause of ship vibration, even though their quantitative evalua¬tion on harmless limit of unbalance seems not always clear.

Cylinder numbers of diesel engines used for marine engines are not strictly limited with four or six, or their multiples, but practically any number is applicable, if proper care for balancing will be taken so that resultant unbalance may become reasonable. On the other hand, however, even such crankshaft arrangement of perfectly balanced type will be required to have extra-balancing weight in view of reducing the internal unbalance forces or moments inside the engine, when structure of engine bed or crankshaft is not sufficiently rigid.

This is the most case for large propulsion engines of slow-running type, while for medium speed engines or high speed engines, whole structure will have sufficient rigidity as well as strength as an integral- unit against either internal or external forcer.

Therefore, it is very important in the former's case, that necessary attention will be paid on engine seating as well as double bottom construction, as they might be expected as supplementary members in view of engine rigidity. The philosophy, on arrangement of side chocks and of holding-down bolts for engine bed may be understood in this view point.

(a) (b)



Fig. 6.11

Often balance weights will be found on the neighbouring crank webs of a journal, in order to reduce bearing pressure of respective journal caused by inertia forces of the neighbouring cylinders. This precaution is based on the assumption that inertia forces on other cylinders have little effect on the journal in question, namely the rigidity of crankshaft is negligibly small.

Similar precaution might be necessary also on the connection of engine bed to engine seating; if either of them is rigid and correctly finished, a few bolts are enough, but if they are flexible, many bolts may be required to be distributed along whole length. This is also the way to make our struc¬tures light and cheap.
Regarding installation of steam turbine reduction gear, we must pay the best of our attention not to give excessive moment on the coupling of thrust bearing to shafting due to the deflection of ship for any reason.

It does not mean that the whole length of engine room to the stern tube is to be stiffened, for shafting seems relatively flexible.

But longitudinal stiffness of the ships bottom, where thrust bearing and reduction gear is installed, should be so that no relative displacement between them may be desirable.

Today, reduction gears are of precision work, they are intal led and adjusted with the accuracy of 0.001 m/m in the strong gear casing with sufficient stiffness, not to give any de¬formation which may affect over this tolerance. They may be regarded as an integral black box, no adjustment on (alignment, of gears in gear casing is needed on board, and what is re¬quired for installation is to prepare well-finished and stiffened beds for gear casing as well as thrust bearing.

Alignment of shafting to thrust bearing is generally carried out so that bearing reaction at the aft-side of thrust bear¬ing may be kept to the instructed value by turbine makers, when whole shafting is completely coupled.

6.5 Vibration of double bottom

When double bottom of engine room is regarded as a simple beam supported on both ends, with a concentrated mass in middle, it will give a typical mode of bending vibration with natural frequency given below;
, /min

where y is a deflection at the centre of beam and is given as follows

, cm

where ρ is supposed to be the engine weight and equivalent water mass effect 0.25B2L tons, B is breadth between centre of knee plates in m, L is length of engine room with 2 frame distance in addition, in m and I is bending moment of inertia of ship's bottom.

Fig. 6.12
Excitation impulse is inertia forces of 1st, 2nd and even 3rd order acting on crankshaft, which are balanced as a whole in most cases. However, as the rigidity of neither crankshaft nor bedplate of engine is sufficient enough to keep local deflections caused by each of the inertia forces on every cylinder within permissible limit, their effect will become periodical impulse on the engine seat¬ing one by one along the whole length of engine with the sequence of crankshaft arrangement. The less becomes longitudinal stiffness of engine structure, the stronger will be the impulse of such kind.

6.6 Associated vibration of double bottom and engine structure

(i) Fig. 6.4 shows fundamental mode of associated vibra¬tion of engine frame and double bottom, when they are represented by a system of masses and springs.

Natural angular frequency ω of the system is given as the solution of following equations of dis¬placement;

where k is the spring constant, namely the force required to give unit deflection, and first suffix represents the point where force will act, while second suffix represents the point of deflection. For example, kyx means that when force of magnitude k will act on y, it will give unit deflection at x.

Fig. 6.13

m is mass for engine, M is mass for half of double bottom including water mass. Spring constant k will be given



where p0 is stiffness of engine frame, namely the amount of horizontal force which will give unit deflection of x. (1 cm)

Thus ω will be given as the root of following equation;

Therefore we will get two value for ω each corresponding to respective swing form of m, different each other.

(ii) Transverse vibration of engine frames is here represented by a model of m and r, which will give the natural (angular) frequency ne (ω0) then fol¬lowing equation holds.

m is equivalent mass of engine reduced at the cylinder height r for one cylinder, and Z is total number of cylinders of engine.

We can estimate natural frequency, if drawings of engine cross-section and weight distribution along engine height are available, and equivalent mass per cylinder will be given so that it may have the vibration (energy m equal to total sum of that of any weight density ω having deflection Δ, namely

is respective deflection of engine frame at r, when deflection Δ along engine height is calculated.

These data will also be obtained, if such record of transverse vibration measurement on test bench is available. ω0 can be measured directly, if res¬onance may be observed, p0 may be also statically measured by experiment or may be assumed by calcula¬tion.

Proper attention would be necessary, in actual measurement, how engine bed is vibrating together with engine frame, as we cannot expect 100% of fixed boundary on the foundation of test bench.

(iii) Measurement results of transverse vibration of multi-cylinder engine have proved, at least, three typical modes of vibration along engine length (H, X and Z type), as shown in Fig. 5, each with respectively different natural frequency.

Fig. 6.14

Type H shows that whole engine cylinders are vibrat¬ing in the same direction, amplitude of each cylinder being not always the same.

X type shows that fore and aft part of engine cyl¬inders are vibrating in different direction, namely it has one node along the length of engine.

Z type may be similar to A, but having two nodes.

As ship's bottom, when assumed as an elastic plate freely supported around periphery, will have various modes of bending vibration, it is quite natural that they will affect the mode of engine frame vibration. While on the other hand, selected mode of engine vibration may as well influence which mode of ship's bottom will be associated with. In another word, this will be the problem of associated vibration of engine and hull.

Exact analysis may well be carried out by means of computer, taking such effects of ship-sides and deck structure, which will give various vibration modes with respective natural frequency. Two of typical modes are shown in Fig. 6.15 and 6.16, one for H type resonance and the other for X type resonance to engine vibration.

Exciting force for transverse vibration of this kind is the reaction of engine torque acting on the engine frames at each cylinder, and if any of the harmonics of engine torque is in resonance with the certain mode of vibration, vibration work done by this harmonics on each cylinder will be summed up at least to certain amount, otherwise amplitude will be damped out.

Such harmonics, which would give large vibration energy to the system will be easily predicted if vibration mode is given, thus we may judge among many resonance condition, which would be the critical revolution to which we should be cautious at least, even though absolute amount of amplitude or accompanied stress might not be accurately estimated.

Fig.6.15 H-Type

Fig.6.16 X-Type

Chapter 7


7.1 Introduction.

Main propulsion shafting is sup¬ported by bearings that maintain the shafting in proper alignment. These propulsion shaft bearings are naturally divided into two groups: bearings inside the watertight, boundary of the hull and bearings outside the hull water¬tight boundary.

The requirements imposed upon the design of propul¬sion shaft bearings are extremely severe. The bearings are required to operate at speeds ranging from about 0.1 rpm, when on the jacking gear, to 100 or more rpm in either direction of rotation. And, unlike some applications, the bearing loads do not vary with rpm but are essentially constant at all speeds. Reliability is heavily emphasized in the design of bearings because there is no redundancy for bearings, and a single bearing failure can incapacitate the propulsion system.

In addition to the radial bearings that support the shaft¬ing, a main thrust bearing is located inside the ship and transmits the propeller thrust from the shafting to the hull structure. Figures 5.1 and 5.2 show the two typical main thrust bearing locations. Figure 5.1 indicates that the thrust bearing is located such that the thrust collar is on the forward end of the reduction gear slow-speed shaft. In this arrangement, the thrust collar is necessarily remov¬able, which may be advantageous if the thrust collar is damaged. However, the thrust bearing foundation stiff¬ness that can be achieved with this arrangement is limited because the continuity of the supporting structure is interrupted by the reduction gear on the after side and the main condenser, which is located on the forward side of the thrust bearing.

The thrust bearing for the shafting arrangement shown in Fig. 5.2 is located aft of the reduction gear, and there is an independent thrust shaft. This arrangement has the potential of providing a more stiff thrust bearing founda¬tion than when the thrust bearing is integrated with the reduction gear. Where the thrust bearing is independent of the reduction gear, with its own thrust shaft, a line shaft bearing is commonly integrated with the thrust bearing housing. If the thrust shaft is located some dis¬tance aft of the reduction gear, an independent thrust bearing oil system may be required.

7.2 Main Thrust Bearings.

In general, the normal practice for propulsion main thrust bearings is to use thrust bearings with tilting pads where the individual shoes are free to pivot as the oil film dictates. There are two basic designs of tilting-pad thrust bearings, the Kingsbury and Michell types. The Michell bearing pads pivot on a radial line across the thrust pad, whereas the Kingsbury type pivots on a radiused button support. The Kingsbury type of main thrust bearing normally has the thrust pads supported on leveling links to distribute the thrust load equally to all the thrust pads; this is referred to as a self-equalizing type of thrust bearing. The Michell marine thrust bearings, which are used primarily in Eu¬rope and Japan, are normally built with the thrust pads supported directly in the thrust bearing housing without the use of leveling links. Theoretically, the self-equalizing type of bearing can carry more load than a non-self-equal¬izing bearing since the individual thrust-pad loads are not affected by the machining accuracy of the thrust bearing parts, or by the deflection of the thrust bearing housing and foundation under load. Figure 7.1 is a photograph of the base ring, leveling links, and thrust shoes of an 8-pad self-equalizing Kingsbury type main thrust

bearing with two thrust pads removed. Figure 7.2 is a section through a main thrust bearing, and shows how the thrust-pad ele¬ments pictured in Fig. 7.1 are arranged in the thrust hous¬ing to carry the thrust load. Figure 7.3, which is a devel¬oped view of the thrust pads and leveling links, shows how the leveling links distribute the load equally among the thrust pads.

Fig. 7.1 Self-equalizing main thrust bearing

U.S. Navy practice is to apply self-equalizing main thrust bearings at unit loads up to a maximum of 500 psi, allowing higher unit loads to occur in transient conditions such as ship turns. The commercial-ship practice with self-equalizing bearings is more conservative than Navy prac¬tice, with a limit to the full-power thrust unit load of about 400 psi. Standard 6-pad self-equalizing main thrust bearings are normally designed such that the load-car¬rying area is equal to one half of the square of the outside diameter of the thrust pads.

Main thrust bearings can be made with any number of thrust pads. A larger number of thrust pads can, in some cases, facilitate the use of a smaller bearing outside diam¬eter. The optimum thrust pad geometry from a hydrodynamic perspective is one with the mean circumferential pad length equal to the pad radial length. With a normal thrust bearing configuration, an 8-pad thrust bearing is the preferred selection to satisfy this 'condition. Main thrust bearings are generally designed with 8 pads.

The thrust bearing housing and foundation deflection under maximum load must be established before the maxi¬mum design unit load is set for non-equalizing bearings; normal practice limits the average maximum loading for these bearings to about 300 psi.

For naval ships, shock loadings must be considered when evaluating the thrust bearing strength and maxi¬mum thrust-pad loads. Because of the rigid design of thrust bearing housings and foundations and the capacity of thrust pads to take large transient loads, shock load¬ings do not normally control the thrust bearing design.
Thrust-pad support disks can be replaced by load-mea¬suring cells in a Kingsbury type thrust bearing to mea¬sure the load on the thrust bearing. Thrust measurements permit verification of the thrust calculations and monitor¬ing of the propulsion system performance. The necessary number and location of the load cells depend on the appli¬cation; however, because of the leveling-link concept, load cells are not required under all pads.

Thrust-pad operating temperatures can be monitored by having a thermocouple or a resistance temperature detector embedded into the babbitt of the thrust pads. This is the most common practice of monitoring bearing performance and operating limits.

Fig. 7.2 longitudinal section through thrust bearing

Fig. 7.3 Developed view of thrust pads and leveling links
Vibration reducer. Thrust bearings and the thrust bearing foundations are designed to be stiff to limit the longitudinal deflection and stress resulting from the steady and alternating thrust. A longitudinal vibration resonance is intolerable in the upper propeller rpm range. One means of avoiding objectionable longitudinal vibra¬tion is to modify the main thrust bearing to incorporate a "vibration reducer," which reduces the longitudinal stiff¬ness of the thrust bearing without increasing the thrust bearing and foundation deflections, and adds dampening to the shafting system. The increased flexibility in the shafting system shifts the resonant frequency downward, thereby reducing the alternating forces and amplitudes of vibration.

Fig. 7.4 Vibration reducer modification if thrust bearing

Fig. 7.5 Schematic of a thrust bearing vibration reducer system
To accommodate a vibration reducer arrangement, the thrust bearing leveling links are removed, and each thrust pad is supported on a piston, as illustrated by Fig.7.4. The pistons are connected to an oil manifold in the thrust bearing, which in turn is connected to oil flasks external to the thrust bearing. A hydraulic valve, which is con¬trolled by the position of the thrust collar, adds or removes oil from the system to maintain the thrust collar in the central operating position within the thrust housing. The thrust-collar positioning system must have a source of oil at a pressure greater than the maximum operating pressure. The maximum operating pressure is equal to the maximum thrust divided by the sum of the thrust-pad piston areas. Figure 7.5 is a diagram of a vibration reducer system.

The reduced thrust bearing spring constant is achieved through the bulk modulus of the oil in the flasks that support the thrust pads.

7.3 Line Shaft Bearings.

Bearings located inside the ship's watertight boundary are called line shaft bearings, although they are sometimes referred to as steady or spring bearings. Almost without exception, these bear¬ings are ruggedly constructed, conservatively designed, babbitt lined, and oil lubricated. Except in special cases, the bearings are self-lubricated by rings or disks arranged in such a manner that lubrication is effected by the rota¬tion of the shaft. Roller bearings have been used in the smaller shaft sizes, but the advantages of lighter weight and lower friction have in general not been sufficient to offset the higher reliability and lower maintenance costs of the babbitt-lined type.

Line shaft bearing housings are made of steel castings or fabricated of steel plates welded together. Completely satisfactory bearing housings are obtained by either method, and manufacturing costs govern the construction method used. Since rigidity is of more concern than strength, low-carbon steel is used as the material for bear¬ing housings with the exception of bearings for naval combatant vessels, in which case high-impact shock re¬quirements may necessitate the use of high-strength steel. Bearing housings are split horizontally at the shaft eenterline. The bottom half of the bearing must be very ruggedly designed since it carries the vertical shaft load and any side load that occurs.

The bearing housing supports a heavy steel removable shell, which is lined with babbitt. The shaft rests on the babbitted surface. The bearing shell can be made with a self-aligning feature by providing a spherical or crowned seat at the interface between the bearing shell and hous¬ing. This allows the axis of the bearing shell to align exactly with that of the shaft. Figure 7.6 is a section through a bearing with a self-aligning feature, and Fig. 7.7 is a section through a bearing that is similar but without a self-aligning capability. The general construction of bear¬ing housings and shells can be observed from Figs. 7.6 and 7.7.

Fig. 7.6 Self-aligning line bearing with oil-disk lubrication

Fig. 7.7 Non self-aligning line bearing with oil-ring lubrication

Except for the aftermost line shaft bearings in mer¬chant applications, it is general practice to babbitt only the bottom half of the bearings since these bearings would never be expected to be loaded in the top. However, the aftermost bearing (the one closest to the stern tube) may become unloaded particularly when the stern tube and propeller bearings are water lubricated. Water-lubricated bearings are subject to a large amount of wear, which can result in severe misalignment. It is considered good practice to provide the maximum practicable amount of babbitt in the top half of the aftermost line shaft bearings when water-lubricated stern tube bearings are used. With oil-lubricated stern tube bearings, the probability of the after bearing becoming unloaded is considerably reduced. In naval practice, the top halves of line shaft bearing shells are babbitted to accommodate upward bearing loads during shock conditions.

Babbitt that is centrifugally cast onto the bearing shell is considered preferable to that which is statically poured. The former technique dependably provides a more secure bond between the babbitt and the bearing shell.

Babbitt can be of either the lead- or tin-base type. Tin-base babbitt has greater strength and is generally pre¬ferred for shaft bearings; it is specified almost exclusively for centrifugally cast bearings. Lead-base babbitt is pre¬ferred where embedding, conforming, and anti-friction are primary considerations. Lead-base babbitt has a lower yield point and a slightly better fatigue resistance.

The oil reservoir that is provided within the line shaft bearing housing must be sized to operate during extreme roll and pitch conditions without leaking oil by the shaft or disabling the bearing lubrication system. Furthermore, the oil quantity and sump surface area must be sufficient to dissipate the heat generated. Line shaft bearings are sometimes designed with cooling coils located in the sumps as shown in Fig.7.7; however, experience has shown that the cooling coils are rarely, if ever, needed.

Line shaft bearings may be lubricated by means of oil rings, an oil disk, or by a supply of oil under pressure. Ring oil-lubricated bearings contain two or three metal rings with diameters of 1.25 to 1.5 times that of the shaft (the ratio decreases with larger shaft diameters). The number of rings in a bearing should be selected such that no ring is required to distribute oil for an axial distance greater than 7 in. on either side of the ring. The rings rest on top of the shaft and dip into an oil reservoir located beneath the bearing shell. Figure 7.7 is an example of a ring-lubricated bearing. As the shaft turns, the rings are rotated by the fractional contact with the top of the shaft. Oil that adheres to the ring in way of the oil reservoir is carried up to the top of the shaft where a part of the oil is transferred to the shaft and is subsequently carried into the contact region of the bearing. Ring-lubricated bearings have proved to be capable of accommodating large angles of list and trim and have proved to be reliable in service with design bearing unit loads of 50 psi. With regard to the possible adverse effects of trim, tests have demonstrated that ring-lubricated bearings can accommo¬date angles of approximately 10 deg from the horizontal with no sacrifice in performance.

Disk-lubricated bearings use a metal disk that is clamped to the shaft at one end of the bearing shell. The disk may have a flange as illustrated by Fig.7.7. As the shaft turns, the lower portion of the disk, which is immersed in an oil reservoir, is coated with oil. This oil is carried to the top where a metal bar scrapes the oil from the disk and guides it into passages where it is admitted to the top of the shaft and then into the contact region of the bearing. When disk-lubricated bearings were first introduced, they were designed with a unit pressure that was about the same as for a ring-lubricated bearing; how¬ever, as experience has been gained with disk-lubricated bearings, the design unit pressure specified for them has continually been increased to a value of about 100 psi.
The results of tests conducted with two sizes of disk-scraper lubrication arrangements (22 and 37 in. diameter), which are representative of those used in line shaft bear¬ings. During the tests an emphasis was placed on obtaining oil-flow data at low shaft speeds. In the lower rpm range (below 35 rpm for the larger disk), the oil flow varied as the 1.5 power-of the disk surface velocity, the 0.5 power of the oil viscosity, and directly with the axial width of the disk. At higher shaft speeds, oil was centrifugally thrown from the disk, and the oil delivery became essentially independent of shaft speed.

In special cases, line shaft bearings may be lubricated with oil supplied by a pump. If the shafting system is very long, and the main engine lubricating oil pump is used to supply the oil, sump pumps would be required to return the oil from the bearings since a gravity drain would not be possible under all conditions of trim and pitch. Another alternative is for each line shaft bearing to have an inde¬pendent closed lubricating system. While this method of lubrication assures an adequate supply of oil at all shaft speeds, and can result in smaller bearing sizes, it has the disadvantages of the extra pumps and added complexity.

The load that can be supported by a babbitted journal bearing is dependent upon the method of lubrication, the bearing configuration, the bearing length to diameter (L/D) ratio, and of course the installation workmanship. In the early designs, babbitted journal bearings had L/D ratios as large as 2, and even with such high L/D ratios, the shafting systems had very closely spaced bearings such that the bearing loads were very sensitive to align¬ment. The use of higher bearing pressures, in conjunction with the advent of more sophisticated techniques for the alignment of bearings, has resulted in more reliable shaft¬ing systems by affording more favorable bearing L/D ratios and more flexible shafting systems. Bearing L/D ratios are normally limited to a maximum of 1.5 in commercial ship design, but not less than 1 shaft diameter for bearings that are ring or disk lubricated to prevent end leakage of the oil from impairing adequate lubrication.

The most severe demands on the lubricating system of a line shaft bearing do not correspond to full-power, full-rpm operation, but to the condition when the shafting is rotated by the turning gear at about 0.1 rpm for extended periods of time to facilitate uniform cooling or heating of the main turbine rotors. If the lubrication system fails to deliver adequate oil to the journal under this condition, damage to the bearing surface may occur. Lubrication provisions have a strong influence on the ability of a bear¬ing to operate satisfactorily in the critical jacking mode of operation; and, consequently, the means of lubrication strongly influences the extent to which line shaft bearings can be loaded. As a guide, it has been determined that as little as 25 drops of oil per minute on the journal surface will sustain indefinite operating in the jacking mode at bearing pressures of about 75 psi.

Tests to determine the conditions under which the tran¬sition from fluid-film lubrication to boundary lubrication occurs in journal bearings. Both tilting-pad and sleeve bear¬ings were tested at shaft speeds as low as those represen¬tative of turning-gear operations. The tilting-pad bearing was immersed in oil, and the sleeve bearing was disk lubricated. The bearings had 13 in. diameters and were tested at a load of 200 psi. An abrupt change in the friction coefficient occurred at 1.3 rpm for the tilting-pad bearing and 2.5 rpm for the sleeve bearing. The oil flow supplied by the disk was more than adequate, even at speeds as low as 0.1 rpm. The tilting-pad bearing was also subjected to a series of high-loading (up to 1000 psi), low-speed (0.012 to 0.2 rpm) tests, with the results showing only light pol¬ishing of the babbitt up to 300 psi and definite movement (wiping) of the babbitt above 750 psi.

With proper attention given to design details, ring-lubri¬cated bearings, disk-lubricated bearings, and pressure-lubricated bearings can carry increasingly higher unit loads in that order. Disk-lubricated bearings can carry a higher unit load than ring-lubricated bearings based on the assumption that the oil scraper functions properly. Very close controls must be maintained in the manufac¬ture of oil scrapers because manufacturing flaws, which are hardly perceptible, can have a large influence on their performance.

7.4 Outboard Bearings.

Outboard bearings can be further classified as stern tube or strut bearings. Figures 5.1 and 5.2 show the locations of these bearings relative to the ship arrangement.

Outboard bearings can either be water lubricated or oil lubricated. Nearly all outboard bearings were water lubricated until about 1960, when a transition to oil-lubri¬cated bearings began. This transition to oil-lubricated bearings was stimulated by the unduly short service life of many of the water-lubricated bearing assemblies dur¬ing that period. It is believed that the shortened life of the water-lubricated bearings was caused by the trend to larger ship sizes, which had higher bearing loads, and more contaminated water passing through the bearings. Larger ships generally operate at deeper drafts; and with less clearance between the hull and channel bottom more contaminants, such as silt, mud, and sand, are drawn into the bearing clearance. The experience of ship operators during that time period regarding the weardown of water-lubricated outboard bearings with lignum vitae staves was generally unsatisfactory. The use of lignum vitae, which is a resinous dense hardwood, as a bearing material for water-lubricated bearings has been supplanted by the use of rubber or laminated phenolic materials. This up¬grade in bearing material has substantially improved the performance of outboard bearings; however, comprehen¬sive resolutions have not been developed for the many external factors that affect the performance of outboard bearings.

The minimization of vibration was also influential in the adoption of oil-lubricated bearings. Particularly with larger and fuller ships, variations in the water inflow velocity to the propeller generate large variable bending forces on the shafting. There have been many reported instances of shafting pounding in the forward stern tube bearing and the stern tube stuffing box on single-screw ships, particularly when five-bladed propellers were used. With proper initial alignment, oil-lubricated bearings, which have close bearing clearances and minimal wear-down, eliminate the pounding and associated maintenance of propeller shafts and stuffing boxes.

Oil-lubricated stern tube bearings also reduce the power losses in the shafting system. For a 22,000-shp ship an efficiency improvement of about 0.2 percent can be ex¬pected with oil-lubricated vice water-lubricated outboard bearings.

Oil-lubricated outboard bearings are favored on com¬mercial ships, but water-lubricated bearings are preva¬lently used for naval ships. Figure 7.8 illustrates a typical water-lubricated strut bearing design. A water-lubricated stern tube bearing design is similar except that the bear¬ing bushing is fitted inside the stern tube rather than inside the strut barrel.

Water-lubricated bearings basically consist of a non-ferrous corrosion-resistant bearing bushing that retains a number of bearing contact elements, which may be a phe¬nolic composition, or be made of rubber that is bonded to brass or nonmetallic backing strips. A sleeve is installed on the shaft to provide a corrosion-resistant contact surface.

When brass-backed rubber strip (rubber stave) bear¬ings are used, as is common in naval practice, dove-tailed slots are accurately cut in the bushing to accommodate the bearing staves. Sufficient metal is left between each slot to hold the staves securely; the space between staves also provides a cooling water flow passage. Continual improvements have been made in the design of water-lubricated rubber bearings. Reducing the rubber thickness, using a more resilient compound, and using nonmetallic backing materials, that enhance the perform¬ance of rubber-stave bearings.

As indicated by Fig.7.8, bearings that use phenolic mate¬rials are similar to rubber stave bearings. A "V" or "U" shaped groove is cut at the longitudinal joints of the blocks to provide lubricating and cooling water flow. Brass re¬taining strips are generally placed at four points around the circumference to secure the contact elements.

Fig.7.8 Water-lubricated strut bearing

Phenolic bearing materials, usually installed when dry, absorb water and consequently tend to swell; therefore, swelling must be considered in the design of these bearings.

Water-lubricated bearings that had lignum vitae as the bearing material were designed with L/D ratios of ap¬proximately 4 for the bearing adjacent to the propeller and 2 for those forward of the propeller bearing. For water-lubricated bearings that have synthetic bearing ma¬terials, when substantiated by test results, an L/D ratio as low as 2 has been used for the propeller bearing, with L/D ratios of 1 for more-forward bearings. The unit load¬ing of the propeller bearing, based on projected area (shaft diameter times bearing length), is normally under 80 psi when an L/D ratio of 2 is used; however, great care must be taken in placing importance on the absolute value of bearing contact pressures that are based on the pro¬jected area. Not only does the eccentricity of propeller thrust alter the loading, but also the load distribution is both difficult to assess and is subject to radical change. Outboard water-lubricated bearing materials may wear 0.2 to 0.5 in. before being replaced.

Water-lubricated outboard bearings can be installed to a slope that corresponds to the static slope of the shaft resulting from the weight of the propeller and shaft. The objective is to obtain a more uniform bearing load and shaft contact in the bearing when initially placed in ser¬vice. Slope boring can facilitate hydrodynamic lubrication at a lower shaft rpm as a result of the lower bearing unit loads; however, this procedure has not proven entirely satisfactory from a weardown standpoint since the eccen¬tric thrust of the propeller is not taken into account.

To provide a more uniform load distribution over the length of water-lubricated propeller shaft bearings, some naval ships have been designed with the sleeve that con¬tains the bearing material mounted within a rubber sup¬port, which is located near the middle of the bearing. The flexible rubber support allows the bearing to conform to the slope of the shaft, and is an effective means of ob¬taining a more uniform bearing load distribution.

Propeller-shaft bearings of the tilting-pad type have also been used to provide a self-adjusting bearing contact feature. However, the average bearing pressure is inher¬ently higher with tilting-pad bearings, and the bearing housing is necessarily much larger in diameter to accom¬modate the tilting-pad feature, which is expensive to pro¬vide and obstructs the flow of water to the propeller.

The shaft breakaway friction torque in water-lubricated bearings can indicate a coefficient of friction as high as 0.4. Depending on the shaft length, shaft torsional stiffness, bearing loads, and the boundary-lubrication coefficient of friction in the bearing, the shafting can rotate intermittently. The stick-slip shaft motion is observed most frequently when operating on the jacking gear, but it may continue up to speeds of about 10 rpm. The resulting nonuniform shaft motion is often accompanied by reduc¬tion gear backlash noises.

Water-lubricated bearing materials have upper op¬erating temperature limits that, if exceeded, will result in material damage. Therefore, each application should be reviewed for possible cooling-water requirements. In gen¬eral, the cooling-water flow requirements are no more than 1 to 10 gpm depending on the maximum design op¬era ting temperature, bearing coefficient of friction, bearing load, and shaft surface velocity. Generally, conserva¬tive design operating temperatures of 140 F or less are used. For instance, the Navy standard brass-backed rubber-stave bearing has a dynamic coeffi¬cient of friction that ranges from 0.006 to 0.013.

Fig. 7.9 Typical oil-lubricated stern bearing

Oil-lubricated bearings, as illustrated by Fig.7.9, have primarily been used in stern tubes and bossings, but have also been adapted for strut bearings. Oil-lubricated bear¬ings do not require a liner to be installed on the shaft since contact with seawater does not occur, nor is there any significant shaft wear. Also, no bushing is inserted in the stern tube; the bearing shells, which have heavy wall thicknesses, are pressed directly into the stern tube. The L/D ratios of the heavily loaded after stern tube bearing have ranged widely. Early designs had ratios of 2.5 but a trend toward a value of 1.5 was subsequently established.

Although the unit bearing pressure based on the pro¬jected area normally falls in the 80 psi range for oil-lubri¬cated bearings, the actual operating pressure is probably closer to twice this value. An inspection of the bearing contact area after operation reveals that the after bearing is loaded only on the after end for a length of about one shaft diameter; shorter bearings are often advocated for this reason. Slope boring the aftermost bearing so that it corresponds to the mean slope of the propeller shaft can provide better bearing contact and reduce the high pres¬sures that would otherwise be applied to the after end of the bearing. Alternatively, tilting-pad propeller shaft bearings have been developed that assure a uniform con¬tact between the bearing and shaft under all operating conditions. Tilting-pad bearings are generally designed with an L/D ratio of 1.

Fig. 7.10 Stern tube bearing lubricating oil diagram

Figure 7.10 illustrates a typical lube-oil diagram for an oil-lubricated stern tube bearing. Oil-lubricated stern tube bearings are totally submerged in oil, and seals on the after and forward ends of the tube prevent the ingress of seawater and the leakage of oil. The pressure differential between the oil in the stern tube and the ambient seawater has been controlled in several ways. For ships that operate at a nearly constant draft, this has been accomplished by means of a head tank that is located about 10 ft above the full-load waterline. Ships that have large draft variations may require two head tanks: one for full-draft operation and one for ballast operation. An alternative means of controlling the differential pressure between the lubricat¬ing oil and the ambient seawater at the seal is to use an automatic control system that senses the seawater pressure and adjusts the oil pressure accordingly, usually by imposing a variable air pressure on the head tank. The operating life of the shaft seals, which retain the oil in the stern tube and prevent the ingress of seawater, can be sensitive to the differential pressure between the seawa¬ter and the oil and to the shaft rubbing velocity. Although several seal designs have been developed for this applica¬tion, the most common design has lip-type seals on a sleeve that is secured to the shaft and rotates it. This type of seal can be subjected to rather large swings in differential pressure without damage. However, instances of excessive liner wear and seal leakage have bees reported with lip-type seals. The seals used were approxi¬mately one-half scale. The test series was not completed, but the tests conducted indicate the importance of a proper selection of the contacting mating materials and the proper manufacture of these materials.

A pump is usually installed, as shown in Fig. 7.10a force oil circulation through the stern tube. The piping is preferably arranged such that oil is circulated through both bearings. Many variations of this system have bees used, including the deletion of the pump. Owners often specify filters, heaters, coolers, and coalescers to condition the oil as it passes through the circuit. Coolers, rarely used as the temperature leaving most stern tubes does not exceed 120 F.

A design variation that was developed to minimize risk of leaking lubricating oil to the seawater incorporates a drained air cavity that is located in the after seal housing between the seawater and the lubricating-oil seal elements. With this arrangement any leakage past the sea-water or lubricating-oil seal elements goes to the air cavity and is drained inboard. The air pressure and lubricating oil pressure in the after seal assembly are automatically adjusted to compensate for variations of draft.

Stern-tube bearings on smaller ships have been installed by fitting the bearing bushings within the stern tube with a poured-in-place epoxy resin. Such an installation eliminates the necessity for an accurate stern tube boring operation. The stern tube bearings can be positioned to provide the best theoretical contact with the shaft, and then fixed in that position by the epoxy resin.

Section 2

Rolling-Contact Bearings

a. General.

Rolling-contact bearings are distin¬guished by the use of a series of rolling elements to posi¬tion the shaft with respect to the housing of the machine. The rolling elements most frequently employed include: balls, needles, and cylindrical, tapered, and convex rollers. The rolling elements of rolling-contact bearings provide much closer positioning of shafts than can be achieved with the use of self-acting sliding bearings. In addition to the close positioning, rolling-contact bearings provide a radially (or axially) stiff bearing that permits heavy load¬ing of machine components with minimum deflection. The lubrication system is usually simpler for rolling-contact bearings, especially where the size, load, and speed are such that grease lubrication can be used. Rolling-contact bearings have much lower starting friction coefficients (0.002 to 0.006) than self-acting sliding-contact bearings (0.15 to 0.25).
The load capacity of rolling-contact bearings is fairly well-defined in terms of the cycles of operation to obtain a fatigue failure in a definite percentage of a given popula¬tion at a single load level. This fatigue failure mode is the normal basis for sizing rolling-contact bearings to satisfy the requirements of a given application. Equations have also been developed to compute the static load to cause surface indentation of a size known to cause rough run¬ning. The static load capacity provides a design limit for slow-speed, high-load applications.

The size variation of rolling-contact bearing elements must be kept to very small values. Size variations within an element or between elements in a bearing must be minimized to provide a uniform distribution of load be¬tween the elements. Any lack of internal uniformity must be compensated for by compression of the rolls and deflec¬tion of the rings and supporting structure. Remarkable advances have been made in achieving uniformity of roll¬ing-element diameters. Military specification MIL-B-17931 restricts the ball size variation within a single bear¬ing to 10 microinches (μin.). Balls with only 3-μin. diamet¬rical variation are available.

Unevenness in mounting surfaces also imposes an un¬equal load distribution on the bearing components and probably accounts for many of the premature bearing failures.

b. Mounting.

The highly desirable rigidity and close-positioning capability of rolling-contact bearings have im¬plications in the incorporation of these bearings into ma¬chinery designs. Careful analysis of the starting and op¬erating temperature gradients of the machine design should be made to prevent internal loading of the bearings as a result of thermal expansion forces. A number of mounting designs have been developed to accommodate the most frequently encountered situations. Two basic alternative principles underlie most of the mounting ar¬rangements, i.e., fixed-free mounting or opposed-shoulder mounting. These arrangements assume that the shaft will be supported by two bearings, one near each end of the shaft. Axial positioning will be determined by either im¬posing the constraint at one end, as in the fixed-free mounting, or allowing the shaft to float between the op¬posed shoulders of the shaft and housing. The free-end play provided in a fixed-free mounting must exceed the sum of the thermal and elastic differential motion be¬tween the shaft and the housing. In cases where the free-end bearing is to be preloaded to provide a quieter installa¬tion, the spring force should be applied so that it is reduced by differential thermal expansion within the machine.

Opposed-shoulder mountings tend to be less expensive than fixed-free mounting in manufacture; however, the axial location is not as close as may be obtained in fixed-free mounting. Some opposed-shoulder mounts are de¬signed to allow adjustment of the free play through the use of shims between the cap shoulder and the housing to obtain the degree of axial control sought.

c. Ball bearings.

Ball bearings consist of one or two rows of balls contained in grooves having a circular cross section. The grooves form raceways and are normally cut into rings that confine the balls. The radius of the raceway cross section is slightly larger than that of the ball. The largest ball possible, consistent with the other design fea¬tures of the bearing, is normally used since this gives the largest load capacity. Ball bearings accept either radial or bidirectional thrust loading. Angular-contact ball bear¬ings provide a very high axial load capacity in one direc¬tion. Duplex pairs of angular-contact ball bearings are used for very high bidirectional axial loadings.

Ball thrust bearings are designed with a row of balls running in grooved washers placed perpendicular to the axis of rotation. The bearing will accept virtually no radial load, and thrust load is limited to one direction. Two-direc¬tion thrust capacity is obtained by adding a second row of balls and a third washer.

d. Cylindrical roller bearings.

Roller bearings are classed as line-contact bearings in contrast to the point-contact designation of ball bearings. Cylindrical roller bearings consist of right-circular cylindrical rollers be¬tween rings of cylindrical inside and outside diameters. The roller length is less than four times its diameter. Rolls are separated by retainers that may be positioned radially by the rolls or by either of the two rings. The rolls are restrained in an axial direction by ribs on either of the two rings. The cylindrical roller bearing has very little thrust capacity, and for this reason it is frequently used to pro¬vide longitudinal freedom in fixed-free shaft mountings. The fixed-end bearing may be any bearing providing axial location. Cylindrical roller bearings with solid rolls usually have a somewhat larger radial play than ball bearings of the same bore size. By the use of hollow rollers, cylindrical roller bearings may be given an internal radial preload. The cylindrical roller bearing has a very high radial load capacity and low friction.

e. Needle bearings.

Needle bearings differ from cy¬lindrical roller bearings in having their roll length more than four times the roll diameter. The needle bearing is normally restricted to shafts less than three inches in diameter and speeds below 3600 rpm. The needle bearing is available as a full complement of needles and as a bear¬ing with the needles separated by a cage. The cage-type bearing is less subject to skewing of the needles than the full-complement bearing. The needle bearing occupies the , least radial space of any roller bearing. Both needle and cylindrical roller bearings may be used without an inner race; in such a case the shaft must be hardened to a Rockwell C hardness of 58-65 and given a fine grind.

f. Tapered roller bearings.

Tapered roller bearings use frustums of a cone as a rolling element. The races have a mating taper. The apex of the tapers on both rings and rolls meet at a single point on the axis of rotation. Cages are used to separate the rollers, and a rib is pro¬vided on the inner ring to accept the roll thrust component resulting from the small angle of divergence of the conical roller. The large end of the roll and its mating rib are shaped to provide a converging load-carrying wedge. Pairs of tapered roller bearings used as fixed-end locating bearings provide a very rigid high-load capacity unit.

g. Roller thrust bearings.

Roller thrust bearings have no radial load capacity and must be used in conjunc¬tion with a radial bearing. The radial bearing must be positioned very carefully if internal loading between the radial and thrust bearing is to be avoided. Roller thrust bearings have a very high thrust capacity. Their speed limits are much lower than radial bearings and more vis¬cous oil is usually employed to prevent smearing of the surfaces. The supporting structure must be very rigid to develop the full capacity of roller thrust bearings. Care must be taken regarding the oil circulation in large roller thrust bearings to avoid thermal distortions.

Chapter 8


8.1 Introduction.

As discussed in Chapter 1, the selec¬tion of the propulsor, which converts engine torque to ship thrust, and the selection of the propulsion machinery are often closely related. Because of the interfaces be¬tween the propulsor, propulsion machinery, and hull, the design of the propeller is often a task of shared responsi¬bility. A naval architect is usually responsible for the de¬velopment of the hull lines and the propulsor hydrodynamic characteristics; but a marine engineer is generally responsible for the equipment and mechanical arrange¬ments that properly interface with the naval architect's area of responsibility. This is the general basis upon which the Society's two publications, Principles of Naval Archi¬tecture and Marine Engineering are presented.

This information gives guidance concerning the relative merits of one propulsor versus another from an efficiency standpoint. However, in the preliminary design stage, more specific information is required to make the necessary trade-off studies required to support a design selection. Systematic model tests of propulsors provide the necessary information for the trade-off studies, and in many cases may be adequate for the final design.

8.2 Propulsor Types.

As noted in Chapter 1, the type of propulsor to be used must be selected very early in the ship design process as the type of propulsor can have a strong impact on the design of the ship itself. The majority of ship propulsors are of the solid fixed-pitch propeller type. Nevertheless, there are a number of other types of propellers that may be more suitable in particular in¬stances. A brief description of the mechanical aspects of the various types of propulsors is as follows:

Conventional fixed-pitch propellers.

Most propel¬lers are of the conventional fixed-pitch type and are made from single castings. Conventional fixed-pitch propellers usually have an efficiency, cost, and simplicity advantage over other types of propellers. The procedures used to develop the hydrodynamic design of fixed-pitch propellers and variants of fixed-pitch propellers, such as propellers in nozzles and controllable-pitch propellers.

Detachable-blade propellers.

Detachable-blade (or built-up) propellers consist of a separately cast hub and blades. The blades are bolted to the hub to form the composite propeller. When operating conditions are such that there is a high probability of propeller blade damage, detachable-blade propellers offer the advantage that indi¬vidual blades can be replaced. Also, some blade attach¬ment designs have elongated bolt holes that offer the advantage of being able to make small modifications in blade pitch, which can be used to adjust the operating rpm. The disadvantages associated with detachable-blade propellers, as compared with propellers made from a sin¬gle casting, are the greater first cost, greater complexity, and greater susceptibility to cavitation in the vicinity of the blade root because of the shorter, thicker sections necessitated by the restriction on blade bolting flange diameter.
Controllable- and reversible-pitch propellers.

Con¬trollable- and reversible-pitch propellers [or, more suc¬cinctly, controllable-pitch (CP) propellers] have a mecha¬nism in the propeller hub that can be operated remotely to change the propeller pitch setting from a maximum design ahead pitch to a maximum design astern pitch. The pitch can be changed while the propeller rotates and develops thrust within these limits, or the pitch can be maintained at any intermediate setting for continuous op¬eration. A CP propeller is advantageous in any of the following situations:

1. Where the operating conditions vary widely and maximum thrust is desired throughout these operating conditions, such as tug, trawler, and offshore supply boat applications.

2. Where shaft reversing capabilities are not readily provided by the main engines (e.g., gas turbines). The unidirectional rotation is also beneficial in applications that require highly skewed blades in that thicker sections from the 0.8 radius to the tip are not required on the trailing half of the blade chord.

3. Where extensive low-speed maneuvering is required for a diesel-powered vessel. The thrust can be varied con¬tinuously from ahead to astern, including zero thrust, while operating in the minimum speed range of the diesel, thus avoiding slipping clutches or stopping and starting the main engine.

4. Where the ship will operate in ice-covered water. The unidirectional rotation of a CP propeller subjects the blades to less ice damage because the leading edges of the blades are thicker and stronger than the trailing edges and because continuous propeller rotation during thrust reversals minimizes fouling of propeller blades by blocks of ice, which sometimes impose loads on the propeller blade sections in their weakest direction.

5. Where an improved maneuverability and a minimum ship stopping distance are desired. An infinitely variable thrust capability in either direction and a more rapid re¬sponse to thrust-reversal commands improve ship maneu¬verability and reduce the ship's headreach.

6. Where a constant shaft rpm is an advantage over a wide range of operating powers. By adjusting the propel¬ler pitch, a constant rpm can be maintained over a range of ship speeds; this can be advantageous with shaft-driven generators. However, a propeller efficiency penalty is in¬curred.

At the propeller design point, the efficiency of a CP propeller approaches the efficiency of a fixed-pitch propel¬ler. However, the larger hub normally prevents the effi¬ciency of a CP propeller from exceeding that of a fixed-pitch propeller. Off the design point, the efficiency of a CP propeller is usually less than that of a fixed-pitch propeller designed for that operating condition. This is because all sections of a CP propeller blade are rotated through the same angle as the pitch is changed; thus, the angles of attack of the various blade sections along the propeller radii are optimum only at the design point.

The blade setting of a CP propeller is controlled by a hydraulic piston, a servo valve, an oil-distribution system, a pitch feedback indicator, and a pitch demand control loop, which' is located within the ship and can be designed to respond to a variety of inputs.

Three basic arrangements of the power piston and servo valve are in general use: (1) those with the power piston and servo valve located in the hub, as in Fig.8.1; (2) those with the power piston in the propeller hub and the servo valve inboard, as in Fig.8.2; and (3) those with both the power piston and the servo valve located inboard, as illus¬trated by Figs. 8.3 and 8.4. In all cases the propeller hub houses the pitch-changing mechanism and structurally contains the torque, thrust, and centrifugal forces.

Fig. 8.1 CP propeller with power piston and servo valve in the hub

Fig. 8.2 CP propeller with power piston in hub and servo valve inboard
The pitch of the blades is changed by rotating the blades about their radial axis. For the configuration shown by Fig. 8.1, the pitch is changed with a Scotch-yoke mecha¬nism, which is shown in more detail by Fig.8.5. Link mech¬anisms, of the types illustrated by Figs. 8.2 and 8.3, are also commonly used. A simplified technique that can be used to analyze mechanisms of the trunnion-link type, as in Fig.8.2.

Fig. 8.3 CP propeller with power piston and servo valve inboard

Fig. 8.4 Inboard pitch-control assembly

When the power piston is located in the propeller hub with the servo valve inboard, the motivating hydraulic oil is transmitted through a distribution assembly to piping that is inside the hollow propulsion shaft. The oil-distribu¬tion assembly can be located along the run of the line shafting or it may be conveniently located at the forward end of the reduction gear slow-speed shaft, in arrange¬ments that have geared drives.

For CP propeller arrangements that have the power pistons inboard, the force required to control the propeller pitch is developed by a pitch-control assembly, such as shown by Fig. 8.4, and is transmitted through a push/pull force rod that is in the hollow propulsion shafting.

Fig. 8.5 Scotch-yoke blade pitch mechanism (see also Fig. 8.1)

The selection of the diameter, rpm, blade area, and blade thickness for a CP propeller proceeds basically the same as for a fixed-pitch propeller except that the regula¬tory bodies generally require that the stress in the propel¬ler blade be calculated at the 0.35 radius, instead of the 0.25 radius, because of the inherently larger hub diame¬ter. It is also noted that there may be an increased suscep¬tibility to cavitation in the vicinity of the blade root of the CP propeller because of the shorter, thicker sections necessitated by the restriction of the propeller blade flange diameter.

Propellers in nozzles.

Two types of arrangements fall into this category, namely, the pump jet and the Kort nozzle. In the pump jet arrangement the propeller is placed in a rather long nozzle with guide vanes either forward, aft, or in both positions relative to the propeller. A pump jet is normally considered where propeller noise is important. Because of the resistance of the nozzle and guide vanes, the overall efficiency of a pump jet arrange¬ment is strongly dependent on particular circumstances. Kort nozzle or ducted-propeller arrangements provide efficiency advantages in applications where the thrust loading is high; examples of such applications are tugs, trawlers, and large slow-speed ships. A Kort nozzle arrangement consists of a propeller lo¬cated in a nozzle of relatively short length; the length diameter ratio of the nozzle is in the range of 0.5 to 0.8. Kort nozzles are used extensively in connection with tug¬boats because the bollard pull and towing pull can be increased 30 to 40% as compared with a propeller op¬erating alone without a nozzle. Nozzles can be of the accelerating or decelerating flow type depending on whether they accelerate or decelerate water flow through the nozzle. The accelerating nozzle also augments the forward thrust of the propeller and is used extensively in cases where the ship screw is heavily loaded.

Tandem propellers.

As the horsepower requirements for a ship increase, a single propeller can become inade¬quate because of restrictions on the propeller diameter, draft limitations, or excessive thrust loading. When this occurs, an increase in the number of propellers is required. Since a single shaft is desirable from an operating and design viewpoint, there could be justification for consider¬ing the installation of two propellers positioned in tandem on the same shaft.

Only small losses in propulsive efficiency (2.2%) were reported from model tests for a tandem arrangement as compared with a twin-screw arrangement for a large tanker. The economy of a single propulsion plant, as opposed to two propulsion plants, in addition to the single-screw simplicity of the shafting arrangement are the ad¬vantages offered by tandem propellers.

Vane wheel.

A vane wheel is a freely rotating propel¬ler that is located abaft a powered propeller. The vane wheel may be supported on an extension of the powered-propeller shaft or it may be supported by the rudder sup¬port structure. The diameter of a vane wheel is larger than that of the powered propeller, and the blades of a vane wheel are designed so that the vane wheel develops torque from the powered-propeller race at the inner radii and simultaneously converts the torque into thrust by the outer radii of the vane wheel, which are outside the race of the powered propeller. Full-scale tests on a research vessel with this type of propulsor showed an improvement of 9% when compared with a conventional propeller. With optimization of the system, it was predicted that a 12% improvement could be achieved. The improvement in the overall efficiency is attributed to a reduction in the rotational energy in the wake of the powered propeller. Vane wheels introduce complications in the outboard ar¬rangement, however, and the increased clear diameter that is required in way of the propeller aperture may not be easily accommodated. The bearing-support arrange¬ment for a vane wheel requires a comprehensive engi¬neering analysis, as does the vibratory interaction effects introduced by a vane wheel.

Contrarotating propellers.

Contrarotating propeller arrangements consist of two propellers positioned in tan¬dem on coaxial shafts that rotate in opposite directions. Higher efficiencies can be achieved with this propeller arrangement because no rotational energy need be left in the propeller wake. A propulsion efficiency improvement of 6.7% for a 136,000-ton-displacement tanker with contrarotating propellers as compared with a conventional single-screw arrangement; similar tests for an 18, 170-ton-displacement dry cargo ship indicated a 12% improvement.

Contrarotating propeller arrangements have not been used extensively in connection with commercial ships be¬cause of the mechanical complications involved with the coaxial propulsion system arrangement. Some naval installations have been made, but their per¬formance has not been made public.

Fully cavitating propellers.

The primary objection to propeller cavitation is the deleterious effect that it has on the propeller blade surfaces and overall propeller per¬formance. Once the propeller loading conditions become such that cavitation can no longer be avoided, as may be the case with very fast ships, then rather than accept a limited amount of cavitation a more satisfactory choice is to design the propeller such that it cavitates fully. In this event, the cloud of vapor, which forms on the suction side of a blade, does not collapse until it is clear of the propeller blade, thus having no deleterious effect on the propeller blades. Operating at off-design conditions may result in severe propeller cavitation erosion, and such operations (accelerating, decelerating, etc.) cannot be entirely avoided in service. For this reason and to withstand the high stresses resulting from the large thrust load, fully cavitating propellers are frequently made of exotic, cavitation-resistant, materials.

In order to achieve fully cavitating performance in a speed range too low for the usual fully cavitating propel¬ler design, but still in the range where conventional pro¬pellers would cavitate excessively, ventilation may be con¬sidered. Ventilation is the term used to describe the introduction of air into the cavitation areas to produce a fully developed cavity. There is little difference in efficiency between fully-cavitating and ventilated propellers once the cavity is formed. Experi¬ence with ventilated propellers is very limited, but some model testing has been carried out.

8.3 Propeller Characteristics.

The characteristics of a propeller have an important influence on the design of the shafting and bearing system. The propeller weight is carried by the propeller shaft, and propeller hydrodynamic loads are imposed on the shafting system. Standard propeller series data, such as reported in reference 1, are commonly used to develop a preliminary estimate of the basic propeller parameters and the related propeller-hull interactions. Propeller series data can be used, with a minimum of cost and time, to obtain results that are ade¬quate for many purposes. To optimize a propeller design for a specific application, propeller calculations are often made using hydrodynamic lifting-surface theory. The following propeller characteristics must be estab¬lished during the design process:

Propeller diameter.

In general, a higher propeller efficiency is associated with a larger propeller diameter and a lower shaft rpm. Therefore, it is usually desirable to install the largest propeller diameter that can be accom¬modated by the hull lines.

Propeller rpm.

The choice of the propeller rpm in¬volves establishing a balance between the propeller effi¬ciency and the weight, cost, and space requirements of the main machinery. This is accomplished by using standard propeller series data to compute a series of points that form a curve which represents the relationship between the propulsive efficiency and the propeller speed over the rpm range of interest. These calculations are based on a propeller diameter that is selected as indicated above. The point of maximum efficiency on this curve is known as the optimum rpm for the propeller diameter selected. This curve is used to assess the penalty in propulsive efficiency associated with an increase in rpm. Data from this curve combined with the effect of the rpm on the weight, cost, and space requirements of the main propulsion machinery permit the final selection to be made.

It will be noted that at an rpm slightly higher than the optimum propeller rpm for a given propeller diameter, the propeller efficiency decreases only slightly. But on the other hand, the effect of a relatively small increase of propeller rpm (with the power remaining the same) on the weight, cost, and space requirements of the main machin¬ery can be significant. In the case of higher-powered ves¬sels, it is usual to select a propeller rpm that is higher than optimum and to accept some sacrifice of propeller efficiency to reduce the size of the propulsion machinery.

Number of blades.

Propellers may have three, four, five, six, seven, or more blades. Over the years, the trend has been to use a larger number of blades; three blades fell into complete disuse for large ships during the 1940's, and the use of six- and seven-bladed propellers has become common. The major factor in the selection of the number of propeller blades is vibration considerations. Both the hull hydrodynamic pressure forces and the forces trans¬mitted through the shafting system bearings are strongly influenced by the selection of the number of propeller blades. In general, the propeller exciting forces decrease rapidly with larger numbers of blades; however, there are exceptions. For more details concerning the relationship between the number of propeller blades and the vibratory forces generated. A prudent selection of the number of propeller blades is an important design criterion that can be used to avoid the excitation of natural frequencies in the propulsion system.

Propeller pitch.

The selection of propeller pitch can be made when the power, ship speed, shaft rpm, propeller diameter, and general hull characteristics have been de¬termined. The pitch ratio may be selected on the basis of standard propeller model series data. However, when a propeller is highly loaded or operates in a nonuniform wake field, it may be desirable to design a propeller with a pitch ratio and pitch distribution tailored to suit the particular operating conditions.

Blade skew.

A propeller blade is termed skewed when its outline is asymmetrical with respect to a straight radial reference line in the plane of the propeller. Skew is usually introduced by successively displacing the blade sections away from the direction of rotation. Propeller blades with skew tend to enter and leave the regions of high wake more gradually. Model test results show that blade skew is an effective means of reducing the fluctuating forces and moments acting on a propeller. It is normal practice to skew propeller blades a moderate amount based on past experience, without specific knowledge regarding the benefits achieved; however, model tests may be conducted to evaluate the effects or an analytical evaluation can be made.

Developed area.

With heavily loaded propellers, which is commonly the case, the developed area must be established with care. Considerations in the selection of the propeller developed area are the penalty in efficiency associated with an excessive developed area and the ef¬fects of cavitation resulting from an inadequate developed area. The effects of an inadequate area can be of greater consequence than those of an excessive area; therefore, prudent practice dictates that a developed area be pro¬vided which is sufficiently large to incur a minimal cavita¬tion hazard. For a more detailed discussion of propeller cavitation, and consequently developed area.

Propeller blade thickness.

Requirements concerning the minimum allowable blade thickness are given in classi¬fication society rules. A thorough discussion of the development of the classification society rules is given in reference 48, which also provides the basis for making an in-depth analysis of the propeller blade stress.

Propeller hub.

The contour of the propeller hub out¬side diameter is shaped to maintain a smooth flow of water over the hub from the stern frame or strut barrel, and the hub length is largely controlled by the propeller blade fore-and-aft length at the interface with the hub. These parameters establish only the lower limits, and thicker hubs may be required to provide adequate strength. Ex¬cessively large propeller hubs are disadvantageous in that they increase the expense of the propeller and propeller weight (and consequently propeller shaft stress).

Propeller weight.

An estimated propeller weight can be obtained in several ways. The most accurate is to calcu¬late the weight based on detailed drawings. Unfortu¬nately, however, the need for the propeller weight is well in advance of the time detailed drawings are available. There are a number of approaches that may be used to approximate propeller weights; there are other methods such as
W = KD3(MWR)(BTF) (1)
W = propeller weight (including hub), lb
K = material density factor, having a value of:
0.26 for Mn-Brz
0.25 for Ni-Mn-Brz
0.235 for Ni-Al-Brz
0.235 for Mn-Ni-Al-Brz
0.225 for cast iron
0.245 for stainless steel
D = propeller diameter, in.
MWR = mean width ratio
= developed area per blade/ D (blade radius – hub radius)
BTF = blade thickness fraction
= maximum blade thickness extrapolated to shaft axis, in./ D

Care must be exercised in the use of approximate meth¬ods because of considerations such as unusual hub dimen¬sions and allowances for ice strengthening.

8.4 Manufacturing Tolerances.

Two distinctly differ¬ent methods are used to verify that propeller blades are in compliance with specified tolerances. The International Standards Organization Recommendation 484 delineates a system of tolerances that is based upon the use of a pitchometer. A pitchometer is a device for determin¬ing the propeller blade pitch angle by measuring the dis¬tance from a reference plane to points on the blade pres¬sure face. Propellers for merchant ships are almost exclusively manufactured and inspected using the pitcho¬meter method. Four classes of tolerances are presented from which the one appropriate for a specific application can be selected. Table 8.1 is a summary of the four tolerance classes and the tolerances.

Table 8.1 Summary of recommended propeller tolerances

A second method to measure the accuracy of propeller blades is based upon the use of a series of sheet-metal template gages. This is the method required by the U.S. Navy. Three types of sheet-metal template gages are used: (1) suction and pressure face cylindrical contour gages; (2) leading edge, trailing edge, and tip gages; and (3) fillet and hub or palm gages. Generally, a minimum of 53 gages is required to in¬spect a propeller. The gage method provides considerably more insight and control over blade geometry than does the pitchometer method; however, there is also an in¬crease in cost. The cost increase is related to: the gages, which must be manufactured for each propeller design; the increased number of measurements, with more than 2.5 times as many required; the data gathering process, which is not easily automated; and the fact that the pro¬cess is subject to errors because of the number of gages and measurements required. But, for applications where propeller accuracy is of critical importance, as is the case with some naval ships, such a rigorous measurement pro¬cedure is a necessity.

A discussion and evaluation of the pitchometer and gage methods of assessing propeller blade accuracy are presented and review of the adequacy of the two tolerance systems rela¬tive to their intended purpose and an assessment of the effect of a tolerance change on the manufacturing process and propeller performance. The propeller manufacturing tolerances reflect the effort re¬quired for accomplishment and be related to performance requirements.

In addition to the tolerances governing the propeller physical dimensions, balance tolerances must also be spec¬ified. Ship's specifications usually require that propellers be balanced (with static or dynamic equipment) such that the static unbalanced force at rated rpm is no greater than 1% of the propeller weight. The following expression may be used to determine the static unbalance correspond¬ing to an unbalanced force equal to 1% of the propeller weight:

U= 352W/N2 (2)
U = static unbalance which will generate an alternat¬ing force equal to 1% of the propeller weight, in.-lb
W = propeller weight, lb
TV= maximum rated propeller rpm

Limits are not generally placed on dynamic unbalance because of the large diameter-length ratio of propellers, but good practice dictates that corrections made for static unbalance be accomplished so as to improve the dynamic unbalance. Dynamic unbalance is generally not found to be a problem; nevertheless, the dynamic unbalance should be limited such that the alternating force generated at the aftermost bearing is no greater than an alternating force at the aftermost bearing corresponding to a static unbal¬ance equal to 1% of the propeller weight. A useful expres¬sion for the maximum allowable dynamic unbalance under these conditions is


D = dynamic unbalance that will produce the same force at the aftermost bearing as a static unbal¬ance equal to 1% of propeller weight applied at propeller center of gravity, in.-lb-in.
W = propeller weight, lb
L1 = distance from propeller center of gravity to the aftermost bearing reaction, in.
L2 = distance from aftermost bearing reaction to the reaction of next bearing forward, in.
N =maximum rated propeller rpm
E = shaft modulus of elasticity, psi
I = shaft rectangular moment of inertia, in.4

Chapter 9


Section 1
Torsional Vibration

9.1.1 General.

Severe torsional vibration difficulties experienced with the early reciprocating-engine drives, particularly diesel engines, placed an emphasis on the importance of torsional vibration as a consideration in the design of shafting systems. Subsequently, the design methodology required to conduct a comprehensive tor¬sional vibration analysis was formulated, and tor¬sional vibration became established as a factor to be care¬fully considered in the design of all types of main propulsion shafting systems.

9.1.2 Modes of Torsional Vibration.

The design of most large ships is such that one or more resonant modes of torsional vibration occur within the operating range.

With the possible exception of propulsion systems that use a power takeoff to drive a component having a large inertia through a torsionally flexible drive train, the first mode of torsional vibration in the shafting system will have the node and the highest torsional alternating stresses occur immediately aft of the propulsion engine. For vessels with fairly long runs of shafting, the first-mode frequency usually occurs at a low shaft rpm (less than 50% of rated rpm). This condition is normally not objectionable for a turbine-driven system because the pro¬peller is the source of excitation, and the alternating tor¬ques developed are of low magnitude. In addition, the damping energy absorbed by the propeller is high enough to result in low vibration amplitudes and stresses. How¬ever, for diesel-engine drives, the engine also can excite the first mode and can cause shaft stresses that must be avoided on a continuous basis. In such cases, a barred speed range is often imposed. In the case of ships that have short runs of shafting, the first mode can occur sufficiently high in the operating range to become of sig¬nificant concern. In these cases, the shafting system may require special design features to avoid deleterious tor¬sional vibrations.

The second and third modes of torsional vibration are determined primarily by the characteristics of the prime mover. With geared-turbine drives, the turbine-gear sys¬tem generally cannot be designed such that the second mode of torsional vibration is out of the operating range. Such being the case, a so-called "nodal drive" is frequently provided. In a nodal drive, the turbine branches are designed to have equal frequencies, which forces the slow-speed gear to be a nodal point. The second mode of tor¬sional vibration then consists of motion in which the two turbines vibrate so that their vibratory torques oppose each other with a nodal point at the gear. This being the case, the turbine branches cannot be excited by the propeller.

In the third mode of torsional vibration of a geared-turbine system, the vibratory torques of the propeller and turbines oppose that of the slow-speed gear. The third mode usually occurs considerably above the operating range; consequently, it is rarely of concern. However, very high propeller speeds or a large number of propeller blades can cause it to occur within the operating range. The third mode is difficult to excite because the antinode occurs at the slow-speed gear, which is not a source of excitation, and a node occurs near the propeller, which is a source of excitation. The mode shapes of the first three modes of torsional vibration for a geared-turbine propul¬sion system are shown by Fig.9.1.

(a) First Mode (b) Second Mode

(c) Third Mode

Fig.9.1 Mode shapes of first three modes of torsional vibration of a turbine-driven propulsion system of the nodal-drive type

The first three modes of vibration of a slow-speed diesel propulsion system are shown by Fig.9.2. The second and third modes of vibration have nodes in the engine crank¬shaft, but these modes can be excited by the higher orders of engine alternating torque. The strengths of the higher of engine alternating torque. The strengths of the higher orders of engine excitation are generally of smaller mag¬nitude; however, some of the higher orders are potentially hazardous and must be evaluated.

9.1.3 Models for Torsional Vibration Analyses.

a. Geared-turbine drives.

A typical steam turbine propulsion system is schematically illustrated by Fig 9.3(a). To simplify the analytical procedure, the system can be reduced to an equivalent model in which all elements referred to the same rotational speed, as illustrated by Fig. 9.3(b). Figure 9.3(b) can be used to evaluate all modes of torsional vibration that would be expected to be of practical interest. However, if only the first three modes of vibration are of interest, which would generally be the case, the model shown in Fig. 9.3(b) can be further simplified to that shown in Fig. 9.3(c)without a serious loss of accuracy because the equivalent inertias of the turbines and stiffnesses of the turbine shafts are very high compared with those of the first-reduction gear ele¬ments.

(a) First Mode

(b) Second Mode

(c) Third Mode

Fig. 9.2 Mode shapes of first three modes of torsional vibration of a direct-drive diesel propulsion system

(a) Schematic illustration of a geared turbine driven propulsion system

(b) Equivalent 6 mass system with all branches referred to the propeller rpm

(c) Four mass system with all branches referred to the propeller rpm for approximating the first three natural frequencies of torsional vibration

(d) Single degree if freedom system for approximating the first natural frequency of torsional vibration

Fig.9.3 Equivalent systems for determining torsional natural frequencies of geared turbine- driven propulsion systems
If only the first mode of torsional vibration is of inter¬est, then it can be approximated by directly adding the equivalent inertias of the turbine branches, JTL and JTH in Fig. 9.3(c), to the slow-speed gear inertia, JG, and making an analysis based on a two-mass system. When the iner¬tias of the turbines and gears are not known, the nodal point in the first mode of vibration is often assumed to be aft of the slow-speed gear, a distance that is equal to 4% of the length between the slow-speed gear and the propeller. With such an assumption, the first-mode natu¬ral frequency can be simply determined by considering the system to be a one-degree-of-freedom model as shown in Fig.9.3(d).

All of the system parameters needed to evaluate the torsional natural frequencies can be directly determined from the physical properties of the system except for the propeller entrained water.

To avoid the tedious labor associated with calculating the moment of inertia of the propeller in air, the propeller radius of gyration is often estimated to be between 0.40 and 0.44 of the propeller radius (the lower end of the range corresponds to larger propeller hubs and smaller numbers of blades).

b. Diesel drives.

The models used to analyze the tor¬sional vibration characteristics of diesel-driven propulsion systems are similar to those used for geared-turbine sys¬tems. If the prime mover is a medium- or high-speed diesel(s) driving through a reduction gear, the model is devel¬oped with the inertias and stiffnesses referred to the propeller rotative speed as discussed for a geared-turbine model.

Fig. 9.4 Torsional vibration analysis for a six-cylinder direct diesel engine
A model representation of a typical slow-speed, direct-drive diesel propulsion system is shown by Fig.9.4. The inertias of the propeller and entrained water are deter¬mined the same as for geared-turbine drives. The inertias of rotating masses and the spring constants of the shafts can be determined in a straightforward manner; however, "effective" inertias are used to represent the inertias of the pistons and connecting rods.

When a piston is at either the top- or bottom-dead-center position, there is no piston motion; however, at crank angles halfway between the top- and bottom-dead-center positions, the reciprocating parts move at approximately crank-pin ve¬locity. When located at the crankpin, the "effective" iner¬tia of the reciprocating mass is one-half the total recipro¬cating mass, that is:


Jr = reciprocating mass effective inertia to be located at crankpin, in.-lb-sec2
Wr= equivalent weight of reciprocating parts, lb
R = one-half of piston stroke, in.
g = gravitational constant, in./sec2

Wr includes the total weight of purely reciprocating masses, such as the piston and crosshead; however, the weight of a connecting rod, which has one end attached to the crankpin and the other end attached to the recipro¬cating element, is broken down into two components. One component is placed at the crankpin and is added directly to the rotary weight of the crankpin, and the other compo¬nent is placed at the reciprocating end of the attachment and is added to Wr in equation (1). The two weights representing the connecting rod are distributed so that the total connecting rod weight and its center of gravity are accurately represented.

The inertia properties of rotating masses attached to the crankshaft or shafting, such as flywheels and moment compensators, can be directly determined from equipment drawings. Also, such data are often available from the engine manufacturer.

9.1.4 Determination of Natural Frequencies.

The Holzer method of computing the natural frequencies of lumped spring-mass systems is a convenient procedure for de¬termining the torsional natural frequencies of propulsion systems, whether turbine or diesel powered. To illustrate the computational procedures used, a turbine-driven ves¬sel, modeled as shown by Fig.9.3 (b), and a direct-drive diesel, modeled as indicated by Fig.9.4, will be analyzed.

a. Geared-turbine drives.

Referring to Fig. 9.3(b), typical values of system inertias and spring constants and calculations for the first torsional natural frequency of geared-turbine drives are given in Table 10. Since the principal source of excitation is the propeller at blade-rate frequency, following conventional practice the calculation is initiated by first assuming the resonant frequency of the system, in terms of the propeller rpm, and then calcu¬lating the corresponding vibratory torque and torsional amplitude at the slow-speed gear (inertia JG) in terms of the amplitude at the terminal end of each branch. For convenience, the amplitudes at the terminal ends of the three branches are initially assumed to be one radian. Since the three branches (propeller, LP turbine, and HP turbine) must have the same amplitude at the slow-speed gear, the amplitudes of the three branches can be ex¬pressed as a function of the same unknown amplitude— for instance, the propeller—thereby obtaining the mode shape. The torques imposed on the slow-speed gear are then summed; if the sum is zero, a resonant condition is established. If the sum is not zero, the process is iterated until the sum is zero by assuming a different resonant frequency.

The same procedure can be repeated to determine the remaining four torsional natural frequencies but, as pre¬viously mentioned, only the first three modes would gen¬erally be of interest. The mode shapes of the first three natural torsional frequencies are shown in Fig.9.1. The node in the first mode is seen to be immediately abaft the slow-speed gear. The two turbine branches are tuned in the second mode such that the slow-speed gear is a nodal point. The third mode is the one in which the slow-speed gear is the antinode with the terminal ends of the three branches being near nodal points.

Table 9.1 Determination of first natural mode of torsional vibration for a turbine-driven propulsion system

b. Diesel drives.

The characteristics of a typical two-stroke, six-cylinder diesel engine are given in Table9.2. A model that can be used to conduct a torsional vibration analysis of that engine is illustrated by Fig.9.4. A calcula¬tion for the first mode of vibration, using the Holzer method, is given in Table 9.3. Unlike the case of geared-turbine drives, the calculation is usually begun by assum¬ing the resonant frequency of the system in terms of radians per second or cpm. Next, an amplitude of one radian is assigned to the mass at the forward end of the crankshaft, and subsequent calculations are based on the reference mass amplitude,θ0. The Jxω2θx column repre¬sents the inertia torque of each mass relative to the refer¬ence mass amplitude.

The ΣJxω2θx column represents the sum of the inertia torques of all preceding masses, and is the torque in the shaft immediately following the mass under consider¬ation. Thus, when this torque is divided by the correspond¬ing shaft stiffness, the incremental torsional deflection between masses, in radians, is determined. The incremen¬tal torsional deflection is subtracted from the amplitude of the mass under consideration to obtain the angular amplitude of the next mass. A system resonant frequency is established when the sum of the oscillating torques developed by all masses, the ΣJxω2θx column, is zero; that is, when no external torque is required to sustain the vibration amplitudes. The same procedure is used to estab¬lish the higher modes of system vibration.
Table 9.2 Characteristics of a typical two-cycle, six-cylinder diesel engine

Table 9.3 Calculation of first mode of torsional vibration of diesel-driven propulsion system

9.1.5 Excitation Factors.

Torsional vibrations in propul¬sion shafting systems are principally excited by the pro¬peller and, in the case of diesel-driven ships, the diesel. Reduction gears are manufactured with such accuracy that gear-tooth excitation is of negligible magnitude. The strength of the propeller alternating torque is influenced by a number of factors, including propeller loading, pro¬peller aperture clearances, appendages that influence the flow of water to the propeller, number of propeller blades, hull lines, and hull draft. The propeller torque variation is often expressed as rQ, where r is the alternating torque as a fraction of the mean torque, Q. Generalization in this area must be used with care; however, typical ranges of blade-rate torque excitation for normal ship proportions are presented. Propeller excitation of a fre¬quency higher than blade rate (propeller rpm times the number of propeller blades) exists and occurs at multiples of the blade-rate order, but the higher orders are gener¬ally of negligible magnitude.

With the propeller excitation torque expressed as rQ, the energy input, Eip, from the propeller per cycle of vibra¬tion is:


where rQ is the alternating torque in inch-pounds and Qp is the propeller amplitude of vibration in radians.

For diesel-driven ships, in addition to the propeller, the diesel is a source of torsional vibration excitation. The varying piston gas pressure and the inertia loads due to the cylinder reciprocating masses cause the diesel to produce a periodically varying torque that is related to crankshaft rotation.

The periodic torque applied to the crankshaft of a diesel engine by the piston gas pressure can be analyzed in terms of the force per cylinder acting on the crankpin in a direction tangent to the crankpin turning radius. This periodic torque is commonly expressed as the tangential effort. A diagram can be drawn that traces the tangential effort acting on the crankpin, which is caused by the gas pressure (and is commonly stated per square inch of pis¬ton area), through the working cycle of one cylinder. For a two-cycle engine, the working cycle is one revolution of the crankshaft, but for a four-cycle engine, the process repeats every two revolutions.

A tangential-effort diagram can be developed from a cylinder gas pressure indicator card where the cylinder pressure is related to the piston crankpin angle. Figure 9.5 is a cylinder indicator card for an engine with the char¬acteristics outlined by Table 9.2; the mean indicated pres¬sure is 261 psi (18 bars).

Fig. 9.5 Full-power indicator card for the engine described in Table 9.2
The cylinder tangential effort at any crankpin position is related to the cylinder gas pressure by a factor. The factor is a function of the ratio of the length of the con¬necting rod to the crank radius and the angular position of the crankpin relative to the top-dead-center position. Figure 9.6 is a tangential-effort diagram that was developed from the indicator card, illustrated by Fig.9.5.

Fig. 9.6 Full-power tangential-effort diagram (with harmonic components) developed from the indicator card shown by Fig. 9.5

The relationship between the mean indicated pressure, Pm, and the mean tangential effort, Tm, shown in Figs. 9.5 and 9.6, respectively, is


Pm = mean indicated pressure, psi
L = stroke of piston, in.
R = crank radius = L/2, in.
A = area of piston, in.2
N = crankshaft speed
Nw = number of working cycles per minute: N/2 for a 4-cycle engine; N for a 2-cycle engine

A tangential-effort diagram caused by the cylinder gas pressure, TEg, can be represented by a Fourier series consisting of a constant term and a series of harmonically varying terms. The constant term is the mean tangential effort, Tm, and does not excite torsional vibration. The harmonically varying terms, however, are the principal source of torsional vibration and do not contribute to the useful work output of the engine.

Table 9.4 Diesel engine harmonic gas-pressure coefficients

A Fourier series representing the gas-pressure tangen¬tial-effort diagram can be written as:


where Agn and Bgn are the Fourier coefficients, θ is the crankshaft angular position from top dead center, and n is the order number of the harmonic component. The order numbers of the harmonics relate to the number of com¬plete cycles that each respective harmonic completes per revolution of the crankshaft. Consequently, the engine speed (in rpm) for resonant harmonic excitation of any system natural frequency is determined by dividing the system natural frequency (in cpm) by the harmonic order number, n, of the engine excitation. For a two-cycle en¬gine, where the tangential-effort curve is periodic every crankshaft revolution, there are only integer orders of the Fourier components. For a four-cycle engine, where the tangential-effort curve is periodic over two crankshaft revolutions, there are Fourier harmonic components of ½, 1,1½, etc. orders.

Equation (4) can also be written as:



and the remaining symbols are as defined above.

The procedure used to derive the Fourier series har¬monic components of the tangential-effort diagram, equa¬tion (4). Six of the Fourier harmonic components are plotted in Fig. 9.6 for the tangential-effort diagram shown on the same figure. It can be seen that the six harmonic orders essentially sum to the original tangential-effort diagram with the axis being at the mean tangential effort, Tm. Normally 12 to 24 harmonic orders are used to represent the tangential-effort diagram. The engine manufacturer can often provide data for the terms TEgn and ygn in equation (5) as a function of n, the har¬monic order, and Pm, the mean indicated pressure. Table 9.4 is a portion of such data that maps the tangential-effort harmonic components for the two-cycle engine described by Table 9.2. The six harmonic orders shown in Fig.9.6 correspond to the data given in Table 9.4 for a mean indi¬cated pressure of 18 bars.

The second component of the alternating torque pro¬duced by a diesel engine is the inertia loads imposed by the reciprocating mass of each piston assembly. A tangential-effort diagram for inertia loads and their harmonic compo¬sition. Nor¬mally, only the first four orders of the inertia loads have a significant magnitude. Both two- and four-cycle engines contain integer orders only, and both are represented by a sine term only; there are no half-orders and no cosine terms. The expression for the alternating inertia load is


TEin = tangential crankshaft force, per square inch of piston area, caused by piston assembly, act¬ing at the crankpin turning radius, psi
Hn = harmonic order coefficient
H1= 0.25/r H3 = -0.75/r
H2 = -0.5 H4 = -0.25/r2
r = connecting rod length /R

A, N, R, Wr, n, and θ are as defined for equations (1), (3), and (4).

To determine the total alternating torque for the first four orders, the gas-pressure and inertia tangential-effort harmonics must be combined. Above the fourth order, the gas pressure harmonics are predominant, and the inertia components can be neglected. To combine the gas and inertia tangential-effort components, the gas harmonic component must be stated in sine and cosine components, as in equation (4). The amplitudes of the sine components caused by the inertia forces, TEin, and gas-pressure loads, Agn, are then added to obtain the total amplitude, Agin, of the sine term. The total sine component can then be combined with the cosine term of the gas-pressure compo¬nent, Bgn, to obtain the resultant combined amplitude, TEgin; and the phase angle, γgin, can be calculated from equation (5).

Table 9.5 Procedure for combining and inertia tangential-effort harmonic components

The procedure used to combine the harmonic tangential-efforts caused by gas pressure and inertia forces is illus¬trated by Table 9.5. It may be noted that in the example given the sine terms of the inertia components oppose those of the gas-pressure components such that the com¬bined gas-inertia amplitude, TEgiri, is less than that of the gas pressure, TEgn, alone.

For the first four harmonic orders, the maximum alter¬nating torque per cylinder at order n, Qn, is determined
from the combined gas and inertia tangential-effort maxi¬mum amplitude, TEgin, as follows:

Qn = AR(TEgin) (7)

For the fifth and higher harmonic orders, only the gas-pressure forces need be considered; therefore
Qn = AR(TEgn) (8)

Equations (7) and (8) are used to determine the alter¬nating torques per cylinder, which can be summed to de¬termine the combined effect of all cylinders. In a linear elastic system, the motions produced by two or more sets of periodically varying forces acting simultaneously are equal to the sum of the motions that would be produced by the separate forces acting alone, recognizing the phase relationships between the different components. Follow¬ing this principle, each torque harmonic order induces in the system a forced torsional vibration of its respective frequency; consequently, the motion of the shaft is the summation of as many harmonics as are present in the applied torque. However, in general, only when the fre¬quency of a harmonic order coincides with a natural fre¬quency in the shafting system is the amplitude of the vibration response significant.
Wcn =Π Qn θ csinβn (9)

Qn = harmonic torque of a cylinder at order n, from equation (7) or (8)
θc = amplitude of vibration of cth cylinder for mode of vibration being analyzed
βn = phase angle between cylinder harmonic torque vector, Qn, and amplitude vector, θc

Qn has the same magnitude for all cylinders since all cylinders nominally fire equally; however, the phases are different because all cylinders do not fire at the same time. At resonant vibration conditions, the amplitude vectors, θc of all cylinders are in phase since all cylinders vibrate at the same frequency and go through zero amplitude at the same instant. However, the magnitude of the θc vector is different from cylinder to cylinder, depending on the normal elastic curve of vibration for the mode being ana¬lyzed. The frequency of the two vector rotations Qn and θc is n times the crankshaft rotation and equals a natural vibration mode of the system.

To obtain the work of all engine cylinders at a giver resonant mode of vibration, it is necessary to determine the resultant of all the θc amplitudes and the phase angle between that resultant and the Qn vector. At resonance the resultant phase angle is 90 deg, which makes the input work a maximum (i.e., sinβ = 1); therefore, the total engine input work per cycle, Eie, at a resonant frequency of order n is:


where Σθc is the vector sum obtained by adding vectors with the phases of the cylinder torques, Qn, and the magni¬tudes of the cylinder vibration displacements, θc.

Figure 9.7 shows the crankshaft angle diagram and fir¬ing order, as well as the phase diagrams for 18 orders of excitation, for the two-cycle engine described by Table 9.2. The phase angles between the θc vectors depend upon the crank arrangement, its firing sequence, and the harmonic order number. The phase diagram is developed by assum¬ing that the number 1 cylinder is at top dead center at its firing position; this is the zero phase angle. The phase angle of the θc vector corresponding to the cth cylinder is found by multiplying the number of degrees the crank must be rotated to fire that cylinder by the order number being investigated. As an example, the fifth-order location of the number three cylinder is found by observing that the number three cylinder must rotate 120 deg to the TDC firing position. The fifth-order vibration vector would ro¬tate 5 X 120 or 600 deg during this period. Six hundred degrees from the TDC firing position measured counter to shaft rotation locates the number three cylinder vector at 240 deg counterclockwise from the number one cylinder firing position, as shown in Fig. 9.7. Note that with two-cycle engines the angle of rotation to bring a cylinder to firing position is the same as the crank angle rotation to bring that cylinder to the TDC position. With a four-cycle engine, the angle to fire may be the crank angle plus 360 deg.

Fig. 9.7 Cylinder phase diagrams versus excitation order and first-mode vector sums for the propulsion system described by Table 9.2 & 9.3

As illustrated by Fig.9.7, a phase diagram can be con¬structed that defines the phase relationships between the cylinders as a function of order. A length is assigned to each vector that is equal to the amplitude of vibration of that mass, which is taken from the mode shape of the mode of vibration being analyzed. The six cylinder ampli¬tudes, θ1 through θ6 are applied to the vector lengths in the phase diagrams and summed. As an example, for the major order 6, the phase diagram shows all six vectors are in phase; therefore, the vector sum is obtained by adding the vector amplitudes. For the first-mode fre¬quency, the sum is 5.6578 θ0.

If all cylinders do not fire equally, as would be the case if the injection of fuel was not uniform for all cylinders, then the Qn value would not be the same for all cylinders. The effects of this condition can be analyzed by determin¬ing the Fourier components of the tangential effort pro¬duced by the misfiring cylinders. When the Fourier com¬ponents for all cylinders are known, the vector sum of the input work per cycle from all cylinders can be calculated from equation (10).

9.1.6 Damping.

There are several sources of damping that control the maximum attainable amplitude of torsional vibration; one of the most important is the propeller, particularly in the first mode. For second and higher modes of vibration, damping within the system caused by elastic hysteresis, sliding fits, and friction elements can be important if these modes of vibration are excited in the operating range of the system. This is particularly true for diesel-driven ships.

Propeller damping can be determined in several ways. In general, the propeller damping coefficient can be expressed as

b = KQ/Ω (11)
b = propeller damping coefficient, in.-lb-sec/rad
K = a constant
Q = mean propeller torque, in.-lb
Ω = rotative speed of propeller, rad/sec

If propeller model test data are available, it may be convenient to use the relationship

where s is the propeller slip.

If the propeller data are given in the form of J, KQ curves:


If given in the form of a Troost diagram (Bp, δ):


As an approximation for many propellers, K = 3.7 to 4, which may be used in the absence of other data. A value of 4 corresponds to a damping constant that is double the slope of the torque-speed curve. In all cases the deriva¬tives are computed at the operating point of the propeller by taking the ratio of small differences in dependent and independent variables, moving along a constant-pitch line.

The energy loss via the propeller per cycle of torsional vibration can be written as

ω = circular frequency of vibration, rad/sec
θp = amplitude of propeller vibration, radians
b = as defined for equation (11)

Energy is also dissipated as a result of elastic hysteresis in the shafting, sliding fits, etc. The elastic hysteresis energy loss per cycle is a function of the material and stress level. Damping from sliding fits is very difficult to estimate. Even for identical machinery, it will vary from one unit to another. The degree of energy loss per cycle varies with clearances, oil viscosity, and the amount of lateral motion the moving part has within the fit. How¬ever, for general guidance, the internal damping vibratory energy loss per cycle is frequently estimated to be be¬tween 1 and 5% of the total system vibratory energy. The energy dissipated because of internal damping can be expressed as:

ar = fraction of energy dissipated at mass x
Jx = moment of inertia of mass x, lb-in.-sec2
θx = amplitude of vibration of mass x, radians

The damping action of the turbines in geared-turbine drives would generally be expected to be of secondary importance especially in modes where the turbines have small relative amplitudes; however, it may warrant as¬sessment under some circumstances. The energy dissi¬pated due to turbine damping can be expressed as

c = turbine damping constant, which can be approxi¬mated as the ratio of turbine torque to turbine rpm at the speed corresponding to the point un¬der study, in.-lb-sec/rad
θt = amplitude of vibration of turbine rotor, radians

If damping is introduced into the vibration calculations, the computational procedure is modified considerably. An external source of damping, such as that at the propeller or turbines, introduces an external moment of —jbωθ on the respective mass concentration; and internal damping, such as shafting hysteresis, between two masses is equiv¬alent to changing a spring constant K to a complex spring constant

k' = k(1+ja/2Π) (18)

where a is the fraction of the elastic energy absorbed by the damper.

Calculations that incorporate damping as just indicated are somewhat tedious; an alternative procedure is to com¬pute the effect of damping at resonance only by equating input energy to damping energy.

9.1.7 Vibratory Torque Calculations.

In many cases, the torsional vibration characteristics of a shafting system can be shown to be satisfactory in the design stage with only a computation of the system natural frequencies and without predicting vibratory torques and amplitudes. Nor¬mally this is possible when a comparison is made with a similar system that has proven satisfactory in service. For designs where the system natural frequencies, vibratory excitation, or anticipated system operation may cause con¬cern, however, an investigation of the magnitude of the vibratory torques and stresses is necessary.

In order to establish the vibratory torques and stresses in a vibrating system, the amplitudes of vibration of the system masses must be established so that the twist in the interconnecting shafts (springs) can be determined. In a system vibrating at resonance, the amplitude of vibra¬tion increases until the damping work per cycle of vibra¬tion is equal to the input work per cycle of vibration.

a. Geared-turbine drives.

A geared-turbine drive, with accurately cut gears, is excited torsionally only by the propeller. Also, in the first mode, internal damping and turbine damping can be ignored without a significant loss of accuracy. Therefore, the propeller excitation en¬ergy, equation (2), can be equated to the propeller damp¬ing energy, equation (15):

By substituting 4Q/Ω equation (26), for the propeller damping coefficient and letting ω = ZΩ, where Z equals the number of propeller blades, the maximum propeller amplitude,θP, is

The maximum amplitude of propeller vibration can be determined from the foregoing expression. The normal¬ized mode shape determined from the system natural fre¬quency calculation, Table 9.1, can then be used to assess the vibratory torque at resonance at any element of the system. The alternating torques in the quill shafts be¬tween the high-speed gears and low-speed pinions are usu¬ally the largest from a relative viewpoint; consequently, it is customary to analyze these elements when investigat¬ing the possibility of torque reversals.

As an example, referring to the calculation in Table 9.1, with a propeller excitation, r, equal to 3% of the mean propeller torque, the alternating torque, q, in the low-pressure quill shaft in the first mode of torsional vibration would be:

q = 1213 θL X 106
q = 1213 (0.06477 θp) X 106
q = 78.57 (r/4Z) X 106
q = 98,210 in.-lb

This is the torque in the low-pressure quill shaft re¬ferred to line-shaft speed. With a second-reduction ratio of 7.5, the actual vibratory torque in the quill shaft will be 98,210/7.5 or 13,090 in.-lb. The mean operating torque corresponding to the resonant frequency can be approxi¬mated by determining the rated propeller torque (the torque corresponding to 22,000 shp at 115 rpm) and as¬suming that the propeller torque varies as the square of the propeller rpm; therefore, the mean operating propeller torque at the resonant frequency is estimated to be

Q = [(63,025)(22,000)/115] [22.38/115] 2
Q = 456,630 in.-lb

In this particular case at the resonant frequency, the low-pressure turbine develops 55% of the total power deliv¬ered to the propeller, and the mean torque in the low-pressure branch at resonance is determined to be 33,490 in.-lb whereas the vibratory alternating torque is esti¬mated to be 13,090 in.-lb; therefore, torque reversals in the low-pressure train at the first resonant mode of torsional vibration are not expected. The vibratory stress in the quill shaft can be calculated using the alternating torque across this shaft of 13,090 in.-lb.

b. Diesel drives.

As with turbine drives, the propel¬ler is the principal means of system damping in the first mode of diesel shafting systems. However, in the follow¬ing discussion concerning the amplitude of vibration and the resulting stress levels in a diesel propulsion system, internal damping will be considered to evaluate its effect. The vibratory work input per cycle from a diesel engine is given by equation (10). The Σ θc term in equation (10) is obtained from Fig.9.7. This term establishes the order that provides the maximum energy input per cycle. In the first mode, when all engine cylinders have essentially the same amplitude, the "major orders" are the principal or¬ders to investigate. For a two-cycle engine, the major orders are integral multiples of the number of cylinders, and for a four-cycle engine they are integral multiples of one-half the number of cylinders; however, the major orders do not always cause the most severe vibration.

Figure 9.7 shows the major orders to be dominant. In this case, the major orders are over 20 times larger than the vector sum of any other order. For the sixth-order, the alternating torque per cylinder, Qn, can be determined from equation (8) and Tables 9.2 and 9.5 as

Qn = AR(TEgn) (8)

= (596.6)(52.64)(22.26)

= 699,100 in.-lb

The vector sum Σ θc for the sixth order is obtained from Fig.9.7, and the engine input work per cycle becomes

Eie = ΠQnΣθc (10)

= Π(699,100)(5.6578) θ0

= (12.43 x 106) θ0 in.-lb

The propeller damping work per cycle, which is the principal source of damping in the first mode, can be com¬puted using equation (15). The propeller damping coeffi¬cient is calculated from equation (11), assuming that K = 4 and Q is proportional to the propeller rpm squared. With the rated torque given by Table9.2:

= 4.21 X 106

The propeller amplitude and first mode natural frequency are given by Table 9.3; therefore

Edp = Π bωθp2 (15)

Edp = Π(4.21 x 106)(25.64)(-1.2180θ0)2

= (503.1 x 106) θ02 in.-lb

With the fraction of internal energy dissipated, ax, as indicated in Table 9.3 for the various masses, the internal damping per cycle of vibration can be calculated and summed as shown in Table 9.3, that is:

Edi = Σ ½ αx Jx ω2 θx2 (16)

= (8.490 x 106) θ02in.-lb

The absolute amplitude of vibration at the first-mode nat¬ural frequency, when excited by the sixth-order excita¬tion, can be found by equating the engine input work per cycle to the sum of the propeller damping and the internal system damping, that is:

Eie = Edp + Edi

(12.43 x 106) θ0 = (503.1 x 106) θ02 + (8.490 x 106) θ02


In this mode the most highly stressed element in the shafting system is the line shaft (spring constant k8 in Fig.9.4 and Table 9.3). The vibratory torsional stress in the line shaft can be determined by calculating the torsional deflection of the line shaft, multiplying the line-shaft de¬flection by the line-shaft spring constant (which equates to the vibratory torque in the line shaft), and dividing the torque by the line-shaft section modulus. Referring to Table 9.3, the line-shaft deflection is

= 1.4340 θ0

With a line-shaft spring constant, k8, of 644 x 106 in.-lb/ rad, and a reference amplitude, θ0, of 0.0243 radians, the line-shaft sixth-order vibratory torque is

Q6 = θ9-8 k8
= [(1.4340)(0.0243)](644 x106) = 22.44 x106 in.-lb

(The same result can be obtained more directly by multi¬plying θ0 by the Σ J8 ω2 θ8 term in Table 9.3) The diameter of the line shaft is 21.5 in., which provides a section modu¬lus of 1951 in.3; therefore, the vibratory torsional stress is 11,500 psi, a value sufficiently high to be of concern.

9.1.8 Acceptable Limits for Torsional Vibration.

As a general guideline for double-reduction geared systems, untuned resonant frequencies of torsional vibration should not occur in the range of 60 to 115% of rated rpm; however, this broad guideline does not ensure satisfactory torsional vibration characteristics. Furthermore, there may be satisfactory operational systems that this limita¬tion would exclude. Such being the case, the details of each particular shafting system must be analyzed to ensure satisfactory performance.

Specific acceptance criteria for torsional vibration in geared-turbine propulsion systems are generally gov¬erned by two considerations: (1) limiting fatigue stresses within the system to safe values, and (2) avoiding torque reversals in the reduction gear elements by ensuring that alternating torques within the reduction gear engage¬ments do not exceed the continuous torques. Generally, these criteria can be satisfied by the appropriate selection of the number of propeller blades, propeller design details, reduction gear design details, and the shafting diameters.

For gear-driven propulsion systems, the classification societies normally require a barred speed range, indepen¬dent of stress level, if the system has a resonant fre¬quency that causes gear-tooth chatter during continuous operations.

Torsional vibration in diesel-driven propulsion systems can lead to damage or failure of propulsion elements, such as the shafting, crankshaft, gears, and couplings. Consequently, the classification societies require torsional vibration calculations to be submitted and also require verification by measurement. The classification societies prescribe criteria that govern stress limits for vibratory torsional stresses; the criteria typically stipulate an upper limit for torsional stresses that occur during continuous operations, but also allow transient operations, below a higher torsional stress limit, as necessary to pass through a torsional critical frequency that occur below 80% of rated speed. A band of propeller speeds extending above and below the critical speed, is specified that forms the "barred speed range." Figure 9.8 illustrate the barred speed range for the propulsion system use for the calculations outlined in Table 9.3. Barred speed ranges are usually not permitted above 80% of rated speed.

For ships that have direct-drive diesels located aft, the torsional characteristics of the propulsion system are generally dominated by a resonance of the first mode that excited by a major order of the engine. For two-eye engines the major orders are multiples of the number of cylinders, and for four-cycle engines they are multiples of one-half the number of cylinders. The number of cylinder in the engine selected is, therefore, an important consideration in the design of the propulsion shafting system. Where an unacceptable critical frequency occurs in the operating range, there are basically three approaches that can be taken to achieve satisfactory propulsion system operation:

1. Lower the critical frequency. This can be accomplished by decreasing the shafting diameter, as permitted by the regulatory bodies, or by adding tuning wheel to the engine crankshaft. While this approach will normally reduce the severity of the critical frequency, a barred speed range will usual be necessary.

2. Raise the critical frequency. This can be accomplished by increasing the shafting diameter. The objective is to shift the major-order critical frequency at least 40% above the operating range. A barred speed range would be avoided, but the shafting would be very stiff. When large-diameter shafting is used, the alternating propeller thrust that induced by torsional vibrations, and the resulting effects on the hull structure, requires a rigorous analysis.

3. Install an engine torsional vibration damper. The objective would be to reduce the torsional vibratory stresses to an acceptable level. However, satisfactory operation of the propulsion system would be come dependent on the reliable operation of the torsional damper.

Fig. 9.8 Limiting torsional vibration stresses in line shaft for diesel propulsion system example

Of the three alternatives, the first is generally the least expensive and is preferred, if practical.

Couplings with a low torsional stiffness can be used decouple vibrating components in a mechanical system. Torsionally flexible couplings are often used to shift a system natural frequency low in the operating range in arrangements where a power takeoff is driven by a slow-speed diesel, and such couplings are also used on the output shafts of medium-speed diesels that drive the propulsor through a reduction gear.

Section 2

Longitudinal Vibration

9.2.1 Introduction.

Severely objectionable longitudinal vibrations in shafting systems were not encountered until the advent of several classes of large naval vessels in early 1941. A description of the difficulties experienced with these ships and also presents the most thorough treatment of longitudinal vibration that has been prepared for steam-turbine-driven ships. The works of Panagopulos, Rigby, Couchman, and others add to the knowledge on the subject, yet the fundamental problem areas remain as those identified by Kane and McGoldrick.

The principles set forth by Kane and McGoldrick are primarily oriented to turbine-driven ships; however, the principles are equally applicable to diesel-driven ships. The treatment of the shafting, thrust bearing, and founda¬tions is directly applicable; and the engine crankshaft can be modeled as masses and springs and analyzed. An axial vibration resonance can cause high crankshaft stresses in a diesel engine and can result in large axial forces going into the thrust bearing; consequently, they are to be avoided.

The axial stresses in line and propeller shafting associ¬ated with even the most violent instance of longitudinal vibration are not sufficiently large to induce failures in the shafting itself; nevertheless, longitudinal vibration can produce effects that are destructive to engine room equipment. Shafting systems having longitudinal vibra¬tion characteristics that are resonant with diesel engine or propeller blade-rate frequency forces produce a signifi¬cant magnification of the exciting forces. Such a force magnification can result in such deleterious effects as:

(a) Accelerated wear of gears, flexible couplings, thrust bearings, etc., and destruction of main engine clear¬ances because of the increased relative axial movements,
(b) Large vibration amplitudes and stresses in attach¬ments to the main engine, condensers, and main and auxil¬iary machinery, which can ultimately result in fatigue failure.
(c) Cracks in foundations and hull structures.

Axial vibration issues should be considered by the en¬gine builder and ship designer during the preliminary de¬sign stage. In addition to the variations in thrust caused by irregularities in the propeller wake field, consideration must also be given to the induced propeller thrust forces resulting from propeller torsional vibration, and, for die¬sel-driven ships, the forces from coupled axial and tor¬sional vibration of the diesel engine and the variable axial forces emanating from the diesel engine crankshaft.

9.2.2 Determination of Natural Frequencies.

There are basically three approaches that may be taken to determine the natural frequencies of longitudinal vibration. The first approach would be to use a simplified method for the purpose of quickly assessing a situation. Approximate methods suitable for investigating the first mode of vibra¬tion.

A second approach is to model the shafting system as discrete masses and springs and use the Holzer method to determine the system natural frequencies. The accuracy obtained with a discrete spring-mass model depends upon the technique used to establish the masses that are used to represent the shafting system.

A third approach is the mechanical impedance method, as proposed by Kane and McGoldrick. This method is inherently more accurate than the Holzer method since the weight of the shafting is considered to be distributed; however, the impedance method has the slight disadvan¬tage of being somewhat more complex and difficult to grasp. For illustrative purposes, a calculation of the natu¬ral modes of longitudinal vibration of the shafting ar¬rangement shown in Fig. 5.1 has been made using the me¬chanical impedance method. Figure 9.9 is a model of the shafting arrangement, which is suitable for analysis by the mechanical impedance method. It may be noted that the difference in the diameter of the inboard and outboard shafting is taken into account; in general, especially with short spans of shafting, this additional degree of accuracy is not warranted.

Fig. 9.9 Representation of a geared turbine propulsion shafting system for a longitudinal vibration analysis

The majority of the system parameters are directly cal¬culated from the system scantlings and, therefore, there is no difficulty in establishing their values. However, the assessment of several of the system parameters can be nebulous. For example, the determination of the water entrained with the propeller does not lend itself to an accurate calculation, but as a first approximation, the en¬trained water weight may be assumed equal to 60% of the propeller weight. The results obtained from the experi¬mental work of Burrill and Robson are widely used in estimating propeller entrained water. Parsons and Vorus provide an analytically derived estimate of the added mass of marine propellers when vibrating as a rigid body.

The behavior of longitudinally flexible couplings, which are affected by the friction between mating surfaces, in connection with vibratory movements similarly cannot be stated with certainty. The consequences of the response of flexible couplings to vibratory loadings, aside from the effect on the couplings themselves, is not great when the thrust bearing is located well forward. But when the thrust bearing is located aft and there is an appreciable vibratory amplitude at the couplings, the effect of flexible coupling behavior can be significant. For a detailed discus¬sion of the response of flexible couplings to vibratory loadings and the complications involved.

Some machinery liquid and foundation weight partici¬pates with the shafting system when vibrating longitudi¬nally as a consequence of being near the main thrust bearing, but assigning a magnitude to these quantities entails numerous uncertainties. An assessment of the ma¬chinery mass, Mc, to be included in the calculations re¬quires judgment, which must be based on the specifics of each system. In instances where the shafting spring constant and the propeller mass are the major determinants of the first-mode frequency, the machinery mass has a small participation; consequently, an accurate assessment of its magnitude is not important. On the other hand, the machinery mass is expected to have a significant participation when the foundation stiffness is a major determinant of the first-mode natural frequency and in the second mode, in which cases a more accurate assessment of the machinery mass is required. In general, the first-reduction gear rotating elements, gear casing, turbines, condenser, foundation structure, or portion thereof may be included as machinery mass. In the assessment of the machinery mass for turbine-driven ships. Interesting approach concerning the treatment of machinery masses in that the center of gravity of a portion of the machinery mass is displaced from the shaft centerline and given a leverage ratio relative to the centerline of the shaft.

The spring constant of the thrust bearing, ktb, may be considered to consist of three components: the spring constants of the thrust-bearing housing, the thrust collar and the thrust elements (or shoes). Aside from the tedious calculations, no difficulty is experienced in calculating the spring constants of the thrust-bearing housing and collar inasmuch as the majority of the deflections are due shear and can be estimated on the basis of well establish techniques. But the spring constant of the thrust elements can be difficult to evaluate because of the oil film and the supporting configuration of the shoes. In the absence more specific information, the data given in reference may be used for guidance in establishing the stiffness thrust elements. However, a more accurate assessment of the thrust-shoe stiffness can be obtained by modeling the shoes using a finite-element procedure.

The determination of the thrust-bearing foundation spring constant can be a difficult and nebulous undertaking even for an experienced analyst. The foundation stiffness is determined by estimating the deflection at I thrust bearing along the shaft centerline due to:

(a) Shear deflection of the thrust-bearing foundation structure.
(b) Bending deflection of the thrust-bearing foundation structure.
(c) Hull bottom longitudinal deflection.
(d)Deflection at shaft centerline resulting from rota¬tion (flexural bending) of the hull structure.

The model used to analyze the thrust-bearing founda¬tion stiffness can take several forms, depending upon the analytical procedure to be used and the information avail¬able concerning the structural details. One model that has been used is based on a fore-and-aft strip through the ship bottom structure that includes the thrust-bearing foundation and the longitudinals that transmit the thrust load into the hull structure. The strip is assumed to be supported at the forward and after engine room bulk¬heads. The strip may extend abaft of the aft engine room bulkhead if the structure there effectively contributes to the thrust-bearing foundation stiffness or if that struc¬ture effectively restrains rotation (flexure) of the bottom structure in way of the thrust bearing.

Longitudinal vibration calculations are frequently con¬ducted such that the natural frequency is expressed in terms of the thrust-bearing foundation stiffness. This pro¬cedure permits a judgment to be made concerning the degree of accuracy required for the thrust-bearing foun¬dation stiffness calculation. In many cases, an approxi¬mate procedure that understates the actual foundation stiffness is found to provide sufficient accuracy.

Table 9.6 contains a calculation for the first and second resonant modes of longitudinal vibration of the shafting system modeled as shown in Fig.9.9. Table 9.6 is based upon the mechanical impedance method and is arranged such that the resonant frequen¬cies can be plotted in terms of the thrust-bearing founda¬tion stiffness. Figure 9.10 is such a plot and indicates the accuracy required of the thrust-bearing foundation stiff¬ness calculations.

Fig. 9.10 Effect of thrust –bearing foundation stiffness on longitudinal resonant frequencies

Table 9.6 Longitudinal vibration calculations for shafting system model shown by Fig. 9.9

In some instances, as may be the case with a ship having a very short run of shafting, an inspec¬tion of the thrust-bearing foundation drawings may be all that is required to provide assurance that the resonant modes of longitudinal vibration will be well clear of the operating range. On the other hand, lengthy and sophisti¬cated thrust-bearing foundation stiffness calculations may be required in order to ensure that ships with long runs of shafting have satisfactory longitudinal vibration characteristics.

The longitudinal vibration characteristics of ships driven by diesel engines are analyzed using the same ana¬lytical approach. The engine crankshaft can be modeled as a series of masses (one for each piston throw) and springs that represent the longitudinal stiffness of the crankshaft between pistons. The mass and stiffness val¬ues representing the crankshaft can be developed from engine drawings. Engine manufacturers provide this in¬formation for shafting system development.

9.2.3 Vibration Reducers.

In cases where design con¬straints make it impossible to design a shafting system such that it is free of objectionable frequencies of reso¬nant longitudinal vibration, use may be made of a "vibra¬tion reducer." Briefly, vibration reducers are thrust bear¬ings, that are modified so that the thrust pads are supported by hydraulic pistons, as illustrated by Figs. 7.4 and 7.5. The volume of oil supporting the thrust pads and the connecting piping can be sized to alter the thrust-bearing spring constant, system effective mass, and damping to avoid objectionable resonant frequencies.

A schematic design of a vibration reducer system is illustrated by Fig.7.5. The major elements establishing the characteristics of a vibration reducer are the oil flask volume and the piping size and length between the thrust bearing and the flasks. The design approach used to size these compo¬nents and control the thrust vibration at the thrust bear¬ing. A complicating factor when using vibration reducers is the necessity to add or remove oil from the oil flasks to keep the thrust pistons from bottoming out. As shown schematically in Fig.7.5, a valve controlled by the thrust collar position adds or dumps oil from the active system. A supply of oil at adequate pressure must be available.

Analytical results and experience confirm that vibration reducers can be very effective in lowering the alternating forces at the thrust bearing and the vibratory amplitudes in the engine space. In general, reductions greater than 4 can be achieved.

9.2.4 Excitation Factors.

Longitudinal vibration of pro¬pulsion shafting systems is often excited by the variable thrust developed by the propeller due to the nonuniform wake pattern in which it operates. The predominant peri¬odic component of the thrust developed by a propeller occurs at blade-rate frequency, i.e., the number of propel¬ler blades times the rotational frequency of the shaft. Higher harmonics of blade-rate frequency occur but, due to their relatively small magnitude, they are generally not of practical importance. A number of factors influence the magnitude of the vibratory thrust; consequently, gen¬eralizations in this area must be used with care. Neverthe¬less, typical ranges of thrust excitation, expressed as a percentage of the mean thrust.

Slow-speed, long-stroke diesel engines can excite longi¬tudinal vibration by:

- The combustion pressure and mass forces in the indi¬vidual cylinders. When the crank throw is loaded by the gas and mass force through the connecting-rod mecha¬nism, the arms of the crank throw deflect in the axial direction of the crankshaft, exciting axial vibrations.
- Propeller thrust variation that is induced by engine torsional vibration. This is particularly troublesome when the major-order critical is above the running speed (stiff shafting system) and the engine variable torque causes an irregular angular velocity of the propeller blades through the water.
- Torsional resonances in the engine that cause axial crankshaft deflections.

9.2.5 Damping.

There are several sources of damping in the longitudinal vibration system, the most important of which is the propeller. Other sources of damping such as hysteresis, and sliding friction are generally relatively small, difficult to estimate, and not readily reflected in the analytical procedures; therefore, their effects are usually considered to be lumped with the propeller damping allowance.

A procedure for estimating propeller damping is de¬scribed, the procedure entails plotting the propeller thrust coefficient versus slip curve at the operating slip point. The propeller damping constant, Cp, is accordingly determined to be

lb-sec/in. (19)
P = propeller pitch, ft
n = propeller speed, rps
D = propeller diameter, ft
CT = propeller thrust coefficient, T/n2P2D2
s = propeller slip = 1 – Va/ Pn
Va = propeller advance velocity, fps

A somewhat different approach for determining system damping was taken by Rigby. Rigby used full-scale data to calculate an equivalent propeller damping con¬stant and concluded that for three-bladed propellers the equivalent damping constant was about 16.5 lb-sec/in. per square foot of propeller developed area; he further concluded that the propeller damping constant tends to increase with larger numbers of blades and suggested that a damping factor equal to 39 lb-sec/in. per foot of blade edge may give better results based on tests made with four- and five-bladed propellers.

An analytically developed esti¬mate of propeller damping of longitudinal vibration based upon Wageningen Series B propeller geometry. The ana¬lytical process recognizes the actual propeller physical attributes in the estimate.

In cases where the thrust bearing is located well aft and there is a significant amplitude of vibration at the slow-speed gear, investigations made and that machinery damping must also be considered; a procedure which may be used to include the effects of machinery damping.

Significant damping can also be provided by a vibration reducer, when incorporated, which must be recognized when evaluating the shafting system vibration character¬istics. The absolute value of the vibration reducer damp¬ing is dependent on the specific design, and can be esti¬mated.

Most slow-speed diesel engines incorporate longitudinal vibration damping features in the crankshaft arrange¬ment. Diesel-engine damping provisions can be effective in minimizing crankshaft axial vibration.

9.2.6 Vibratory Thrust Calculations.

A meaningful pre¬liminary indication of the importance of a resonant mode of longitudinal vibration can be obtained by assessing and comparing the alternating thrust component with the mean thrust component at the main thrust bearing and the vibratory amplitude, velocity, and acceleration at the slow-speed gear, when installed. This can readily be ac¬complished by assuming that the only source of system damping is the propeller (the restriction need not be quite so severe in that an "equivalent propeller damping" may be used which incorporates other system damping effects) and that the propeller is also the only source of excitation. With these assumptions, the propeller input work per cy¬cle can be expressed as:

E = ΠtXa in.-lb/cycle (20)

where t is the maximum amplitude of alternating thrust (pounds) and Xa is the maximum amplitude of propeller vibration (in inches). This can be equated to the damping per cycle

D = ΠCpωXa2 in.-lb/cycle (21)

where Cp is the propeller damping constant (lb-sec/in.) and co is the resonant frequency of vibration (rad/sec), to obtain the following expression for the amplitude of vibration at the propeller:

Xa = t/ωCp (22)

Once the amplitude of vibration at the propeller has been established, the alternating force at other points in the system can be determined by using the mechanical imped¬ance method.

The procedure of determining the alternating force on the main thrust bearing may be illustrated by referring to Table 9.6 and Fig.9.9. In addition, the following data are required:

Mean propeller thrust at 75 rpm
(thrust is assumed to vary as the rpm squared) .............................................. 110,000 lb
Propeller damping constant................................................. …………...……...5800 lb-sec/in.
Ratio of alternating to mean propeller thrust
(based on an analysis of the propeller wake)........................................................... 3%

With these data the exciting force from the propeller is established to be 3300 Ib and from equation (22) the amplitude of vibration at the propeller is

Xa = 3300/[2Π (75)(6)/60][5800]
Xa = 0.012 in.

The procedure outlined can be used to establish the amplitude of vibration at the thrust bearing (point d in Fig.9.9). The amplitude of vibration at point b becomes

Xb = Xa cos (tan-1 Zb/k1Є1)/cos (tan-1 Za/k1Є1) (23)

and the amplitude of vibration at point c becomes

Xc = Xb cos (tan-1 Zc /k2Є2)/cos (tan-1 Zb /k2Є2) (24)

(see Table 9.6 for a definition of terms.) A numerical evalu¬ation of the foregoing expression indicates a vibratory amplitude of ± 0.008 in. at point d (the same as c). This is the amplitude at the slow-speed gear from which the velocity and acceleration can be calculated knowing the frequency of vibration. The alternating force at point d is then determined from

Fd = ZdXd (25)

By interpolating the data shown in Table9.6, Zd is estab¬lished to be 2.95 X 106; therefore, Fd= 23,600 lb and the ratio of the alternating thrust to the mean thrust is established to be 0.215, an entirely acceptable value in view of the low power level at which it occurs.

9.2.7 Acceptable Limits for Longitudinal Vibration.

Sev¬eral attempts have been made to enumerate acceptance criteria for longitudinal vibration characteristics. Other acceptance criteria have stated that reversals of thrust in thrust bearings are not permitted. One crite¬rion has specified that the acceleration of the slow-speed gear should not exceed 3 ft/sec2; but this recom¬mended criterion is accompanied with the statement: “It is emphasized that particular case warrants individual attention and that the thrust variation levels must be given equal consideration”.

There are so many variables which must be considered when analyzing the vibration characteristics of a system that there appears to be no satisfactory alternative to conducting an analysis of each particular system and studying each system individually.

Section 3

Whirling Vibration

9.3.1 Introduction.

Whirling vibration can best be visu¬alized by considering the motion to be the resultant of two shaft vibrations each in perpendicular planes passing through the shaft neutral position. Depending upon the manner in which the vibratory motions combine in the two perpendicular planes, the resultant motion may be circular (analogous to the motion of a skip-rope), elliptical, or in a single plane (if one of the two combining vibrations is of negligible magnitude). Visualization of whirling vi¬bration is further complicated by the fact that the whirling frequency may be either at the frequency of shaft rotation or a multiple of shaft rotation, and the whirling motion can be either in the direction of shaft rotation or opposite to the direction of shaft rotation.

9.3.2 Determination of Whirling Natural Frequen¬cies.

The shafting system whirling natural frequencies are determined by analyzing a model that: considers the shafting system to be a continuous beam, represents sig¬nificant concentrated masses (such as propellers), in¬cludes an allowance for the propeller entrained water, recognizes the gyroscopic effect of the propeller, and allows for flexibility in the shaft bearing supports. Com¬puter programs are commonly used to conduct such con¬tinuous-beam calculations; however, as an alternative, a method based on the Rayleigh approximation is simple to apply and is useful as a means of assessing the potential for a whirling natural frequency. To apply this method, an assumption must be made with regard to the shape of the shaft centerline when the amplitude of vibration is at its maximum. It is not necessary that the assumed curve have exactly the same shape as the actual vibration deflec¬tion curve, but it should have the same general character¬istics. In problems concerning the vibration of beams it has been found satisfactory to use the deflection curve corresponding to the static loading condition, and this as¬sumption is considered sufficiently accurate in connection with propulsion shafting.

The total energy of vibration at any instant consists of two parts: kinetic energy due to the motion of the shaft masses and potential energy due to the bending stresses caused by the shaft deflection. At the point of maximum amplitude, the masses of the shafting are all stationary, so the kinetic energy is zero; but the potential energy stored up in the shaft is at its maximum. On the other hand, when the amplitude is zero, there is no bending in the shaft, so the potential energy is zero; but the kinetic energy is at its maximum. During vibration the total en¬ergy in the shaft system remains constant; therefore, the potential energy at the point of maximum amplitude is equal to the kinetic energy at the point of zero amplitude. The maximum kinetic and potential energies are deter¬mined by the shaft deflections, the masses carried by the shaft, and the frequency of vibration. These energies so determined may be equated, and this equation is then solved for the critical speed, Arc in cycles per minute, as follows:


In this formula dW is the weight of a short section of shafting whose mass may be considered concentrated or the weight of any concentrated mass carried by the shaft (such as the propeller), and y is the deflection of the center of gravity of this mass. The summations include all of the masses in the shaft system.

The static deflection curve can be calculated as de¬scribed in any standard book on strength of materials. It should be noted, however, that the loads on the shafting should be reversed in direction in alternate spans; that is, the weights are assumed to act down in one span and up in the next. This reversal is necessary to produce a deflection curve that has the same general form as the vibration curve corresponding to the lowest natural fre¬quency.

Such calculations were made for the shafting system shown in Fig. 7.1, and a plot of the mode shape for the whirling mode of vibration is shown in Fig.9.11. It may be seen from Fig.9.11 that the large amplitudes of vibration are confined to the aftermost regions of the shafting sys¬tem. From an inspection of the Rayleigh equation it is evident that only the regions of the shafting system that have relatively large amplitudes have an important effect on the whirling critical frequency. This fact can be exploited to greatly simplify the calculation procedure.

Fig. 9.11 Mode shape of shafting arrangement shown in Fig. 5.1 during whirling mode of vibration

The computation of whirling critical frequencies, by necessity, entails several approximations. One is the assumed location of the resultant reaction in the bearing just forward of the propeller. Assessing the load distribution in this bearing is difficult because neither the shaft alignment conditions nor the slope of the shaft in way c the bearing is known with certainty; furthermore, in ft case of water-lubricated bearings, the position of the bearing reaction moves due to bearing weardown. With shafting arrangements similar to that shown in Fig. 7.2 (close spaced stern tube bearings), the forward stern tube bearing can become unloaded or even possibly develop a downward reaction. Since the load condition of the forward stern tube bearing strongly affects the whirling natural frequency, computations are usually made with that bear¬ing assumed to be loaded and also unloaded, particularly with water-lubricated bearings that are subject to large amounts of wear.

The effects of entrained water can be estimated, but are normally approximated by increasing the weight of the propeller by a percentage (usually 25%). Bearing flexibilities are normally neglected in the Rayleigh calcu¬lations as the problem would otherwise be considerably more complex. However, neglecting bearing flexibility may not be justified if the bearings are softly mounted in rubber to achieve self-aligning capabilities. Propeller gyroscopic effects, which tend to stiffen the system, are similarly neglected. Fortunately, the inaccuracies associated with considering bearings rigid and neglecting pro¬peller gyroscopic effects tend to offset each other.

N. H. Jasper developed a calculation procedure that takes bearing flexibility and propeller gyroscopic effects into account. The procedure is relatively simple due to the fact that only the aftermost region of the shaft¬ing is considered. The results obtained with the Jasper procedure are in very good agreement with the results obtained by using the Rayleigh method; this is attributed to the opposite effects of the additional factors taken into consideration.

9.3.3 Acceptable Limits for Whirling Vibration.

Impor¬tant sources of whirling vibration excitation are propeller and shafting unbalance and occur at a frequency corres¬ponding to propeller rpm. Also, where Z is the number of propeller blades, the kZ ± 1 harmonics of the propeller wake field produce exciting frequencies; however, these are generally not significant due to the small exciting force and the dampening resulting from the relatively higher frequency. Only the frequency corresponding to the propeller rpm is considered to be important by some authorities; however, this point can be debated. In any case, it must be agreed that the severity of excitation at blade-rate frequencies must be investigated for a specific case before blade-rate vibration can be categorically dis¬missed.

In order for the whirling natural frequency to be coinci¬dent with the propeller rpm, conditions considerably dif¬ferent from those on the usual large ship must exist. For example, bearing spans would have to be abnormally long, shaft diameters would have to be abnormally small, a bearing would have to become unloaded for some reason, etc. Whirling frequencies corresponding to blade-rate fre¬quencies can and do fall within the operating range. Fortu¬nately, however, the exciting forces at blade rate frequen¬cies are generally not of great severity unless coupled with other adverse conditions, such as the forward stern tube bearing becoming unloaded.

Perhaps the only generalization which can be made with respect to acceptance criteria for whirling vibration is that shafting arrangements should be designed such that, in the upper operating range, whirling resonant frequencies do not come into close proximity to the propeller rpm or the blade-rate frequencies that have strong exciting forces.
Chapter 10

Reliability concept on marine engineering

It is one of the most important problems how to prevent such damages or troubles as would affect navigation schedules and economy, not to say of the safety of the lives and properties on board. This problem has been studied, however in most cases, from the aspect of searching the causes of troubles or damages at the occasion of happening, in order to find the remedy not to repeat the same case again. It is our in¬tension to study those failures as a whole, trying to find universal characters if any, as well as effective preventive methods to minimize those of respective character.

10.1 Reliability

Reliability is expressed with probability of success to attain aimed purpose, or in another word, / - (probabil¬ity of the failure).

When we had expected, for example, all pieces of N0 work¬ing satisfactory for t hours, among which Nf have failed under way while Ns have survived, we define probability of failure up to time t as follows;

Therefore reliability up to time t is given as follows;

It may be noted that Nf or Ns are variables depending on time t, consequently provability of failure as well as reliability are given as function of time t.

If we will define instantaneous rate of failure occuring a t t, as follows;

we may have following expression of reliability;


We have had in total N0 pieces, among which α Ns pieces have lost their lives at t. Therefore average life m will be calculated by following equation.

If λ is given as a constant,


and we may have following expression of


m is average life or we may call it also MTBF (mean time between failures).


t/n 1.0 1/10 1/102 1/103 1/104

R 0.368 0.9 0.99 0.999 0.9999

10.2 Pattern of failure

As one of the index to denote how failures distribute along time elapsed, we define density function f(t), to express the rate of failure occurrence at certain time t against total number,

Fig.10.1 shows statistic representation of human life, where f(t) shows the percentage of those, whose life is t, while λ(t) gives rate of death of those whose ages are t. Q(t) shows how death percentage will increase, while R(t) shows how survivals will decrease in percentage as year elapses.


Those will be noted three kinds of pattern of distribu¬tion of failures, 1st period of high failure, but decreas¬ing quickly, 2nd period of low and rather constant λ, and 3rd period of high failure having its peak. Failure of the first pattern has usually been observed at earlier stage of service period and consequently called infantile failure. They are due to those of poor quality, which should have been rejected by proper quality control during production stage. Failure of third pattern is regarded as wear-out type, where strength or function have been gradually deteriorated until most of them would reach their limit of durability. Those in between are called accidental failure, whose occurrence seems not depending on time.

It may be noted that these names does not always mean the physical cause of failures belonging to respective patterns.

If we use density function f(t) to represent these three kinds of pattern, for random or accidental failure we will have,


and for wear-out type, we may use what is called normal distribution, namely


as shown in Fig. 10.2 where σ is called normal deviation. Recently Weibl's distribution is also used to represent these three pattern in common expression as

as shown in Fig. 10.3. When m<1 it will give the character of infantile failure. If m =1 , it will be same as equation (5), and with m>1, it will give wear-out type.

It is convenient, if we can apply any of the pattern as a model of actual failure occurrence, to estimate probability of failure in future.

Example: -

If a piece once used for T hours, is again in service for T hours, how will be its reliability R'(t)? If reliability of an original piece for T+t hours service may be given as R(T+t), reliability for T hours will be given also as R(T). As to a used piece, it may have reliability of R' (t) for t hours of further use.



and it may be written as follows;


Namely failure rate of a used piece is subjected to the value T in case of wear-out failure, as position of T will decide the rest of its life. However, in case of failure having random character,

Reliability is not affected whether it is once used or not. We may, therefore, regard time duration in which -failures are of random character, as the effective life of the piece.

10.3 Reliability of systems

Ships or machinery of ships are consisted of numbers of various parts organized for five purpose. Such system, which fails its function if any of its components fails, will be called series and the reliability will be given as:

(10 )

If system does not fail unless all of its components will fail, we call it paralled system, those reliability will be given as:

For example, a system having two boilers will have the higher reliability than that of one boiler, whose reliability is 0.9,

R=1-(1-0.9)2 = 0.99

Under investment doubled, we can reduce the failure chance to 1/10.

If we have a spare system, with which we can replace failed one, reliability of such system may be considera¬bly improved as shown in following example:

Supposing machine 1 works satisfactory for τ hours before it fails, probability for this condition may be expressed as

The probability of failure, which will occur during time ατ is given as follows:

as λ1 is instantaneous rate of failure of machine 1. Then machine 2 will take place of machine 1 and will work for further hours of t-τ until time t without failure. This probability will be given as:

Therefore, probability of such happenings which are in series, will be R1, R2, R3, and as such chance may occur along whole time duration of t, we can obtain total of such probability as in the followings:


Beside, we have the chance that machine 1 may work without failure for t hours, and as a whole, the reliability of this system is


where , , the reliability of machine No. 1 and No. 2 respectively.

In case λ1=λ2=λ equation (12) will become


and (13) will become



Assuming failure of random character, we can get λ as 1/m where

Table 10.1 shows an example of analysis based on the data of a ship over ten years. R is given for working 6000 hours. Table 10.2 shows the comparison of reliability of various engine systems, which are given in Fig.

It may be noted that such low value of reliability does not mean the danger nor losses of ship operation. Most of these failures have been remedied on board by crews immediately and practically of no importance in view of sailing schedules etc., though there might have been included such serious troubles that had affected actually on economy of ships.

Such evaluation of failures may be necessary, when we are to discuss reliability or to make investigation on actual data or record statistically, otherwise they may give us wrong information for prediction of reliability.

10.4 Failure characters of ship's machineries

Among various kind of failures experienced on ship's machineries, we may note following problems as the typical characteristics common to them.

(1) Deterioration of material strength under corrosive atmosphere.
Any material used in machineries is subjected to the change among its molecular structure owing to the load applied or energy attack of various nature from environment, which results in enlarging potential defect or weakening the tie of the structure in the material in course of time, as we call deterioration of strength.

Typical example is observed on reduction of mechanical strength as function of time, which is expressed in the following equation:

where S and S0 are the values of strength correspond¬ing to time t and initial condition. Q is activation energy, E is environmental energy to promote reaction, and K is the constant given by case, ie. combination of material and substances in atmosphere.

With larger Q, strength drops less, while with larger E, strength falls rapidly in course of time.

S-N curve of steel shows clearly that steep reduction of fatigue limit in sea water due to corrosive at¬mosphere.

The environmental energy, which will promote deterio¬ration of strength is not only such chemical reaction, but also temperature or even the stress in the material itself will be the cause. Creep at high temperature or fatigue behavior under combined low cycle and high cycle repeated stresses are the cases of this kind.

As strength will fall gradually in course of time, it cannot be avoided that will come across the limit required to stand against the load, under which failure of material is inevitable. Life of part with the material is thus determined. It may be quite obvious that longer life of machine parts will be obtained, (1) by reduced load, (2) by increasing strength, (3) by reducing deterioration speed, namely improving atmosphere.

(2) Nature of load

As we have observed on those forces acting on shaft¬ing of ship at sea, all of external forces are of varying nature, having certain frequency distribution along magnitude like a spectrum. For instance, stressed in shafting seem rather low in average during one voyage, but peak stress of several times as large as average will be some times observed.

Such random peak stress may directly cause failure as it surpasses strength limit at that instant, or will accelerate deterioration of strength quickly, which will result in failure near future.

When distribution f(x) of variable x is given, probability of all the measured values of x being less than x during n time measurement, will be calculated by;

In other words, P(x) gives the probability of maximum value of x occuring during n time measurement.
If f(x) is normal distribution of logarithmic type,

with n being infinity, or expressed in following expression:

Actual data of observation is shown in Fig., where x is maximum value of stress observed during every voyage of trans-Atlantic route, and P(x)is proba¬bility of occurrence corresponding to x. Average value of x is 5x 103 lbs/ where P(x) = 0.5, and probability with which stress more than two times of average may happen, will be 3%, or l/l-P(x) = 33, namely once for 33 times of voyages. This kind of information is useful to estimate frequency of such dangerous case as stress might surpass limit of strength.

(3) Probability of failures and safety factor as mentioned above, load as well as strength of material are not definite value but have certain distribution as given with L(x) and S(x) respectively, where L (x) means probability of stress due to load being larger than value x, while S(x) means probability of material strength being less than value x. Fig. shows these relations, where L'(x) or S'(x) are function of distribution of each probability density.

If we assume that failure will occur at any instance when stress surpass strength, we may give probability of such condition as follows:

It is obvious that probability of failure F will be decided how L (x) and S (x) are close and overlapped each other. Let and are respectively modes of S' and L', and we may define safety factor as .

In Fig., probability function of L and S is shown, where L(x) gives the probability of stress being greater than x, while S (x) gives that of strength less than x. Comparing relation of these two curves referring to most probable case of mode of stress, namely p(x)=0.5 on L(x.), we may get p(x)=0.995 under same x, which means the chance that strength is less than x is only 0.5%. We also see that safety factor in this case is Ca 7.5 - 3.5 / 3.5 = 1.3.

Fig. shows the case where strength is deteriorated in course of time t. We may observe at t=o, probability of failure is ca 1/180, but it will increase as the time elapses until L=S or it reaches 1/2.

10.5 Concept on improving reliability

Investigation on failures of large diesel engines has proved that they are divided into two kind of groups, one contains mostly those of large components such as piston, cylinder cover, cylinder, namely heat affected members around combustion chamber, as well as bearings in power transmission system, whose MTBF are of several ten-thousand hours. They are wear-out failure by nature, but with broad deviation in life, and it is difficult to keep reasonable maintenance before hand. Another group is consisted mostly those of small parts such as valves on cylinders as well as fuel pumps etc., whose MTBF are of several thousand hours. They are easy to access by crews on board and may be well kept, if proper preventive maintenance system will be applied.

Therefore, what we can take as the measure to improve reliability of those in first category, is:

(1) To keep load or strength of material as uniform as possible. To avoid abnormal load, governor or safety device shall be improved. Quality control will be strengthened with necessary and sufficient standard limit as well as ingenious methods of measurement.

(2) To select ample safety factor.

(3) To select material having anti-deterioration properties.

(4) Precaution against instantaneous failure so that a machine part can stand for some time before complete break-down of its function.

(5) Repair maintenance under regular inspection system. Inspection interval will be so determined that failure once overlooked may not become fatal before next inspection.

The most important problem in reliability design is how we shall set the expected life on each of those machine parts. For instance, durability and high earning efficiency will be required especially when parts are expensive consumable goods. They may become more expensive, using material of higher quality produced under higher quality control, with more ample margin against load to ensure longer life and better availability so far as balance of cost against earning will allow.

Contrary to this tendency, such small parts as mentioned above have been regarded as ordinary consumable goods, which will require cheaper cost and easy handling for replacement, even at the cost of higher stress and shorter life. However, high reliability should be strongly needed, as even single failure of them will stop whole function of machinery. Therefore, neces¬sary measures will be considered as follows:

1) Strict quality control during production to ensure uniform durability in service.

2) Preventive maintenance system, replacing all working parts after certain service hours.

Under this condition, it may be seen how important as well as difficult to set the expected life-time on such parts of second category also, because longer life does not always mean cheaper mainte¬nance cost, not to say of better reliability.

Our present knowledge and information on material strength as well as stress induced in machine parts in service seems still not enough to predict life-time or reliability on each of designed parts with such exactness as you may expect. But I hope those principles mentioned above will help you, when you are required to control ships and their operations as a whole. It will give you also the idea how to grasp whole aspect not coming into details.

Table 10.1

Failures of ship machinery

no of set no of failure
total working hours MTBF
λ x 10-6

feed pump
4 85,680

M condensate pump
2 4

A condensate pump

M circulation pump

A circulation pump

sea water pumps

L.O pumps

F.O. supply pump

F.O. transfer pump
0. 6452


tubes for boiler


fire bricks


super heater header


safety valve


soot blower




temp. regulator


feed regulator



main turbine

reduction gear


HP feed heater

LP feed heater


M ejector

A ejector

evaporator ejector

M condenser

A condenser

air heater

air blower
0 85,680

Table 10.2

Comparison of reliability of systems

Chapter 11

Weight-Based Designs

Machinery Weight

11.1 Machinery type

- the almost universal choice for the machinery of most medium to large cargo ships is a slow speed diesel engine;
- medium speed geared diesels are the general choice for smaller cargo ships, ferries, tugs and supply boats;
- large cruise liners are frequently fitted with diesel electric installations as are many specialist vessels such fishery research and oceanographic vessels.

Gas turbines and/or high speed diesels are the choice for warships where the need for a high power/weight ratio is all important. An unusual feature of warship machinery is the fact that it usually has to provide both a high speed sprint capability and a reasonable endurance at a slow to medium speed. The machinery provided for these two roles may be arranged so that the two component parts always operate separately (the “or” configuration) or combine together (the “and” configuration) for the high speed role.

Obviously the aggregate power for both configurations must be used as the basis for estimating the machinery weight.

As the weights per unit of power vary considerably between the extremes of slow speed diesels and gas turbines, a decision on machinery type is a necessary preliminary to the assessment of the machinery weight.

As with outfit weights, accurate machinery weights are best obtained by synthesis from a number of group weights and a suggested system for this is given later in this section.

11.2 Approximate machinery weight estimation

The simplest possible way of estimating the machinery weight is by the use of a graph of total machinery weight plotted against total main engine power (MCR), with a line for each of the four different main machinery types described in the last section and preferably with the data spots on it identified with the ship types to which they refer. This last suggestion stems from a recognition that the different auxiliaries required by different ship types can exercise a considerable influence on the total weight.

11.3 Two or three group methods

A slightly more sophisticated treatment would divide the machinery weight into two components: propulsion machinery and remainder. In the 1976 paper where this two-group method was suggested, the propulsion machinery was limited to the dry weight of the main engine which can be obtained from manufacturers’ catalogues with everything else being taken with the remainder.

Largely because of the availability of data in this format, this demarcation is followed again in this book, although the author can now see advantages in the alternative three-group demarcation. In this demarcation the propulsion group is enlarged to include main engine lubricating oil and cooling water, any gearing, the shafting, bearings and glands and propeller(s) as well as the dry main engine weight. The second group would then consist of generators, boilers and heat exchangers, all pumps, valves and piping, compressors and other auxiliaries. The third group would consist of items such as ladders, gratings, uptakes and vents, the funnel, sundry tanks, etc. As these items are generally a good deal cheaper per tonne than machinery items, keeping these separate helps cost estimating. As the total weight of these items will generally be more dependent on the propulsion machinery type and power and the general size of the engine room than on the auxiliaries fitted segregating them into a separate group helps to improve weight estimation.

The original two-group treatment has the advantage that the weight of the main engine can usually be obtained from a catalogue and this significant portion of the weight can therefore be presumed to be correct limiting any error in the machinery weight estimation to that occurring in the estimation of the remainder, the treatment of which as a single entity has the merit of simplicity.

The two-component demarcation is, however, unsuitable for recording the weights of diesel-electric machinery installations in which an aggregate of generators provides both the propulsion power and the electricity supply for other purposes. Weights for diesel-electric machinery seem best kept as a single unit and plotted against the total power which can be generated with all engines on full load.

11.4 Propulsion machinery weight

If catalogues giving dry machinery weights are not readily available approximate values for slow and medium speed diesels can be obtained from Fig. 11.1 which is a modified version of a plot from the 1976 paper.

Fig. 11.1 Main engine weight-slow and medium speed diesels (dry)
The base parameter used in this plot is the maximum torque rating of the engines as represented by MCWRPM and in 1976 it was commented that most of the current engines conformed remarkably closely to a mean line represented by the formula:


where MCR = maximum continuous power in kilowatts and in this case RPM is engine RPM and not propeller RPM.

The weight given by this equation is about 5% higher than that represented by a line through the data spots to allow for the fact that the graph really ought to be a stepped line corresponding to cylinder numbers with approximately 10% weight steps for the addition of each cylinder.

The constant in the formula now quoted has been modified to allow for the power being in kilowatts and for a slight change in the line to accord with 1992 data but the index remains unchanged.

Apart from its use when catalogues are not immediately handy it may be useful when it is thought wise to use a “mean” weight figure in advance of taking a decision on the make of diesel which will be fitted.

An alternative approach to dry machinery weights is provided by the use of average weights in tonnes per kilowatt, values for each of the main types of engine being as follows:

Slow speed diesels: 0.035-0.045, most usual value 0.037 tonnes/kW or 22 to 28 kW/tonne
Medium speed diesels: 0.010-0.020, most usual value 0.013 tonnes/kW or 50-100 kW/tonne;
vee engines tend to be lighter and in-line engines tend to be heavier
High speed diesels: 0.003-0.004 tonnes/kW or 250-330 kW/tonne
Gas turbines: 0.001 tonnes/kW or 1000 kW/tonne

For some reason the reciprocal kW/tonne figures seem to be easier to remember.

11.5 Weight of the remainder

In the 1976 paper two alternative parameters were considered as possible bases for plotting the remainder of the machinery weight. These were:

(1) The Maximum Continuous rating of the main engine(s); and once again
(2) The engine torque as represented by the quotient MCR/RPM.

The argument for the use of the first of these parameters lies in the fact that the shafting and propellers and many of the auxiliaries, exhaust gas boilers, uptakes are related to MCR of the propulsion machinery.

The argument for the second parameter lies in the fact that the use of torque as a base reduces the parameter of a medium speed engine and still more that of a high speed engine when compared with that of a slow speed engine of the same power in a way that may correspond approximately to the reduced weight of auxiliaries that can be expected in such installations and the smaller size of engine room required with correspondingly reduced weight of piping, floorplates, ladders and gratings, vent trunks, etc.

The best “fit” with the data available was, however, obtained when MCR was used as the base. Figure 4.16 is a revision of the figure presented in the 1976 paper with the MCR altered to kilowatts and with account taken both of the altered demarcation now suggested and of some additional data.

The Maximum Continuous rating of the main engine(s); and once again The engine torque as represented by the quotient MCR/RPM.
Expressed as a formula:


where MCR is in kW.

The constants noted below have been updated to allow for the power now being in kilowatts and weights to 1992 practice.
K = 0.69 for bulk carriers and general cargo ships
= 0.72 for tankers
= 0.83 for passenger ships
= 0.19 for frigates and corvettes

Fig. 11.2 Weight of remainder of machinery weight versus main engine MCR (kW)
Chapter 12

Machinery Selection

12.1 Introduction and criteria for choosing the main engine

The selection, arrangement and specification of the main and auxiliary machinery is the province of the marine engineer. In this chapter only those aspects of these tasks which directly affect the naval architect as the overall ship designer are dealt with - and the treatment is necessarily a simplified one. It commences with an examination of the criteria against which the choice of main engines is made, which include:

12.2 Required horsepower
12.3 Weight
12.4 Space
12.5 Capital cost
12.6 Running costs
12.7 The ship’s requirement for electrical power and heat
12.8 Reliability and maintainability
12.9 The ship’s requirement for manoeuvring ability and/or for slow-speed operation
12.10 Ease of installation
12.11 Vibration
12.12 Noise and other signatures

The importance of each of these criteria differs from one ship type to another. In some ships only a few of the criteria need be considered, in others all must be taken into account although with different degrees of emphasis. Each criterion is considered briefly in the following sections.

12.2 Required horsepower

The naval architect, when calculating the power to specify to the marine engineer, has to make a number of assumptions. The most important of these assumptions relates to the number and type of propulsors and to the propeller revolutions. All these must be known to enable the quasi propulsive coefficient to be estimated and this has, of course, a major influence on the required power. A secondary influence on the power stems from the effect on the displacement of whatever assumption is made in respect of machinery type with the influence this exercises on machinery and fuel weights etc.

All these assumptions must be relayed to the marine engineer, who should feel free to question them. If by changing any or all of the assumptions the marine engineer can offer a technically better and/or cheaper solution, a dialogue with the naval architect should ensue and the power estimate adjusted to suit what are then agreed as the main technical features of the machinery.

Apart from adjustments of this sort the power is of course the fundamental criterion.

12.3 Weight

This is not generally a very important matter for the majority of merchant ships, although it undoubtedly plays quite a significant part in the selection of machinery for ferries and similar relatively fast, fine lined ships, particularly if these are also subject to a draft limitation.

In the design of warships, planing craft and catamarans, the need for a high speed from a relatively small ship makes the power/weight ratio a matter of vital importance.

12.4 Space

Much of what has been just been said about weight also applies to space. As far as the main engines are concerned space and weight generally go together, but if a trade-off between weight and space is possible, then ships designed on a deadweight basis should be fitted with the lighter machinery, even if this takes more space, whilst those designed on a volume basis should be fitted with the less bulky machinery even if this is heavier.

On warships space, like weight, is at a premium and the power/volume ratio is very important.

12.5 Capital cost

The cost of the main engine itself must be considered along with any differential costs which may arise from its installation. Such differential costs could include another may use direct drive and have engine driven pumps included in the main engine price.

12.6 Running costs

Usually, the most important item of running costs is the annual fuel bill. In recent years fuel prices have been very volatile, as Fig 9.1 shows. Whilst at the time of writing (1995) fuel prices are well down from their peak in the period 1979-1985, the lessons learnt then ensure that these costs remain a very major factor in machinery selection.

For a required horsepower there are, in principle, two fundamentally different ways of minimising expenditure on fuel:

(i) by fitting as fuel efficient an engine as possible even if this requires a relatively expensive fuel; or
(ii) by the use of machinery which can bum a cheap fuel even if its specific consumption is comparatively high;

and, of course a compromise between these extremes, with the ideal being an engine capable of achieving a low specific consumption whilst burning a cheap fuel.

Whilst seeking minimum fuel costs, however, it is important not to overlook other running costs, such as lubricating oil, spare gear, annual maintenance and not least - the cost of manning. A reduction of one in the number of engine room staff may reduce running costs by as much as, or more than, can be achieved by expensive improvements in engine efficiency.

Fig.9.1. Fuel prices through the years.

12.7 The ship’s requirement for electrical power and heat

Because the main engine will generally be able to bum a cheaper fuel than is required by the generators, the use of the main engine(s) to provide electrical energy and/or heat for engine auxiliary plant and hotel services via shaft driven alternator(s) and exhaust gas boiler(s) respectively can have an important influence on running costs.

On passenger and other ships with high electrical loads this can lead to a preference for diesel electric propulsion.

12.8 Reliability and maintainability

These aspects --- very dear to all practical seagoing marine engineers --- must be considered on all ships, but become of outstanding importance on ships for which the consequences of a breakdown may be particularly severe. Such ships include passenger ships where not only are particularly high costs incurred in dealing with the immediate emergency but future profitability may be prejudiced by attendant publicity. On warships reliability is made the subject of very detailed studies and redundancy is introduced to minimise the consequences of any loss of capability whether this is caused by mechanical breakdown or enemy action.

Some marine engineers tend to favour the use of a slow-speed diesel because this will have fewer cylinders, reducing the parts requiring maintenance, whilst others prefer the lighter and more easily handled parts of a medium-speed engine.

12.9 The ship’s requirement for manoeuvring ability and/or slow-speed operation

An ability to manoeuvre quickly and accurately can be an important factor in the choice of main engines and, of course, their associated propulsors on ships which berth or use canals or constricted waters frequently.

A need to be able to operate at slow speeds using low power, particularly if this may have to be for protracted periods, can rule out certain machinery options, unless this function is undertaken by an auxiliary system, such as a controlled slipping clutch device or an auxiliary propulsion system such as a thruster.
12. 10 Ease of installation

This is probably a second-order criterion, but there is no doubt that some engines, particularly of the slow-speed type have much simpler systems than others of the same type and this may be taken into account when the choice is finely balanced.

12.11 Vibration

Any vibratory forces or couples that may emanate from a main engine under consideration must be carefully assessed before it is accepted as suitable. An engine which develops even a moderate couple should only be considered if it can be clearly shown that the resulting vibration is within acceptable limits at all parts of the ship where it could affect personnel or equipment. It is worth noting that the relativity of the position in which the engine is to be fitted to the nodes and anti-nodes of the ship’s vibration profile can have a significant effect.

12.12 Noise and other signatures

In some vessels such as fishery and oceanographic vessels and warships operating submarine detection equipment such as towed array, the minimisation of the under-water noise signature becomes a driving factor in the whole machinery installation.

Where the noise targets are stringent, consideration must be given to raft mounting the engine(s) and enclosing them in an acoustic enclosure. Both of these requirements impose limits of both weight and space on the choice of engines.

Even if these measures are taken, the required performance will demand the choice of an engine with minimum vibration and noise characteristics.

In mine hunters the magnetic signature becomes so important that all machinery must be constructed of non-magnetic materials.
Chapter 13

Cost Estimating
13.1 Cost and Price

The words cost and price are used colloquially as though they had the same meaning, but as used here they are fundamentally different.

Costs can be divided into two categories - estimated and actual. The estimated cost is that calculated when the shipyard is tendering; the actual cost is that ascertained to have been incurred at the end of the contract. The price is the sum of money which the shipyard quotes to, and eventually receives, from his customer.

The tender price is that given in the quotation, the contract price that agreed in subsequent negotiations whilst the final price is the sum for which the contract is concluded. The tender and contract prices are based on the estimated cost and on the state of the market.

The difference between the cost and price will take account of any allowances necessary for cash flow finance, for any anticipated inflation, for the shipyard’s profit with these additions being reduced by any Government subsidy which can be claimed. If the price has to be quoted in a foreign currency it may also be wise for it to include some provision for possible exchange rate fluctuations.

The price may be a fixed price or there may be provision for it to vary with inflation. In some circumstances where it is impossible to specify exactly what is required, the tender price may be little more than an indication with the contract agreed on an ascertained cost basis. Needless to say this is not very desirable for the buyer, but may be the only way to get work under way on a novel project.

The final price depends very much on the contract. If this has stipulated a “fixed” price, then the final price will be based on the tender price adjusted as necessary by the agreed variations to contract.

When there have been difficulties with the contract or the specification/design have been inadequately defined, there may be considerable extra costs due to changes required by the owner or due to delays that the shipyard can claim were the responsibility of the owner. With inflation and possibly with a variety of different currency exchange rates entering the equation there can be fierce arguments before a final price is agreed.

13.2 Machinery material costs – general

Machinery material costs are obtained mainly from subcontractor’s quotations but partly by costing items either on unit, unit power or unit weight basis. Where greater accuracy is required more subcontractor’s prices should be used, but where speed is essential the cost per tonne basis is necessarily used for most items.

13.3 Machinery material costs - merchant ships

For merchant ships a split into three groups seems to provide a way of bringing together items whose costs per unit weight are fairly similar and which can be related to an easily assessed parameter.

It could be argued that it would be better to make controls and switchboards into a separate group because of their high cost and low weight, but they are so closely connected with propulsion and generation respectively that groups 1 and 2 seem the best homes for them.

Group1. Propulsion
Main engine(s)
Propeller( s)
Main engine controls
Group2. Auxiliary machinery
Generators and switchboard
Compressors, etc.
Group3. Structure related
Funnel and uptakes
Ladders and gratings
Pipework and ventilation trunking within engine room.
A machinery materials estimate summary sheet is given in Fig. 13.1.

Fig.13.1. Machinery material cost calculations.

13.4 Machinery labour costs

Machinery labour costs are estimated as the product of the manhours required and the average wage rate applicable. The manhours can be obtained either by a detailed work assessment --- the most accurate way but a lengthy process --- or for approximate estimates by proportioning from available data on the manhours and total machinery power (P) of a suitable reference ship using this in the ratio (P) to the power 0.82, again as recommended by Carreyette.
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