Vibration Characteristicsof Two-stroke Low Speed Diesel Engines

Abstract

This paper gives a general introductionto the vibration characteristics associ-ated with two-stroke, low speed marinepropulsion diesel engines, and ou#inesmeasures t h a t can be taken to counter-act any adverse influences arising in theship.

A few years ago, vibrations were en-countered in some ships propelled byengines wtih a low number of cylnders.These cases led to intensified investiga-tions of the vibration conditions on boardsome of these ships, and prompted afurther careful theoretical investigationinto the vibratory excitation sources.

The vibratory conditions relating to thecoupling betwean torsional vibrations ofthe propeller and axial vibrations of theshaft system, engine and huff wi// bethoroughly dealt with. These appear es-pecialy where shaft system diametershave been increased considerably inorder to avoid a barred speed range:

Introduction

Developments in world economy dur-ing the last two decades have led todrastic changes in the traditions of theshipping and shipbuilding industries.

On the technical side, two-stroke, lowspeed diesel engines with a low num-ber of cylinders have become verypopular for the propulsion of ocean-going ships, mainly on account of theirlow instaI!ation and operating costs.

Fig. 1 shows how the number of 4 andScylinder engines has increased overthe years at the expense of 7 and 8-cylinder engines. The same illustrationalso indicates how the stroke/bore ratioand the ratio between mean indicatedpressure and maximum pressure havedeveloped with the aim of reducing thespecific fuel consumption and reducingthe engine speed, with consequentlyincreased propeller efficiency.

In the same period, it has bean verifiedthat constant pressure turbochargingand uniRow air scavenging are the work-ing principles which ~provide the lowestspecie fuel consumption of two-strokelow speed diesel engines.

From a vibration point of view, theabove changes have resulted in certainvibration charactenstics playing a moredomi- nant role than others. However,the fundamental excitation principles inthe engine remain the same. The en-closed reference list refers to some re-cently published papers dealing withthese subjects.

The concern about vibrations on boardships most often stems from a wish toprovide comfortable conditions. How-ever, if not adequately dealt with, vibra-tions can reach a level which threatensthe safe operation of mechanical andelectronic components and even thestabilw of major parts of the ships steelstructure.

As a major licenser, MAN B&W Dieselare obviously interested in having asmany MAN B&W engines as possibleinstalled with the optimum overall costefficiency. With rward to vibrations, thismeans that the optimum combinationof vibration countermeasures are to beimplemented on every propulsion unit.

According to the authors experience,actual contract conditions have in somecases prevented the necessary counter-measures from being taken or have evencaused unnecessary countermeasuresto be implemented.

Terminology

Before undertaking a detailed exami-nation of the vibration characteristics ofthe diesel propulsion plant, it may beuseful to study a simple mass-springsystem in order to recapitulate the ter-minology used in a discussion of vibra-tions.

Fig. 2 illustrates the following:

1) Mass-elastic system:model used to calculate the physicalsystem comprising masses, springand damping elements

2) Excitation:Forces or moments acting on themass-elastic system

3) Mode shape, or vibration modes,and natural frequency:A characteristic deflection fom- of themass-elastic system and a corre-sponding characteristic frequency atwhich the system can perform sinu-soidal vibrations once excited, afterwhich jt is left to vibrate freely

4) Harmonic excitation:In the case of a periodic excitation, itis possible to describe the excitationas a sum of sine functions with dif-ferent amplitudes, phase angles andperiods (Fourier analysis). The pertodsof the sine functions will be 1, i/Z.l/3, i/4 _.. of the period for the basicexcitation. These sine excitation com-ponents are also called the lst, 2nd.3rd, 4th order harmonic excitations

5) Resonance:The frequency of a harmonic excita-tion coincides with the natural fre-quency of the mass-elastic system.Depending on the damping of thesystem, a considerable magnitica-tion of the response will take placeat resonance. Magnifications of 5 to50 times will not be unusual

6) Main critical resonance is the condi-tion at which the main harmonicexcitation has resonance

Overcritical condition refers to the con-dition at which the frequency of themain harmonic excitation is higher thanthe natural frequency.

Conversely, undercritical conditionrefers to the condition at which the fre-quency of the main harmonic excitationis lower than the natural frequency.

1

Influence of bordstroke ratio

Influence of Pmax ratioPO

ASKJOC

15,000 EIHP 1979-1992

Fig, 1: Developments in the parameters of two stroke low-sped diesel engines

2

P. excitation of nth order:

Pn = Qn sin (m3t + ~1

Q,: nth order excitation amplitude

El: engine angular velocity

93: nth order excitation phase angleFWMCy

44,: N*,ralfrqecy for system I A periodic excitation F can be split into a number

of harmonic orders P,,:

A, (response Of P. angular frequency

f *vJwept mm 0 - -,

F

0

0 -node naturalN

F=C Q,sin(nwtxm)

M2n=,

,-node natural

(excitation synth+s)

YW= response of nth order

X, = A, sin (nti + qr.)

A, = nth order response amplitude

V = nth order response phase angle

For linear system nth order excitation P,, will giveonly nth order response x,

atural,quency: Characteristic frequencv for the mass-elastic svstem

Sub- and super-harmonic response

ode shape: Characteristic deflection form in which mass-elastic system responds whenNon-linear response of order dierent ulan theexcitation order

excited at a frequency equal to the natural frequencyThese effects are considered in standard torsional

esonance: Where natural frequency coincides with excitation frequency no vibration calculations

Fig. 2: Explanation of vibration terms

3

Excitation - General

Excitations generated by the enginecan be divided into two categories:

1) Primary excitations, which are forcesand moments originating from thecombustion pressure and the inertiaforces of the rotating and recipro-cating masses. These are character-istics of the engine as such, andthey can be calculated in advanceand be stated as part of the enginespecification, with reference to a cer-tain speed and power

2) Secondary excitations, stemmingfrom a forced vibratory response in asub-structure. The vibration charac-teristics of sub-structures are almostindependent of the remaining shipstructure

Examples of secondary excitationsources from sub-structures could beanything from transverse vibration ofthe engine structure to longitudinal vi-bration of a radar or light mast on topof the deckhouse. Such sub-structuresof the complete ship might have reson-ance or be close to resonance condi-tions, resulting in considerable dynam-ically magnified reaction forces at theirinterface with the rest of the ship.

Secondary excitation sources cannotbe directly quantified for a certain en-gine type, but must be calculated atthe design stage of the specific propul-sion plant.

Primary excitation sources

The primary excitation sources are veryclosely connected to the crankshaft/connecting rod mechanism and the en-gine process pressure acting through it.Even though the function of this mech-anism is simple, it can be difficult to ax-plain the origin and distribution of itsassociated internal/external forces andmoments.

F;+G+

S Sand S:Cbnnecting rod force acting on crosshead, equal to connecting rod force acting oncrankpin, equal to force on main beating journals

M M Mand Ml:ITorque on main bearing journals from combustion pressure forces and inertia forces

T and R:S, S and Scan at the crankpin be given as a sum of a radial component Rand atangential component T

Resulting forces on engine frame in vertical direction: C, F I, F and FJ

Resulting forces on engine frame in horizontal direction: C and Fi

Resulting moment on engine frame: M+M+M=lx(G+G+G)

Fig. 3 shows the forces and momentsof a 1 -cylinder engine. As an approxi-mation for calculation purposes, the Fig. 3: Resulting forces and moments on the engine frame from one cylinder

4

mass of fhe connecting rod has beendivided into two and concentrated atthe centre of the crankpin and thecentre of the crosshead, respectively.This means that only inertia forces ac-ting on two masses, i.e. the reciprocat-ing mass at the centre of the cross-head and an equivalent rotating massat the centre of the crankpin, need tobe considered.

The gas force P will, through the con-necting rod, act on the crankshaft witha torque M, causing an equivalent reac-tion torque on the engine frame G x I = M.M and G will contain harmonic excita-tions of all orders. In MAN B&Ws ex-perience, only excitations of the 1 st to16th order need to be considered.

At a certain uniform speed of the crank-shaft, an inertia force F arises from theaccelerations of the reciprocating massM,, and a centrifugal force C acts onthe rotating mass M,: The force F willcontain harmonic excitations of the 1st2nd, 4th, 6th and higher even orders,however, normally only the 1st and 2ndorder are taken into account. Force Cwill only give 1st order excitation.

For a multi-cylinder engine, Fig. 4. thefiring order will determine the vectorialsum of the forces and moments fromthe individual cylinders.Distinction should be made between:

External forces and moments, andInternal forces and moments

The external forces and moments willact as resultants on the engine andthereby also on the ship through thefoundation and top bracing of the en-gine. The internal forces and momentswill tend to deflect the engine as such.

External forces and moments:

. 1st order moments in vertical andhorizontal direction. These are ofequal size in MAN B&W engines withstandard balancing.

. 2nd order moments in vertical direc-tion. 4th and higher even order exter-nal forces and moments will exist on

Rg. 4: Forces and moments of a multi-cylinder engine

engines with certain numbers of cy-linders, however, they will be smalland can be ignored.

l The H-type guide force moment is amoment between the stationary en-gine frame and the rotating/oscillat-ing parts of the engine. From a prac-tical engineering point of view, itshould be applied to the engine frameas an external moment.

Internal forces and moments:

It is the responsibility of the engine de-signer to provide the engine frame withsufficient stiffness to cope with the in-ternal forces and moments so that de-flections and corresponding stressescan be kept within acceptable limits.

If the engine frame could be assumedto be infinitely stiff, internal momentsand forces would not be able to giveexcitations to the ships structure. How-ever, it is obvious that an infinitely stiffengine frame cannot be obtained and,therefore, it is the relative stiffness be-tween the engine frame and the con-nected hull structure which has to beconsidered.

In MAN B&Ws experience, the internalforces and moments of 1st and 2ndorder, caused by the inertia forces onrotating and reciprocating masses, willnot be able to excite vibrations in theship.

The X-type guide force moment should,however, be taken into account be-cause of its higher excitation frequen-cies and because it acts on the enginein one of its less rigid directions, par-ticularly in the case of engines with ahigh number of cylinders.

Secondary excitation soyces

Torsional vibrations

Torsional vibrations of the entire shaftsystem are mainly excited by the tan-gential force T, Fig. 3. Torsional vibra-tion can, as will be demonstrated inthe next paragraphs, excite vibration inthe hull through the coupling phenom-ena present in the connecting rodmechanism and in the propeller.

5

FA FAA

Vibration of bladesection due toaxial vibration

Coupling between vibratory torsionaltorque and vibratoty thrust due toadded mass.

FA: Total force on propeller bladefrom added mass will be per-pendicular to the blade, inde-pendent of vibration direction

F~I: Force component contributingto added moment of inertia(entrained water) used in tar-sional vibration calculation

FAA: Force component contributingto added mass used in axialvibration c&culation

Fig. 5: Torsional vibration induced propellerI thrust

Torsional vibration induced momentsand forces due to connecting rodmechanism

~,. If a harmonic angular velocity is super-imposed upon the nonal uniform rota-tion of the crankthrow, as in the caseof torsional vibrations, this will causeharmonic forces and moments to occur.However, due to the connecting rodmechanism, the reaction forces will notsolely be of the same order as the super-imposed torsional vibration, but signifi-cant orders of n-2, n-l, n+l and n+2will also appear.

One of the best known effects of this isthe (n-2)th and (n+2)th orders in the tar-gential force T, which are responsible

6

for the so-called sub- and super-har-monic torsional vibrations. But also ex-ternal forces F of (n+l)th and (n-1)thorder will appear for the 1 -cylinder en-gine, see Fig. 3.

Appendices A, B and C give, as ex-amples, the values of these sacondatyforces and moments for relevant tor-sional vibration condition of multi-cylin-der engines.

Torsional vibration induced propellerthrustThe propeller can be considered as ascrew, optimized to transform powerfrom a uniform rotating torque into a uni-form translatofy moving force, pushingthe ship (the propeller thrust).

With this concept in mind, it is not diffi-cult to imagine that if a varying compo-nent is superimposed on the mean in-put rotational speed (or input torque)due to vibration of propeller and shaft-ing, this variation will also appear in thepropeller thrust. An investigation of suchan effect is given in Ref. (2).

Fig. 5 shows that this coupling effectcan be explained partly as an addedmass effect, which is also in accord-ance with the theory in Ref. (2).

Hydrodynamic forces on the propellerdue to vibration of propeller and shafi-ing will also be able to set up pressurefluctuations on the hull surface abovethe propeller, which can give rise to an-noying vibrations.

These phenomena have nothing to dowith the non-uniform wake field.

Axial vibrations

Axial vibrations are excited in the crank-shaft from the radial force R as well asthe tangential force T, Fig. 3. The before-mentioned torsional vibration inducedpropeller thrust will also excite axial vi-bration in the shaft system. Axial vibra-tions will create a reaction force in thethrust bearing which can be consideredas an excitation source for the rest ofthe ship.

Propeller excitations due tonon-uniform wake field

Excitations due to the propeller workingin the non-uniform wake field will betransmitted to the hull either through theshaft system as forces and moments orthrough the water as pressure fluctua-tions acting on the hull surface,

lhe forces and moments should alsobe considered when calculating the tor-sional, axial, and lateral vibrations ofthe shaft system.

The excitation can be reduced by mod-ifying wake field and propeller design,however, this subject is beyond thescope of this paper.

Vibration Modes, TheirExcitation and Control

The general excitations listed in the pre-vious section and the vibration modeson which they act will be discussedtheoretically and illustrated by relevantexamples in this section. Furthermore,available countermeasures will be dis-cussed.

Torsional vibrations

The control of torsional vibrations is ofvital importance for the propulsionplant because excessive vibration ofthis kind can lead to damage or evenfracture of the crankshaft or the propul-sion elements, such as intermediateshafts, propeller shaft, gears and flex-ible couplings.

This is also the reason why the classifi-cation societies, since the early days,have required calculation and verifica-tion by measurements for this kind ofvibrations.

The classification societies prescribetwo limits, T, and T*, for the torsionalstress in the speed range up to 80 percent of MCR, see Fig. 6.

At engine speeds where the lower limit7, is exceeded, it will be necessary to

Solution A Solution B

Rg. 6a and 66: Different shaft systems for a 5L7OMC engine

introduce a barred speed range inwhich continuous operation is pro-hibited. The upper limit me must not beexceeded. Above 80 per cent speedonly limit 7, is applicable.

lhe following propulsion systems andtheir torsional vibration characteristicswill be treated in the following:

1) Engines with 4, 5 and 6 cylinders,directly coupled to the propeller

2) Engines with more than 6 cylinders,directly coupled to the propeller

i fig. 6~: Different shaft systems for a 5L7OMC engine

3) Engines directly coupled to thepropeller and with a small powertake-off

4) Engines with a large power take-offand the possibility of disconnectingthe propeller

Engines with 4,5 and 6 cylinders

With the conventional aft end engine in-stallation, the torsional characteristicsof these engines are dominated by aresonance of the 1 -node torsional vi-bration mode excited by the harmonicorder equal to the cylinder number (Le.5th order 1 -node resonance in case ofa 5-cylinder engine, referred to as maincritical resonance).

This resonance will normally occur some-where in the middle between minimumand maximum speed of the engine,mainly depending on the lengths anddiameters of the shaft system (i.e. totaltorsional flexibility of shaft system be-tween propeller and engine).

The response at resonance will lead totorsional stresses in the shaft systemwhich have to be compared to the limitsstipulated by the classification societyin question. The magnitude of the res-onance stresses will depend on the ex-citations and the damping of the system.Generally, it can be said that the excita-tion increases with increasing enginespeed. The system damping will dependon the ratio between moment of inertia

for propeller and engine, the dampingof the propeller, and the presence ofpossible torsional vibration dampers.

Figs. 6 and 7 illustrate three possibil-ities A, B and C, which are relevant forthe layout of the shafting system fora &cylinder engine directly coupled tothe propeller, but which have widely dif-ferent torsional vibration conditions.

Frequency

wmExcitation order

6th /

Solution C

6 0 0

Solution A is characterised by a rela-tively flexible shaft system. The materialstrength has been increased in order toreduce the diameter of the shafts, thera-by making them even more flexible. Atuning wheel has been mounted on thefront end of the crankshaft to increasethe ratio between engine and propellermass moment of inertia, resulting inhigher damping in the system. The res-onance will occur below engine MCRspeed (over-critical).

400

rImin*

100 120 140

The torsional stresses will be below theF-limit, but above the 1 -limit, with a ?

Engine speed 5L70MC

oarrea speea range as a consequence. ng. 7: Engine speed versus excitation frequency. Natural frequencies for 1 -node torsionalvibration modes art? indicated for solutions A, E and C. Optimum positions of natural

Solution E is characterised by a rela- frequency of PTO systems indicated by shaded areastively stiff shaft system, e.g. due to theshort distance between propeller andengine or due to implemented stiffshaft elements such as shrink-fit coup-lings, oil distribution box to CP-propel-ler and ice class requirements on shaftdiameters. This has brought the maincritical resonance relatively close toMCR, and the resonance stresses willexceed the upper limit 2 prescribed bythe classification society. In this casethere will be four possibilities:

1) Mounting a torsional vibration damp-er of appropriate size which will re-duce stresses to below the 2 limit,and the plant will have a barredspeed range

2) Mounting a torsional vibration damp-er of appropriate size which will re-duce stresses to below the 1 limit,and the plant will have no barredspeed range

3) Increasing shaft diameters in orderto move the main critical reso-nance to above MCR (solution C)

4) QPT (Quick Passage through abarred speed range Technique) forCPP-installation, Ref. 12

The procedure can be described asfollows:

a. The carrying out of ordinarytorsional vibration calculations inmaximum pitch condition

b. The carrying out of ordinarytorsional vibration calculations inminimum pitch condition usingrather pessimistic propellerdamping values

c. The establishment of a simulationmodel of ship/propeller/shafUng/engine/governor which, in thebarred speed range during steadystate operation, Fig. 8 (upperpart), gives results coincidingwith the results of the ordinarytorsional vibration calculations

d. The simulation of engine startingand stopping with rapid passagethrough the barred speed range,Fig. 9 (upper part)

e. The evaluation of stresses in thebarred speed range based onresults of the start and stop testsimulations for rapid passagethrough the barred speed range

In order to ensure the rapid pas-sage through the barred speedrange, a so-called critical speedunit should be installed. Thisunit operates on the speed set-ting signal in such a way thatautomatic rapid passage throughthe barred speed range is ob-tained when the engine is ope-rated via the bridge manoeu-vring system, as well as whenoperating from the engine con-trol room

9

(~

Calculation SimulationStart of simulation I< Steady state >I kNnl1

818

Time I sec.Tinw sec.

I Measurementr Calculationt

I II Toraw

Enlarged time scale tki4m I I

1227

1 818

409D

- 409

- 818

.I 0

1\ Fig. 9: Comparison between simulated and measured torque in

I the intermediate shaft during starting of main engine and passageMeasurement through thebarred speed range (minimum propeller pitch). (As an

! example, a 5L5OMC engine is used)

Solution C is obtained by increasing thediameter of shafts until the main criticalresonance is positioned approximately40-45 per cent above the nominalspeed (undercritical). Due to the largeshaft diameter (large moment of resist-ance), only moderate torsional stressesappear even though the varying torsionaltorque in the shaft is high.

Soletjon C is chosen either as an un-0.0 is i.0 i.5 2.0Time sec. avoidable consequence tor a very

short shaft system or because the ship-i

.I. .,I .~.~

~1fig, 8: Simulated steady state torque and measured torque at mini- owner nas speclrlea mar me sn,p musrmum pitch. (As an example, a 5L5OMC engine is used) not have any barred speed range.

Besides avoiding a barred speed range,solution C is characterised by a ratherhigh varying torque in the shaft which,-as already explained, will induce a ratherhigh varying thrust, called torsional vi-bration induced propeller thrust.

It should be mentioned that under ad-verse conditions the varying thrust canreach levels of up to 50% per cent ofthe mean thrust, which is far abovewhat a propeller designer would acceptas an excitation from the non-uniformwake field.

Of the three alternatives, A will normallyinvolve the lowest cost. Solutions A, Bor C cannot be directly related to aspecific engine type, only detailed tor-sional vibration calculation at the designstage will reveal the optimum solution.

Trends in the choice and feasibility ofthe solutions can be summarised asfollows:

4-cylinder engines:Solution A:less feasible -not very commonSolution B:feasible -not very commonSolution C:feasible -very common

5-cylinder engines:Solution A:feasible -very commonSolution S:feasible -not very commonSolution C:feasible -common

6-cylinder engines:Solution A:feasible also without tuning wheel -very commonSolution B:feasible -not very commonSolution C:not feasible

Engines with 7 or more cylinders

For such engines, the 1 -node maincritical resonance is not normally impor-tant, because it will occur close to or be-low the minimum speed of the engine.Furthermore, the 7th order or higherorder excitations of the torsional vibra-tion are considerably smaller than the4th, 5th and 6th order, which meansthat barred speed ranges are not nor-mally required.

However, the Z-node torsional vibra-tion mode (one node in the crankshaft)begins to be important and needs at-tention.

Major resonances for this vibration modeshould be avoided close to MCR. Smalltorsional vibration dampers might berelevant.

Engines with small power take-off

It has become very popular to connecta power take-off (PTO) to the crank-shaft or propulsion shaft system. Someyears ago, also exhaust gas drivenpower turbines were introduced, de-livering their power to the propulsionshafting power take-in (PTI). A commonfeature of both the PTO and the PTI isthat they are connected to a gear sys-tem which needs protection from therelatively high torsional excitation fromthe crankshaft.

In the MAN B&W standard designs, thePTO and PTI are mounted on the foreend of the crankshaft, as a compactunit, and the protection is obtained byinstalling an elastic coupling betweenthe propulsion shafting and the above-mentioned gear.

Normally, when the PTO/PTI representsa power of less than 10 per cent of themain engine power, the vibration modesof the PTO/PTI system will not influencethe vibration modes of the propulsionshaft system. This means that the mainpropulsion shaft system can be de-signed and determined regardless ofwhether a PTO/PTI is to be installedlater on.

As a rule of thumb, the lowest natu-ral frequency of the PTO/PTI mass-elastic system should not be higher than75 per cent of the frequency corre-sponding to the main engine speed.This will give low torsional loads in thePTO system due to the fact that over-critical vibration condition is obtainedfor all harmonic excitations from themain engine at MCR, see Fig. 7.

Engines with large power take-off

Certain types of ships, such as ferries,cement carriers and shuttle tankers,have operating conditions that requirehigh auxiliary power, simultaneouslywith propulsive power. This has beenmet by controllable pitch propellerscombined with relatively large powertake-offs comprising clutches, elasticcouplings, gears, generators and/or hy-draulic power packs.

The torsional vibrations of such installa-tions are very complex, and need care-ful investigation dunng the design stage.

The design philosophy with respect totorsional vibrations in a power take-off is:

l The elastic couplings are necessaryto facilitate alignment and to protectthe gears from the high frequencytorsional excitation of the main en-gine. Such excitation may, in combi-nation with backlash, produce harm-ful vibration in the gear

l The elastic coupling, or couplings,should be sufficiently flexible to en-sure a natural frequency in the PTO-system of either approx. 1.5 timesthe mainengine speed, or below0.75 times the main engine speed,see Fig. 7. This will give main criticalresonances in the PTO-system (4th,5th and 6th order) at very low speedor even below the minimum speed.Furthermore, the 1 st and 2nd orderexcitation, which becomes dominantin case of misfiring, will have reson-ance away from the nominal speed.Such tuning of the natural frequen-cies will normally require very elasticcouplings

11

Shafting system

Mass-elastic system

2) Coupling of torsional vibrations ofthe crankshaft to responses in theaxial direction (mechanism: twist ofcrankshaft will cause axial deflection).This coupling depends on the geom-etry of the crankshaft and is foundwhere pronounced torsional re-sponses exist. For engines with arelatively low number of cylinders, itwill almost exclusk&y be found in con-nection with barred speed ranges

For the following reasons, the axial vi-bration damper is standard for a// cylin-der numbers of MC engines:

l First and foremost, the axial vibrationamplitudes are to be kept below acertain level to protect the crankshaftagainst too heavy extra stressescaused by axial vibrations. For thisreason, MC engines with six or morecylinders are provided with an axialvibration damper

kg. 10: Mass-elastic system for axial vibration calculations. Axial deflections of O-node andl-node mode shape

The combination of low natural frequen-cy and high moment of inertia in thePTO-system will require special facili-ties in the engine governor if insta-bilities in the system are to be avoided.

Axial Vibrations

Axial vibrations are longitudinal shaftingvibrations. Fig. IO shows the mass-elastic system used for axial vibrationcalculations and the mode shapes ofthe two lowest modes which are of re-levance.

MC engines with more than six cylin-ders will have main critical resonancewith O-node vibration mode belowMCR speed. For 4,5, and 6-cylinderengines, the main critical resonancewill occur outside the normal speedrange. However, for 5cylinder S-MCand 6-cylinder K-MC, L-MC, and S-MC engines, the main critical 5th and6th order resonance, respectively, willbe situated very close to MCR speed.

The 1 -node vibration mode is normallyof less importance. Its natural frequen-cy is determined by the mass and stiff-ness of the entire shafting system. Espe-cially the stiffness of the thrust bearingand its support is very decisive.

12

Normally, the natural frequency is sohigh that no dynamic amplification ofthis mode will occur.

Axial vibrations are excited by:

. Radial and tangential components ofthe combustion pressure and massforces in the individual cylinders. Thefact that the pmaJPe ratio of modernengines has increased considerably(see Fig. 1) means that especially theradial components of orders higherthan the 4th order have increased

. Propeller excitation of the blade fre-quency and multiples hereof from thenon-uniform wake field

Excitations caused by responses fromother vibration modes, such es:

1) Torsional vibration induced propellerthrust, the magnitude of which de-pends on how the torsional vibra-tions (see Fig. 6) are situated. Thisexcitation may initiate heavy varyingforces in the thrust bearing

l The second reason for installing anaxial vibration damper is to be ableto control varying forces in the thrustbearing, which may excite the hullstructure. In order to control thesevarying forces, 4 and 5-cylinder en-gines are also provided with an axialvibration damper

The axial vibration damper effectivelyreduces the varying forces generatedin the crankshaft and acting on thethrust bearing. The varying forces orig-inating from torsional vibration inducedpropeller thrust are, on the other hand,left practically unaffected by the axial vi-bration damper.

Fig. 11 shows measurements of thevarying thrust in the intermediate shaftof a 4L60MCE engine with an activeaxial vibration damper. The figure showsthe thrust originating from the 8th order1 -node torsional resonance and the4th order flank. With an inactive dam-per, the magnitude of the varying thrustis the same.

For plants on which the torsional vibra-tion induced propeller thrust is negli-gible, it will still, despite the use of anaxial vibration damper, be necessary to

4L6OMCE thrust-variation86.111 dmin

(Wmo

2 0

00 ,5 10 15 2 0 25 30 35 40 45 50

4L60MCE thrust-variation (Hz)60-W r/min

Fig. 11: Torsional vibration induced propeller thrust measured in the intermediate shaft ofa4L60MCE engine. Response of 8th order 1 -node torsional resonance and 4th order flank isseen

predetermine the varying force in thethrust bearing. The damper will leave avarying force in the thrust bearing of amagnitude corresponding to the staticdeflection of the crankshaft caused bythe mass and gas forces. On accountof the evolution in the pmJpe ratio ofmodern longstroke engines, especiallythe radial components of these forceshave increased, resulting in a consider-able static deflection of the crankshaft.

The above shows that the axial vibra-tion and related torsional vibrationproblems should be solved at the de-sign stage of the ship through cooper-ation between the engine builder andthe shipyard. Especially the force in thethrust bearing should be determined ineach individual case by combining theforces from the torsional vibration in-duced propeller thrust, the forces fromaxial vibrations of the crankshaft, andthe forces from coupled axial and tor-sional vibrations in the crankshaft.

In order to be able to present solutionsto such cases, MAN B&W use a com-puter program including FEM (FiniteElement Method) based crankshaftmodels (Fig. 12) which allows the firingorder, crank throw geometry, and bear-ing stiffnesses to be represented. It alsoallows the model to be excited directlyby the tangential and radial forces ac-tingon the crankpins, Fig. 13.

An example:When designing the shafting for a 5-cylinder engine, a choice can be madebetween an overcritical layout, i.e. usingsmall diameter shafts and, if neces-sary, a barred speed range, or an under-critical layout, i.e. the use of large diam-eter shafts and no barred range.

The reason for the interest in Scylinderengines is that many of these installa-tions are apparently designed for under-critical operation without sufficientallowance being made in the hull struc-ture for excitations from the thrustbearing originating from axial vibrationsand the vibrations coupled to them.

13

Degree of freedom

fig. 12: Half crantihrow FEM-mode/led in fig. 13: Crankshaft modelorder to cauy out vibration and stress ana-lysis. Complete crankshaft is mode/led fromthis half w&throw by the dedicated sys-tem HIFINEL-CIWNK

To illustrate the issues with, in particu-lar, undercritical operation, it will benecessary to recapitulate some conclu-sions relating to torsional vibrations inthe two layouts.

The aspects of the undercritical layoutare illustrated in Fig. 14, upper. At MCR,the 5th order l-node torsional vibrationresonance is situated above MCR. The5th order O-node torsional vibrationmode, normally referred to as irregu-larity, can be considered as over-criti-cal. Thus it can be assumed that thetorsional amplitude on the propeller isa sum of the two contributing torsionalamplitudes.

When passing through a resonance,Fig. 14, lower, the phase of the pertain-ing amplitude is changed 180 degrees.Accordingly, when the shaft system lay-out is overcritical at MCR, relative toboth the 5th order 1 -node torsional

14

mode and the O-node torsional mode, For a shafting design where the mainthe conditions in Fig. 14, centre, are ob- critical is situated below but rathertained. The torsional amplitude on the close to MCR, and a torsional vibrationpropeller is the difference between the damper is used to control the stress-two contributions. As these are typical- levels (Fig. 6, solution B), the result willly of the same magnitude, the resultant be a relatively high torsional amplitudepropeller amplitude at MCR is small com-pared with that of an undercritical lay-

at the propeller. This will give a signifi-cant contribution to torsional vibration

out. induced propeller thrust.

In the case of undercritical layout, theresonance at the main critical order (inthis case 5th order) should be situated40-45% above MCR. Measuring re-sults on the thrust bearing of a 5L70MCconfirm the calculations of the 5th ordervarying thrust. Depending on propellerand shafting, values of +200 to +400kN have bean found at MCR.

Corresponding values for the 5th ordervarying thrust on the thrust bearing,when having overcritical layout, aretypically 60 to 100 kN.

The FLS-M vibration compensator, Fig.15, has been successfully applied as aso-called thrust pulse compensator inorder to reduce the torsional vibrationinduced propeller thrust on 5-cylinderengines that are coupled to large-diameter shafting.

The thrust pulse compensator counter-acts the varying thrust from a positionon a foundation on the tanktop closeto the thrust bearing; Fig. 16, of a5L60MC engine.

Under-critical runningPropeller: 5th order response of O-node and 1 -node adds at MCR

EE[,,er

free end

n n

8

Over-critical runningPropeller: 5th order response of O-node and 1 -node subtract at MCR

Enginefree end

Propeller

Phase change due to passage of natural frequencyPropeller amplitude (torsion) for 5 cylinder engines

fig. 14: Torsional response for 5cylinder engines shown in order to illustrate torsionalvibration induced propeller thrustUpper : situation when running under-criticalCentre: situation when running over-criticalLower : phase change when passing through a resonance

A: AC ServomotorB: Gear wheelsC: Flyweights

fig. 15: FLS-M Vibration compensator

1

Fig. 17 outlines the results of vibrationmeasurements at the wheelhouse levelof the superstructure in the longitudinal

: direction. It is seen that with the opti-~ mum phase of the counterweights ofI the thrust pulse compensator, a reduc-~ tion of the vibration level with a factor

,; of 8-10 is obtained.

:~:T~.~ External Forces and Moments

The entire ship forms a mass-elasticsystem, with natural frequencies and vi-bration modes. The horizontal and ver-

~ tical bending modes of the hull girderand the corresponding natural frequen-ties can be calculated. Determinationof vibration modes with 4, 5 and more

: nodes requires comprehensive calcu-:: lating procedures, whereas modes1 with 2 and 3 nodes can be calculated

I by more simple procedures.

fig. 17: 5LtiOMC. Measurements at 92 r/mn at the wheelhouse inlongitudinal direction

In order to obtain the correct decisionbasis at the engine contract stage, in-formation about these vibration modesshould be available, as this will make itpossible to decide the measures to betaken to control the responses fromthese vibration modes.

Hull girder vibration modes are excitedby forces and moments acting on thehull girder, Fig. 18. Excitations of hullgirder vibration modes originating fromthe engine are external forces and mo-

ments generated by the inertia forcesof unbalanced rotating and reciprocat-ing masses.

For MAN B&W engines, the externalforces can -for all practical purposes -be considered to be zero, due to theirsmall size. Normally, only the externalmoments of 1st and 2nd order need tobe considered. However, modest mo-ments of other orders exist; an exampleis shown in Appendix A.

f=Fsin(qwt+v$

Jewantinodes (translatory deflection):dear nodes (angular deflection):

Forces excitation, F, gives forced responsesMoment excitation, M, gives forced responses

fig. 18: Excitation of the hull girder modesCharacteristics of mode shapes and their excitations

According to 1st and 2nd order external moments in layout point LI

0 1 st order- 2nd order

1301

Compensator most likaely

i t20(

Com!xnsator likelv t

fig. 19: Power related unbalance for the MC enginesDefined to judge the size of the external moments

1 st order moments act in both the veni-Cal and horizontal directions. For MANB&W engines with standard balancing,these moments are of identical magni-tudes.

For engines with five cylinders or more,the 1 st order moment is very rarely harn-ful to the ship. However, with 4.cylinderengines, precautions need to be con-sidered.

The 2nd order moment acts only in avertical direction Precautions need onlybe considered for 4, 5, and 6-cylinderengines.

To judge the size of the external mo-ments, the so-called Power RelatedUnbalance (PRU) has been defined,Fig. 19.

On 4-cylinder engines, the 1 st ordermoment is controlled in the followingway:

l standard:adjustable counterweights

l option:1 st order moment compensator

Resonance between the vertical mo-ment and the 2-node vertical hull gir-der mode may often be criiical, where-as the resonance between the horizon-tal moment and the 2-node horizontalhull girder mode normally occurs at en-gine speeds higher than nominal. Asstandard, 4-cylinder engines are fittedwith adjustable counterweights. as illus-trated in Fig. 26. These counterweightsreduce the vertical moment to an insig-nificant value (although simultaneouslyincreasing the horizontal moment); thus,this resonance of the 2-node verticalhull girder mode is easily dealt with.

In rare cases, where the 1 st order mo-ments will cause resonance with boththe vertical and the horizontal 2-nodehull girder mode in the normal speedrange of the engine, a 1 st order momentcompensator, as shown in Fig. 21, canbe introduced in the chain tightenerwheel, reducing the horizontal 1 st ordermoment to a harmless value. The com-

17

Standard balancing

Balancing givingreduced MW

reduced MIH

Fig. 20: Adjustable counterweights for 1st order external momentcontrol

Fig. 21: Compensation of 1st order external moment

pensator comprises two counter-rotat-ing masses, rotating at the same speedas the engine is running.

Since resonance with both the verticaland the horizontal hull vibration modesis rare, the standard engine is not pre-pared for the fitting of such compen-sators

Resonance between the 2nd order ver-tical moment and the 3,4, and 5.nodehull girder vibration modes are possiblein the normal running range of the en-gine, Fig. 22, upper. In order to controlthe resulting vibratory responses, asecond order compensator can be in-stalled on 4, 5, and 6.cylinder engines.

Several solutions, from which the mostcost-efficient one can be chosen, are

18

available to cope with the 2nd ordervertical moment:

a) No compensators, if considered un-necessary on the basis of the naturalfrequency, nodal point, and size ofthe 2nd order moment

b) A compensator mounted on the aftend of the engine, driven by the mainchain drive, Fig. 22

c) A compensator mounted on thefore end, driven from the crank-shaft through a separate chain drive

d) An electrically driven compensator,synchronized to the correct phaserelative to the free moment. Thistype of compensator requires anextra seating to be prepared,

preferably in the steering gear roomwhere deflections are largest andthe compensator therefore has thegreatest effect

e) Compensators on both the aft andfore ends of the engine, completelyeliminating the external 2nd ordermoments, Fig. 22

Solutions (b), (c) and (d) are force gene-rating compensators, which are ineffec-tive if they are placed in a node of theactual hull girder mode, but effective ifthey are placed away from the node,i.e. close to an antinode.

If the node of the critical hull girdermode is situated close to the engine,solutions (d) and (e) should be con-sidered.

Frequency of engine moment cpm cpmMZV = 2 x engine speed

Natural frequency vertical hull vibrations

Statistics of tankers andbulk carriersin the actual power range /I ! r-1 /

20,000 40,000 60,000 60.000 dwt

Compensating moment

Moment from compensator

fig. 22: Compensation of 2nd order vertical external moment. 3, 4 and 5.node vertical hullgirder mode should be considered

Expected node positionExpected node positionn u

FD: Compensating force ofelcectttcally driven compensator

FB: Compensating force ofcompensator in the main chaindrive

M2V: 2nd order external moment tobe outbalanced

FDL!K!LLc node

M2VFB = Lg node

As LB node is given with greater relativeuncertainty than Ls node, Fo can be-determined more precisely than Fe

fig. 23: 2nd order moment balancing.SensWW of force generating compensatorsdue to the node position

If placed in the steering gear room, theelectrically driven compensator d) hasthe advantage -compared to the othercompensators (b) and (c) -that it is notas sensitive to the positioning of thenode, Fig. 23.

If compensator(s) are omitted, the en-gine can be delivered with preparationfor the later fitting of compensators. Thispreparation must be decided at the con-tract stage of the engine. Measurementstaken during the sea trial, or later dur-ing service with special loadings of theship, will show whether compensator(s)have to be fitted or not.

19

2. X-mode:i J

Transverse vibration mode of Iengine top where the foremost partand the aftmost part of the engine Iare 180 degrees out of phase,

L,

having node at the centre part of Ithe engine, Fig. 24 L2

3. L-mode:I

Longitudinal vibration mode withanti-node at the engine top level,

Lsi oooooc

Fig. 24 L6

The natural frequencies of these vibra-tion modes are to a large extent deter-mined by the stiffness of the seating andthe double bottom on which the engineis installed. Fig. 25 shows the mea-sured mode shape of a longitudinaldouble bottom engine column vibrationmode for a 5L80MCE engine. It appearsthat the majority of the elastic deforma-tions occur in the double bottom. The.

Engine Structure andDouble Bottom Vibrations fig. 24: The three major modes of the engine column structure, H, X and L-mode

The vibration modes of the engineframe are part of more comprehensivevibration modes in the aft end of the I- f 0.61 mm 1

In addition to these above discussedexternal forces and moments, thereare also secondary external forces andmoments,originating from torsional vi-brations. An example concerning an8S60MCE is given in Appendix A. Sec-ondary external forces and momentsoriginating from torsional vibrations aremainly of higher order and will be ca-pable of exciting local vibration modes.These secondary forces and moments,which have not so far been reportedas a source of vibration, should be con-sidered at the design stage. They willappear as a result of thorough torsionalvibration calculations.

H - mode X mode L - mode

ship. There are three major modes:

1. H-mode:Transverse vibration mode with anti-node at the engine top level.In-phase amplitudes from the firstcylinder to the last cylinder, Fig. 24

natural rrequency 1s tneretore mainlydetermined by this structure, as the en-

fig. 25: Longitudinal double bottom engine column vibration mode measured on a5LBOMCE engine. Main critical 5th order has resonance in the running range

20

gine as such, compared to the doublebottom, has a much greater stiffness.A similar example could be given forthe H-vibration mode.

H and X-modes are excited by guideforce moments of the H and X-types,Fig. 4. The primary values of theseguide force moments can be calcu-lated for each engine type on the basisof its gas and mass forces. This kind ofexcitation is inherent in all engines.

Secondary values of the H and X-typeguideforce moments originate from tor-sional vibrations and will, therefore, bedifferent for each installation, even forthe same type of engine. Appendix Bshows primary and secondary valuesof guide force moments for a 5L70MCengine with two different shafting lay-outs. It is seen that the secondaryvalues are moderate.

The guide force moments of an 6S6OMCengine for two alternative firing ordersare given in Appendix C. In this case,values for the guide force momentsoriginating from the Z-node torsionalmode are noticed.

L-modes are excited by secondary phe-nomena only, i.e. installation depend-ent forces. The example in Fig. 25shows a case where the L-mode shapeis excited mainly by varying forces inthe thrust bearing initiated by torsionalvibration induced propeller thrust.

Another source of excitation is varyingforces in the thrust bearing caused byaxial vibrations of the crankshaft.

H and X-vibration modes are tradition-ally controlled by bracing the enginetop to the hull structure so as to obtainresonances with the critical orders situ-ated above the relevant speed range,thus detuning the system. In order toobtain a sufficient detuning effect, i.e.to bring certain resonances with criticalorders above the relevant speed range,stiffness requirements are specified forthe attachment of the bracing to theengine room structure.

We have experienced some caseswhere a proper detuning effect was notobtained, even though the stiffness re-quirements had been fulfilled: In this con-nection, it is relevant to bear in mindthe development during the past ffieenyears, see Fig. 1. Today an engine witha specified output typically has fewercylinders and is considerably higher thanprevious engine types, i.e. the height/length ratio is different. To cope with thisdevelopment, classification societiesand shipyards should consider revisingtheir requirements to the double bot-tom design.

For two reasons, L-vibration modeshave attracted increasing attention:

l The excitation of the thrust bearinghas increased

l The L-mode has in many casesbecome resonant with the main criti-cal order in the relevant speed range(example: see Fig. 25). This is themost important reason and, again, itis suggested that the requirementsto the double bottom design shouldbe reconsidered

In certain cases, longitudinal top brac-ing has been introduced in order to de-tune critical orders and the natural fre-quency of the L-mode. By means ofthis arrangement, vibrations in the lon-gitudinal direction have been reducedto a satisfactory level.

Where axial vibrations of the crankshaftare the main source of excitation, thelongitudinal vibration levels can also bereduced by means of an axial vibrationdamper.

As mentioned earlier, L-mode excita-tions are of a secondary type. Thismeans that the excitation level is deter-mined by vibration characteristics ofother vibration modes. L-mode excita-tions are determined by means of axialand torsional vibration characteristics,and these are to be calculated and syn-thesized at the design stage of the shipin order that appropriate precautionscan be taken.

As an alternative to the traditional fric-tion type of top bracing, Fig. 26, the hy-draulically adjustable top bracing hasbeen designed for use on vessels hav-ing large deflections due to heavy sea,loading/unloading, etc.

This system, shown in Fig. 27, consistsbasically of a hydraulic cylinder and twospherical bearings. Oil is supplied fromthe camshaft lubricating oil system, anda relief valve prevents the build-up ofexcessive forces.

This hydraulically adjustable top brac-ing is intended for one-side mounting,and will provide a constant force be-tween engine and hull, irrespective ofdeflection and, as such, will still act asa detuner of the double bottom/mainengrne system.

The system has been commercially ap-plied in a number of newbuildings withgood results.

Obviously, this system increases theoverall costs and, therefore, it will re-place the friction type only when neces-sary.

It should be noted that the hydraulicallyadjustable top bracing does not in-crease the building width of an engine,compared to the friction type bracing.

Vibration Levels and TheirAcceptability

There are two basic criteria for deter-mining acceptability level of vibrations:

1) The vibration level must not result instress levels that may cause fatiguedamage to the engine, or theconnected hull structure

2) Vibration must not result inannoyance and/or discomfort forthe operating personnel

21

Rg. 26: Friction type top bracing

With a view to fulfilling these criteria,certain limits to vibration levels can beprescribed, and it is common practiceto specify different limits in different fre-quency ranges:

a) Lower frequency range:displacement limit

b) Intermediate frequency range:velocity limit

c) Upper frequency range:acceleration limit

The displacement limit in the lower fre-quency range is determined by staticstress level considerations, In the inter-mediate range, the velocity limit will keepthe kinetic energy constant throughoutthe range, resulting in decreasing per-missible displacements, The accelera-tion limit in the upper frequency rangedecreases the permissible displace-ments further so as to control noiseradiation.

The limits applying to MAN B&W two-stroke engines are given as single orderpeak amplitudes, X:

S = *xsin(flmt+@tt)

The two-stroke low speed diesel en-gine is designed to cope with ratherhigh internal varying forces and, conse-quently, rather high limits are allowedfor vibration levels in its main structure.Fig. 28 shows the limits which are ac-ceptable for MAN B&W two-stroke en-gines.

If vibration levels in zone II (see Fig. 28)have been measured under a certaincondition of the ship, it should be bornein mind that zone Ill readings, i.e. notacceptable, might occur under otherconditions, such as:

1: different draught of the vessel2: different trim of the vessel3: different distribution of ballast load4: different engine loading5: changing sea condition

i Fg. 27: Hydraulically adjustable top bracing

Zone I: AcceptableZone I(: Vibration will not damage the main engine, however, under adverse

conditions, annoying/harmful vibration responses may appear in theconnected structures

Zone Ill: Not acceptable

Conclusion

Mechanical vibrations of steel structuresare of a complex nature. When the steelstructure comprises a ship and a two-stroke low speed diesel, a coagency ofthe excitation sources and the naturalfrequencies of the structures may leadto situations of annoying vibration un-less due consideration is paid to thispoint.

Based on all the experience gatheredup till now, we are confident that thenecessary means for predicting andcounteracting vibration on board shipswith two-stroke diesel engines areavailable today.

The fact that, even today, ships are,from time to time, delivered with unsat-isfactory vibration conditions reflectsthat the whole procedure from projectto actual ship in service is subject tocompromises which consider other as-pects than the vibrational and that pre-dictions of vibrational behaviour, evenwhen based on advanced computerprograms, are still subject to uncertain-ties.

In order to utilise the available possi-bilities, its is recommended that yards,owners, and engine builders discussthe vibration aspects at an early stage,at least before signing the contract, soas to ensure that the best possible sol-utions are selected and incorporated inthe project right from the start.

Fig. 28: Vibration limits

23

References

1) Prevention and Remedy of ShipVibration (Parts 1 and 2)By Masaki Mano, Yoshio Ochi andKaatsuya Fujii, Ishikawajima-HarfmaHeavy Industries, Co., Ltd. JapanShipbuilding & Marine Engineering,Vol. 12, No. 2, 1978

2) Hydrodynamic Reactions toPropeller VibrationsBy Dr. S. Hylarides andDr. W. van GentTrans I Mar E (C) Vol. 91Conference No. 4. Paper C37, 1979

3)Recommendations Designed toLimit the Effects of Vibrations OnBoard ShipsBureau Veritas, 1979. GuidanceNote NI 138 A RD3, June 1979

4 )Guidelines for Prevention ofExcessive Ship VibrationBv H. Johannessen and K.T. SkaarSiAME Transactions, Vol. 88,1980, pp. 319-356

5)Balancing the First Order ExternalMoments of MAN B&W FourCylinder Low Speed EnginesBy H. LindquistMAN B&W Diesel A/S, CopenhagenThe Motor Ship, March 1983

6)Vibration of Long Stroke TypeMarine Diesel EngineBy Koji Kagawa, Kazunobu Fujitaand Tadahiko HaraMitsubishi Heavy Industries Ltd.International Symposium on ShipVibrations, Geneva 1984

1 7)New Calculation Method onComplicated Vibratory Behaviourof A&Part of ShiosBy Yasuo Yoshida andMakoto MaedaIshikawajima-Harima HeavyIndustries Co., Ltd., Tokyo, Japan.International Symposium on ShipVibrations, Geneva, 1984

8) Fore and Aft Vibration of MainEngine and Ship Vibrations due tothe Torsional Vibration of 5.cylinderMain EngineBy Shinji KumazakiIshikawajima-Harima HeavyIndustries Co., Ltd., JapanICMES Conference, 1984

9) Exciting Forces of Ship VibrationInduced by Torsional andLongitudinal Vibration of theShafting SystemBy K. Fujii and K. Tanida,Ishikawajima-Harima HeavyIndustries Co., Ltd., JapanICMES Conference, 1984

IO) Vibration of Long Stroke DieselEngine with a Small Number ofCylindersBy MitSUN Mizuuchi, KoheiMatsumoto, Toshimasa Saitoh.March, 1985

11) Vibration Control in ShipsBy VERITEC Marine TechnologyConsultants, Veritasveien 1,N-l 322 H&k, Norway, 1985

12) A theoretical and experimentalinvestigation of propeller dampingand transient torsional resonanceresponseBy L. Bryndum and S.B. Jakobsen,MAN B&W Diesel A/SM. Matosevfc, Uljanik EngineeringCompany Ltd.ICMES Conference, 1990, Newcastle

13) Vibration Aspects of Long-StrokeDiesel EnginesBy L. Bryndum, S.B. Jakobsen andM.C. JensenMAN B&W Diesel Xi2nd International MarineEngineeringConference 1991 Shanghai, China

14) Axial Vibrations of Crankshafts ofLong-Stroke Diesel Engines, andthe Control of Their Influence onCrankshaft Strength and HullVibration ConditionsBy S.B. Jakobsen and L. Bryndum,MAN B&W Diesel A/ST. Fukuda and M. OhtsuMitsui Enaineerina & ShiobuildinaCo. Ltd.&pan - -CIMAC 91, Florence Paper 061

15) Coupled Axial and TorsionalVibration Calculations on Long-stroke Diesel EnginesBy S.B. JakobsenMAN B&W Diesel A/SThe Society of Naval Architectsand Marine Engineers1991 Annual Meeting, New York,Paper No. 14

! 24j

Appendix A

Example: ES60MCE. 102 r/min, 12,000 kW

External Forces and Moments (vertical)

Firing order:6 8

Firing order:

7 a5*

3 3 32 4

7 +k5 64

Primaly valuesgiven at Secondary values due to

Primary values

102 rlmin Torsional Vibration Responsesgiven at Secondary values due to

102 r/min Torsional Vibration Responses

I st order moment:b348 kNm

Excitation (torsional amplitudes): 1st order moment:f174 kNm

Excitation (torsional amplitudes):

11 th order (92 r/min)Ith order moment: zk2.5 nmd

t75 kNm

%

11 th order (92 r/rain)4th order moment:

+I .O mrad

*300 kNmX2.5 mrad

~c1w*1 .o mra,

Cyl. No. 1 2 3 4 5 6 7 6 Cyl. No. 1 2 3 4 5 6 7 8Secondary values at 92 r/min: Secondary values at 92 rfmin:Free forces: 12th order: *198 kN Free forces:

13th order: +104 kN12th order: +299 kN

Free moments: 10th order: &986 kNm Free moments: 10th order: * 92 kNm

Excitation (torsional amplitudes):

fo.5 mrad12th order (84 rlmin)

%fo.5 mrad

Cyl. No. 12 3 4 56 78Secondary values at 84 r/min:Free forces: 1 lth order: f101 kN

13th order: +122 kN

Free moments: 14th order: * 38 kNm

1

Excitation (torsional amplitudes):

GO mrad12th order (84 rfmin)

%f2.0 mrar

Cyl. No. 1 2 3 4 5 8 7 6Secondary values at 64 r/min:Free forces: 11 th order: -01 kN

13th order: +245 kN

Free moments: 11 th order: f 61 kNm13th order: + 75 kNm14th order: f 38 kNm

EXCitatiOn (torsional amplitudes):

3il85 m?ad12th order (78 r/min)

%XMS mrad

Cyl. No. 1 2 3 4 5 6 7 8

Secondary values at 78 r/min:Free forces: 12th order: ? 52 kN

Free moments: 14th order: f376 kNm

Excitation (torsional amplitudes):

f0.8 mrad13th order (78

%

rlmin)

f0.8 mm

Cyl. No. 12 3 4 56 78Secondary values at 78 rlmin:Free forces: 12th order: -08 kN

Free moments: 14th order: f 94 kNrr15th order: f 67 kNrr

2 5

!~.:

.~

._

Appendix B

Example: 5L70MC, 95 rlmin. 10,400 kW

Guide Force Moments -H-type

1 2 3 4 5Secondary values of guide force mom& (95 rImin):5th order: 5213 kNm 7th order: *I3 kNm 2nd order: f4 kNm

8th order: f 7 kNm

1 2 3 4 5 Secondary values of guide force moments (96 rimin):7th order: +15 kNm

5th order: f571 kNm 5th order: ti5 kNm1Mh order: -3 kNm

Secondary values of guide force moments (68 rimin):10th order: +I74 kNm

Example: SL70MC. 95 rlmin, 10,400 kW

Guide Force Moments -X-type

Order Moment Excitation (torsional amplitudes): 5th order at 95 dmin1st

Excitation (torsional ampliiudes): 5th order at 95 rimin

2nd3rd4th5th

Fii ~33.0mrad mi

6th k 31 kNm Cyl. No.

cy;OmdflI5mrad

1 2 3 4 57th 522 kNm8th

Secondary values of guide force moments (95 rlmin):Secondaly values of guide force moments (95 r/min):

51h order: f18 kNm 3rd order: f12 kNmf137 kNm 7th order: +75 kNm 3rd order: f3S kNm 71h order: f25 kNm 2nd order: * 9 kNm

9th f 6kNm 8th order: *39 kNm 2nd order: k27kNm 8th order: fl3 kNm10th 011th + 3 k N m12th k 20 kNm Excitation (torsional amplitudes): 7th order at 96 rimin

m0.7 mrad hkO.35 mrad

Cy.No. 1 2 3 4 5Secondary values of guide force moments (96 rlmin):

I 7th order: *35 kNm

26

Appendix C

Example: 6S60MCE. 102 Urnin. 12.000 kW

Guide Force Moments -H-type

13th order: +222 kNm

11 th order (92 rImin)

1 2 3 4 5 6

13lh order: H33 kNm1 Ith order: k 54 kNm161h order: f 63 kNm

1 2 3 4 5678

1 lib order: T? 76 kNm

Example: 8S60MCE, 102 rImin, 12.000 kW

Guide Force Moments -X-type

3rder Moment Excitation (torsional amplitude): Order Moment1st f181 kNrn 1 Itk order (92 rimin)2nd 0

3rd HI 7 kNm

+2.5 mrad

4th +350 kNm5th SO2 kNm6th 0 %

Excitation (torsional amplitude):1st k 9 1 kNm lZh order (64 r/min)2nd 0 32.0 mrad3rd f 209 kNm4th f1401 kNm

ti.5 mrad 5th f 451 kNm 22.0 mrad6th 0 %

7th + 29 kNm C y l . N o . 12 3 4 5 6 7 6 71h f 14kNm CyLNo. 1 2 3 4 5 6 7 66th 0 Secondary values of guide lorce moments (92 rImin): 6th 09th + 11 kNm 6th order: f 63 kNm

Seandaly values of guide force moments (64 r/m9th f 5 kNm 9th order: f 39 kNm

1Mh 0 91h order: f 45 kNm 10th 0 10th order: f 16 kNmllth + 56 kNm lOth order: k 40 kNm llth + 2 8 k N m12th + 11 kNm 12th f 4 3 k N m

Excitation (torsional amplaud@:13th order (76 rfmin)

Excitation (torsional amplitudes):

M.65 mrad

%

1 Ith order (92 rimin)fl .O mrad

ti.65 mrad

C y l . N o . 12 3 4 5 6 7 6Seconday values of guide force moments (76 rImin):16th order: + 35 kNm15th order: + 21 kNm

%fl .O mrad

12 3 4 5 6 7 8Cyl. NO.Seccn* values of guide face moments (92 rImin

9th order: f 34 kNm10th order: + 35 kNm

in):

I:

11:27