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An In t roduc t ion to V ib ra t ion Aspec t s o f Tw o-s t rok e Diese l Engines i ,n Ships

Introduction

The purpose of this paper is to give aprovide a straight-forward descriptionof the vibration characteristics of two-stroke low speed diesel engines, and ofcountermeasures to be taken in con-nection with their use in ships.

For those who want to study the subjectin more detail, we refer to our publica-tion “Vibration Characteristics of Two-

stroke Low Speed Diesel Engines”.Copies of this publication are availableon request.

First, a number of general terms usedin vibration terminology are explained:

Excitation Sources

An excitation source is the disturbing in-fluence which generates and maintainsvibrations. This source may be a freemoment, a guide force moment pro-

duced by the engine, the influence onengine frame and ship‘s structure aris-ing from the axial vibration of the shaftsystem, or the influence on the sameparts from the torsional vibration of theshaft system.

The excitation sources in a diesel en-gine are cyclic by nature, meaning thatthey vary periodically during the work-ing cycle of the engine, see Fig. 1.

In order to evaluate the influence of anexcitation source, a so-called har-

monic analysis is performed, by whichan excitation source is represented by asum of excitations acting with differentfrequencies, which are multiples of theengine’s rotational frequency.

Mathematically, this is expressed as fol-lows:

F = F, x co+ + v,) +F,xcos(Za+~J+....

a = crank angle

qn= phase angles

I I

Fig, 7: internal forces in a crosshead engine

The first contribution Fl cos (a + cp,) iscalled the first order force, because itacts once per revolution.

F2 cos 2 (2~ + cp,) is called the secondorder force, as it acts twice per revolu-tion, and so on.

Natural Frequency andResonance

A natural frequency is a character-istic frequency at which a solid ob-

ject will vibrate freely, if subjected toan impact. Any system of solid ele-ments, a violin string, a beam, a shaftline or a ship, has several natural fre-quencies, each corresponding to acertain vibration mode as outlinedbelow.

Resonance occurs when the frequencyof the excitation coincides with a natu-ral frequency and, when this happens,quite high vibration levels can be theresult.

To take an example:

It is planned to install a 4L60MC enginein a vessel.

Calculations have revealed that avert-cal hull vibration has a natural frequency

of 3.83 Hz. This corresponds to:

3.83 x 60 cycles/min =230 cycles/min

If 4L60MC engine runs 117 r/min atMCR, so obviously there is no risk ofresonance with the first order moment,as its maximum excitation frequency is:

117 x 1 cycle/min =117 cycleslmin

The 2nd order moment has an excita-

tion frequency of up to:

117 x 2 cycleslmin =234 cycles/min

This means that resonance with the2nd order moment may occur at:

?=115r/min

corresponding to$ sx 100i 1

which equals 95% load.

Therefore, it is relevant to consider out-balancing the 2nd order moment in Casea 4L60MC engine is installed.

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Fig. 2 shows the deflection line of thehull for the vibration mode mentioned.

Vibration Modes

Often the phrase “vibratory response”is met with: this means the deflection ofthe system caused by~excitations on thesystem.

A system can have several natural fre- Damping

quencies, each corresponding to a cer-tain characteristic vibration mode. for As there is some kind of energy-absorb- 1

Deflection:

2 nodes

- I

3 nodes

iFig. 3: Vibration modes

As can be seen, the upper deflectionmode has two points that do not move,the lower one has three.

These points are called “nodes”, andthe vibration nodes are called “2.nodevibration”, and “3-node vibration”, re-spectively.

Also other forms exist, e.g. deflectionsin the longitudinal direction, torsionaldeflections and combinations of these,

mplitudeefleclion~

8 Frequency t

5 excitation

.5

r!

ing friction in all systems, the deflectionwill only reach a certain value. This value fig. 4: Deflection curve with and without

will depend on the magnitude of the ex- damping

citation and damping (Friction) as wellas on the excitation frequency in rela-tion to the system’s natural frequency.

The magnitude of the damping, whichmust be known in order to calculate

The four categories of excitation sourcesmentioned are the following, see Fig. 5:

stresses and deflections, can be basedon theoretical studies or on experience.

I External unbalanced moments, clas-sified as 1st order moments (acting

Fig. 4 illustrates the deflection with andin both the horizontal and vertical

without damping.directions) and 2nd order moments(acting in the vertical direction only),see Fig. 5

Description and Examples

The description of excitation sources isdivided into four sections, because thevibration characteristics of two-strokelow speed diesel engines are normallysplit up into four categories,

Each section gives a basic explanationof a so-called excitation source in termsof origin and nature, and describes thecountermeasures to be taken to mini-mise or eliminate the consequences ofthe excitation source.

II Guide force moments (see Fig. 5)

Ill Axial vibrations

IV Torsional vibrations

During the working cycle of an enginethere are inertia forces as well as gasforces acting on the drive train.

The inertia forces are divided into inertiaforces acting on rotating masses andon reciprocating masses.

The inertia forces acting on rotatingmasses are constant in magnitude,when the engine speed is constant, butthe direction changes

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A -Combustion pressureB -Guide forceC - Staybolt forceD -Main bearing force

1st Order moment vertical 1 cyclelrev

2nd Order moment, vertical 2 cycles/rev

1st Order moment,horizontal 1 cycle/rev

Guide force moment, H transverse Z cycles/revZ is 1 or 2 times the number of cylinders

--

.c-Guide force moment, X transverse Z cycles/revz= 1,2 1 2

-s

fig. 5: External force s and m ome nts

The inertia forces acting on reciprocatingmasses, however, depend on the actualposition of the piston, even though theengine speed is constant.

The same applies to the gas forces;they are not constant during the work-ing cycle.

In order to give a mathematical descrip-tion of the behaviour of the forces, a har-monic analysis is normally carried out.

These forces are counteracted by reac-tion forces in the crankshaft, thus mak-ing the resultant force equal to zero, butthe external unbalanced moments willstill exist.

I External unbalanced moments

The external moments are known as the1 st ,order moments (acting in both thevertical and horizontal directions) and2nd order moments (acting in the verti-

cal direction only, because they origin-ate solely in the inertia forces on thereciprocating masses.

Moments of higher orders exist, but arenormally ignored, as they are very small.

1st order momentThe 1 st order moments acts with a fre-quency corresponding to the enginespeed x 1.

Generally speaking, the 1 st order mo-ment causes no vibration problems. For

4-cylinder engines, however, ti is recom-mendable to evaluate the risk becausein rare cases this cylinder configurationmay cause vibration levels of a disturb-ing magnitude.

Resonance with a 1st order momentmay occur for hull vibrations with 2 and/ or 3 nodes. This resonance can be cal-culated with reasonable accuracy, andthe calculation for the specific plant willshow whether or not a compensator isnecessary on a given four-cylinder en-gine.

Resonance with the vertical moment forthe 2 or 3-node hull vibration can be

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Standard balancing A aft

Balancing reducingthe vertical moment

a

‘1 .

MlV

MlH

I~ Fig. 6: AQusfable counteweights for 1st order moment

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i critical, whereas resonance with the ho+zontal moment normally occurs at a~: higher engine speed than the nominal

because of the higher natural frequencyof horizontal hull vibrations,

1 As standard, four-cylinder versions ofthe 50MC and larger engine types are

~ fitted with adjustable counterweights.For S26MC, L35MC and L42MC adju-stable counterweights can be orderedas an option.

~: These counterweights can reduce the

vertical moment to an insignificant value(although they simultaneously increase

(

the horizontal moment), so this reso-nance is easily dealt with. A solution with

zero horizontal moment is also avail-able should this be desirable, see Fig. 6.

An example:

A Panama bulk carrier, previouslydesigned and delivered with a 5-cylinder engine, was ordered with a4L90GBE.

The hull girder vibration characteris-tics had been measured on the “hullwise” identical sistership and were,as such, well-known. The engine was

derated from the nominal 97 r/minto 84 r/min in order to optimise thepropeller. The 1 st order moment atthe derated 64 r/min represents

1,000 kNm vertically as well as hori-zontally in standard balancing.

As the natural frequency for the ver-tical 3-node hull girder vibration modewas approximately 80 cycles/min,resonance would occur with excita-tion from the 1st order vertical exter-nal moment in the normal runningrange.

It was decided to adjust the counter-

weights so as to neutralise the vert-Cal moment, and to accept the in-creased horizontal moment. If vibra-tion excited by the horizontal 1 storder moment would cause harmfulvibration (possible horizontal 2.nodevibration mode), an additional balan-cing of the engine could be carriedout.

It should be mentioned that 2ndorder moment compensators werefitted from the start.

Measurements on the trial trip andwith the ship in loaded conditionconfirmed a satisfactory vibrationlevel.

In rare cases, where the 1 st order mo-ment may cause resonance with boththe vertical and the horizontal hull vibra-tion mode in the normal speed rangeof the engine, the adjustable counter-weights should be positioned so as tomake the vertical moment harmless,and a 1st order compensator fitted in

the chain tightener wheel in order toneutralise the horizontal moment.

The compensator comprises twocounter-rotating masses running at thesame speed as the main engine crank-shaft, see Fig. 7.

Experience from actual vibration mea-surements shows that the aftmost nodein the 2-node horizontal hull vibrationmode is positioned reasonably far fromthe compensator in the chain drive.

Since resonance with both the verticaland the horizontal hull vibration mode israre, the standard MAN B&W two-strokeengine is not prepared for the fitting of

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Balancing reducingthe vertical moment 4k. ..

Balancing reducingthe horizontal moment

Flc resulting horizontalcompensating force

rotating with the crankshaft

fig. 7: Compensation of Ist order horizonfalmoment

such compensators. If there is a risk ofsuch resonance, it should be consideredto prepare the engine for the fitting ofcompensators.

2nd order momentThe 2nd order moment acts with a fre-quency corresponding to twice the en-gine speed. As mentioned earlier, the2nd order moment acts in the verticaldirection only.

Owing to the magnitude of the 2nd ordermoment, it is only relevant to compen-sate this moment on 4, 5 and B-cylinderengines, for which reason it is necas-

sary to analyse the situation only on suchengines. Resonance with 4 and 5.nodevertical hull girder vibration modes canoccur in the normal engine speed range.

In order to control the resulting vibra-tory responses, a 2nd order compen-sator can be installed.

Experience has shown, however, thatvessels of a size propelled by theS26MC, L35MC and L42MC enginesare less sensitive to hull vibrations, forwhich reason engine-mounted 2ndorder moment compensators are notapplied on these smaller types,

However, should the need for compen-sators arise, solution (e) as mentionedbelow, may be applied.

The calculation of the vibration modesmentioned above requires advanced cal-culation systems and is often subject toa high degree of uncertainty. Therefore,it is essential that owner, shipyard andengine builder discuss the question atthe project stage, because later reme-dies can be very costly.

Several solutions, from which the mostcost-efficient one can be chosen, areavailable to cope with the 2nd order vert-cal moment:

a) No compensators, if consideredunnecessary on the basis of thenatural frequency, nodal point andsize of the 2nd order moment

b) A compensator mounted on the aftend of the engine driven by the mainchain drive, see Fig. 8

c) A compensator mounted on the frontend, driven from the crank shaftthrough a separate chain drive

d) Compensators on both the aft andfore ends of the engine, completelyeliminating the external 2nd ordermoments, see Fig. 9

e) An electrically driven compensator,synchronised to the correct phaserelative to the free moment, This typeof compensator needs preparationsin the form of an extra seating, prefer-

able in the steering gear room, wheredeflections are largest and thecompensator, therefore, will havethe greatest effect, see Fig. 10

Compensation of an external momentby means of a compensating force ispossible if there is an adequate dis-tance from the position where the forceis acting to the node of the vibration(i.e. an excitation force is inefficientwhen acting in a node).

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Compensating moment F2C x Lnoderender M2V harmless

Lnode

fig, 8: 2nd order moment compenstor located on aft end

Moment from compensatorM2C outbalances M2V

Centre line crankshaft

Fig. 9: 2nd order moment compensator located on fore end

The counterweights on the chain wheelproduce a centrifugal force which cra-ates a moment, the size of which isfound by multiplying the force by thedistance to the node.

Due to the positioning of these counter-weights, the direction of the compen-sating moment will always be oppositeto the direction of the external moment.Obviously this method of compensa-tion, solutions (b), (c) and (e), requiresknowledge of the distance from the po-sition of the compensating force to thenode in order to choose the correctcompensating force. Such knowledgemay be acquired by calculation, but itis often necessary to take measure-ments during the sea trial.

If the node is placed in the same posi-tion (or close to) the compensatingforce, no compensating moment willbe created. Thus, solution (d) must beapplied, because the fitting of compen-sators on both the fore and aft ends

of the engine form a compensatingmoment which neutralises the free mo-ment. In this case independence of thenode position is achieved, and no know-ledge of the hull vibrations forms isnecessary.

When placed in the steering gear room,the electrically driven compensator (e)has the advantage -compared to theother compensators (b) and (c) -that itis not as sensitive to the position of thenode. Such a device does not take upmuch room, approximately 1 x 2 x 3 m,and is driven by an electric motor ofabout 15 kW.

More than 70 ships are currently in ser-vice with the electrically driven compen-sator and have an excellent low vibrationlevel.

If compensator(s) are omitted, the en-gine can be delivered prepared for thelater fitting of compensators. This prep-aration must be decided at the projectstage or, at the latest, when ordering

the engine.

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!

I

Compensatiirg moment FZE x LnodeoutbalancesM2V

Lnode-I

Fig. 10: 2nd order moment comoensation from electrical driven compensator in steer;ng gearroom

Measurements taken during the seatrial, or later during service, with diffar-

ent loadings of the ship, will showwhether or not compensator(s) needto be fitted.

An example:

A 40,000 dwt general cargo ship wasto be equipped with a 6-cylinder engine of the L67GFCA-type. A roughcalculation showed only a small riskof excitation of vibration from the 2ndorder external moment of 760 kNm,but still there was a certain degreeof uncertainty.

Discussion between the owner, yardand engine builder materialised intoan agreement that the engine shouldbe delivered prepared for later mount-ing of 2nd order compensators.

Only in cases where the vibrationlevel would exceed the value givenin IS0 recommendations, shouldcompensators be fitted.

The measurements showed satis-factory conditions at fully loaded

ship, but at the specified ballastcondition the level was measuredto 11 mm/set. The IS0 recommen-dation stated 9 mm/set as beingacceptable.

However, the measurements alsoshowed that the node or the vibra-tion (4-node hull girder vibration) wassituated very close to the aft end ofthe engine, nearly independent of theship’s load.

As mentioned earlier, a compensatorfitted at the aft end would be ineffi-cient, so only the forward compen-sator was fitted.

II Guide force moments

The so-called guide force moments arecaused by the gas force on the piston,and by inertia forces.

When the piston is not exactly in its topor bottom position, the gas force, trans-ferred through the connecting rod, willhave a component acting on the crank-shaft perpendicular to the axis of the cy-linder. Its resultant is acting on the guideshoe and, together, they form a guideforce moment, see Fig. 1.

In a multi-cylinder engine, gas and iner-tia forces and their resultants form asystem of guide force moments con-taining all orders.

Two kinds of guide force moments exist:

The so-called H and X-moments.

The H-type guide force moment, whichis dominating on engines with less than

seven cylinders, tends to rock the en-gine top in the transverse direction, seeFig. 5. The main order of the H-momentis equal to the cylinder number, i.e. fora 5-cylinder engine the frequency of theexcitation is 5 times the number ofrevolution.

The X-type guide force moment is thedominating for engines with more thansix cylinders, see Fig. 5. The X-momenttends to twist the engine in an X-likeshape, and the main order is equal tohalf the number. For engines with odd

numbers of cylinders, the main ordersare mostly the two orders closest tohalf the number of cylinders, In orderto counteract the possible impact onthe hull from guide force moments, werecommend the installation of a set oftop bracings between the upper galleryof the main engine and the hull struc-ture (casing side). The top bracing caneither be mechanical with frictional con-nection or hydraulically adjustable, seeFig. 11 and Fig. 12.

These bracings act as detuners of thesystem double bottom and main en-gine, which means that the natural fre-quency of the vibration system will be

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I fig. 17: Mechanical top bracing fig. 12: Hydraulic top bracing

increased to such an extent that rason-ance occurs above the running rangeof engine speed and the guide forcemoments will, therefore, be harmless,

Measurements on plants in selviceprove that, with adequately fitted brac-ings, resonance occurs above the nor-mal running range.

III Axia l v ibrat ions

When the crankthrow is loaded by thegas force through the connecting rodmechanism, the arms of the crank throwdeflect in the axial direction of the crank-shaft, exciting axial vibrations which,through the thrust bearing, may be trans-ferred to the ship’s hull.

The dominating order of the axial vibra-tion is equivalent to the number of cy-linders for engines with less than sevencylinders. For engines with more thansix cylinders, the dominating order isequal to half the numbers of cylinders.

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For engines with odd numbers of cylin-ders, the dominating orders are mostlythe two orders closest to half the cylin-der number.

In order to counteract the influence onthe hull from the axial vibration, all en-gines are equipped with an axial vibra-tion damper although, for the crankshaftitself, such a damper is only necessary

on larger cylinder numbers.

The damper is shown in Fig. 13.

An example:

At the introduction of our MC en-gine series, an axial vibration dam-per was only standard on engineswith six or more cylinders, where thedamper was needed because reso-nance with the order correspondingto the cylinder number would other-

wise have caused too high stressesin the crankthrows.

Shortly after we experienced a casein which a 5L50MC engine installedin an LPG tanker recorded excessiveaxial vibration of the crankshaft dur-ing the trial trip.

A closer analysis of this case re-vealed that the crankshaft was notin resonance, and that the situationwas caused by a coupled vibration

phenomenon The crankshaft vibra-tion was coupled to the engine frameand double bottom which, in turn,transferred vibration energy back tothe crankshaft. As a result, both thewhole engine and the superstructuresuffered from heavy longitudinal vi-bration.

We decided to tackle the problemfrom two sides:

An axial vibration damper was retro-

fitted to the crankshaft, and top brac-ing in the longitudinal direction wasfitted on the aft end of the engine.

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fig. 13: Axial vibration damper

Crankshaftfree end ,

Main bearingsupport NO. 1

Abs. max. limit

Barred speedrange required

I - Speed

Resonances !-Normal

If the barred speed range is close to normal speed,

this solution can not be used

Fig. 14: Engine located aft and shaftk diameter according to Class Rules

These two countermeasures both influ-enced the vibration behaviour of thecrankshaft, the engine frame, and thesuperstructure.

The axial vibration damper alone actu-ally eliminated the problems, and thelongitudinal top bracing alone reducedthe vibration level in the deck house tobelow the IS0 recommended values.With both countermeasures in action,the longitudinal top bracing had only in-significant influence.

This incident, together with experiencefrom some other 5-cylinder engines, ledus to install axial vibration dampers asstandard on all our engines.

IV Torsional vibration

The varying gas pressure in the cylin-ders during the working cycle and thecrankshaft/connecting rod mechanismcreate a varying torque in the crank-shaft. It is these variations that causethe excitation of torsional vibration ofthe shaft system.

Like the other excitation sources, thevarying torque is cyclic of nature andcan thus be subject to harmonic ana-lysis.

As explained in the section “ExcitationSource” this analysis makes it possibleto represent the varying torque as a sumof torques acting with different frequen-cies which are multiples of the engine’s

rotational frequency.

Like other kinds of vibration, torsionalvibration causes extra stresses, whichmay be detrimental to the shaft system.The stresses will show peak values atresonances, i.e. where the number ofrevolutions multiplied by the order ofexcitation corresponds to the naturalfrequency.

Therefore, the Classification Societiesrequest that the torsional vibrationcharacteristics of the engine/shafting

system be calculated, and they havelaid down limits for the extra strasses.

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:

Small varying ning wheel

_ -torque improved material

fig. 15: Over-critical condition

Two limits exist: quency. Also the introduction of a tun-ing wheel will lower the natural frequency.

The lower I,:

Determines a stress level which The Classification Societies have alsomay only be exceeded for a short laid down rules determining the shafttime, i.e. not during continuous run- diameter. It is permitted to increase thening, which means that the propul- diameter, whereas a reduction will re-sion plant requires a barred speed quire the use of a material with a higherrange of revolutions. ultimate tensile strength.

The upper limit za :

May not be exceeded at all,For the different numbers of cylindersthe following guidelines can be givenbased on our experience:

Considering a shaftline of a certainlength, it is possible to adjust its natu-ral frequency of torsional vibration byadjusting the diameter. A small diameter

results in a low natural frequency, anda larger diameter in a high natural fre-

4-cylinder engines normally have themain critical resonance (4th order) posi-tioned above but close to normal revo-

lutions and thus, in the worst cases,require an increased diameter of theshaft-line relative to the diameters re-

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quired by the class rules in order to in-crease the natural frequency andthereby bringing it 40.45% above nor-mal running range.

For 5cylinder engines the main critical(5th order) is also positioned close to,but below, normal revolutions.

If the diameter of the shafting is chosenaccording to the class rules, the reso-nance with main critical will be posi-tioned quite close to the normal service

speed, thus introducing a barrad speedrange, see Fig. 14. The usual and cor-rect way to tackle this unacceptable po-sition of a barred speed range is to mounta tuning wheel on the front end of thecrankshaftand design the intermediateshaft with reduced diameter relative tothe class diameter and to use bettermaterial with a higher ultimate tensilestrength. This is called over-critical run-ning, because the normal speed rangeis placed above the resonance, seeFig. 15.

In some cases, the solution chosenhas been to install a large diameter in-termediate shaft in order to increase theresonance to above the MCR. This iscalled under-critical running, because thenormal speed range is placed below theresonance, see Fig. 16.

Besides avoiding a barred speed range,this solution is characterised by arather high varying torque in the shaftwhich will induce a rather high varyingthrust, called Torsional Vibration In-

duced Propeller thrust.

For 6-cyknder engines the normal ex-ecution is a shaftline with a diameteraccording to the class rules and, con-sequently, a barred speed range.

For engines with seven or more cyfin-

der. the excitations are smaller, and abarred speed range is not normallynecessary.

An example:

A series of tankers equipped with5L80MCE engines was fitted with ashaft system of a larger diameter than

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Large vaying torque

and large vajing thrustincreased diameter

when or if resonance is related to class rules

I - Speed

Normal

Approx. 40-45% of rlmin

Recommended distance

“from resonance”

No barred speed range required

fig, 16: Under-cr;tical condition

required by the Classification Societies

and had no tuning wheel in order toavoid a barred speed range. The tor-sional vibration induced propeller thrustwas approximately 30% of the meanthrust and, during the sea trial, heavylongitudinal vibration of the engine frameas well as the superstructure excitedby the varying thrust was experienced.

As replacement of the whole shaft sys-tem was considered virtually impossible(expensive and time consuming), effortsto restrict the heavy longitudinal vibra-tion were concentrated on longitudinal

top bracing. After a few attempts it be-came evident that the steel work of thedeck in way of the fore end of the engine

had to be strengthened in order to pos-

sess sufficient rigidity. After this streng-thening had been carried out, the vibra-tion levels became accedable.

Conclusion

If proper consideration is given to thevibration aspects at an early stage, thecountermeasures available provide agood safety margin against potential vi-bration problems.

It is emphasised that the all-important

issue in these questions is the interac-tion with the ship, and not the meremagnitude of the excitation source.

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