07

7 Vibration Aspects

The vibration characteristics of the two-stroke low

speed diesel engines can for practical purposes be,

split up into four categories, and if the adequate

countermeasures are considered from the early

project stage, the influence of the excitation

sources can be minimised or fully compensated.

In general, the marine diesel engine may influence

the hull with the following:

? External unbalanced moments These can be

classified as unbalanced 1st and 2nd order ex-

ternal moments, which need to be considered

only for certain cylinder numbers

Guide force moments

Axial vibrations in the shaft system

Torsional vibrations in the shaft system.

The external unbalanced moments and guide force

moments are illustrated in Fig. 7.01.

In the following, a brief description is given of their

origin and of the proper countermeasures needed to

render them harmless.

External unbalanced moments

The inertia forces originating from the unbalanced

rotating and reciprocating masses of the engine

create unbalanced external moments although the

external forces are zero.

Of these moments, the 1st order (one cycle per revo-

lution) and the 2nd order (two cycles per revolution)

need to be considered for engines with a low number

of cylinders. On 7-cylinder engines, also the 4th order

external moment may have to be examined. The iner-

tia forces on engines with more than 6 cylinders tend,

more or less, to neutralise themselves.

Countermeasures have to be taken if hull resonance

occurs in the operating speed range, and if the vi-

bration level leads to higher accelerations and/or

velocities than the guidance values given by inter-

national standards or recommendations (for in-

stance related to special agreement between ship-

owner and shipyard).

The natural frequency of the hull depends on the

hull’s rigidity and distribution of masses, whereas

the vibration level at resonance depends mainly on

the magnitude of the external moment and the en-

gine’s position in relation to the vibration nodes of

the ship.

MAN B&W Diesel A/S L70MC-C Project Guide

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7.01

D

B

A

C C

Fig. 7.01: External unbalanced moments and guide force

moments

178 06 82-8.0

A–

B–

C–

D–

Combustion pressure

Guide force

Staybolt force

Main bearing force

1st

2nd

1st

order moment

vertical 1 cycle/rev

order moment

Vertical 2 cycle/rev

order moment,

horizontal 1 cycle/rev.

Guide force moment,

H transverse Z cycles/rev.

Z is 1 or 2 times number of

cylinder

Guide force moment,

X transverse Z cycles/rev.

Z = 1,2 ...12

1st order moments on 4-cylinder engines

1st order moments act in both vertical and horizon-

tal direction. For our two-stroke engines with stan-

dard balancing these are of the same magnitudes.

For engines with five cylinders or more, the 1st order

moment is rarely of any significance to the ship. It

can, however, be of a disturbing magnitude in

four-cylinder engines.

Resonance with a 1st order moment may occur for

hull vibrations with 2 and/or 3 nodes, see Fig. 7.02.

This resonance can be calculated with reasonable

accuracy, and the calculation will show whether a

compensator is necessary or not on four-cylinder

engines.

A resonance with the vertical moment for the 2 node

hull vibration can often be critical, whereas the reso-

nance with the horizontal moment occurs at a higher

speed than the nominal because of the higher natu-

ral frequency of horizontal hull vibrations.

As standard, four-cylinder engines are fitted with

adjustable counterweights, as illustrated in Fig.

7.03. These can reduce the vertical moment to an in-

significant value (although, increasing correspond-

ingly the horizontal moment), so this resonance is

easily dealt with. A solution with zero horizontal mo-

ment is also available.

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7.02

Fig. 7.03: Adjustable counterweights: 4 31 151

Adjustable

counterweights

178 16 78-7.0

Fig. 7.02: Statistics of tankers and bulk carriers with 4 cylinder MC engines

178 06 84-1.0

Fixed

counterweights

Fore

Adjustable

counterweights

Fixed

counterweights

Aft

MAN B&W Diesel A/S L70MC-C Project Guide

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Fig. 7.04: 1st order moment compensator Fig. 7.05: Statistics of vertical hull vibrations in tankers

and bulk carriers

7.03

2nd order moments on 4, 5 and 6-cylinder

engines

The 2nd order moment acts only in the vertical di-

rection. Precautions need only to be considered for

four, five and six cylinder engines.

Resonance with the 2nd order moment may occur

at hull vibrations with more than three nodes. Con-

trary to the calculation of natural frequency with 2

and 3 nodes, the calculation of the 4 and 5 node nat-

ural frequencies for the hull is a rather comprehen-

sive procedure and, despite advanced calculation

methods, is often not very accurate. Consequently,

only a rather uncertain basis for decisions is avail-

able relating to the natural frequency as well as the

position of the nodes in relation to the main engine

A 2nd order moment compensator comprises two

counter-rotating masses running at twice the en-

gine speed. 2nd order moment compensators are

not included in the basic extent of delivery.

178 06 76-9.0 178 06 92-4.0

In rare cases, where the 1st order moment will

cause resonance with both the vertical and the hori-

zontal hull vibration mode in the normal speed

range of the engine, a 1st order compensator, as

shown in Fig. 7.04, can be introduced (as an option:

4 31 156), in the chain tightener wheel, reducing the

1st order moment to a harmless value. The compen-

sator comprises two counter-rotating masses run-

ning at the same speed as the crankshaft.

With a 1st order moment compensator fitted aft, the

horizontal moment will decrease to between 0 and

30% of the value stated in the last table of this chap-

ter, depending on the position of the node. The 1st

order vertical moment will decrease to about 30% of

the value stated in the table.

Since resonance with both the vertical and the hori-

zontal hull vibration mode is rare, the standard en-

gine is not prepared for the fitting of such compen-

sators.

Several solutions are shown in Fig. 7.06 for com-

pensation or elimination of the 2nd order moment.

The most cost efficient solution must be found in

each case, e.g.:

1) No compensators, if considered unnecessary

on the basis of natural frequency, nodal point

and size of the 2nd order moment

2) A compensator mounted on the aft end of the

engine driven by the main chain drive, option:

431203

3) A compensator mounted on the front end,

driven from the crankshaft through a separate

chain drive, option: 4 31 213

4) Compensators on both aft and fore end com-

pletely eliminating the external 2nd order mo-

ment, options: 4 31 203 and 4 31 213

Briefly speaking, compensators positioned on a

node or near it are inefficient. If it is necessary, solu-

tion no. 4 should be considered.

A decision regarding the vibration aspects and the

possible use of compensators must be reached at

the contract stage preferably based on data from

sister ships. If no sister ships have been built, we

recommend to make calculations to determine

which of the above solutions should be chosen.

If no compensators are chosen, the engine can be

delivered prepared for retro-fitting of compensators

on the fore end, see option: 4 31 212. The decision

to prepare the engine must also be made at the con-

tract stage. Measurements taken during sea trial or

in service with fully loaded ship can show whether

there is a need for compensators.

If no calculations are available at the contract stage

we advise ordering the engine with a 2nd order mo-

ment compensator on the aft end, option: 4 31 203,

and to make preparations for the fitting of a com-

pensator on the front end, option: 4 31 212.

If it is decided neither to use compensators nor pre-

pare the main engine for retro-fitting,the following

solution can be used:

An electrically driven compensator, option: 4 31

601, synchronised to the correct phase relative to

the external force or moment can neutralise the ex-

citation. This type of compensator needs an extra

seating fitted, preferably in the steering gear room

where deflections are largest, and the compensator

will have the greatest effect.

The electrically driven compensator will not give rise

to distorting stresses in the hull, but it is more ex-

pensive than the engine-mounted compensators as

listed above. More than 70 electrically driven com-

pensators are in service with good results.

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7.04

MAN B&W Diesel A/S L70MC-C Project Guide

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178 06 80-4.0

Moment compensator

Aft end, option: 4 31 203

Compensating moment

F2C x Lnode

outbalances M2V

3node

4node

Node AFT

M2V

F2C

Lnode

M2V

M2V

Centreline

crankshaft

Moment compensator

Fore end, option: 4 31 213

7.05

Moment from compensator

M2C outbalances M2V

Fig. 7.06: Optional 2nd order moment compensator

Power Related Unbalance (PRU)

To evaluate if there is a risk that 1st and 2nd order

external moments will excite disturbing hull vibra-

tions, the concept Power Related Unbalance can be

used as a guidance, see fig. 7.07.

PRU

External moment

Engine power

= Nm/kW

With the PRU-value, stating the external moment

relative to the engine power, it is possible to give an

estimate of the risk of hull vibrations for a specific

engine. Based on service experience from a greater

number of large ships with engines of different types

and cylinder numbers, the PRU-values have been

classified in four groups as follows:

PRU Nm/kW. . . . . . . . . . . . Need for compensator

from 0 to 60 . . . . . . . . . . . . . . . . . . . . not relevant

from 60 to 120 . . . . . . . . . . . . . . . . . . . . . . unlikely

from 120 to 220 . . . . . . . . . . . . . . . . . . . . . . . likely

above 220. . . . . . . . . . . . . . . . . . . . . . . most likely

In the table at the end of this chapter, the external

moments (M1) are stated at the speed (n1) and MCR

rating in point L1 of the layout diagram. For other

speeds (n

A

), the corresponding external moments

(M

A

) are calculated by means of the formula:

MMx kNm

A1

2

=

?

?

?

?

?

?

?

?

?

n

n

A

1

(The tolerance on the calculated values is 2.5%).

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MAN B&W Diesel A/S L70MC-C Project Guide

Fig. 7.07: 1st and 2nd order moment compensator

7.06

178 49 23-6.0

Guide Force Moments

The so-called guide force moments are caused by

the transverse reaction forces acting on the

crossheads due to the connecting rod/crankshaft

mechanism. These moments may excite engine vi-

brations, moving the engine top athwartships and

causing a rocking (excited by H-moment) or twisting

(excited by X-moment) movement of the engine as

illustrated in Figs. 7.08a and 7.08b.

The guide force moments corresponding to the

MCR rating (L

1

) are stated in the last table.

Top bracing

The guide force moments are harmless to the en-

gine but may excite relative large vibrations if a reso-

nance occur in the engine/ship structure system.

As a detailed calculation of the system is normally

not available, MAN B&W Diesel recommend that a

top bracing is installed between the engine''s upper

platform brackets and the casing side for the first

vessel in a series. For further information please see

section 5 ‘Top bracing’.

The mechanical top bracing, option: 4 83 112 com-

prises stiff connections (links) with friction plates

and alternatively a hydraulic top bracing, option: 4

83 122 to allow adjustment to the loading condi-

tions of the ship. With both types of top bracing

the above-mentioned natural frequency will in-

crease to a level where resonance will occur above

the normal engine speed. Details of the top brac-

ings are shown in section 5.

MAN B&W Diesel A/S L70MC-C Project Guide

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Fig. 7.08a: H-type guide force moments Fig. 7.08b: X-type guide for moments

178 06 81-6.2

7.07

Definition of Guide Force Moments

During the years it has been discussed how to define

the guide force moments. Especially now that com-

plete FEM-models are made to predict hull/engine in-

teraction, the proper definition of these moments has

become increasingly important.

H-type Guide Force Moment (M

H

)

Each cylinder unit produces a force couple consist-

ing of:

1: A force at crankshaft level.

2: Another force at crosshead guide level. The po-

sition of the force changes over one revolution,

as the guide shoe reciprocates on the guide.

As the deflection shape for the H-type is equal for

each cylinder the N

th

order H-type guide force mo-

ment for an N-cylinder engine with regular firing or-

der is:

N M

H(one cylinder)

.

For modelling purpose the size of the forces in the

force couple is:

Force = M

H

/L kN

where L is the distance between crankshaft level

and the middle position of the crosshead guide (i.e.

the length of the connecting rod).

As the interaction between engine and hull is at the

engine seating and the top bracing positions, this

force couple may alternatively be applied in those

positions with a vertical distance of (L

Z

). Then the

force can be calculated as:

Force

Z

=M

H

/L

Z

kN

Any other vertical distance may be applied, so as to

accommodate the actual hull (FEM) model.

The force couple may be distributed at any number

of points in the longitudinal direction. A reasonable

way of dividing the couple is by the number of top

bracing and then applying the forces in those

points.

Force

Z,one point

= Force

Z,total

/N

top bracing, total

kN

X-type Guide Force Moment (M

X

)

The X-type guide force moment is calculated based

on the same force couple as described above. How-

ever as the deflection shape is twisting the engine

each cylinder unit does not contribute with an equal

amount. The centre units do not contribute very

much whereas the units at each end contributes

much.

A so-called ‘Bi-moment’ can be calculated (Fig. 7.08):

’Bi-moment’ =c83[force-couple(cyl.X) distX]

in kNm

2

The X-type guide force moment is then defined as:

M

X

= ‘Bi-Moment’/ L kNm

For modelling purpose the size of the four (4) forces

(see Fig. 7.05) can be calculated:

Force = M

X

/L

X

kN

where:

L

X

: is horizontal length between ’force points’ (Fig. 7.05)

Similar to the situation for the H-type guide force

moment, the forces may be applied in positions

suitable for the FEM model of the hull. Thus the

forces may be referred to another vertical level L

Z

above crankshaft centreline.These forces can be

calculated as follows:

Force

Z,one point

=

M L

L L

x

zx

kN

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MAN B&W Diesel A/S L70MC-C Project Guide

For calculating the forces the length of the

connectiing rod is to be used: L= 2660mm

7.08

Torsional Vibrations

The reciprocating and rotating masses of the engine

including the crankshaft, the thrust shaft, the inter-

mediate shaft(s), the propeller shaft and the propel-

ler are for calculation purposes considered as a

system of rotating masses (inertias) interconnected

by torsional springs. The gas pressure of the engine

acts through the connecting rod mechanism with a

varying torque on each crank throw, exciting tor-

sional vibration in the system with different frequen-

cies.

In general, only torsional vibrations with one and

two nodes need to be considered. The main critical

order, causing the largest extra stresses in the shaft

line, is normally the vibration with order equal to the

number of cylinders, i.e., five cycles per revolution

on a five cylinder engine. This resonance is posi-

tioned at the engine speed corresponding to the

natural torsional frequency divided by the number of

cylinders.

The torsional vibration conditions may, for certain

installations require a torsional vibration damper,

option: 4 31 105.

Based on our statistics, this need may arise for the

following types of installation:

Plants with controllable pitch propeller

Plants with unusual shafting layout and for special

owner/yard requirements

Plants with 8-cylinder engines.

The so-called QPT (Quick Passage of a barred

speed range Technique), option: 4 31 108, is an al-

ternative to a torsional vibration damper, on a plant

equipped with a controllable pitch propeller. The

QPT could be implemented in the governor in order

to limit the vibratory stresses during the passage of

the barred speed range.

The application of the QPT has to be decided by the

engine maker and MAN B&W Diesel A/S based on fi-

nal torsional vibration calculations.

Four, five and six-cylinder engines, require special

attention. On account of the heavy excitation, the

natural frequency of the system with one-node vi-

bration should be situated away from the normal op-

erating speed range, to avoid its effect. This can be

achieved by changing the masses and/or the stiff-

ness of the system so as to give a much higher, or

much lower, natural frequency, called undercritical

or overcritical running, respectively.

Owing to the very large variety of possible shafting

arrangements that may be used in combination with

a specific engine, only detailed torsional vibration

calculations of the specific plant can determine

whether or not a torsional vibration damper is

necessary.

MAN B&W Diesel A/S L70MC-C Project Guide

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Axial Vibrations

When the crank throw is loaded by the gas pressure

through the connecting rod mechanism, the arms of

the crank throw deflect in the axial direction of the

crankshaft, exciting axial vibrations. Through the

thrust bearing, the system is connected to the ship`s

hull.

Generally, only zero-node axial vibrations are of in-

terest. Thus the effect of the additional bending

stresses in the crankshaft and possible vibrations of

the ship`s structure due to the reaction force in the

thrust bearing are to be considered.

An axial damper is fitted as standard: 4 31 111 to all

MC engines minimising the effects of the axial vibra-

tions.

The five and six-cylinder engines are equipped with

an axial vibration monitor (4 31 117).

7.09

Undercritical running

The natural frequency of the one-node vibration is

so adjusted that resonance with the main critical or-

der occurs about 35-45% above the engine speed

at specified MCR.

Such undercritical conditions can be realised by

choosing a rigid shaft system, leading to a relatively

high natural frequency.

The characteristics of an undercritical system are

normally:

Relatively short shafting system

Probably no tuning wheel

Turning wheel with relatively low inertia

Large diameters of shafting, enabling the use of

shafting material with a moderate ultimate tensile

strength, but requiring careful shaft alignment,

(due to relatively high bending stiffness)

Without barred speed range, option: 4 07 016.

When running undercritical, significant varying

torque at MCR conditions of about 100-150% of the

mean torque is to be expected.

This torque (propeller torsional amplitude) induces a

significant varying propeller thrust which, under ad-

verse conditions, might excite annoying longitudinal

vibrations on engine/double bottom and/or deck

house.

The yard should be aware of this and ensure that the

complete aft body structure of the ship, including

the double bottom in the engine room, is designed

to be able to cope with the described phenomena.

Overcritical running

The natural frequency of the one-node vibration is

so adjusted that resonance with the main critical or-

der occurs about 30-70% below the engine speed

at specified MCR. Such overcritical conditions can

be realised by choosing an elastic shaft system,

leading to a relatively low natural frequency.

The characteristics of overcritical conditions are:

Tuning wheel may be necessary on crankshaft

fore end

Turning wheel with relatively high inertia

Shafts with relatively small diameters, requiring

shafting material with a relatively high ultimate

tensile strength

With barred speed range (4 07 015) of about

±10% with respect to the critical engine speed.

Torsional vibrations in overcritical conditions may,

in special cases, have to be eliminated by the use of

a torsional vibration damper, option: 4 31 105.

Overcritical layout is normally applied for engines

with more than four cylinders.

Please note:

We do not include any tuning wheel, option: 4 31

101 or torsional vibration damper, option: 4 31 105

in the standard scope of supply, as the proper coun-

termeasure has to be found after torsional vibration

calculations for the specific plant, and after the deci-

sion has been taken if and where a barred speed

range might be acceptable.

For further information about vibration aspects

please refer to our publications:

P.222: ‘An introduction to Vibration Aspects of

Two-stroke Diesel Engines in Ships’

P.268: ‘Vibration Characteristics of Two-stroke

Low Speed Diesel Engines’

These publications, are available at the Internet

address: www.manbw.dk under ‘Libraries’, from

where they can be downloaded.

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MAN B&W Diesel A/S L70MC-C Project Guide

7.10

MAN B&W Diesel A/S L70MC-C Project Guide

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7.11

a 1st order moments are, as standard, balanced so as to obtain equal values for horizontal and vertical moments

for all cylinder numbers.

b By means of the adjustable counterweights on 4-cylinder engines, 70% of the 1st order moment can be moved

from horizontal to vertical direction or vice versa, if required.

No.fcyl.45678

Firing order 1-3-2-4 1-4-3-2-5 1-5-3-4-2-6 1-7-2-5-

4-3-6

1-8-2-6-

4-5-3-7

External forces in kN

00000

External moments in kNm

Order:

1st a 994 b 315 0 188 315

2nd 2629 c 3272 c 2276 c 661 0

4th 0 16 124 353 573

Guide force H-moments in kNm

Order:

1 x No. of cyl. 1506 1524 1133 853 599

2 x No. of cyl. 299 108 84

3 x No. of cyl. 56

Guide force X-moments in kNm

Order:

1st 578 183 0 109 183

2nd 201 250 174 51 0

3rd 112 395 715 782 501

4th 0 76 584 1658 2695

5th 193 0 0 137 860

6th 338 38 0 23 0

7th 77 271 0 0 24

8th 0 167 116 9 0

9th 24 8 154 17 8

10th 39 0 33 95 0

11th 10 3 0 70 45

12th 0 31 0 6 100

178 23 46-2.0

Fig. 7.09: External forces and moments in layout point L

1