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Section 16

Torsional Vibrations

A. Definition

For the purposes of these requirements, torsional vi-bration loads are additional loads due to torsionalvibrations. They result from the alternating torquewhich is superimposed on the mean torque.

B. Calculation of Torsional Vibrations

1. A torsional vibration analysis covering thetorsional vibration stresses to be expected in the mainshafting system including its branches is to be submit-ted to GL for approval. The following data shall beincluded in the analysis:

Input Data

equivalent torsional vibration system

moments of inertia and inertialess torsional ela-sticities/stiffnesses for the complete system

prime mover

engine type, rated power, rated speed, cycles perrevolution, design (in-line/V-type), number ofcylinders, firing order, cylinder diameter, stroke,stroke to connecting rod ratio, oscillating massof one crank gear, excitation spectrum of enginein the form of tangential coefficients (for new/unconventional types of engines)

vibration damper

type, damping coefficient, moments of inertia,dynamic stiffness

elastic couplings

type, damping coefficient, moments of inertia,dynamic stiffness

reduction / power take off (PTO) gears

type, moment of inertia for wheels and pinions,individual gear's ratios per mesh, effective stiff-ness

shafting

shaftdiameterofcrankshafts, intermediateshafts,gearshafts,thrustshaftsandpropellershafts

propeller

type, diameter, number of blades, pitch andexpanded area ratio, moment of inertia in air,moment of inertia of entrained water (for zeroand full pitch for CP propellers)

Output Data / Results

natural frequencies

with their relevant vibration forms (modes)

forced vibratory loads (torques or stresses)

calculatedtorsionalvibrationtorques/shearstres-ses inall importantelementsof thesystem withparticularreference toclearlydefinedresonancespeedsfor the whole operating speed range.Theresultsshallincludethesynthesisedvalues(vec-torial sum over all harmonics) for the torques/stresses

2. The calculations are to be performed both fornormal operation (uniform pressure distribution overall cylinders or small deviations in the pressure distri-bution e.g. + 5%) and misfiring operation (one cylin-der without ignition, compression of the cylinder stillexisting).

3. Where the installation allows various opera-tion modes, the torsional vibration characteristics areto be investigated for all possible modes, e.g. in instal-lations fitted with controllable pitch propellers for zeroand full pitch, with power take off gear integrated inthe main gear or at the forward crankshaft end forloaded and idling generator, with clutches for engagedand disengaged branches.

4. The calculation of torsional vibrations shallalso include the stresses / torques resulting from thesuperposition of several harmonics (synthesised val-ues) so far relevant for the overall assessment of the

system, see also 1., output data.

5. If modifications are introduced into the sys-tem which have a substantial effect on the torsionalvibration characteristics, the calculation of the tor-sional vibrations is to be adapted and re-submitted forapproval.

6. Where an electrical machine (e.g. static con-verter controlled motors) can generate periodic excita-tion leading to relevant torsional vibration stresses inthe system as a whole, this is to be taken into accountin the calculation of the forced torsional vibration. Themanufacturer of the electrical machine is responsiblefor defining the excitation spectrum in a suitable man-ner for performing forced torsional vibration calcula-tions.

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C. Permissible Torsional Vibration Stresses

1. Shafting

1.1 In no part of the shafting may the alternating

torsional vibration stressesexceed the followingvalues

of 1 for continuous operation or of 2 under transient

conditions. Fig. 16.1 indicates the 1 and 2 limits as a

reference for intermediate and propeller shaftsof com-

mondesignandfor the locationdeemed tobemostse-

verely stressed (cK = 0,55 or cK = 0,45 for propeller

shafts,andcK=1,0andcK=0,8forintermediateshafts).

Thelimitsdependonthedesignandthelocationconsid-

eredandmayinparticularcaseslieoutsidetheindicated

rangesaccordingtoFig.16.1.Theyaretobedetermined

in accordance with equations (1) - (4) and Table 16.1.

Speed ranges in the n/no0,8 area, in which the per-

missible values of 1 for continuous operation areexceeded shall be crossed through quickly (barred

speed ranges for continuous operation), provided thatthe limit for transient operation 2is not exceeded.

1 = cWcKcD(32 2) [N/mm2] (1)

for speed ratio values < 0,9

= cWcKcD1,38 [N/mm2] (2)

for speed ratio values 0,9 1,05

2 = 1,7 6,0 1

K Wc c

[N/mm2] (3)

Alternatively and depending on the material and de-sign the following formula may be used instead (3)

2 = 1,7 1

Kc

[N/mm

2] (3)

d = shaft diameter [mm]

= speed ratio []

= n/no

n = speed [min-1]

no = nominal speed [min-1]

Rm = tensile strength of shaft material [N/mm2]

cw = material factor []

=18

160R m + (4)

For direct coupled plants in general materials with a

tensile strength Rm >500 N/mm2 shall be used, for

geared plants or other plants with low torsional vibra-

tion level shafting materials with Rm >400 N/mm2

may be accepted.For the purpose of the formulas (1), (2), (3), (3) thetensile strength calculation value applied shall notexceed the following limits:

Rm = 600 N/mm2

for propeller shafts in general

for other shafts particularly intermediate

shafts, madeofforged, lowalloycarbonor

carbonmanganesesteel

Rm = 800N/mm2

forallshaftsexceptpropellershaftsmadeof

forgedhighalloysteels.Formula(3)should

be applied in conjunction with such steels

and special design features only.

cD = size factor []

= 0,35 + 0,93 d0,2

cK = formfactorforintermediateandpropellershafts

dependingondetailsofdesignandconstruction

oftheappliedmechanicaljointsintheshaftline

The value for cK

is given in Table 16.1.[]

1.2 In the speed range 0,9 1,05 the alternat-ing torques in the shafting system may not exceed75 % of the mean full-load torque transmitted by theshafting. With the consent of GL, 90 % of the meantorque may be permitted provided that the torque isonly transmitted in the connection by friction only orintegrally forged flanges are applied.

1.3 For controllable pitch propeller systems the

permissible values of 2within a barred speed range

may be exceeded provided that the system is operated

at a low pitch and the additional shear stresses remain

below the 2 value for = 0,6 calculated by for-mula (3). Applying this alternative, which is subject to

special approval, requires an adequate design case by

case. Especially a fast crossing of barred speed range

has to be guaranteed additionally by adequate meas-

ures. In such cases an adequate dimensioning of all

connections in the shaft system for dynamic torque at

resonance speed has to be proven individually.

2. Crankshafts

2.1 Crankshaftsappliedforenginesforshipsclas-

sedbyGLshallbeapprovedonthebasisofVIAddi-

tional Rules and Guidelines, Part 4 Diesel Engines,Chapter 2 Guidelines for the Calculation of Crank-

shafts for Internal Combustion Engines. For applica-

tionof thisguidelineagaspressuredistribution in the

cylinderoverthecrankangleissubmittedbythemaker

oftheengine.Themakeroftheenginealsoappliesfor

approval of a maximal additional (vibratory) shearstress, which is referred to the crank with the highest

loadduetomeantorqueandbendingforces.Normally

thisapprovedadditionalshearstressmaybeappliedfor

first evaluation of the calculated vibratory stresses in

thecrankshaftvia the torsionalvibrationmodel.Com-

monvaluesarebetween30and70N/mm2formedium

andhighspeedenginesandbetween25and40N/mm2for twostrokeengines,butspecialconfirmationofthe

value considered for judgement by GL is necessary.

For further details see also Section 2, C.1.

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1,

2

[N/mm

2]

140

120

100

80

60

40

20

00 0,2 0,4 0,6 0,8 1,0 1,2

Speed ratio [ - ]

2

1

cK= 1,0

d = 100 mm

cK= 0,80

d = 700 mm

cK= 0,80

d = 700 mm

cK= 1,0

d = 100 mm

Intermediate shafts

2

100

80

60

40

20

00 0,2 0,4 0,6 0,8 1,0 1,2

Speed ratio [ - ]

1

,

2

[N/mm

2]

1

cK= 0,55

d = 100 mm

cK= 0,45

d = 700 mm

cK= 0,45

d = 700 mm

cK= 0,55

d = 100 mm

Propeller shafts

Fig. 16.1 Permissible torsional vibration stresses in shafting systems in accordance with

formulas (1) (3) for shaft materials with a tensile strength of 450 N/mm2

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Table 16.1 Form factors for intermediate and propeller shafts

ck [] Shaft type / design

1,0Intermediate shafts

with integral forged flanges and / or hydraulic oil mounted shrink fit couplings

0,6

Intermediate shafts

with keyway / key flange connection (in general not to be used for plants with barred speed

ranges)


with radial holes of standard design 1(for example oil distribution (OD) shaft of CP plants)


with longitudinal slots of standard design 2(for example for OD shaft of CP plants)

0,85Thrust shafts

transmitting thrust, additionally to the torque, by means of a collar (bending)

0,80Propeller shafts

in the fwd. propeller shaft area 3within the stern tube

0,55

Propeller shafts

with forged or hydraulic shrink fit flange and keyless propeller fit within the aft.4propeller shaft

area

0,45

Propeller shafts

with key fitted propellers (in general not to be used for plants with barred speed ranges) and oil

lubrication in the stern tube within the aft4propeller shaft area

0,40Propeller shafts

with grease lubrication in the stern tube and in the aft4propeller shaft area

The part of propeller shafts outside the stem tube (engine room area) is subject to the same c kfactors as the intermediate shaft.

1 The ckfactor as given above covers the stress concentration for bores with good manufacturing quality and adequately smoothened up in

the transitions for hole diameters not exceeding 30% of the shaft's outer diameter. For other special designs individual stressconcentration factors may be applied based on special considerations to be approved by GL.

2 The ckfactor as given above covers the stress concentration for slots with good manufacturing quality and adequately smoothened up in

the transitions for slots with axial extension less than 80% of the shaft's outer diameter, width of the slot less tan 10% of the shaft's outer

diameter and a rounding at the ends not less than the width of the slot (half circle). For other special designs or arrangements with more

than one slot individual stress concentration factors may be applied based on special considerations to be approved by GL.

3 The fwd. propeller shaft area is the area inside the stem tube (up to the fwd. stern tube seal) next to the after bearing position as defined

under 4. For designs with shaft bossings, the fwd. area is that adjoining and lying forward of the position of the aft bossing bearing.

4 The aft propeller shaft area is the area inside the stem tube extending from the aft stem tube bearing to the forward supporting edge of the

propeller hub. For designs with shaft bossings, it is the area between the aft bossing bearing and the fwd. supporting edge of the propeller

hub. The aft propeller shaft area is defined for an axial extent of at least 2,5d.

2.2 When the generally approved limit for thevibratory stresses for the crankshaft of the engine asdefined under 2.1 is exceeded, special considerationsmay be applied to define a higher limit for the specialinvestigated case. For this detailed system calculations(combined axial / torsional model) and application ofthe actual calculated data within the model in accor-dance to VI Additional Rules and Guidelines, Part 4 Diesel Engines, Chapter 2 Guidelines for the Cal-culation of Crankshafts for Internal Combustion En-gines, as quoted under 2.1 are necessary. Such specialconsiderations, especially the application of combinedaxial and torsional vibration calculations, may only beconsidered for direct coupled two stroke engine plants.

For such evaluations in no case the acceptability factorin accordance to the GL Guideline shall be less than1,15 over the whole speed range.

2.3 Torsional vibration dampers which are aim-ing to reduce the stresses in the crankshaft shall besuitable for use for diesel engines. GL reserve theright to call for proof of this, compare also F.

Torsional vibration dampers shall be capable of beingchecked for their performance ability in the assembledcondition or shall be capable of being dismountedwith reasonable ease for checking purposes. This re-quirement does not apply for small medium or high

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speed engines, so far the exchange of the damper is apart of the regular service of the engine and a fixedexchange interval is part of the engine's crankshaftapproval.

3. Gears

3.1 In the service speed range 0,9 1,05, noalternating torque higher than 30 % of the mean nomi-nal torque for this stage shall normally occur in anyloaded gear's mesh. In general the value for the maxi-mum mean torque transmitted by the gear stage has tobe applied for evaluation purposes as the mean nomi-nal torque.

If the gearing is demonstrably designed for a higherpower, then, in agreement with GL, 30 % of the de-sign torque of the concerned gear's mesh may be ap-

plied as the load limit.

3.2 When passing through resonant speeds belowthe operational speed range during starting and stop-ping of the plant, the alternating torque in the gearshall not exceed twice the nominal mean torque forwhich the gear has been designed.

3.3 Load reversal due to alternating torques isnormally permitted only while passing through the

lower speed range up to 0,35.

If, in special cases, gear hammering in the 0,35

speed range is unavoidable, a barred speed range inaccordance with E.1.is to be specified.

This requirement does not apply to gear stages whichrun without load (e.g. the idling stage of a reversinggear or the idling gears of an unloaded shaft-drivengenerator). These are covered by the provisions inaccordance to 3.4.

3.4 In installations where parts of the gear trainrun without load, the torsional vibration torque incontinuous operation shall not exceed 20 % of thenominal torque in order to avoid unacceptable stressesdue to gear hammering. This applies not only to gearstages but also to parts which are particularly subjectto torsional vibrations (e.g. multiple-disc clutchcarriers). For the loaded parts of the gear system theprovisions in accordance to 3.1apply.

Higher alternating torques may be approved by GL ifproof is submitted that design measures have beenintroduced considering these higher loads, see 3.1.

4. Flexible couplings

4.1 Flexible couplings shall be designed to with-stand the torsional vibration loads which occur duringoperation of the ship. In this context, the total loadresulting, in accordance with B.4., from the superim-position of several orders is to be taken into account,see also Section 5.

4.2 Flexible couplings shall be capable of trans-mitting for a reasonable time the increased alternatingtorques which occur under abnormal operating condi-tions in accordance with B.2.A reasonable time is ingeneral the time consumed until the misfiring opera-

tion is detected and the propulsion plant is transferredto a safe operating condition.

Speed ranges within which, under abnormal operatingconditions, continuous operation is not allowed shallbe indicated in accordance with E.2.

5. Shaft-driven generators

5.1 In installations with generators directly andrigidly coupled to the engine (free crankshaft end) it isnecessary to ensure that the accelerations do not ex-ceed the values prescribed by the manufacturer in anypart of the generator.

The applicable criterion in such cases shall be thetangential acceleration, which is the product of theangular acceleration and the effective radius. Theangular acceleration is determined by means of forcedtorsional vibrations calculations and is to be regardedas the synthesised value of all major orders. However,for simplified consideration of excited resonant speedsthe value of the individual harmonics may be usedinstead for assessment.

5.2 The torsional vibration amplitude (angle) ofshaft-driven generators shall normally not exceed an

electrical value of 5. The electrical vibration am-

plitude is obtained by multiplying the mechanical vi-brationamplitudebythenumberofpolepairs.WhetherGLisabletopermithighervaluesdependsonthecon-figuration of the ship's electrical system.

6. Connected units

6.1 If further units, e.g. power turbines or com-pressors, are coupled to the main propulsion systemwith or without the ability to declutch, due attention isto be paid to these units when investigating the tor-sional vibration loadings.

In the assessment of their dynamic loads, the limits asdefined by the respective makers are to be consideredin addition to the criteria as stated in 1.If these limitsare exceeded, the units concerned are to be disengagedor prohibited ranges of operation in accordance withE.1. are to be declared. Dismounting of such unitsshall generally not lead to substantial overloading of

the main system in terms of exceeding the 2limit for

shafting systems, the maximum torque for flexiblecouplings or the like.

6.2 In special critical cases, the calculations offorced torsional vibrations, including those for dis-turbed operation (dismounted unit), as stated in B.1.will be required to be submitted to GL. In such casesGL reserve the right to stipulate the performance ofconfirmatory measurements (compare D.), includingsuch as related to disturbed operation.

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D. Torsional Vibration Measurements

1. During the ship's sea trials, the torsional vi-brations of the propulsion plant are to be measuredover the whole operating range. Measuring investiga-

tions shall cover the normal as well as the misfiringcondition. Speed ranges, which have been declared asbarred speed ranges in accordance with E.1. for mis-firing operation shall not be investigated by measure-ments, as far as these ranges are finally declared as"barred" on the base of reliable and approved calcula-tions and adequately documented.

Measurements are required by GL for all plants with anominal torque exceeding 40 kNm. For other plantsnot meeting this condition, GL reserve the right to askfor measurements depending on the calculation re-sults. The requirement for measurements will be com-municated to the yard/engine supplier with the ap-

proval letter for the torsional vibration calculation.

Where measurements of identical propulsion plants(specifically sister vessels) are available, further tor-sional vibration measurements for repeat ships may,with the consent of GL, be dispensed with.

In case that the measuring results are not conclusiveenough in respect to the calculations, GL reserve theright to ask for further investigations or new approvalof a revised and adapted calculation model.

2. Where existing propulsion plants are modi-fied, GL reserve the right to require a renewed inves-tigation of the torsional vibration characteristics.

E. Prohibited Ranges of Operation

1. Operating ranges, which due to the magni-tude of the torsional vibration stresses and / or torquesmay only be passed through quickly (transient opera-tion), are to be indicated as prohibited ranges of opera-tion by red marks on the tachometer or in some othersuitable manner at the operating station.

In normal operation the speed range

0,8 is to bekept free of prohibited ranges of operation.

In specifying prohibited ranges of operation it has tobe observed that the navigating and manoeuvringfunctions are not severely restricted. The width of thebarred speed range(s) is (are) to be selected in a waythat the stresses in the shafting do not exceed the per-missible 1 limit for continuous operation with anadequate allowance considering the inaccuracies ofthe tachometers and the speed setting devices. Forgeared plants the barred speed ranges, if any, refer tothe gear meshes and elastic couplings and are to bedetermined in the same way with reference to thepermissible vibratory torques or permissible powerloss for these components (see also C.4.and C.5.).

2. Measures necessary to avoid overloading ofthe propulsion plant under abnormal operating condi-tions are to be displayed on instruction plates to beaffixed to all engine control stations.

F. Auxiliary Machinery

1. Essential auxiliary machinery such as dieselgenerators and bow thrusters shall be designed in away that the operating speed range is free of unaccept-able stresses due to torsional vibrations in accordancewith C.

2. Generators

2.1 For diesel generator sets with a mechanical

output of more than 150 kW torsional vibration calcu-lations shall be submitted to GL for approval. Theinvestigations shall include natural frequencies as wellas forced vibration calculations. The speed range 90 %to 105 % of the nominal speed shall be investigatedunder full load conditions.

2.2 For rigidly coupled generators (without elas-tic coupling) the vibratory torque in the input part ofthe generator's shaft shall not exceed 250 % of thenominal torque. For the purposes of these Rule nomi-nal torque is the torque which can be calculated byapplying the actual data of the diesel engine (nominaloutput / nominal speed).

The compliance of the limit of 250 % within the speedrange 90 % to 105 % of the nominal speed shall beproven. The calculation for this speed range shall becarried out by using the excitation corresponding tothe nominal torque of the engine.

Exceeding the limit of 250 % may be considered inexceptional cases, provided that the generator's manu-facturer has designed the generator for a higher dy-namical torque. But also in such cases a highest valueof 300 % of the actual nominal torque of the set asdefined above shall not be exceeded.

3. Bow thruster

3.1 Forbowthrustersaswellasforfurtheressentialauxiliary machinery driven by a diesel engine with amechanicaloutput higher than150kW,naturalas wellas forced torsional vibration calculations shall be sub-mittedtoGLforapproval.Thetorsionalvibrationcalcu-lationshallfocusontotheactualloadprofileoftheset.

3.2 For bow thrusters as well as for further essen-tial auxiliary machinery driven by electrical motor thesupplier shall take care that relevant excitation forces(e.g. propeller blade frequency or similar) may notlead to unacceptable torsional vibration loadings. Inspecial cases GL may require the submission of corre-sponding calculations.

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