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Rules for Classification and Construction

VI Additional Rules and Guidelines

4 Diesel Engines

2 Calculation of Crankshafts for Internal Combustion Engines

Edition 2012

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The following Rules come into force on 1 May 2012.

Alterations to the preceding Edition are marked by beams at the text margin.

Germanischer Lloyd SE

Head OfficeBrooktorkai 18, 20457 Hamburg, Germany

Phone: +49 40 36149-0Fax: +49 40 36149-200

[email protected]

www.gl-group.com

"General Terms and Conditions" of the respective latest edition will be applicable(see Rules for Classification and Construction, I - Ship Technology, Part 0 - Classification and Surveys).

Reproduction by printing or photostatic means is only permissible with the consent ofGermanischer Lloyd SE.

Published by: Germanischer Lloyd SE, Hamburg

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Table of Contents

Section 1 Calculation of Crankshafts for Internal Combustion EnginesA. General ............................................................ .............................................................. ............. 1- 1B. Calculation of Stresses .................................................................. ............................................. 1- 3C. Calculation of Stress Concentration Factors ................................................................... ........... 1- 7D. Additional Bending Stresses ................................................................................... ................... 1- 10E. Calculation of Equivalent Alternating Stress .............................................................................. 1- 10F. Calculation of Fatigue Strength .............................................................................. .................... 1- 10G. Acceptability Criteria ................................................................... .............................................. 1- 11H. Calculation of Shrink-fits of Semi-built Crankshafts ....................................................... ........... 1- 11

Annex A Definition of Stress Concentration Factors in Crankshaft Fillets

Annex B Stress Concentration Factors and Stress Distribution at the Edge of Oil Drillings

Annex C Alternative Method for Calculation of Stress Concentration Factors in theWeb Fillet Radii of Crankshafts by utilizing Finite Element Method

A. General ............................................................ ............................................................... ............ C- 1B. Model Requirements ................................................................... ............................................... C- 1C. Load Cases ........................................................ ............................................................. ............ C- 2

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Section 1

Calculation of Crankshafts for Internal Combustion Engines

A. General

1. Scope

These Rules for the scantlings of crankshafts are to beapplied to diesel engines for main propulsion andauxiliary purposes, where the engines are so designedas to be capable of continuous operation at their rated

power when running at rated speed.

Crankshafts which cannot satisfy these Rules will besubject to special consideration as far as detailed cal-culations or measurements can be submitted.

In case of:

surface treated fillets

tested parameters influencing the fatigue behav-iour

measured working stresses

these data can be considered on special request.

2. Field of application

These Rules apply only to solid-forged and semi-builtcrankshafts of forged or cast steel, with one crankthrow between main bearings.

3. Principles of calculation

The design of crankshafts are based on an evaluationof safety against fatigue in the highly stressed areas.

The calculation is also based on the assumption thatthe areas exposed to highest stresses are:

fillet transitions between the crankpin and webas well as between the journal and web,

outlets of crankpin oil bores.

When journal diameter is equal or larger than thecrankpin one, the outlets of main journal oil bores areto be formed in a similar way to the crankpin oil

bores. Otherwise, the engine manufacturer if requested by GL shall submit separate documentation of fatiguesafety.

Calculation of crankshaft strength consists initially indetermining the nominal alternating bending andnominal alternating torsional stresses which, multi-

plied by the appropriate stress concentration factorsusing the theory of constant energy of distortion(v. Mises' Criterion), result in an equivalent alternatingstress (uni-axial stress). This equivalent alternating

stress is then compared with the fatigue strength of theselected crankshaft material. This comparison willthen show whether or not the crankshaft concerned isdimensioned adequately.

4. Drawings and particulars to be submitted

For the calculation of crankshafts, the documents and particulars listed in the following are to be submitted:

crankshaft drawing which must contain all datain respect of the geometrical configuration ofthe crankshaft

type designation and kind of engine (in-lineengine or V-type engine with adjacent connect-ing rods, forked connecting rod or articulated-type connecting rod)

operating and combustion method (2-stroke or4-stroke cycle, direct injection, precombustionchamber, etc.)

number of cylinders rated power [kW]

rated engine speed [min -1]

sense of rotation (see Fig. 1.1 )

ignition sequence with the respective ignitionintervals and, where necessary, V-angle v (seeFig. 1.1 )

cylinder diameter [mm]

stroke [mm]

maximum cylinder pressure p max [bar]

charge air pressure [bar] (before inlet valves orscavenge ports, whichever applies)

nominal compression ratio []

connecting rod length L H [mm]

oscillating weight of one crank gear [kg] (incase of V-type engines, where necessary, alsofor the cylinder unit with master and articulated-type connecting rod or forked and inner con-

necting rod) digitalized gas pressure curve presented at equi-

distant intervals (bar versus crank angle, but notmore than 5 CA)

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Fig. 1.1 Designation of the cylinders

for engines with articulated-type connecting rod(see Fig. 1.2 )

- distance to link point L A [mm]

- link angle N []

- connecting rod length L N [mm]

Fig. 1.2 Articulated-type connecting rod

for the cylinder with articulated-type connectingrod

- maximum cylinder pressure p max [bar]

- charge air pressure [bar] (before inlet valvesor scavenge ports, whichever applies)

- nominal compression ratio []

- digitalized gas pressure curve presented atequidistant intervals [bar/CA]

details of crankshaft material

- material designation (according to ISO, DIN,AISI, etc.)

- mechanical properties of material (minimumvalues obtained from longitudinal test speci-mens)

The minimum requirements of the GL RulesII Materials and Welding must complywith:

- tensile strength [N/mm 2]

- yield strength [N/mm 2]

- reduction in area at fracture [%]

- elongation A 5 [%]

- impact energy KV [J]

- method of material melting process (open-hearth furnace, electric furnace, etc.)

- type of forging (free form forged, continuousgrain flow forged, drop-forged, etc., with de-scription of the forging process)

heat treatment

surface treatment of fillets, journals and pins(induction hardened, flame hardened, nitrided,rolled, shot peened, etc. with full details con-cerning hardening)

- hardness at surface [HV]

- hardness as a function of depth of hardening

- extension of surface hardening

particulars for alternating torsional stresses, seeB.2.

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Section 1 Calculation of Crankshafts for Internal Combustion Engines VI - Part 4GL 2012

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B. Calculation of Stresses

1. Calculation of alternating stresses due tobending moments and radial forces

1.1 Assumptions

The calculation is based on a statically determinatesystem, so that only one single crank throw is consid-ered of which the journals are supported in the centreof adjacent bearings and which is subject to gas andinertia forces. The bending length is taken as the

length between the two main bearings (distance L 3)see Figs. 1.3 and 1.4 .

The bending moments M BR , M BT are calculated in therelevant section based on triangular bending momentdiagrams due to the radial component F R and tangen-tial component F T of the connecting-rod force, respec-tively (see Fig.1.3).

For crank throws with two connecting-rods acting upon one crankpin the relevant bending moments are ob-tained by superposition of the two triangular bending moment diagrams according to phase (see Fig.1.4).

Fig. 1.3 Crankthrow for in-line engine Fig. 1.4 Crank throw for Vee enginewith 2 adjacent connecting rods

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1.1.1 Bending moments and radial forces actingin web

The bending moment M BRF and the radial force Q RF are taken as acting in the centre of the solid web (dis-tance L 1) and are derived from the radial componentof the connecting-rod force.

The alternating bending and compressive stresses dueto bending moments and radial forces are to be relatedto the cross-section of the crank web. This referencesection results from the web thickness W and the webwidth B (see fig. 1.5).

Mean stresses are neglected.

Fig. 1.5 Reference area of crankweb cross section

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1.1.2 Bending acting in outlet of crankpin oilbore

The two relevant bending moments are taken in thecrankpin cross-section through the oil bore.

MBRO = bending moment of the radial componentof the connecting-rod force

MBTO = bending moment of the tangential compo-nent of the connecting-rod force

Fig. 1.6 Crankpin section through the oil boreThe alternating stresses due to these bending mo-ments are to be related to the cross-sectional area ofthe axially bored crankpin.

Mean bending stresses are neglected.

1.2 Calculation of nominal alternating bend-ing and compressive stresses in web

The radial and tangential forces due to gas and inertialoads acting upon the crankpin at each connecting-rod position will be calculated over one workingcycle. A simplified calculation of the radial and tan-gential forces may be used at the discretion of GL.Using the forces calculated over one working cycleand taking into account of the distance from the main

bearing midpoint, the time curve of the bending mo-ments M BRF , M BRO , M BTO and radial forces Q RF (defined in 1.1) will then be calculated.

In case of V-type engines, the bending moments progressively calculated from the gas and inertiaforces of the two cylinders acting on one crankthrow are superposed according to phase, the differ-ent designs (forked connecting rod, articulated-typeconnecting rod or adjacent connecting rods) shall be

taken into account.Where there are cranks of different geometrical con-figuration (e.g. asymmetric cranks) in one crankshaft,the calculation is to cover all crank variants.

The decisive alternating values will then be calcu-lated according to:

N max min1

X X X2

=

X N = considered as alternating force, moment orstress

Xmax = maximum value within one working cycle

Xmin = minimum value within one working cycle

1.2.1 Nominal alternating bending and com-pressive stresses in web cross section

The calculation of the nominal alternating bendingand compressive stresses is as follows:

3BRFNBFN

eqw

M10 Ke

W =

RFNQFN

QKe

F =

BFN = nominal alternating bending stress related tothe web [N/mm 2]

MBRFN = alternating bending moment related to thecentre of the web [Nm] (see Fig. 1.3 and 1.4)

BRFN BRFmax BRFmin1

M M M2

=

W eqw = section modulus related to cross-section ofweb [mm 3]

2

eqwB W

W6=

Ke = empirical factor considering to some extentthe influence of adjacent crank and bearingrestraint with:

Ke = 0.8 for 2-stroke enginesKe = 1.0 for 4-stroke engines

QFN = nominal alternating compressive stress dueto radial force related to the web [N/mm 2]

QRFN = alternating radial force related to the web[N] (see Fig. 1.3 and 1.4)

RFN RFmax RFmin1

Q Q Q2

=

F = area related to cross-section of web [mm 2]

F = B W

1.2.2 Nominal alternating bending stress inoutlet of crankpin oil bore

The calculation of the nominal alternating bendingstress is as follows:

3BONBON

e

M10

W =

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BON = nominal alternating bending stress related tocrank pin diameter [N/mm 2]

MBON = alternating bending moment calculated at theoutlet of crankpin oil bore [N/mm 2]

BON BOmax BOmin1

M M M2

=

MBO = M BTO cos + M BRO sin

= angular position [] (see Fig. 1.6)

We = section modulus related to cross-section ofaxially bored crankpin [mm 3]

4 4BH

eD D

W32 D

=

1.3 Calculation of alternating bendingstresses in fillets

The calculation of stresses is to be carried out for thecrankpin fillet as well as for the journal fillet.

For the crankpin fillet:

BH B BFN( ) =

BH

= alternating bending stress in crankpin fillet[N/mm 2]

B = stress concentration factor for bending incrankpin fillet [] (determination, see C.)

For the journal fillet:

( )BG B BFN Q QFN = +

BG = alternating stresses in journal fillet [N/mm 2]

B = stress concentration factor for bending in journal fillet [] (determination, see C.)

Q = stress concentration factor for shearing [](determination, see C.)

1.4 Calculation of alternating bendingstresses in outlet of crankpin oil bore

( )BO B BON =

BO = alternating bending stress in outlet of crankpin oil bore [N/mm 2]

B = stress concentration factor for bending incrankpin oil bore (determination, see C.)

2. Calculation of alternating torsional stresses

2.1 General

The calculation for nominal alternating torsionalstresses is to be undertaken by the engine manufac-turer according to the information contained in 2.2.

The maximum value obtained from such calculationswill be used by GL when determining the equivalentalternating stress, according to E. In the absence ofsuch a maximum value it will be necessary for GL toincorporate a fixed value in the calculation for thecrankshaft dimensions on the basis of an estimation.

In case GL is entrusted with carrying out a forced vibra-tion calculation on behalf of the engine manufacturer to determine the torsional vibration stresses to be expected in the engine and possibly in its shafting, the following data are to be submitted to GL additionally to A.4. :

Equivalent dynamic system of the engine com- prising

- mass moment of inertia of every mass point[kgm 2]

- inertialess torsional stiffnesses [Nm/rad]

Vibration dampers

- type designation

- mass moments of inertia [kgm 2]

- inertialess torsional stiffnesses [Nm/rad]

- damping coefficients [Nms] Flywheels

- mass moment of inertia [kgm 2]

If the whole installation is to be considered, the aboveinformation is to be extended by the following:

Coupling

- dynamic characteristics and damping data

Gearing data

- shaft diameter of gear shafts, thrust shafts,intermediate shafts and propeller shafts

Shafting- diameter of thrust shafts, intermediate shafts

and propeller shafts

Propellers

- propeller diameter

- number of blades

- pitch and area ratio

Natural frequencies with their relevant modesof vibration and the vector sums for the har-monics of the engine excitation.

Estimated torsional vibration stresses in allimportant elements of the system with particu-lar reference to clearly defined resonancespeeds of rotation and continuous operatingranges.

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2.2 Calculation of nominal alternating tor-sional stresses

The maximum and minimum alternating torques areto be ascertained for every mass point of the systemand for the entire speed range by means of a har-monic synthesis of the forced vibrations from the 1storder up to and including the 15th order for 2-strokecycle engines and from the 0,5th order up to andincluding the 12th order for 4-stroke cycle engines.Whilst doing so, allowance must be made for thedampings that exist in the system and for unfavour-able conditions (misfiring in one of the cylinders).The speed ranges shall be selected in such a way thatthe transient response can be recorded with sufficientaccuracy.

The values received from such calculation are to besubmitted.

The nominal alternating torsional stress in every mass point, which is essential to the assessment, resultsfrom the following equation:

3T N

p

M10

W =

TN Tmax Tmin1

M (M M )2

=

4 44 4G BGBH

p pG

D DD DW or W

16 D 16 D

= =

N = nominal alternating torsional stress referredto crankpin or journal [N/mm 2]

MTN = nominal alternating torque [Nm]

W p = polar section modulus related to cross-sectional area of bored crankpin or bored

journal [mm 3]MTmax , MTmin = extreme values of the torque with

consideration of the mean torque[Nm]

For the purpose of the crankshaft assessment, thenominal alternating torsional stress considered infurther calculations is the highest calculated value,

according to above method, occurring at the mosttorsionally loaded mass point of the crankshaft.Where barred speed ranges are necessary, the tor-sional stresses within these ranges are to be neglectedin the calculation of the acceptability factor.

Barred speed ranges are to be so arranged that satis-factory operation is possible despite of their exis-tence. There are to be no barred speed ranges above aspeed ratio of 0,8 of the rated speed.The approval of crankshafts is to be based on theinstallation having the largest nominal alternatingtorsional stress (but not exceeding the maximumfigure specified by engine manufacturer).

Thus, for each installation, it is to be ensured bysuitable calculation that the approved nominal alter-nating torsional stress is not exceeded. This calcula-tion is to be submitted for assessment.

2.3 Calculation of alternating torsional stresses in fillets and outlet of crankpin oilbore

The calculation of stresses is to be carried out for thecrankpin fillet, the journal fillet and the outlet of thecrankpin oil bore.


H = (T N)H = alternating torsional stress in crankpin fillet

[N/mm 2]

T = stress concentration factor for torsion incrankpin fillet [] (determination, see C.)

N = nominal alternating torsional stress related tocrankpin diameter [N/mm 2]

For the journal fillet (not applicable to semi-built crank-shafts):

G = (T N)G = alternating torsional stress in journal fillet

[N/mm 2]

T = stress concentration factor for torsion in journal fillet [] (determination, see C.)


For the outlet of crankpin oil bore:

( )TO T N = TO = alternating stress in outlet of crankpin oil

bore due to torsion [N/mm 2]

= stress concentration factor for torsion inoutlet of crankpin oil bore [] (determina-tion, see C.)


C. Calculation of Stress Concentration Fac-tors

1. GeneralThe stress concentration factors are evaluated bymeans of the formulae according to 2., 3. and 4. ap-

plicable to the fillets and crankpin oil bore of solidforged web-type crankshafts and to the crankpinfillets of semi-built crankshafts only. It must be no-ticed that stress concentration factor formulae con-cerning the oil bore are only applicable to a radiallydrilled oil hole. All formulae are based on investiga-tions of FVV (Forschungsvereinigung Verbren-nungskraftmaschinen) for fillets and on investigations

of ESDU (Engineering Science Data Unit) for oilholes.

Where the geometry of the crankshaft is outside the boundaries of the analytical stress concentration fac-

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tors (SCF) the calculation method detailed in AnnexC may be undertaken.

All crank dimensions necessary for the calculation ofstress concentration factors are shown in Fig. 1.7.

The stress concentration factors for bending ( B, B)are defined as the ratio of the maximum equivalentstress (von Mises) - occurring in the fillets under

bending load - to the nominal stress related to theweb cross-section, see Annex A .

The stress concentration factor for compression ( Q)in the journal fillet is defined as the ratio of the maxi-mum equivalent stress (von Mises) - occurring in thefillet due to the radial force - to the nominal compres-sive stress related to the web cross-section.

The stress concentration factor for torsion ( T, T) isdefined as the ratio of the maximum equivalent shearstress - occurring in the fillets under torsional load -to the nominal torsional stress related to the axially

bored crankpin or journal cross-section (see AnnexA).

The stress concentration factors for bending ( B) andtorsion ( T) are defined as the ratio of the maximum

principal stress - occurring at the outlet of the crankpin oil-hole under bending and torsional loads - to thecorresponding nominal stress related to the axially

bored crankpin cross section (see Annex B ).

When reliable measurements and/or calculations areavailable, which can allow direct assessment of stressconcentration factors, the relevant documents andtheir analysis method have to be submitted to Classi-fication Societies in order to demonstrate theirequivalence to present rules evaluation.

Actual dimensions:

D = crankpin diameter [mm]

DBH = diameter of axial bore in crankpin [mm]

DO = diameter of oil bore in crankpin [mm]

R H = fillet radius of crankpin [mm]

TH = recess of crankpin [mm]

DG = journal diameter [mm]

DBG = diameter of axial bore in journal [mm]

R G = fillet radius of journal [mm]

TG = recess of journal [mm]E = pin eccentricity [mm]

S = pin overlap [mm]

= GD D

E2

+

W*) = web thickness [mm]

B*) = web width [mm]

*) in case of semi-built crankshafts:

when TH

> R H

the web thickness must be considered as equal toWred = W (T H R H)see Fig. 1.7

web width B must be taken in way of crankpinfillet radius centre acc. to Fig. 1.7

The following related dimensions will be applied forthe calculation of stress concentration factors in:

Crankpin fillets Journal fillets

r = R H /D r = R G /D

s = S/Dw = W/D crankshafts with overlap

W red/D crankshafts without overlap

b = B/DdO = D O/D

dG = D EG/D

dH = D BH /D

tH = T H/D

tG = T G/D

Fig. 1.7 Crank dimensions necessary for the calculation of stress concentration factors

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Stress concentration factors are valid for the ranges ofrelated dimensions for which the investigations have

been carried out. Ranges are as follows:

s 0,5

0,2 w 0,81,1 b 2,20,03 r 0,130 dG 0,80 dH 0,80 dO 0,2

Low range of s can be extended down to large nega-tive values provided that:

if calculated f (recess) < 1 then the factor f (re-cess) is not to be considered (f (recess) = 1)

if s < 0,5 then f (s, w) and f (r, s) are to beevaluated replacing actual value of s by 0,5

2. Crankpin fillet

The stress concentration factor for bending B is:

B = 2,6914 f (s, w) f(w) f(b) f(r) f(d G) f(dH) f (recess)

f (s, w) = 4,1883 + 29,2004 w 77,5925 w2 + 91,9454 w3 40,0416 w4 + (1 s)

(9,5440 58,3480 w + 159,3415 w2 192,5846 w3 + 85,2916 w4 ) + (1 s) 2 ( 3,8399 + 25,0444 w 70,5571 w2 + 87,0328 w3 39,1832 w4)

f (w) = 2,1790 w 0,7171

f (b) = 0,6840 0,0077 b + 0,1473 b2

f (r) = 0,2081 r 0,5231

f (d G) = 0,9993 + 0,27 dG 1,0211 2Gd

+ 0,5306 3

Gdf (d H) = 0,9978 + 0,3145 dH 1,5241

2Hd

+ 2,4147 3Hd

f (recess) = 1 + (t H + t G) (1,8 + 3,2 s)

The stress concentration factor for torsion ( T) is:

T = 0,8 f (r, s) f (b) f (w)

f (r, s) = r ( 0,322 + 0,1015 (1 s))

f (b) = 7,8955 10,654 b + 5,3482 b2 0,857 b3

f (w) = w 0,145

3. Journal fillet(not applicable to semi-built crankshaft)


B = 2,7146 f B (s, w) f B (w) f B (b) f B (r) f B (dG) f B (dH) f (recess)

f B (s,w) = 1,7625 + 2,9821 w 1,5276 w2 + (1 s) (5,1169 5,8089 w + 3,1391 w2 ) + (1 s) 2 ( 2,1567 + 2,3297 w

1,2952 w2)

f B (w) = 2,2422 w 0,7548

f B (b) = 0,5616 + 0,1197 b + 0,1176 b2

f B (r) = 0,1908 r 0,5568

f B (dG) = 1,0012 0,6441 dG + 1,2265 2Gd

f B (dH) = 1,0022 0,1903 dH + 0,0073 2Hd

f (recess) = 1 + (t H + tG) (1,8 + 3,2 s)

The stress concentration factor for compression Q due to the radial force is:

Q = 3,0128 f Q (s) f Q (w) f Q (b) f Q (r) f Q (dH) f (recess)

f Q (s) = 0,4368 + 2,1630 (1 s) 1,5212 (1 s)2

f Q (w) =w

0, 0637 0, 9369 w+

f Q (b) = 0,5 + b

f Q (r) = 0,5331 r 0,2038

f Q (dH) = 0,9937 1,1949 dH + 1,7373 2Hd

f (recess) = 1 + (t H + tG) (1,8 + 3,2 s)

The stress concentration factor for torsion T is:

T = T

if the diameters and fillet radii of crankpin and journalare the same, and if crankpin and journal diametersand/or radii are of different sizes:

T = 0,8 f (r,s) f (b) f (w)

f (r,s), f (b) and f (w) are to be determined in accor-dance with 2. (see calculation of T), however, theradius of the journal fillet is to be related to the journaldiameter:

G

G

R r

D=

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4. Outlet of crankpin oil bore


B = 3 5,88 dO + 34,6 dO2

The stress concentration factor for torsion T is

T = 4 6 dO + 30 dO2

D. Additional Bending Stresses

In addition to the alternating bending stresses in fillets(see B.1.3 ) further bending stresses due to mis-alignment and bedplate deformation as well as due toaxial and bending vibrations are to be considered byapplying add as given by the following table:

Type of engine add [N/mm 2]

Crosshead engines 30 *)

Trunk piston engines 10

*) The additional stress of 30 N/mm 2 is composed of twocomponents:

an additional stress of 20 N/mm 2 resulting fromaxial vibration

an additional stress of 10 N/mm 2 resulting frommisalignment / bedplate deformation

It is recommended that a value of 20 N/mm 2 be usedfor the axial vibration component for assessment purposewhere axial vibration calculation results of the completedynamic system (engine / shafting / gearing / propeller)are not available.

Where axial vibration calculation results of the completedynamic system are available, the calculated figures may

be used instead.

E. Calculation of Equivalent Alternating

Stress

1. General

In the fillets, bending and torsion lead to two different biaxial stress fields which can be represented by a vonMises equivalent stress with the additional assump-tions that bending and torsion stresses are time phasedand the corresponding peak values occur at the samelocation (see Annex A ).

As a result the equivalent alternating stress is to becalculated for the crankpin fillet as well as for the

journal fillet by using the von Mises criterion.

At the oil hole outlet, bending and torsion lead to twodifferent stress fields which can be represented by anequivalent principal stress equal to the maximum of

principal stress resulting from combination of these

two stress fields with the assumption that bending andtorsion are time phased (see Annex B ).

The above two different ways of equivalent stressevaluation both lead to stresses which may be com-

pared to the same fatigue strength value of crankshaftassessed according to von Mises criterion.

2. Equivalent alternating stress

The equivalent alternating stress is calculated in ac-cordance with the formulae given.


2 2v BH add H( ) 3 = + +

For the journal fillet:

2 2v BG add G( ) 3 = + +

For the outlet of crankpin oil bore:

2TO

v BOBO

1 91 2 1

3 4

= + +

v = equivalent alternating stress [N/mm 2]

For other parameters, see B.1.3 , B.2.3 and D.

F. Calculation of Fatigue Strength

The fatigue strength is to be understood as that valueof equivalent alternating stress (von Mises) which acrankshaft can permanently withstand at the mosthighly stressed points; the fatigue strength may beevaluated by means of the following formulae:

Related to the crankpin diameter:

( )DW B0,2 B

B X

K 0, 42 39,3

7850, 264 1, 073 D

4900196 1

R

= +

+ +

+

R X = R H in the fillet area

R X = D O/2 in the oil bore area

Related to the journal diameter:

( )DW B0,2 B

G

B G

K 0, 42 39,3

7850, 264 1, 073 D

4900196 1

R

= +

+ +

+

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DW = allowable fatigue strength of crankshaft[N/mm 2]

K = factor for different types of crankshafts with-out surface treatment []

Values greater than 1 are only applicable tofatigue strength in fillet area.

= 1,05 for continuous grain flow forged ordrop-forged crankshafts

= 1,0 for free form forged crankshafts

= factor for cast steel crankshafts with coldrolling treatment in fillet area []

= 0,93 for cast steel crankshafts manufac-tured by companies using a GL ap-

proved cold rolling process

B = minimum tensile strength of crankshaft mate-rial [N/mm 2]For other parameters see C.1.

When a surface treatment process is applied, it must be approved by GL.

These formulae are subject to the following condi-tions:

surface of the fillet, the outlet of the oil bore andinside the oil bore (down to a minimum depthequal to 1,5 times the oil bore diameter) shall besmoothly finished.

for calculation purposes R H, R G or R X are to betaken as not less than 2 mm.

As an alternative the fatigue strength of the crankshaftcan be determined by experiment based either on fullsize crankthrow (or crankshaft) or on specimens takenfrom a full size crankthrow.

In any case the experimental procedure for fatigueevaluation of specimens and fatigue strength of crank-shaft assessment have to be submitted for approval toGL (method, type of specimens, number of specimens(or crankthrows), number of tests, survival probability,

confidence number ).

G. Acceptability Criteria

The sufficient dimensioning of a crankshaft is con-firmed by a comparison of the equivalent alternatingstress and the fatigue strength. This comparison has to

be carried out both for the crankpin fillet, the journalfillet, the outlet of crankpin oil bore and is based onthe formula:

DW

v

Q =

Q = acceptability factor []

Adequate dimensioning of the crankshaft is ensured ifthe smaller of both acceptability factors satisfies thecriterion:

Q 1,15

H. Calculation of Shrink-fits of Semi-builtCrankshafts

1. General

All crank dimensions necessary for the calculation ofthe shrink-fit are shown in Fig. 1.8 .

DS = shrink diameter [mm]

LS = length of shrink-fit [mm]

Fig. 1.8 Crank throw of semi-built crankshaft

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DA = outside diameter of web [mm] or

twice the minimum distance x between cen-tre-line of journals and outer contour of web,whichever is less.

y = distance between the adjacent generatinglines of journal and pin [mm]

y 0,05 DS

Where y is less than 0,1 D S, special consid-eration is to be given to the effect of the stressdue to the shrink on the fatigue strength at thecrankpin fillet.

For other parameter, see C.1. (Fig. 1.7 ).

Regarding the radius of the transition from the journalto the shrink diameter, the following must be ob-

served:R G 0,015 DG and R G 0,5 (DS D G)

where the greater value is to be considered.

The actual oversize Z of the shrink-fit must be withinthe limits Z min and Z max calculated in accordance withitems 2. and 3.

In the case where H.2. condition cannot be fulfilledthen H.3. and H.4. calculation methods of Z min andZmax are not applicable due to multizone-plasticity

problems. In such case Z min and Z max have to be estab-

lished based on FEM calculations.

2. Maximum permissible hole in the journalpin

The maximum permissible hole diameter in the jour-nal pin is calculated in accordance with the followingformula:

R maxBG S 2

S S SP

4000 S MD D 1

D L

=

SR = safety factor against slipping []A value not less than 2 is to be taken unlessdocumented by experiments.

Mmax = absolute maximum value of the torque M Tmax in accordance with B.2.2 [Nm]

= coefficient for static friction []

A value not greater than 0.2 is to be takenunless documented by experiments.

SP = minimum yield strength of material for jour-nal pin [N/mm 2]

This condition serves to avoid plasticity in the hole ofthe journal pin.

3. Necessary minimum oversize of shrink-fit

The necessary minimum oversize is determined by thegreater value calculated according to:

SW Smin

m

DZ

E

and

( ) ( )2 2

R max A Smin 2 2

m S S A S

S M 1 Q Q4000Z

E D L 1 Q 1 Q

Zmin = minimum oversize [mm]

Em = Youngs modulus [N/mm]

SW = minimum yield strength of material for crankweb [N/mm]

QA = web ratio [-]S

A A

D

Q D=

QS = shaft ratio [-]BG

SS

DQ

D= .

4. Maximum permissible oversize ofshrink-fit

The maximum permissible oversize is calculated inaccordance with the following formula:

SW S Smax

m

D 0,8 DZ

E 1000

+

Zmax = maximum oversize [mm]

The condition serves to restrict the shrinkage inducedmean stress in the fillet.

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Annex A

Definition of Stress Concentration Factors in Crankshaft Fillets

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Annex B

Stress Concentration Factors and Stress Distribution at the Edge of Oil Drillings

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Annex B Stress Concentration Factors and Stress Distribution at the Edge ofOil Drillings

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Annex C

Alternative Method for Calculation of Stress Concentration Factors in theWeb Fillet Radii of Crankshafts by utilizing Finite Element Method

A. General

1. The objective of the analysis is to developFinite Element Method (FEM) calculated figures as analternative to the analytically calculated Stress Con-centration Factors (SCF) at the crankshaft fillets. Theanalytical method is based on empirical formulaedeveloped from strain gauge measurements of various

crank geometries and accordingly the application ofthese formulae is limited to those geometries.

2. The SCFs calculated according to the rulesof this Annex are defined as the ratio of stresses calcu-lated by FEM to nominal stresses in both journal and

pin fillets. When used in connection with the presentmethod or the alternative methods, von Mises stressesshall be calculated for bending and principal stressesfor torsion.

3. The procedure as well as evaluation guide-lines are valid for both solid cranks and semibuiltcranks (except journal fillets).

4. The analysis is to be conducted as linearelastic FE analysis, and unit loads of appropriate mag-nitude are to be applied for all load cases.

5. The calculation of SCF at the oil bores is notcovered by this Annex.

6. It is advised to check the element accuracy ofthe FE solver in use, e.g. by modeling a simple ge-ometry and comparing the stresses obtained by FEMwith the analytical solution for pure bending and tor-sion.

7. Boundary Element Method (BEM) may beused instead of FEM.

B. Model Requirements

1. General

The basic recommendations and perceptions for build-ing the FE-model are presented in 2. It is obligatoryfor the final FE-model to fulfill the requirement in4.

2. Element mesh recommendations

In order to fulfil the mesh quality criteria it is advisedto construct the FE model for the evaluation of StressConcentration Factors according to the followingrecommendations:

The model consists of one complete crank, fromthe main bearing centreline to the opposite sidemain bearing centreline

Element types used in the vicinity of the fillets:

10 node tetrahedral elements

8 node hexahedral elements

20 node hexahedral elements

Mesh properties in fillet radii. The followingapplies to 90 degrees in circumferential direc-tion from the crank plane:

Maximum element size a = r/4 through the entire fillet as well as in the circumferential direction.When using 20 node hexahedral elements, the

element size in the circumferential direction may be extended up to 5a. In the case of multi-radiifillet r is the local fillet radius. (If 8 node hexa-hedral elements are used even smaller elementsize is required to meet the quality criteria.)

Recommended manner for element size in filletdepth direction

First layer thickness equal to element size of a

Second layer thickness equal to element tosize of 2a

Third layer thickness equal to element to sizeof 3a

Minimum 6 elements across web thickness.

Generally the rest of the crank should be suit-able for numeric stability of the solver.

Counterweights only have to be modeled onlywhen influencing the global stiffness of thecrank significantly.

Modeling of oil drillings is not necessary as longas the influence on global stiffness is negligibleand the proximity to the fillet is more than 2r,see Fig. C.1.

Drillings and holes for weight reduction have to be modeled.

Sub-modeling may be used as far as the soft-ware requirements are fulfilled.

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Annex C Alternative Method for Calculation of Stress Concentration Factors inthe Web Fillet Radii of Crankshafts by utilizing Finite Element Method

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Fig. C.1 Oil bore proximity to fillet

3. Material

These Rules do not consider material properties suchas Youngs Modulus (E) and Poissons ratio ( ). In FEanalysis those material parameters are required, asstrain is primarily calculated and stress is derived fromstrain using the Youngs Modulus and Poissons ratio.Reliable values for material parameters have to beused, either as quoted in literature or as measured onrepresentative material samples.

For steel the following is advised: E = 2.05 105 MPaand = 0.3.

4. Element mesh quality criteria

If the actual element mesh does not fulfil any of thefollowing criteria at the examined area for SCF

evaluation, then a second calculation with a refinedmesh is to be performed.

4.1 Principal stresses criterion

The quality of the mesh should be assured by checkingthe stress component normal to the surface of the fillet

radius. Ideally, this stress should be zero. With principal stresses 1, 2 and 2 the following criterion isrequired:

( ) ( )1 2 3 1 2 3min , , 0.03 max , , <

4.2 Averaged/unaveraged stresses criterion

The criterion is based on observing the discontinuityof stress results over elements at the fillet for the cal-culation of SCF:

Unaveraged nodal stress results calculated from each element connected to a node i should differ less than by 5 % from the 100 % averaged nodal stress results at this node i at the examined location.

C. Load Cases

1. General

To substitute the analytically determined SCF in theseRules the following load cases have to be calculated.

1.1 Torsion

In analogy to the testing apparatus used for the inves-tigations made by FVV the structure is loaded puretorsion. In the model surface warp at the end faces issuppressed.

Torque is applied to the central node located at thecrankshaft axis. This node acts as the master nodewith 6 degrees of freedom and is connected rigidly toall nodes of the end face.

Boundary and load conditions are valid for both in-line and V-type engines.

Fig. C.2 Boundary and load conditions for the torsion load case

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For all nodes in both the journal and crank pin fillet principal stresses are extracted and the equivalenttorsional stress is calculated:

2 3 1 31 2

equivmax , ,

2 2 2

=

The maximum value taken for the subsequent calcula-tion of the SCF:

equiv,

N

=

equiv,

N

=

where N is nominal torsional stress referred to the

crankpin and respectively journal as per Section 1, B. 2.2 with the torsional torque T:

NP

TW

=

1.2 Pure bending (4 point bending)

In analogy to the testing apparatus used for the inves-tigations made by FVV the structure is loaded in pure

bending. In the model surface warp at the end faces issuppressed.

The bending moment is applied to the central nodelocated at the crankshaft axis. This node acts as themaster node with 6 degrees of freedom and is con-nected rigidly to all nodes of the end face.

Boundary and load conditions are valid for both in-line- and V- type engines.

For all nodes in both the journal and pin fillet vonMises equivalent stresses equiv are extracted. Themaximum value is used to calculate the SCF accord-ing to:

equiv,B

N

=

equiv,B

N

=

Nominal stress N is calculated as per Section 1, B.1.2.1 with the bending moment M:

Neqw

MW =

1.3 Bending with shear force (3-point bending)

This load case is calculated to determine the SCF for pure transverse force (radial force, Q) for the journalfillet.

In analogy to the testing apparatus used for the inves-tigations made by FVV, the structure is loaded in 3-

point bending. In the model, surface warp at the bothend faces is suppressed. All nodes are connected rig-

idly to the centre node; boundary conditions are applied to the centre nodes. These nodes act as masternodes with 6 degrees of freedom.

Fig. C.3 Boundary and load conditions for the pure bending load case

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Fig. C.4 Boundary and load conditions for the 3-point bending load case of an inline engine

Fig. C.5 Load applications for in-line and V-type engines

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The force is applied to the central node located at the pin centre-line of the connecting rod. This node isconnected to all nodes of the pin cross sectional area.Warping of the sectional area is not suppressed.

Boundary and load conditions are valid for in-line andV-type engines. V-type engines can be modeled withone connecting rod force only. Using two connectingrod forces will make no significant change in the SCF.

The maximum equivalent von Mises stress 3P in the journal fillet is evaluated. The SCF in the journal filletcan be determined in two ways as shown below.

1.3.1 Method 1

This method is analogue to the FVV investigation.The results from 3-point and 4-point bending arecombined as follows:

3P N3P B Q3P Q = +

where:

3P as found by the FE calculation.

N3P Nominal bending stress in the web centre due tothe force F 3P [N] applied to the centre-line of the ac-tual connecting rod, see Fig. C.5

B as determined in 1.2 .

Q3P = Q 3P /(B W) where Q 3P is the radial (shear)force in the web due to the force F 3P [N] applied to thecentre-line of the actual connecting rod, see alsoSection 1, Fig. 1.3 and 1.4.

1.3.2 Method 2This method is not analogous to the FVV investiga-tion. In a statically determined system with one crankthrow supported by two bearings, the bending momentand radial (shear) force are proportional. Therefore the

journal fillet SCF can be found directly by the 3-point bending FE calculation.

The SCF is then calculated according to

3PBQ

N3P

=

For symbols see 1.3.1 .

When using this method the radial force and stressdetermination becomes superfluous. The alternating

bending stress in the journal fillet as per Section 1,B.1.3 is then evaluated:

BG BQ BFN =

Note that the use of this method does not apply to thecrankpin fillet and that this SCF must not be used inconnection with calculation methods other than thoseassuming a statically determined system.

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