M53

M53
M53(1986)(cont)(Rev.1,
Dec 2004)(Rev.2
Jan 2011)(Rev.3June 2017)(Rev.4
Aug 2019)(Rev.5
May 2023)

Calculations for I.C. Engine Crankshafts
TABLE OF CONTENTS
M 53.1 GENERAL
1.1

Scope

1.2

Field of application

1.3

Principles of calculation

1.4

Drawings and particulars to be submitted

M 53.2 CALCULATION OF STRESSES
2.1

Calculation of alternating stresses due to bending moments and radial forces

2.1.1 Assumptions
2.1.1.1 Bending moments and radial forces acting in web
2.1.1.2 Bending acting in outlet of crankpin oil bore
2.1.2 Calculation of nominal alternating bending and compressive stresses in web
2.1.2.1 Nominal alternating bending and compressive stresses in web cross section
2.1.2.2 Nominal alternating bending stress in outlet of crankpin oil bore
2.1.3 Calculation of alternating bending stresses in fillets
2.1.4 Calculation of alternating bending stresses in outlet of crankpin oil bore

Note:
1.

Rev.1 is to be applied to crankshafts whose application for design approval is dated on
or after 1 January 2007.

2.

Rev.2 is to be applied to crankshafts whose application for design approval is dated on
or after 1 January 2012.

3.

Rev.3 is to be applied to crankshafts whose application for design approval is dated on
or after 1 July 2018.

4.

Rev.4 is to be applied to crankshafts whose application for design approval is dated on
or after 1 January 2021.

5.

Rev.5 is to be applied to crankshafts whose application for design approval is dated on
or after 1 July 2024.

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2.2

Calculation of alternating torsional stresses

2.2.1 General
2.2.2 Calculation of nominal alternating torsional stresses
2.2.3 Calculation of alternating torsional stresses in fillets and outlet of crankpin oil bore
M 53.3 EVALUATION OF STRESS CONCENTRATION FACTORS
3.1

General3.2

Crankpin fillet

3.3

Journal fillet (not applicable to semi-built crankshaft)

3.4

Outlet of crankpin oil bore

M 53.4 ADDITIONAL BENDING STRESSES
M 53.5 CALCULATION OF EQUIVALENT ALTERNATING STRESS
5.1

General

5.2

Equivalent alternating stress

M 53.6 CALCULATION OF FATIGUE STRENGTH
M 53.7 ACCEPTABILITY CRITERIA
M 53.8 CALCULATION OF SHRINK-FITS OF SEMI-BUILT CRANKSHAFTS
8.1

General

8.2

Maximum permissible hole in the journal pin

8.3

Necessary minimum oversize of shrink-fit

8.4

Maximum permissible oversize of shrink-fit

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Appendix I

Definition of Stress Concentration Factors in crankshaft fillets

Appendix II

Stress Concentration Factors and Stress Distribution at the edge of oil
drillings

Appendix III Guidance for Calculation of Stress Concentration Factors in the web fillet
radii of crankshafts by utilizing Finite Element Method
Appendix IV Guidance for Evaluation of Fatigue Tests
Appendix V Guidance for Calculation of Surface Treated Fillets and Oil Bore Outlets
Appendix VI Guidance for Calculation of Stress Concentration Factors in the Oil Bore
Outlets of crankshafts through utilization of the Finite Element Method

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M 53.1 GENERAL
1.1

Scope

These Rules for the design of crankshafts are to be applied to I.C. engines for propulsion andauxiliary purposes, where the engines are capable of continuous operation at their rated
power when running at rated speed.
Where a crankshaft design involves the use of surface treated fillets, or when fatigue
parameter influences are tested, or when working stresses are measured, the relevant
documents with calculations/analysis are to be submitted to Classification Societies in orderto demonstrate equivalence to the Rules.
1.2

Field of application

These Rules apply only to solid-forged and semi-built crankshafts of forged or cast steel, with
one crankthrow between main bearings.
1.3

Principles of calculation

The design of crankshafts is based on an evaluation of safety against fatigue in the highly
stressed areas.
The calculation is also based on the assumption that the areas exposed to highest stresses
are :• fillet transitions between the crankpin and web as well as between the journal andweb,• outlets of crankpin oil bores.
When journal diameter is equal or larger than the crankpin one, the outlets of main journal oil
bores are to be formed in a similar way to the crankpin oil bores, otherwise separate
documentation of fatigue safety may be required.
Calculation of crankshaft strength consists initially in determining the nominal alternating
bending (see § M53.2.1) and nominal alternating torsional stresses (see § M53.2.2) which,multiplied by the appropriate stress concentration factors (see § M53.3), result in an
equivalent alternating stress (uni-axial stress) (see § M53.5). This equivalent alternatingstress is then compared with the fatigue strength of the selected crankshaft material (see §M53.6). This comparison will show whether or not the crankshaft concerned is dimensioned
adequately (see § M53.7).
1.4

Drawings and particulars to be submitted

For the calculation of crankshafts, the documents and particulars listed below are to besubmitted :• crankshaft drawing(which must contain all data in respect of the geometrical configurations of the
crankshaft)• type designation and kind of engine(in-line engine or V-type engine with adjacent connecting-rods, forked connecting-rod
or articulated-type connecting-rod)• operating and combustion method(2-stroke or 4-stroke cycle/direct injection, precombustion chamber, etc.)• number of cylinders
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rated power [kW]rated engine speed [r/min]direction of rotation (see. fig. 1)
firing order with the respective ignition intervals and, where necessary,
V-angle αv [º] (see fig. 1)

Fig. 1 – Designation of the cylinders
•
•
•
•
•
•
•
•
•

cylinder diameter [mm]stroke [mm]maximum net cylinder pressure Pmax [bar]charge air pressure [bar](before inlet valves or scavenge ports, whichever applies)
connecting-rod length LH [mm]all individual reciprocating masses acting on one crank [kg]digitized gas pressure curve presented at equidistant intervals [bar versus Crank
Angle] (at least every 5° CA)for engines with articulated-type connecting-rod (see fig. 2)
o distance to link point LA [mm]o link angle αN [°]connecting-rod length LN [mm]Page 5 of 69

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Fig. 2 – articulated-type connecting-rod•••

details of crankshaft materialo material designation(according to ISO,EN,DIN, AISI, etc..)
o mechanical properties of material(minimum values obtained from longitudinal test specimens)- tensile strength [N/mm²]- yield strength [N/mm²]- reduction in area at break [%]- elongation A5 [%]- impact energy – KV [J]o type of forging(free form forged, continuous grain flow forged, drop-forged, etc… ; withdescription of the forging process)Every surface treatment affecting fillets or oil holes shall be specified so as to enablecalculation according to Appendix V.
Particulars of alternating torsional stress calculations, see item M 53.2.2.

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Connecting-rod
acting component forces(FR or FT)

Radial shear force diagrams(QR)

Bending moment diagrams(MBR or MBT)

onnecting-rod
acting component forces(FR or FT)

Fig. 3 Crankthrow for in line engine

Fig. 4 Crankthrow for V engine
with 2 adjacent connecting-rods

L1 = Distance between main journal centre line and crankweb centre(see also Fig 5 for crankshaft without overlap)
L2 = Distance between main journal centre line and connecting-rod centre
L3 = Distance between two adjacent main journal centre lines

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M 53.2 CALCULATION OF STRESSES
2.1

Calculation of alternating stresses due to bending moments and radial forces

2.1.1 Assumptions
The calculation is based on a statically determined system, composed of a single crankthrow
supported in the centre of adjacent main journals and subject to gas and inertia forces. The
bending length is taken as the length between the two main bearing midpoints (distance L3,
see fig. 3 and 4).
The bending moments MBR, MBT are calculated in the relevant section based on triangularbending moment diagrams due to the radial component FR and tangential component FT ofthe connecting-rod force, respectively (see fig. 3).
For crankthrows with two connecting-rods acting upon one crankpin the relevant bending
moments are obtained by superposition of the two triangular bending moment diagrams
according to phase (see fig. 4).
2.1.1.1 Bending moments and radial forces acting in web
The bending moment MBRF and the radial force QRF are taken as acting in the centre of thesolid web (distance L1) and are derived from the radial component of the connecting-rod
force.
The alternating bending and compressive stresses due to bending moments and radial forces
are to be related to the cross-section of the crank web. This reference section results from the
web thickness W and the web width B (see fig. 5).
Mean stresses are neglected.

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Overlapped crankshaft

Th

Wred

W

Crankshaft without overlap
Fig. 5 – Reference area of crankweb cross section

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2.1.1.2 Bending acting in outlet of crankpin oil bore
The two relevant bending moments are taken in the crankpin cross-section through the oil
bore.

MBRO is the bending moment of the radial component of theconnecting-rod force

MBTO is the bending moment of the tangential component of
the connecting-rod force

Fig. 6 – Crankpin section through the oil bore
The alternating stresses due to these bending moments are to be related to the crosssectional area of the axially bored crankpin.
Mean bending stresses are neglected.
2.1.2 Calculation of nominal alternating bending and compressive stresses in web
The radial and tangential forces due to gas and inertia loads acting upon the crankpin at eachconnecting-rod position will be calculated over one working cycle.
Using the forces calculated over one working cycle and taking into account of the distancefrom the main bearing midpoint, the time curve of the bending moments MBRF, MBRO, MBTO andradial forces QRF - as defined in M53 2.1.1.1 and 2.1.1.2 - will then be calculated.
In case of V-type engines, the bending moments - progressively calculated from the gas andinertia forces - of the two cylinders acting on one crankthrow are superposed according tophase. Different designs (forked connecting-rod, articulated-type connecting-rod or adjacentconnecting-rods) shall be taken into account.
Where there are cranks of different geometrical configurations in one crankshaft, thecalculation is to cover all crank variants.
The decisive alternating values will then be calculated according to:

XN = ±

1
X max − X min
2

where:
XN

is considered as alternating force, moment or stressXmax

is maximum value within one working cycle

Xmin

is minimum value within one working cycle

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2.1.2.1 Nominal alternating bending and compressive stresses in web cross section
The calculation of the nominal alternating bending and compressive stresses is as follows:σ BFN = ±3
MBRFN
• 10 • Ke
Weqw

σ QFN = ±

QRFN
• Ke
F

where:σBFN [N/mm²]

nominal alternating bending stress related to the web

MBRFN [Nm]alternating bending moment related to the centre of the web (see fig. 3 and 4)

M BRFN = ±Weqw [mm3]1
M BRFmax − M BRFmin
2

section modulus related to cross-section of web
Weqw =

B • W2
6Keempirical factor considering to some extent the influence of adjacent crankand bearing restraint
with: Ke = 0.8 for 2-stroke engines
Ke = 1.0 for 4-stroke engines

σQFN [N/mm²]

nominal alternating compressive stress due to radial force related to the web

QRFN [N]alternating radial force related to the web (see fig. 3 and 4)

Q RFN = ±F [mm²]

1
Q RF − Q RF
max
min
2

area related to cross-section of web
F = B•W

2.1.2.2 Nominal alternating bending stress in outlet of crankpin oil bore
The calculation of nominal alternating bending stress is as follows:

σ BON = ±Page 11 of 69

3
MBON
•10
We

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where:σBON [N/mm²]

nominal alternating bending stress related to the crank pin diameter

MBON [Nm]alternating bending moment calculated at the outlet of crankpin oil bore

M BON = ±with1
M BO − M BO
max
min
2

MBO = (MBTO • cos ψ + MBRO • sin ψ)and ψ ° angular position (see fig. 6)

We [mm3]

section modulus related to cross-section of axially bored crankpin

We =

4
4
π  D − D BH 
32 D 

2.1.3 Calculation of alternating bending stresses in fillets
The calculation of stresses is to be carried out for the crankpin fillet as well as for the journal
fillet.
For the crankpin fillet:

σ BH = ±(α B • σ BFN)

where:
σBH [N/mm2]

alternating bending stress in crankpin fillet

αB [-]

stress concentration factor for bending in crankpin fillet (determination - seeitem M53.3)

For the journal fillet (not applicable to semi-built crankshaft):σ BG = ±(β B • σ BFN + β Q • σ QFN)
where:σBG [N/mm2 ]alternating bending stress in journal fillet

βB [-]

stress concentration factor for bending in journal fillet (determination - seeitem M53.3)

βQ [-]

stress concentration factor for compression due to radial force in journal
fillet (determination - see item M53.3)

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2.1.4 Calculation of alternating bending stresses in outlet of crankpin oil bore

(cont)σ BO = ±(γ B • σ BON)
where:
σBO [N/mm2]

alternating bending stress in outlet of crankpin oil bore

γB [-]

stress concentration factor for bending in crankpin oil bore (determination see item M53.3)

2.2

Calculation of alternating torsional stresses

2.2.1 General
The calculation for nominal alternating torsional stresses is to be undertaken by the engine
manufacturer according to the information contained in item M 53.2.2.2.
The manufacturer shall specify the maximum nominal alternating torsional stress.
2.2.2 Calculation of nominal alternating torsional stresses
The maximum and minimum torques are to be ascertained for every mass point of thecomplete dynamic system and for the entire speed range by means of a harmonic synthesisof the forced vibrations from the 1st order up to and including the 15th order for 2-stroke cycle
engines and from the 0.5th order up to and including the 12th order for 4-stroke cycle engines.
Whilst doing so, allowance must be made for the damping that exists in the system and forunfavourable conditions (misfiring [*] in one of the cylinders). The speed step calculation shallbe selected in such a way that any resonance found in the operational speed range of theengine shall be detected.
Where barred speed ranges are necessary, they shall be arranged so that satisfactory
operation is possible despite their existence. There are to be no barred speed ranges abovea speed ratio of λ ≥ 0.8 for normal firing conditions.
The values received from such calculation are to be submitted to Classification Society.
The nominal alternating torsional stress in every mass point, which is essential to theassessment, results from the following equation:

τN = ±

MTN = ±

Wp =4
π  D4 − DBH 

16 
D


M TN
• 10 3
WP[

1
MT max − MT min
2
or

Wp =

π
16

]
 DG 4 − DBG 4 




D
G



*) Misfiring is defined as cylinder condition when no combustion occurs but only compression cycle.

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where:
τN [N/mm²]

nominal alternating torsional stress referred to crankpin or journal

MTN [Nm]

maximum alternating torque

WP [mm3]polar section modulus related to cross-section of axially bored crankpin orbored journal

MTmax [Nm]maximum value of the torqueMTmin [Nm]minimum value of the torqueFor the purpose of the crankshaft assessment, the nominal alternating torsional stressconsidered in further calculations is the highest calculated value, according to above method,
occurring at the most torsionally loaded mass point of the crankshaft system.
Where barred speed ranges exist, the torsional stresses within these ranges are not to beconsidered for assessment calculations.
The approval of crankshaft will be based on the installation having the largest nominal
alternating torsional stress (but not exceeding the maximum figure specified by engine
manufacturer).
Thus, for each installation, it is to be ensured by suitable calculation that this approved
nominal alternating torsional stress is not exceeded. This calculation is to be submitted forassessment.
2.2.3 Calculation of alternating torsional stresses in fillets and outlet of crankpin oil
bore
The calculation of stresses is to be carried out for the crankpin fillet, the journal fillet and theoutlet of the crankpin oil bore.
For the crankpin fillet:τ H = ±(α T • τ N)

where:
τH [N/mm2]

alternating torsional stress in crankpin fillet

αT [-]

stress concentration factor for torsion in crankpin fillet (determination - seeitem M53.3)

τN [N/mm2]

nominal alternating torsional stress related to crankpin diameter

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

τ G = ±(β T • τ N)

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where:
τG [N/mm2]

alternating torsional stress in journal fillet

βT [-]

stress concentration factor for torsion in journal fillet (determination - seeitem M53.3)

τN [N/mm2]

nominal alternating torsional stress related to journal diameter

For the outlet of crankpin oil bore:

σ T O = ±(γ T • τ N)

where:σTO [N/mm2]

alternating stress in outlet of crankpin oil bore due to torsion

γT [-]

stress concentration factor for torsion in outlet of crankpin oil bore
(determination- see item M53.3)

τN [N/mm2]

nominal alternating torsional stress related to crankpin diameter

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M 53.3 EVALUATION OF STRESS CONCENTRATION FACTORS
3.1

GeneralThe stress concentration factors are evaluated by means of the formulae according to items
M53.3.2, M53.3.3 and M53.3.4 applicable to the fillets and crankpin oil bore of solid forgedweb-type crankshafts and to the crankpin fillets of semi-built crankshafts only. It must be
noticed that stress concentration factor formulae concerning the oil bore are only applicable
to a radially drilled oil hole. All formulae are based on investigations of FVV(Forschungsvereinigung Verbrennungskraftmaschinen) for fillets and on investigations of
ESDU (Engineering Science Data Unit) for oil holes.
Where the geometry of the crankshaft is outside the boundaries of the analytical stressconcentration factors (SCF) the calculation method detailed in Appendix III may beundertaken.
All crank dimensions necessary for the calculation of stress concentration factors are shownin figure 7.
The stress concentration factor for bending (αB, βB) is defined as the ratio of the maximum
equivalent stress (VON MISES) – occurring in the fillets under bending load – to the nominal
bending stress related to the web cross-section (see Appendix I).
The stress concentration factor for compression (βQ) in the journal fillet is defined as the ratioof the maximum equivalent stress (VON MISES) – occurring in the fillet due to the radial force– to the nominal compressive stress related to the web cross-section.
The stress concentration factor for torsion (αT, βT) is defined as the ratio of the maximum
equivalent shear stress – occurring in the fillets under torsional load – to the nominal torsional
stress related to the axially bored crankpin or journal cross-section (see Appendix I).
The stress concentration factors for bending (γB) and torsion (γT) 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 the corresponding nominal stress related to the axially bored crankpin
cross section (see Appendix II).
When reliable measurements and/or calculations are available, which can allow direct
assessment of stress concentration factors, the relevant documents and their analysis
method have to be submitted to Classification Societies in order to demonstrate theirequivalence to present rules evaluation. This is always to be performed when dimensions areoutside of any of the validity ranges for the empirical formulae presented in 3.2 to 3.4.
Appendix III and VI describes how FE analyses can be used for the calculation of the stressconcentration factors. Care should be taken to avoid mixing equivalent (von Mises) stresses
and principal stresses.

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Actual dimensions:Fig. 7 – Crank dimensions

D

[mm]

crankpin diameter

DBH

[mm]

diameter of axial bore in crankpin

Do

[mm]

diameter of oil bore in crankpin

RH

[mm]

fillet radius of crankpin

TH

[mm]

recess of crankpin fillet

DG

[mm]

journal diameter

DBG

[mm]

diameter of axial bore in journal

RG

[mm]

fillet radius of journal

TG

[mm]

recess of journal fillet

E

[mm]

pin eccentricity

S

[mm]

pin overlap
S=

D + DG
−E
2

W (*)

[mm]

web thickness

B (*)

[mm]

web width(*) In the case of 2 stroke semi-built crankshafts:• when TH > RH, the web thickness must be considered as equal to:
Wred = W – (TH – RH) [refer to fig. 5]• web width B must be taken in way of crankpin fillet radius centre according to
fig. 5
The following related dimensions will be applied for the calculation of stress concentration
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Crankpin fillet

Journal fillet

r = RH / D

r = RG / D(cont)

s

=

S/D

w

=

W/D crankshafts with overlap

Wred/D crankshafts without overlap
b

=

B/D

do

=

DO/D

dG

=

DBG/D

dH

=

DBH/D

tH

=

TH/D

tG

=

TG/D

Stress concentration factors are valid for the ranges of related dimensions for which theinvestigations have been carried out. Ranges are as follows:s ≤ 0.5
0.2 ≤ w ≤ 0.8
1.1 ≤ b ≤ 2.2
0.03 ≤ r ≤ 0.13
0≤ dG ≤ 0.8
0≤ dH ≤ 0.8
0≤ dO ≤ 0.2
Low range of s can be extended down to large negative values provided that:• If calculated f (recess) < 1 then the factor f (recess) is not to be considered(f (recess) = 1)
• If s < - 0.5 then f (s,w) and f (r,s) are to be evaluated replacing actual value of s by - 0.5.
3.2

Crankpin fillet

The stress concentration factor for bending (αB) is:αB = 2.6914 • f (s, w) • f (w) • f (b) • f (r) • f (dG) • f (dH) • f (recess)where: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

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(cont)f ( r)= 0.2081 • r (-0.5231)

f (dG)= 0.9993 + 0.27 • dG – 1.0211 • dG² + 0.5306 • dG3

f (dH)= 0.9978 + 0.3145 • dH – 1.5241 • dH² + 2.4147 • dH3

f (recess) = 1 + (tH + tG) • (1.8 + 3.2 • s)
The stress concentration factor for torsion (αT) is:αT = 0.8 • f (r,s) • f (b) • f (w)where: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)

3.3

Journal fillet (not applicable to semi-built crankshaft)

The stress concentration factor for bending (βB) is:βB = 2.7146 • fB (s,w) • fB (w) • fB (b) • fB (r) • fB (dG) • fB (dH) • f (recess)where:fB (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)

fB (w)= 2.2422 • w 0.7548

fB (b)= 0.5616 + 0.1197 • b + 0.1176 • b²

fB (r)= 0.1908 • r (-0.5568)

fB (dG)= 1.0012 – 0.6441 • dG + 1.2265 • dG²

fB (dH)= 1.0022 – 0.1903 • dH + 0.0073 • dH²

f (recess) = 1 + (tH + tG) • (1.8 + 3.2 • s)
The stress concentration factor for compression (βQ) due to the radial force is:βQ = 3.0128 • fQ (s) • fQ (w) • fQ (b) • fQ (r) • fQ (dH) • f (recess)where:fQ (s)= 0.4368 + 2.1630 • (1-s) – 1.5212 • (1-s)²Page 19 of 69

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w
0.0637 + 0.9369 • w

fQ (w)=

fQ (b)= - 0.5 + b

fQ (r)= 0.5331 • r (-0.2038)

fQ (dH)= 0.9937 – 1.1949 • dH + 1.7373 • dH²(cont)f (recess) = 1 + (tH + tG) • (1.8 + 3.2 • s)
The stress concentration factor for torsion (βT) is:βT = αT
if the diameters and fillet radii of crankpin and journal are the same.
If crankpin and journal diameters and/or radii are of different sizes
βT = 0.8 • f (r,s) • f(b) • f(w)where:f (r,s), f (b) and f (w) are to be determined in accordance with item M 53.3.2. (seecalculation of αT), however, the radius of the journal fillet is to be related to the journal
diameter:
r=

3.4

RG
DG

Outlet of crankpin oil bore

The stress concentration factor for bending (γB) is:γ B = 3 − 5.88 • d o + 34.6 • d o 2
The stress concentration factor for torsion (γT) is:γ T = 4 − 6 • d o + 30 • d o 2

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M 53.4 ADDITIONAL BENDING STRESSESIn addition to the alternating bending stresses in fillets (see item M 53.2.1.3) further bending
stresses due to misalignment and bedplate deformation as well as due to axial and bending
vibrations are to be considered by applying σadd as given by table:
Type of engine
Crosshead engines
Trunk piston engines

σadd[N/mm²]± 30 (*)± 10(*) The additional stress of ± 30 N/mm² is composed of two components
1) an additional stress of ± 20 N/mm² resulting from axial vibration
2) an additional stress of ± 10 N/mm² resulting from misalignment / bedplate deformation
It is recommended that a value of ± 20 N/mm2 be used for the axial vibration component forassessment purposes where axial vibration calculation results of the complete dynamic
system (engine/shafting/gearing/propeller) are not available. Where axial vibration calculation
results of the complete dynamic system are available, the calculated figures may be usedinstead.
M 53.5 CALCULATION OF EQUIVALENT ALTERNATING STRESS
5.1

GeneralIn the fillets, bending and torsion lead to two different biaxial stress fields which can be
represented by a Von Mises equivalent stress with the additional assumptions that bending
and torsion stresses are time phased and the corresponding peak values occur at the same
location (see Appendix I).
As a result the equivalent alternating stress is to be calculated 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 two different stress fields which can be
represented by an equivalent principal stress equal to the maximum of principal stressresulting from combination of these two stress fields with the assumption that bending andtorsion are time phased (see Appendix II).
The above two different ways of equivalent stress evaluation both lead to stresses which may
be compared to the same fatigue strength value of crankshaft assessed according to Von
Mises criterion.
5.2

Equivalent alternating stress

The equivalent alternating stress is calculated in accordance with the formulae given.
For the crankpin fillet:22

σ v = ± (σ BH + σ add) + 3 • τ H

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M53

For the journal fillet:(cont)22

σ V = ± (σ BG + σ add) + 3 • τ G

For the outlet of crankpin oil bore:21
9  σ TO  σ v = ± σ BO • 1+ 2 1+ 
3
4  σ BO  where:
σv [N/mm2]

equivalent alternating stressfor other parameters see items M53.2.1.3, M53.2.2.3 and M53.4.
M 53.6 CALCULATION OF FATIGUE STRENGTH
The fatigue strength is to be understood as that value of equivalent alternating stress (VonMises) which a crankshaft can permanently withstand at the most highly stressed points. The
fatigue strength may be evaluated by means of the following formulae.
Related to the crankpin diameter:σ DW = ±K • (0.42 • σ B + 39.3) • 0.264 + 1.073 • D −0.2 +

785 − σ B 196
1 
+
•

σB
4900
R X 

with:
RX = RH

in the fillet area

RX = Do/2 in the oil bore area
Related to the journal diameter:σ DW = ±K • (0.42 • σ B + 39.3) • 0.264 + 1.073 • DG −0.2 +

785 − σ B 196
1 
+
•

σB
4900
RG 

where:σDW [N/mm2]

allowable fatigue strength of crankshaft

K [-]factor for different types of crankshafts without surface treatment. Values
greater than 1 are only applicable to fatigue strength in fillet area.
= 1.05 for continuous grain flow forged or drop-forged crankshafts= 1.0 for free form forged crankshafts (without continuous grain flow)
factor for cast steel crankshafts with cold rolling treatment in fillet area
= 0.93 for cast steel crankshafts manufactured by companies using aclassification society approved cold rolling process

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(cont)

σB [N/mm2]

minimum tensile strength of crankshaft material

For other parameters see item M53.3.3.
When a surface treatment process is applied, it must be approved by Classification Society.
Guidance for calculation of surface treated fillets and oil bore outlets is presented in Appendix
V.
These formulae are subject to the following conditions:• surfaces of the fillet, the outlet of the oil bore and inside the oil bore (down to aminimum depth equal to 1.5 times the oil bore diameter) shall be smoothly finished.
• for calculation purposes RH, RG or RX are to be taken as not less than 2 mm.
As an alternative the fatigue strength of the crankshaft can be determined by experimentbased either on full size crankthrow (or crankshaft) or on specimens taken from a full size
crankthrow. For evaluation of test results, see Appendix IV.
M 53.7 ACCEPTABILITY CRITERIA
The sufficient dimensioning of a crankshaft is confirmed by a comparison of the equivalentalternating stress and the fatigue strength. This comparison has to be carried out for the
crankpin fillet, the journal fillet, the outlet of crankpin oil bore and is based on the formula:
Q=

σ DW
σv

where:
Q [-]acceptability factor

Adequate dimensioning of the crankshaft is ensured if the smallest of all acceptability factors
satisfies the criteria:Q ≥ 1.15
M 53.8 CALCULATION OF SHRINK-FITS OF SEMI-BUILT CRANKSHAFT
8.1

GeneralAll crank dimensions necessary for the calculation of the shrink-fit are shown in figure 8.

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(cont)

Fig. 8 – Crankthrow of semi-built crankshaft
where:DA [mm]outside diameter of webortwice the minimum distance x between centre-line of journals and outer
contour of web, whichever is lessDS [mm]shrink diameter

DG [mm]journal diameter

DBG [mm]diameter of axial bore in journal

LS [mm]length of shrink-fit

RG [mm]fillet radius of journalydistance between the adjacent generating lines of journal and pin
y ≥ 0.05 • DS
Where y is less than 0.1 • DS special consideration is to be given to theeffect of the stress due to the shrink-fit on the fatigue strength at the
crankpin fillet.

[mm]

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(cont)

Respecting the radius of the transition from the journal to the shrink diameter, the following
should be complied with:
RG ≥ 0.015 • DG
andRG ≥ 0.5 • (DS – DG)
where the greater value is to be considered.
The actual oversize Z of the shrink-fit must be within the limits Zmin and Zmax calculated inaccordance with items M53.8.3 and 8.4.
In the case where 8.2 condition cannot be fulfilled then 8.3 and 8.4 calculation methods ofZmin and Zmax are not applicable due to multizone-plasticity problems.
In such case Zmin and Zmax have to be established based on FEM calculations.
8.2

Maximum permissible hole in the journal pin

The maximum permissible hole diameter in the journal pin is calculated in accordance withthe following formula:
D BG = D S • 1 −4000 • S R • Mmaxµ • π • D S2 • L S • σ SP

where:SR [-]

safety factor against slipping, however a value not less than 2 is to betaken unless documented by experiments.

Mmax [Nm]absolute maximum value of the torque MTmax in accordance with
M 53 2.2.2µ [-]coefficient for static friction, however a value not greater than 0.2 is to betaken unless documented by experiments.

σSP [N/mm2]

minimum yield strength of material for journal pin

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

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8.3

Necessary minimum oversize of shrink-fit

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

Z min ≥σ sw • D S
EmZmin ≥SR • Mmax4000•µ • π Em • DS • L S

and•1 − Q 2A • QS2
1 − Q 2A • 1 − QS2

(

) (

)

where:
Zmin [mm]minimum oversize

Em

Young’s modulus[N/mm²]σSW [N/mm²]

minimum yield strength of material for crank web

QA

web ratio, Q = DS
A

[-]

DA

QS

[-]

shaft ratio, QS = DBG
DS

8.4

Maximum permissible oversize of shrink-fit

The maximum permissible oversize is calculated according to:σ
0 .8 

Z max ≤ D S •  SW +1000 
 Em
This condition serves to restrict the shrinkage induced mean stress in the fillet.

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M53
Definition of Stress Concentration Factors in crankshaft fillets

M53(cont)

B

Torsional loading

A

StressLocation of maximal
stressesMax ||σ3||A

Max σ1
C

σ2

σ

σ1

Bending loading

Typical principal
stress system

S.C.F. =τ equiv
τn

B

for α

σ1

T,βT

B

B

τ

σ2 ≠ 0σ

σ3Page 27 of 69

σ2σ1 ≈ ||σ3||

Mohr‘s circle diagramwith σ3 = 0

Equivalent stressand S.C.F.

σ3

σ1 > ||σ3||σ −σ3
τ equiv = 1
2

Equivalent stressand S.C.F.

C

σ

σ1

σ2

σ3

||σ3|| > σ1

Location of maximal
stresses

τ

σ

σ3

B

τ

τ

Typical principal stresssystemMohr‘s circle diagramwith σ2 = 0

Appendix Iσ2σ1σ equiv = σ 1 ² + σ 2 ² − σ 1 .σ 2
σ equiv
S.C.F. =for α , β , β
B B Q
σn

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Stress Concentration Factors and stress distribution at the edge of oil drillings(cont)

StresstypeαUniaxial stress distribution around the edge

Mohr‘s circle diagram

σα = σn γB / 3 [1+2 cos (2 α)]τσn 0
 0 0



σ

σ max

x

γ B = σ max σ n for α = kπdd = hole
diameterShear

σα = γT τn sin (2α)

0
 n
τ

τ

τn
0 

σ

σ max

γ T = σ max τ n for α = π + k π
4σα =Tension + shearσ(α)

TensionyNominalstresstensorAppendix II

σn
 n
τ

τn
0 



 
3 γ T τnγB
σ n 1 + 2cos( 2α ) +sin(2α ) 
3
2 γ B σn


 

8

0

τ

τn/σ n
σ

0.5

6

σ max

1

4

1.5
Max

2

2


2 
9  γ T τn  
σ max =σ n 1 + 2 1 + 
3
4  γ B σn  for α = 1 tg−1 3γ Tτ n 
 2γ σ 2 B n

γB

0
-2
-4
-6

0

30

Page 28 of 69

60

90

120

150

α

180

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(cont)

Appendix III

Guidance for Calculation of Stress Concentration Factors in the web
fillet radii of crankshafts by utilizing Finite Element Method
Contents
1. General
2. Model requirements
2.1. Element mesh recommendations
2.2. Material
2.3. Element mesh quality criteria
2.3.1. Principal stresses criterion
2.3.2. Averaged/unaveraged stresses criterion
3. Load cases
3.1. Torsion
3.2. Pure bending (4 point bending)
3.3. Bending with shear force (3 point bending)
3.3.1. Method 1
3.3.2. Method 2

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(cont)

1.

GeneralThe objective of the analysis is to develop Finite Element Method (FEM) calculated figures as
an alternative to the analytically calculated Stress Concentration Factors (SCF) at the
crankshaft fillets. The analytical method is based on empirical formulae developed from strain
gauge measurements of various crank geometries and accordingly the application of theseformulae is limited to those geometries.
The SCF’s calculated according to the rules of this document are defined as the ratio ofstresses calculated by FEM to nominal stresses in both journal and pin fillets. When used inconnection with the present method in M53 or the alternative methods, von Mises stresses
shall be calculated for bending and principal stresses for torsion.
The procedure as well as evaluation guidelines are valid for both solid cranks and semibuilt
cranks (except journal fillets).
The analysis is to be conducted as linear elastic FE analysis, and unit loads of appropriatemagnitude are to be applied for all load cases.
The calculation of SCF at the oil bores is not covered by this document.
It is advised to check the element accuracy of the FE solver in use, e.g. by modeling a simple
geometry and comparing the stresses obtained by FEM with the analytical solution for purebending and torsion.
Boundary Element Method (BEM) may be used instead of FEM.
2.

Model requirements

The basic recommendations and perceptions for building the FE-model are presented in 2.1.
It is obligatory for the final FE-model to fulfill the requirement in 2.3.
2.1. Element mesh recommendations
In order to fulfil the mesh quality criteria it is advised to construct the FE model for theevaluation of Stress Concentration Factors according to the following recommendations: The model consists of one complete crank, from the main bearing centerline to the
opposite side main bearing centerline
 Element types used in the vicinity of the fillets:o 10 node tetrahedral elements
o 8 node hexahedral elementso 20 node hexahedral elements
 Mesh properties in fillet radii. The following applies to ±90 degrees in circumferential
direction 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 thecircumferential direction may be extended up to 5a. In the case of multi-radii fillet r is
the local fillet radius. (If 8 node hexahedral elements are used even smaller element
size is required to meet the quality criteria.)
 Recommended manner for element size in fillet depth directiono First layer thickness equal to element size of ao Second layer thickness equal to element to size of 2ao Third layer thickness equal to element to size of 3a Minimum 6 elements across web thickness.
 Generally the rest of the crank should be suitable for numeric stability of the solver.
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 Counterweights only have to be modeled only when influencing the global stiffness ofthe crank significantly.
 Modeling of oil drillings is not necessary as long as the influence on global stiffness is
negligible and the proximity to the fillet is more than 2r, see figure 2.1.
 Drillings and holes for weight reduction have to be modeled.
 Sub-modeling may be used as far as the software requirements are fulfilled.

Figure 2.1. Oil bore proximity to fillet.
2.2. Material
UR M53 does not consider material properties such as Young’s Modulus (E) and Poisson’s
ratio (ν ). In FE analysis those material parameters are required, as strain is primarily
calculated and stress is derived from strain using the Young’s Modulus and Poisson’s ratio.
Reliable values for material parameters have to be used, either as quoted in literature or as
measured on representative material samples.
For steel the following is advised: E= 2.05· 10 5 MPa and ν =0.3.
2.3. Element mesh quality criteria
If the actual element mesh does not fulfil any of the following criteria at the examined area for
SCF evaluation, then a second calculation with a refined mesh is to be performed.
2.3.1. Principal stresses criterion
The quality of the mesh should be assured by checking the stress component normal
to the surface of the fillet radius. Ideally, this stress should be zero. With principal
stresses σ 1 , σ 2 and σ 3 the following criterion is required:min (σ 1 , σ 2 , σ 3 ) < 0.03. max(σ 1 , σ 2 , σ 3 )2.3.2. Averaged/unaveraged stresses criterion
The criterion is based on observing the discontinuity of stress results over elements at thefillet for the calculation of SCF:o

Unaveraged nodal stress results calculated from each element connected to a node ishould differ less than by 5 % from the 100 % averaged nodal stress results at thisnode i at the examined location.
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3. Load cases
To substitute the analytically determined SCF in UR M53 the following load cases have to be
calculated.
3.1. Torsion
In analogy to the testing apparatus used for the investigations made by FVV the structure isloaded pure torsion. In the model surface warp at the end faces is suppressed.
Torque is applied to the central node located at the crankshaft axis. This node acts as themaster node with 6 degrees of freedom and is connected rigidly to all nodes of the end face.
Boundary and load conditions are valid for both in-line and V-type engines.

Figure 3.1 Boundary and load conditions for the torsion load case.
For all nodes in both the journal and crank pin fillet principal stresses are extracted and theequivalent torsional stress is calculated: σ1 − σ 2 σ 2 − σ 3 σ1 − σ 3 

,
,

2
2
2



τ equiv = maxThe maximum value taken for the subsequent calculation of the SCF:

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τ equiv , βτNwhere τ N is nominal torsional stress referred to the crankpin and respectively journal as perβT =UR M53 2.2.2 with the torsional torque T:

τN =

T
WP

3.2. Pure bending (4 point bending)
In analogy to the testing apparatus used for the investigations made by FVV the structure isloaded in pure bending. In the model surface warp at the end faces is suppressed.
The bending moment is applied to the central node located at the crankshaft axis. This nodeacts as the master node with 6 degrees of freedom and is connected rigidly to all nodes of theend face.
Boundary and load conditions are valid for both in-line- and V- type engines.

Figure 3.2 Boundary and load conditions for the pure bending load case.

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M53
(cont)For all nodes in both the journal and pin fillet von Mises equivalent stresses σ equiv are
extracted. The maximum value is used to calculate the SCF according to:σ equiv ,ασNσ equiv , β
βB =
σN

αB =

Nominal stress σ N is calculated as per UR M53 2.1.2.1 with the bending moment M:

σN =

M
Weqw

3.3. Bending with shear force (3-point bending)This load case is calculated to determine the SCF for pure transverse force (radial force, β Q )for the journal fillet.
In analogy to the testing apparatus used for the investigations made by FVV, the structure isloaded in 3-point bending. In the model, surface warp at the both end faces is suppressed. All
nodes are connected rigidly to the centre node; boundary conditions are applied to the centre
nodes. These nodes act as master nodes with 6 degrees of freedom.
The force is applied to the central node located at the pin centre-line of the connecting rod.
This node is connected 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 and V-type engines. V-type engines can bemodeled with one connecting rod force only. Using two connecting rod forces will make nosignificant change in the SCF.

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(cont)

Figure 3.3. Boundary and load conditions for the 3-point bending load case of an inline
engine.

Figure 3.4 Load applications for in-line and V-type engines.

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M53
(cont)The maximum equivalent von Mises stress σ 3 P in the journal fillet is evaluated. The SCF in
the journal fillet can be determined in two ways as shown below.
3.3.1. Method 1
This method is analogue to the FVV investigation. The results from 3-point and 4-point
bending are combined as follows:

σ 3 P = σ N 3 P .β B + σ Q 3 P .β Q
where:

σ 3 P as found by the FE calculation.
σ N 3 P Nominal bending stress in the web centre due to the force F3 P [N] applied to thecentre-line of the actual connecting rod, see figure 3.4.
β B as determined in paragraph 3.2.

σ Q3 P = Q3 P /( B.W ) where Q3 P is the radial (shear) force in the web due to the force F3 P [N]applied to the centre-line of the actual connecting rod, see also figures 3 and 4 in M53.
3.3.2. Method 2This method is not analogous to the FVV investigation. In a statically determined system with
one crank throw supported by two bearings, the bending moment and radial (shear) force areproportional. Therefore the journal fillet SCF can be found directly by the 3-point bending FE
calculation.
The SCF is then calculated according toβ BQ =σ 3P
σ N 3PFor symbols see 3.3.1.
When using this method the radial force and stress determination in M53 becomessuperfluous. The alternating bending stress in the journal fillet as per UR M53 2.1.3 is thenevaluated:

σ BG = ± β BQ .σ BFNNote that the use of this method does not apply to the crankpin fillet and that this SCF mustnot be used in connection with calculation methods other than those assuming a staticallydetermined system as in M53.

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(cont)

Appendix IV

Guidance for Evaluation of Fatigue Tests
Contents
1. Introduction
1.1. Small specimen testing
1.2. Full-size crank throw testing
2. Evaluation of test results
2.1. Principles
2.2. Staircase method
2.3. Modified staircase method
2.4. Calculation of sample mean and standard deviation
2.5. Confidence interval for mean fatigue limit
2.6. Confidence interval for standard deviation
3. Small specimen testing
3.1. Determination of bending fatigue strength
3.2. Determination of torsional fatigue strength
3.3. Other test positions
3.4. Correlation of test results
4. Full size testing
4.1. Hydraulic pulsation
4.2. Resonance tester
4.3. Use of results and crankshaft acceptability
5. Use of existing results for similar crankshafts

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M53
(cont)

1. Introduction
Fatigue testing can be divided into two main groups; testing of small specimens and full-size
crank throws. Testing can be made using the staircase method or a modified version thereof
which is presented in this document. Other statistical evaluation methods may also be
applied.
1.1. Small specimen testing
For crankshafts without any fillet surface treatment, the fatigue strength can be determined by
testing small specimens taken from a full-size crank throw. When other areas in the vicinity of
the fillets are surface treated introducing residual stresses in the fillets, this approach cannot
be applied.
One advantage of this approach is the rather high number of specimens which can be thenmanufactured. Another advantage is that the tests can be made with different stress ratios(R-ratios) and/or different modes e.g. axial, bending and torsion, with or without a notch. Thisis required for evaluation of the material data to be used with critical plane criteria.
1.2. Full-size crank throw testing
For crankshafts with surface treatment the fatigue strength can only be determined throughtesting of full size crank throws. For cost reasons, this usually means a low number of crankthrows. The load can be applied by hydraulic actuators in a 3- or 4- point bending
arrangement, or by an exciter in a resonance test rig. The latter is frequently used, although it
usually limits the stress ratio to R = -1.
2. Evaluation of test results
2.1. Principles
Prior to fatigue testing the crankshaft must be tested as required by quality control
procedures, e.g. for chemical composition, mechanical properties, surface hardness,hardness depth and extension, fillet surface finish, etc.
The test samples should be prepared so as to represent the “lower end” of the acceptance
range e.g. for induction hardened crankshafts this means the lower range of acceptablehardness depth, the shortest extension through a fillet, etc. Otherwise the mean value test
results should be corrected with a confidence interval: a 90% confidence interval may be
used both for the sample mean and the standard deviation.
The test results, when applied in M53, shall be evaluated to represent the mean fatigue
strength, with or without taking into consideration the 90% confidence interval as mentioned
above. The standard deviation should be considered by taking the 90% confidence into
account. Subsequently the result to be used as the fatigue strength is then the mean fatigue
strength minus one standard deviation.
If the evaluation aims to find a relationship between (static) mechanical properties and thefatigue strength, the relation must be based on the real (measured) mechanical properties,
not on the specified minimum properties.
The calculation technique presented in Chapter 2.4 was developed for the original staircase
method. However, since there is no similar method dedicated to the modified staircase
method the same is applied for both.

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(cont)

2.2. Staircase method
In the original staircase method, the first specimen is subjected to a stress corresponding to
the expected average fatigue strength. If the specimen survives 107 cycles, it is discarded
and the next specimen is subjected to a stress that is one increment above the previous, i.e.
a survivor is always followed by the next using a stress one increment above the previous.
The increment should be selected to correspond to the expected level of the standard
deviation.
When a specimen fails prior to reaching 107 cycles, the obtained number of cycles is noted
and the next specimen is subjected to a stress that is one increment below the previous. With
this approach, the sum of failures and run-outs is equal to the number of specimens.
This original staircase method is only suitable when a high number of specimens areavailable. Through simulations it has been found that the use of about 25 specimens in astaircase test leads to a sufficient accuracy in the result.
2.3. Modified staircase method
When a limited number of specimens are available, it is advisable to apply the modified
staircase method. Here the first specimen is subjected to a stress level that is most likely well
below the average fatigue strength. When this specimen has survived 107 cycles, this same
specimen is subjected to a stress level one increment above the previous. The increment
should be selected to correspond to the expected level of the standard deviation. This iscontinued with the same specimen until failure.
Then the number of cycles is recorded and the next specimen is subjected to a stress that is
at least 2 increments below the level where the previous specimen failed.
With this approach, the number of failures usually equals the number of specimens.
The number of run-outs, counted as the highest level where 107 cycles were reached, also
equals the number of specimens.
The acquired result of a modified staircase method should be used with care, since someresults available indicate that testing a runout on a higher test level, especially at high meanstresses, tends to increase the fatigue limit. However, this “training effect” is less pronounced
for high strength steels (e.g. UTS > 800 MPa).
If the confidence calculation is desired or necessary, the minimum number of test specimens
is 3.
2.4. Calculation of sample mean and standard deviation
A hypothetical example of tests for 5 crank throws is presented further in the subsequent text.
When using the modified staircase method and the evaluation method of Dixon and Mood,the number of samples will be 10, meaning 5 run-outs and 5 failures, i.e.:
Number of samples,

n=10

Furthermore, the method distinguishes between
Less frequent event is failures
Less frequent event is run-outs

C=1
C=2

The method uses only the less frequent occurrence in the test results, i.e. if there are more
failures than run-outs, then the number of run-outs is used, and vice versa.
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M53
(cont)In the modified staircase method, the number of run-outs and failures are usually equal.
However, the testing can be unsuccessful, e.g. the number of run-outs can be less than thenumber of failures if a specimen with 2 increments below the previous failure level goes
directly to failure. On the other hand, if this unexpected premature failure occurs after a rather
high number of cycles, it is possible to define the level below this as a run-out.
Dixon and Mood’s approach, derived from the maximum likelihood theory, which also may be
applied here, especially on tests with few samples, presented some simple approximate
equations for calculating the sample mean and the standard deviation from the outcome ofthe staircase test. The sample mean can be calculated as follows:when C=1

when C=2

The standard deviation can be found by

where:
Sa0 is the lowest stress level for the less frequent occurrenced is the stress increment
F = Σ fiA = Σ i·fi
B = Σ i2·fi
i is the stress level numberingfi is the number of samples at stress level iPage 40 of 69

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The formula for the standard deviation is an approximation and can be used when(cont)

andIf any of these two conditions are not fulfilled, a new staircase test should be considered or
the standard deviation should be taken quite large in order to be on the safe side.
If increment d is greatly higher than the standard deviation s, the procedure leads to a lower
standard deviation and a slightly higher sample mean, both compared to values calculated
when the difference between the increment and the standard deviation is relatively small.
Respectively, if increment d is much less than the standard deviation s, the procedure leads
to a higher standard deviation and a slightly lower sample mean.
2.5. Confidence interval for mean fatigue limit
If the staircase fatigue test is repeated, the sample mean and the standard deviation will most
likely be different from the previous test. Therefore, it is necessary to assure with a given
confidence that the repeated test values will be above the chosen fatigue limit by using a
confidence interval for the sample mean.
The confidence interval for the sample mean value with unknown variance is known to be
distributed according to the t-distribution (also called student’s t-distribution) which is a
distribution symmetric around the average.

Figure 2.1. Student’s t-distribution

The confidence level normally used for the
sample mean is 90 %, meaning that 90 % ofsample means from repeated tests will be
above the value calculated with the chosenconfidence level. The figure shows the tvalue for (1 - α) · 100% confidence interval
for the sample mean.

If Sa is the empirical mean and s is the empirical standard deviation over a series of nsamples, in which the variable values are normally distributed with an unknown sample mean
and unknown variance, the (1 - α) · 100% confidence interval for the mean is:Page 41 of 69

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(cont)The resulting confidence interval is symmetric around the empirical mean of the sample
values, and the lower endpoint can be found as:

which is the mean fatigue limit (population value) to be used to obtain the reduced fatigue
limit where the limits for the probability of failure are taken into consideration.
2.6. Confidence interval for standard deviation
The confidence interval for the variance of a normal random variable is known to possess achi-square distribution with n - 1 degrees of freedom.
The confidence level on the standard deviation isused to ensure that the standard deviations for
repeated tests are below an upper limit obtained
from the fatigue test standard deviation with aconfidence level. The figure shows the chisquare for (1 - α) · 100% confidence interval forthe variance.
Figure 2.2. Chi-square distribution
An assumed fatigue test value from n samples is a normal random variable with a variance ofσ2 and has an empirical variance s2. Then a (1 - α) · 100% confidence interval for thevariance is:

A (1 – α) · 100% confidence interval for the standard deviation is obtained by the square rootof the upper limit of the confidence interval for the variance and can be found byThis standard deviation (population value) is to be used to obtain the fatigue limit, where thelimits for the probability of failure are taken into consideration.

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(cont)

3. Small specimen testing
In this connection, a small specimen is considered to be one of the specimens taken from acrank throw. Since the specimens shall be representative for the fillet fatigue strength, theyshould be taken out close to the fillets, as shown in Figure 3.1.
It should be made certain that the principal stress direction in the specimen testing isequivalent to the full-size crank throw. The verification is recommended to be done by utilising
the finite element method.

Figure 3.1. Specimen locations in a crank throw
The (static) mechanical properties are to be determined as stipulated by the quality control
procedures.
3.1. Determination of bending fatigue strength
It is advisable to use un-notched specimens in order to avoid uncertainties related to thestress gradient influence. Push-pull testing method (stress ratio R = -1) is preferred, but
especially for the purpose of critical plane criteria other stress ratios and methods may be
added.
In order to ensure principal stress direction in push-pull testing to represent the full-size crankthrow principal stress direction and when no further information is available, the specimen
shall be taken in 45 degrees angle as shown in Figure 3.1.
A.

If the objective of the testing is to document the influence of high cleanliness, test
samples taken from positions approximately 120 degrees in a circumferential direction
may be used. See Figure 3.1.

B.

If the objective of the testing is to document the influence of continuous grain flow (cgf)forging, the specimens should be restricted to the vicinity of the crank plane.

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(cont)

3.2. Determination of torsional fatigue strengthA.

If the specimens are subjected to torsional testing, the selection of samples should
follow the same guidelines as for bending above. The stress gradient influence has tobe considered in the evaluation.

B.

If the specimens are tested in push-pull and no further information is available, thesamples should be taken out at an angle of 45 degrees to the crank plane in order toensure collinearity of the principal stress direction between the specimen and the fullsize crank throw. When taking the specimen at a distance from the (crank) middle planeof the crankshaft along the fillet, this plane rotates around the pin centre point making it
possible to resample the fracture direction due to torsion (the results are to beconverted into the pertinent torsional values).

3.3. Other test positions
If the test purpose is to find fatigue properties and the crankshaft is forged in a manner likely
to lead to cgf, the specimens may also be taken longitudinally from a prolonged shaft piece
where specimens for mechanical testing are usually taken. The condition is that thisprolonged shaft piece is heat treated as a part of the crankshaft and that the size is so as toresult in a similar quenching rate as the crank throw.
When using test results from a prolonged shaft piece, it must be considered how well thegrain flow in that shaft piece is representative for the crank fillets.
3.4. Correlation of test results
The fatigue strength achieved by specimen testing shall be converted to correspond to thefull-size crankshaft fatigue strength with an appropriate method (size effect).
When using the bending fatigue properties from tests mentioned in this section, it should be
kept in mind that successful continuous grain flow (cgf) forging leading to elevated values
compared to other (non cgf) forging, will normally not lead to a torsional fatigue strength
improvement of the same magnitude.
In such cases it is advised to either carry out also torsional testing or to make a conservative
assessment of the torsional fatigue strength, e.g. by using no credit for cgf. This approach isapplicable when using the Gough Pollard criterion. However, this approach is not recognised
when using the von Mises or a multi-axial criterion such as Findley.
If the found ratio between bending and torsion fatigue differs significantly from √3, one should
consider replacing the use of the von Mises criterion with the Gough Pollard criterion. Also, if
critical plane criteria are used, it must be kept in mind that cgf makes the material
inhomogeneous in terms of fatigue strength, meaning that the material parameters differ withthe directions of the planes.
Any addition of influence factors must be made with caution. If for example a certain addition
for clean steel is documented, it may not necessarily be fully combined with a K-factor for cgf.
Direct testing of samples from a clean and cgf forged crank is preferred.

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(cont)

4. Full size testing
4.1. Hydraulic pulsation
A hydraulic test rig can be arranged for testing a crankshaft in 3-point or 4-point bending aswell as in torsion. This allows for testing with any R-ratio.
Although the applied load should be verified by strain gauge measurements on plain shaft
sections for the initiation of the test, it is not necessarily used during the test for controlling
load. It is also pertinent to check fillet stresses with strain gauge chains.
Furthermore, it is important that the test rig provides boundary conditions as defined inAppendix III (section 3.1 to 3.3).
The (static) mechanical properties are to be determined as stipulated by the quality control
procedures.
4.2. Resonance tester
A rig for bending fatigue normally works with an R-ratio of -1. Due to operation close toresonance, the energy consumption is moderate. Moreover, the frequency is usually relatively
high, meaning that 107 cycles can be reached within some days. Figure 4.1 shows a layout of
the testing arrangement.
The applied load should be verified by strain gauge measurements on plain shaft sections. It
is also pertinent to check fillet stresses with strain gauge chains.

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Figure 4.1. An example of testing arrangement of the resonance tester for bending loading
Clamping around the journals must be arranged in a way that prevents severe fretting which
could lead to a failure under the edges of the clamps. If some distance between the clamps
and the journal fillets is provided, the loading is consistent with 4-point bending and thus
representative for the journal fillets also.
In an engine, the crankpin fillets normally operate with an R-ratio slightly above -1 and thejournal fillets slightly below -1. If found necessary, it is possible to introduce a mean load
(deviate from R = -1) by means of a spring preload.
A rig for torsion fatigue can also be arranged as shown in Figure 4.2. When a crank throw issubjected to torsion, the twist of the crankpin makes the journals move sideways. If one
single crank throw is tested in a torsion resonance test rig, the journals with their clamped-on
weights will vibrate heavily sideways.
This sideway movement of the clamped-on weights can be reduced by having two crankthrows, especially if the cranks are almost in the same direction. However, the journal in the
middle will move more.

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Figure 4.2. An example of testing arrangement of the resonance tester for torsion loading withdouble crank throw section
Since sideway movements can cause some bending stresses, the plain portions of the
crankpins should also be provided with strain gauges arranged to measure any possible
bending that could have an influence on the test results.
Similarly, to the bending case the applied load shall be verified by strain gaugemeasurements on plain shaft sections. It is also pertinent to check fillet stresses with strain
gauge chains as well.
4.3. Use of results and crankshaft acceptability
In order to combine tested bending and torsion fatigue strength results in calculation of
crankshaft acceptability (see M53.7), the Gough-Pollard approach and the maximum principal
equivalent stress formulation can be applied for the following cases:
Related to At the crankpin diameter fillet:−1

𝜎𝜎𝐵𝐵𝐵𝐵 + 𝜎𝜎𝑎𝑎𝑎𝑎𝑎𝑎 2
𝜏𝜏𝐻𝐻 2
𝑄𝑄 = ���
� +�� �𝜎𝜎𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
𝜏𝜏𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷

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(cont)

where:

σDWCT
τDWCT

fatigue strength by bending testing
fatigue strength by torsion testingfor other parameters see items M53.2.1.3, M53.2.2.3 and M53.4
Related to crankpin oil bore:

where:σDWOT

fatigue strength by means of largest principal stress from torsion testing

Related to At the journal diameter fillet:
2

2

𝜏𝜏𝐺𝐺
𝜎𝜎𝐵𝐵𝐵𝐵 + 𝜎𝜎𝑎𝑎𝑎𝑎𝑎𝑎
𝑄𝑄 = ���
� +�� �𝜎𝜎𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
𝜏𝜏𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷−1

where:

σDWJT
τDWJT

fatigue strength by bending testing
fatigue strength by torsion testingfor other parameters see items M53.2.1.3, M53.2.2.3 and M53.4
In case increase in fatigue strength due to the surface treatment is considered to be similar
between the above cases, it is sufficient to test only the most critical location according to thecalculation where the surface treatment had not been taken into account.
5. Use of existing results for similar crankshafts
For fillets or oil bores without surface treatment, the fatigue properties found by testing may
be used for similar crankshaft designs providing:•Material:• Similar material type
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• Cleanliness on the same or better level• The same mechanical properties can be granted (size versus hardenability)

M53(cont)•

Geometry:• Difference in the size effect of stress gradient is insignificant or it is considered• Principal stress direction is equivalent. See Chapter 3.

•

Manufacturing:• Similar manufacturing process

Induction hardened or gas nitrited crankshafts will suffer fatigue either at the surface or at thetransition to the core. The surface fatigue strength as determined by fatigue tests of full size
cranks, may be used on an equal or similar design as the tested crankshaft when the fatigue
initiation occurred at the surface. With the similar design, it is meant that a similar material
type and surface hardness are used and the fillet radius and hardening depth are withinapproximately ± 30 % of the tested crankshaft.
Fatigue initiation in the transition zone can be either subsurface, i.e. below the hard layer, orat the surface where the hardening ends. The fatigue strength at the transition to the core canbe determined by fatigue tests as described above, provided that the fatigue initiation
occurred at the transition to the core. Tests made with the core material only will not be
representative since the tension residual stresses at the transition are lacking.
It has to be noted also what some recent research has shown: The fatigue limit can decreasein the very high cycle domain with subsurface crack initiation due to trapped hydrogen that
accumulates through diffusion around some internal defect functioning as an initiation point.
In these cases, it would be appropriate to reduce the fatigue limit by some percent per
decade of cycles beyond 107. Based on a publication by Yukitaka Murakami “Metal Fatigue:
Effects of Small Defects and Non-metallic Inclusions” the reduction is suggested to be 5 %per decade especially when the hydrogen content is considered to be high.

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(cont)

Appendix V

Guidance for Calculation of Surface Treated Fillets and Oil Bore
Outlets
Contents
1. Introduction
2. Definition of surface treatment
2.1. Surface treatment methods
3. Calculation principles
3.1. Evaluation of local fillet stresses
3.2. Evaluation of oil bore stresses
3.3. Acceptability criteria
4. Induction hardening
4.1. Local fatigue strength
5. Nitriding
5.1. Local fatigue strength
6. Cold forming
6.1. Stroke peening by means of a ball
6.1.1. Use of existing results for similar crankshafts
6.2. Cold rolling
6.2.1. Use of existing results for similar crankshafts

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1. Introduction
This appendix deals with surface treated fillets and oil bore outlets. The various treatments
are explained and some empirical formulae are given for calculation purposes. Conservative
empiricism has been applied intentionally, in order to be on the safe side from a calculation
standpoint.
Please note that measurements or more specific knowledge should be used if available.
However, in the case of a wide scatter (e.g. for residual stresses) the values should bechosen from the end of the range that would be on the safe side for calculation purposes.
2. Definition of surface treatment‘Surface treatment’ is a term covering treatments such as thermal, chemical or mechanicaloperations, leading to inhomogeneous material properties – such as hardness, chemistry or
residual stresses – from the surface to the core.
2.1. Surface treatment methods
The following list covers possible treatment methods and how they influence the properties
that are decisive for the fatigue strength.
Table 2.1. Surface treatment methods and the characteristics they affect.
Treatment method•Induction hardening•Nitriding•Case hardening•Die quenching (no temper)•Cold rolling•Stroke peening•Shot peening•Laser peening•Ball coining

Affecting
Hardness and residual stresses
Chemistry, hardness and residual stresses
Chemistry, hardness and residual stresses
Hardness and residual stresses
Residual stresses
Residual stresses
Residual stresses
Residual stresses
Residual stresses

It is important to note that since only induction hardening, nitriding, cold rolling and stroke
peening are considered relevant for marine engines, other methods as well as combination of
two or more of the above are not dealt with in this document. In addition, die quenching canbe considered in the same way as induction hardening.
3. Calculation principles
The basic principle is that the alternating working stresses shall be below the local fatigue
strength (including the effect of surface treatment) wherein non-propagating cracks may
occur, see also section 6.1 for details. This is then divided by a certain safety factor. Thisapplies through the entire fillet or oil bore contour as well as below the surface to a depth
below the treatment-affected zone – i.e. to cover the depth all the way to the core.
Consideration of the local fatigue strength shall include the influence of the local hardness,
residual stress and mean working stress. The influence of the ‘giga-cycle effect’, especiallyfor initiation of subsurface cracks, should be covered by the choice of safety margin.

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It is of vital importance that the extension of hardening/peening in an area with concentrated
stresses be duly considered. Any transition where the hardening/peening is ended is likely tohave considerable tensile residual stresses.
This forms a ‘weak spot’ and is important if it coincides with an area of high stresses.
Alternating and mean working stresses must be known for the entire area of the stressconcentration as well as to a depth of about 1.2 times the depth of the treatment. The
following figure indicates this principle in the case of induction hardening. The base axis iseither the depth (perpendicular to the surface) or along the fillet contour.

Figure 3.1. Stresses as functions of depth, general principles
The acceptability criterion should be applied stepwise from the surface to the core as well asfrom the point of maximum stress concentration along the fillet surface contour to the web.
3.1. Evaluation of local fillet stresses
It is necessary to have knowledge of the stresses along the fillet contour as well as in thesubsurface to a depth somewhat beyond the hardened layer. Normally this will be found via
FEA as described in Appendix III. However, the element size in the subsurface range will
have to be the same size as at the surface. For crankpin hardening only the small element
size will have to be continued along the surface to the hard layer.
If no FEA is available, a simplified approach may be used. This can be based on theempirically determined stress concentration factors (SCFs), as in M53.3 if within its validity
range, and a relative stress gradient inversely proportional to the fillet radius.
Bending and torsional stresses must be addressed separately. The combination of these isaddressed by the acceptability criterion.
The subsurface transition-zone stresses, with the minimum hardening depth, can be
determined by means of local stress concentration factors along an axis perpendicular to thefillet surface. These functions αB-local and αT-local have different shapes due to the different
stress gradients.
The SCFs αB and αT are valid at the surface. The local αB-local and αT-local drop with increasing
depth. The relative stress gradients at the surface depend on the kind of stress raiser, but forPage 52 of 69

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crankpin fillets they can be simplified to 2/RH in bending and 1/RH in torsion. The journal fillets
are handled analogously by using RG and DG. The nominal stresses are assumed to be linear
from the surface to a midpoint in the web between the crankpin fillet and the journal fillet forbending and to the crankpin or journal centre for torsion.
The local SCFs are then functions of depth t according to Equation 3.1 as shown in Figure
3.2 for bending and respectively for torsion in Equation 3.2 and Figure 3.3.

(3.1)

(3.2)

Figure 3.2. Bending SCF in the crankpin fillet as a function of depth. The corresponding SCF
for the journal fillet can be found by replacing RH with RG

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Figure 3.3. Torsional SCF in the crankpin fillet as a function of depth. The corresponding SCF
for the journal fillet can be found by replacing RH with RG and D with DG
If the pin is hardened only and the end of the hardened zone is closer to the fillet than threetimes the maximum hardness depth, FEA should be used to determine the actual stresses inthe transition zone.
3.2. Evaluation of oil bore stresses
Stresses in the oil bores can be determined also by FEA. The element size should be lessthan 1/8 of the oil bore diameter Do and the element mesh quality criteria should be followed
as prescribed in Appendix III. The fine element mesh should continue well beyond a radial
depth corresponding to the hardening depth.
The loads to be applied in the FEA are the torque – see Appendix III item 3.1 – and thebending moment, with four-point bending as in Appendix III item 3.2.
If no FEA is available, a simplified approach may be used. This can be based on theempirically determined SCF from M53.3 if within its applicability range. Bending and torsional
stresses at the point of peak stresses are combined as in M53.5.

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Figure 3.4. Stresses and hardness in induction hardened oil holes
Figure 3.4 indicates a local drop of the hardness in the transition zone between a hard andsoft material. Whether this drop occurs depends also on the tempering temperature after
quenching in the QT process.
The peak stress in the bore occurs at the end of the edge rounding. Within this zone thestress drops almost linearly to the centre of the pin. As can be seen from Figure 3.4, forshallow (A) and intermediate (B) hardening, the transition point practically coincides with thepoint of maximal stresses. For deep hardening the transition point comes outside of the pointof peak stress and the local stress can be assessed as a portion (1-2tH/D) of the peakstresses where tH is the hardening depth.
The subsurface transition-zone stresses (using the minimum hardening depth) can be
determined by means of local stress concentration factors along an axis perpendicular to theoil bore surface. These functions γB-local and γT-local have different shapes, because of thedifferent stress gradients.
The stress concentration factors γB and γT are valid at the surface. The local SCFs γB-local and
γT-local drop with increasing depth. The relative stress gradients at the surface depend on thekind of stress raiser, but for crankpin oil bores they can be simplified to 4/Do in bending and2/Do in torsion. The local SCFs are then functions of the depth t:

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(3.3)

(cont)(3.4)

3.3. Acceptability criteria
Acceptance of crankshafts is based on fatigue considerations; M53 compares the equivalentalternating stress and the fatigue strength ratio to an acceptability factor of Q ≥ 1.15 for oilbore outlets, crankpin fillets and journal fillets. This shall be extended to cover also surface
treated areas independent of whether surface or transition zone is examined.
4. Induction hardening
Generally, the hardness specification shall specify the surface hardness range i.e. minimum
and maximum values, the minimum and maximum extension in or through the fillet and also
the minimum and maximum depth along the fillet contour. The referenced Vickers hardness is
considered to be HV0.5...HV5.
The induction hardening depth is defined as the depth where the hardness is 80% of theminimum specified surface hardness.

Figure 4.1. Typical hardness as a function of depth. The arrows indicate the defined
hardening depth. Note the indicated potential hardness drop at the transition to the core. Thiscan be a weak point as local strength may be reduced and tensile residual stresses may
occur.
In the case of crankpin or journal hardening only, the minimum distance to the fillet shall be
specified due to the tensile stress at the heat-affected zone as shown in Figure 4.2.

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Figure 4.2. Residual stresses along the surface of a pin and fillet
If the hardness-versus-depth profile and residual stresses are not known or specified,
one may assume the following:•

The hardness profile consists of two layers (see figure 4.1):••

Constant hardness from the surface to the transition zone
Constant hardness from the transition zone to the core material•

Residual stresses in the hard zone of 200 MPa (compression)•

Transition-zone hardness as 90% of the core hardness unless the local hardness drop
is avoided•

Transition-zone maximum residual stresses (von Mises) of 300 MPa tension

If the crankpin or journal hardening ends close to the fillet, the influence of tensile residual
stresses has to be considered. If the minimum distance between the end of the hardening
and the beginning of the fillet is more than 3 times the maximum hardening depth, theinfluence may be disregarded.
4.1. Local fatigue strength
Induction-hardened crankshafts will suffer fatigue either at the surface or at the transition to
the core. The fatigue strengths, for both the surface and the transition zone, can be
determined by fatigue testing of full size cranks as described in Appendix IV. In the case of atransition zone, the initiation of the fatigue can be either subsurface (i.e. below the hard layer)
or at the surface where the hardening ends.
Tests made with the core material only will not be representative since the tensile residual
stresses at the transition are lacking.
Alternatively, the surface fatigue strength can be determined empirically as follows where HVis the surface Vickers hardness. The Equation 4.1 provides a conservative value, with which
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the fatigue strength is assumed to include the influence of the residual stress. The resulting
value is valid for a working stress ratio of R = -1:(4.1)
It has to be noted also that the mean stress influence of induction-hardened steels may besignificantly higher than that for QT steels.
The fatigue strength in the transition zone, without taking into account any possible local
hardness drop, shall be determined by the equation introduced in UR M53.6.
For journal and respectively to crankpin fillet applies:(4.2)
where:
Y = DGY = D
Y = D

and X = RG
and X = RH
and X = Do/2

for journal fillet
for crankpin fillet
for oil bore outlet

The influence of the residual stress is not included in 4.2.
For the purpose of considering subsurface fatigue, below the hard layer, the disadvantage oftensile residual stresses has to be considered by subtracting 20% from the value determined
above. This 20% is based on the mean stress influence of alloyed quenched and tempered
steel having a residual tensile stress of 300 MPa.
When the residual stresses are known to be lower, also smaller value of subtraction shall be
used. For low-strength steels the percentage chosen should be higher.
For the purpose of considering surface fatigue near the end of the hardened zone – i.e. in theheat-affected zone shown in the Figure 4.2 – the influence of the tensile residual stresses canbe considered by subtracting a certain percentage, in accordance with Table 4.1, from thevalue determined by the above formula.
Table 4.1. The influence of tensile residual stresses at a given distance from the end of thehardening towards the fillet
I.
II.
III.
IV.

0 to 1.0 of the max. hardening depth:
1.0 to 2.0 of the max. hardening depth:
2.0 to 3.0 of the max. hardening depth:
3.0 or more of the max. hardening depth:

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20%
12%
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5. Nitriding
The hardness specification shall include the surface hardness range (min and max) and theminimum and maximum depth. Only gas nitriding is considered. The referenced Vickers
hardness is considered to be HV0.5.
The depth of the hardening is defined in different ways in the various standards and theliterature. The most practical method to use in this context is to define the nitriding depth tN
as the depth to a hardness of 50 HV above the core hardness.
The hardening profile should be specified all the way to the core. If this is not known, it may
be determined empirically via the following formula:(5.1)

where:t=
HV(t)=HVcore=
HVsurface =tN=

The local depth
Hardness at depth t
Core hardness (minimum)
Surface hardness (minimum)
Nitriding depth as defined above (minimum)

5.1. Local fatigue strength
It is important to note that in nitrided crankshaft cases, fatigue is found either at the surface orat the transition to the core. This means that the fatigue strength can be determined by tests
as described in Appendix IV.
Alternatively, the surface fatigue strength (principal stress) can be determined empirically andconservatively as follows. This is valid for a surface hardness of 600 HV or greater:(5.2)
Note that this fatigue strength is assumed to include the influence of the surface residual
stress and applies for a working stress ratio of R = -1.
The fatigue strength in the transition zone can be determined by the equation introduced in
UR M53.6. For crankpin and respectively to journal applies:(5.3)

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where:
Y = DGY = D
Y = D

and X = RG
and X = RH
and X = Do/2

for journal fillet
for crankpin fillet
for oil bore outlet

Note that this fatigue strength is not assumed to include the influence of the residual
stresses.
In contrast to induction-hardening the nitrited components have no such distinct transition to
the core. Although the compressive residual stresses at the surface are high, the balancing
tensile stresses in the core are moderate because of the shallow depth. For the purpose ofanalysis of subsurface fatigue the disadvantage of tensile residual stresses in and below thetransition zone may be even disregarded in view of this smooth contour of a nitriding
hardness profile.
Although in principle the calculation should be carried out along the entire hardness profile, it
can be limited to a simplified approach of examining the surface and an artificial transition
point. This artificial transition point can be taken at the depth where the local hardness isapproximately 20 HV above the core hardness. In such a case, the properties of the corematerial should be used. This means that the stresses at the transition to the core can befound by using the local SCF formulae mentioned earlier when inserting t=1.2tN.

Figure 5.1. Sketch of the location for the artificial transition point in the depth direction
6. Cold forming
The advantage of stroke peening or cold rolling of fillets is the compressive residual stresses
introduced in the high-loaded area. Even though surface residual stresses can be determinedby X-ray diffraction technique and subsurface residual stresses can be determined throughneutron diffraction, the local fatigue strength is virtually non-assessable on that basis since
suitable and reliable correlation formulae are hardly known.
Therefore, the fatigue strength has to be determined by fatigue testing; see also Appendix IV.
Such testing is normally carried out as four-point bending, with a working stress ratio of
R = -1. From these results, the bending fatigue strength – surface- or subsurface-initiateddepending on the manner of failure – can be determined and expressed as the representative
fatigue strength for applied bending in the fillet.

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In comparison to bending, the torsion fatigue strength in the fillet may differ considerably fromthe ratio √3 (utilized by the von Mises criterion). The forming-affected depth that is sufficient
to prevent subsurface fatigue in bending, may still allow subsurface fatigue in torsion. Anotherpossible reason for the difference in bending and torsion could be the extension of the highly
stressed area.
The results obtained in a full-size crank test can be applied for another crank size provided
that the base material (alloyed Q+T) is of the similar type and that the forming is done so as
to obtain the similar level of compressive residual stresses at the surface as well as throughthe depth. This means that both the extension and the depth of the cold forming must be
proportional to the fillet radius.
6.1. Stroke peening by means of a ball
The fatigue strength obtained can be documented by means of full size crank tests or byempirical methods if applied on the safe side. If both bending and torsion fatigue strengths
have been investigated and differ from the ratio √3, the von Mises criterion should be
excluded.

If only bending fatigue strength has been investigated, the torsional fatigue strength should
be assessed conservatively. If the bending fatigue strength is concluded to be x% above thefatigue strength of the non-peened material, the torsional fatigue strength should not beassumed to be more than 2/3 of x% above that of the non-peened material.

As a result of the stroke peening process the maximum of the compressive residual stress isfound in the subsurface area. Therefore, depending on the fatigue testing load and the stressgradient, it is possible to have higher working stresses at the surface in comparison to the
local fatigue strength of the surface. Because of this phenomenon small cracks may appear
during the fatigue testing, which will not be able to propagate in further load cycles and/orwith further slight increases of the testing load because of the profile of the compressive
residual stress. Put simply, the high compressive residual stresses below the surface ‘arrest’small surface cracks.
This is illustrated in Figure 6.1 as gradient load 2.

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Figure 6.1. Working and residual stresses below the stroke-peened surface.
Straight lines 1…3 represent different possible load stress gradients.
In fatigue testing with full-size crankshafts these small “hairline cracks” should not be
considered to be the failure crack. The crack that is technically the fatigue crack leading to
failure, and that therefore shuts off the test-bench, should be considered for determination of
the failure load level. This also applies if induction-hardened fillets are stroke-peened.
In order to improve the fatigue strength of induction-hardened fillets it is possible to apply thestroke peening process in the crankshafts’ fillets after they have been induction-hardened andtempered to the required surface hardness. If this is done, it might be necessary to adapt thestroke peening force to the hardness of the surface layer and not to the tensile strength of thebase material. The effect on the fatigue strength of induction hardening and stroke peening
the fillets shall be determined by a full-size crankshaft test.
6.1.1. Use of existing results for similar crankshafts
The increase in fatigue strength, which is achieved by applying stroke peening, may beutilized in another similar crankshaft if all of the following criteria are fulfilled:•

Ball size relative to fillet radius within ±10% in comparison to the tested crankshaft•

At least the same circumferential extension of the stroke peening

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•

Angular extension of the fillet contour relative to fillet radius within ±15% in comparison
to the tested crankshaft and located to cover the stress concentration during engine
operation•

Similar base material, e.g. alloyed quenched and tempered•

Forward feed of ball of the same proportion of the radius•

Force applied to ball proportional to base material hardness (if different)•

Force applied to ball proportional to square of ball radius(cont)

6.2. Cold rolling
The fatigue strength can be obtained by means of full size crank tests or by empiricalmethods, if these are applied so as to be on the safe side. If both, bending and torsion fatigue
strengths have been investigated, and differ from the ratio √3, the von Mises criterion should
be excluded.
If only bending fatigue strength has been investigated, the torsional fatigue strength should
be assessed conservatively. If the bending fatigue strength is concluded to be x% above thefatigue strength of the non-rolled material, the torsional fatigue strength should not beassumed to be more than 2/3 of x% above that of the non-rolled material.
6.2.1. Use of existing results for similar crankshafts
The increase in fatigue strength, which is achieved applying cold rolling, may be utilized inanother similar crankshaft if all of the following criteria are fulfilled:•

At least the same circumferential extension of cold rolling•

Angular extension of the fillet contour relative to fillet radius within ±15% in comparison
to the tested crankshaft and located to cover the stress concentration during engine
operation•

Similar base material, e.g. alloyed quenched and tempered•

Roller force to be calculated so as to achieve at least the same relative (to fillet radius)
depth of treatment

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Appendix VI

Guidance for Calculation of Stress Concentration Factors in the Oil
Bore Outlets of crankshafts through utilisation of the Finite Element
MethodContents
1. General
2. Model requirements
2.1. Element mesh recommendations
2.2. Material
2.3. Element mesh quality criteria
2.3.1. Principal stresses criterion
2.3.2. Averaged/unaveraged stresses criterion
3. Load cases and assessment of stress3.1. Torsion
3.2. Bending

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1. General
The objective of the analysis described in this document is to substitute the analytical
calculation of the stress concentration factor (SCF) at the oil bore outlet with suitable finite
element method (FEM) calculated figures. The former method is based on empirical formulaedeveloped from strain gauge readings or photo-elasticity measurements of various roundbars. Because use of these formulae beyond any of the validity ranges can lead to erroneous
results in either direction, the FEM-based method is highly recommended.
The SCF calculated according to the rules set forth in this document is defined as the ratio of
FEM-calculated stresses to nominal stresses calculated analytically. In use in connection withthe present method in UR M53, principal stresses shall be calculated.
The analysis is to be conducted as linear elastic FE analysis, and unit loads of appropriatemagnitude are to be applied for all load cases.
It is advisable to check the element accuracy of the FE solver in use, e.g. by modelling asimple geometry and comparing the FEM-obtained stresses with the analytical solution.
A boundary element method (BEM) approach may be used instead of FEM.
2. Model requirements
The basic recommendations and assumptions for building of the FE-model are presented in
Subsection 2.1. The final FE-model must meet one of the criteria in Subsection 2.3.
2.1. Element mesh recommendations
For the mesh quality criteria to be met, construction of the FE model for the evaluation ofstress concentration factors according to the following recommendations is advised:•

The model consists of one complete crank, from the main bearing centre line to the
opposite side‘s main bearing centre line.

•

The following element types are used in the vicinity of the outlets:
•
•
•

•

10-node tetrahedral elements
8-node hexahedral elements
20-node hexahedral elements

The following mesh properties for the oil bore outlet are used:•

Maximum element size a = r / 4 through the entire outlet fillet as well as in thebore direction (if 8-node hexahedral elements are used, even smaller elements
are required for meeting of the quality criterion)•

Recommended manner for element size in the fillet depth direction•••

First layer’s thickness equal to element size of aSecond layer’s thickness equal to element size of 2a
Third -layer thickness equal to element size of 3a•

In general, the rest of the crank should be suitable for numeric stability of the solver•

Drillings and holes for weight reduction have to be modelled
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Submodeling may be used as long as the software requirements are fulfilled.
2.2. Material
UR M53 does not consider material properties such as Young’s modulus (E) and Poisson’s
ratio (ν). In the FE analysis, these material parameters are required, as primarily strain is
calculated and stress is derived from strain through the use of Young’s modulus andPoisson’s ratio. Reliable values for material parameters have to be used, either as quoted in
the literature or measured from representative material samples.
For steel the following is advised: E = 2.05·105 MPa and ν = 0.3.
2.3. Element mesh quality criteria
If the actual element mesh does not fulfil any of the following criteria in the area examined for
SCF evaluation, a second calculation, with a finer mesh is to be performed.
2.3.1. Principal -stresses criterion
The quality of the mesh should be assured through checking of the stress component normal
to the surface of the oil bore outlet radius. With principal stresses σ1, σ2 and σ3 the following
criterion must be met:

2.3.2. Averaged/unaveraged -stresses criterion
The averaged/unaveraged –stresses criterion is based on observation of the discontinuity ofstress results over elements at the fillet for the calculation of the SCF:•

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

3. Load cases and assessment of stress
For substitution of the analytically determined SCF in UR M53, calculation shall be performed
for the following load cases.
3.1. Torsion
The structure is loaded in pure torsion. The surface warp at the end faces of the model issuppressed.
Torque is applied to the central node, on the crankshaft axis. This node acts as the masternode with six degrees of freedom, and is connected rigidly to all nodes of the end face.
The boundary and load conditions are valid for both in-line- and V- type engines.

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Figure 3.1 Boundary and load conditions for the torsion load case
For all nodes in an oil bore outlet, the principal stresses are obtained and the maximum value
is taken for subsequent calculation of the SCF:

where the nominal torsion stress τN referred to the crankpin is evaluated per M53.2.2.2 withtorque T:

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3.2. Bending
The structure is loaded in pure bending. The surface warp at the end faces of the model issuppressed.
The bending moment is applied to the central node on the crankshaft axis. This node acts as
the master node, with six degrees of freedom, and is connected rigidly to all nodes of the end
face.
The boundary and load conditions are valid for both in-line- and V- type engines.

Figure 3.2. Boundary and load conditions for the pure bending load case

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(cont)For all nodes in the oil bore outlet, principal stresses are obtained and the maximum value istaken for subsequent calculation of the SCF:

where the nominal bending stress σN referred to the crankpin is calculated per M53.2.1.2.2
with bending moment M:

End ofDocument

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