INTERNAT IONAL COUNCIL
ON COMBUST ION ENGINESCONSEIL INTERNATIONAL
DES MACHINES A COMBUSTION

CO-ORDINATING WORKING GROUP"CLASSIFICATION SOCIETIES – DIESEL"(WG2)

Proposal by CIMAC WG4
ST-08-044

29.06.2009

IACS UR M53, Appendix III“Guidance for calculation ofStress Concentration Factors
in the web fillet radii of crankshafts by utilizing
Finite Element Method”

-2-Index
1.
2.

General................................................................................................................ 3
Model requirements............................................................................................. 3
2.1. Element mesh recommendations..................................................................... 32.2. Material ............................................................................................................ 42.3. Element mesh quality criteria ........................................................................... 42.3.1. Principal stresses criterion......................................................................... 52.3.2. Averaged/unaveraged stresses criterion ................................................... 5
3. Load cases .......................................................................................................... 53.1. Torsion ............................................................................................................. 5
3.2. Pure bending (4 point bending)........................................................................ 73.3. Bending with shear force (3 point bending)...................................................... 83.3.1. Method 1.................................................................................................. 10
3.3.2. Method 2.................................................................................................. 10

-3-

1. General
The objective of the analysis is to substitute the analytically calculated Stress
Concentration Factors (SCF) at the crankshaft fillets by suitable Finite Element
Method (FEM) calculated figures. The analytical method is based on empiricalformulae developed from strain gauge measurements of various crank geometries.
Use of these formulae beyond any of the various validity ranges can lead toerroneous results in either direction, i.e. results that are more inaccurate thanindicated by the mentioned standard deviations. Therefore the FEM-based method ishighly recommended.
The SCF’s calculated according to the rules of this document are defined as the ratioof stresses calculated by FEM to nominal stresses in both journal and pin fillets.
When used in connection with the present method in M53 von Mises stresses shallbe calculated for bending and principal stresses for torsion or when alternative
methods are considered.
The procedure as well as evaluation guidelines are valid for both solid cranks andsemibuilt cranks (except journal fillets).
The analysis is to be conducted as linear elastic FE analysis, and unit loads ofappropriate magnitude are to be applied for all load cases.
The calculation of SCF at the oil bores is at present not covered by this document.
It is advised to check the element accuracy of the FE solver in use, e.g. by modellinga simple geometry and comparing the stresses obtained by FEM with the analyticalsolution for pure bending 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 arepresented in 2.1. It is obligatory for the final FE-model to fulfil 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:o The model consists of one complete crank, from the main bearing centreline tothe opposite side main bearing centreline.
o Element types used in the vicinity of the fillets:
10 node tetrahedral elements
8 node hexahedral elements
20 node hexahedral elementso Mesh properties in fillet radii. The following applies to ±90 degrees incircumferential direction from the crank plane:

-4-oooooo

Maximum element size a=r/4 through the entire fillet as well as in thecircumferential direction. When using 20 node hexahedral elements, theelement size in the circumferential direction may be extended up to 5a. In thecase 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 qualitycriteria.)
Recommended manner for element size in fillet depth direction
First layer thickness equal to element size of aSecond layer thickness equal to element to size of 2a
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 thesolver.
Counterweights only have to be modelled only when influencing the global
stiffness of the crank significantly.
Modelling 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 modelled.
Submodeling 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) andPoisson’s ratio ( ). In FE analysis those material parameters are required, as strain isprimarily calculated and stress is derived from strain using the Young’s Modulus andPoisson’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= 2.05·105 MPa

and=0.3.

2.3. Element mesh quality criteria
If the actual element mesh does not fulfil any of the following criteria at the examinedarea for SCF evaluation, then a second calculation with a refined mesh is to beperformed.

-5-

2.3.1. Principal stresses criterion
The quality of the mesh should be assured by checking the stress component normalto the surface of the fillet radius. Ideally, this stress should be zero. With principal
stresses 1, 2 and 3 the following criterion is required:
min

1,2,

3

0.03 max

1,2,3

2.3.2. Averaged/unaveraged stresses criterion
The criterion is based on observing the discontinuity of stress results over elements
at the fillet for the calculation of SCF:
Unaveraged nodal stress results calculated from each element connected to anodei should differ less than by 5 % from the 100 % averaged nodal stressresults at this nodei at the examined location.

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 thestructure is loaded pure torsion. In the model surface warp at the end faces issuppressed.
Torque is applied to the central node located at the crankshaft axis. This node acts
as the master node with 6 degrees of freedom and is connected rigidly to all nodes ofthe end face.
Boundary and load conditions are valid for both in-line and V-type engines.

-6-Multi-point constraint:
All nodes of crosssection are rigidly
connected to central
node (= master)

yxz

Load:
Torque T
applied tocentral node

BoundaryConditions:
DOFs for all
nodes arefully restrained
u x,y,z = 0

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 the equivalent torsional stress is calculated:

equiv

max

122,

232,

1

32The maximum value taken for the subsequent calculation of the SCF:
equiv ,TN
equiv ,

TN

where N is nominal torsional stress referred to the crankpin and respectively journal
as per UR M53 2.2.2 with the torsional torque T:

NTWP

-73.2. Pure bending (4 point bending)
In analogy to the testing apparatus used for the investigations made by FVV thestructure is loaded in pure bending. In the model surface warp at the end faces issuppressed.
The bending moment is applied to the central node located at the crankshaft axis.
This node acts as the master 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.

Multi-point constraint:
All nodes of crosssection are rigidly
connected to central
node (= master)

yxz

Load:
In-planebending by
moment M
applied at
central node

BoundaryConditions:
DOFs for all
nodes arefully restrained
u x,y,z = 0

Figure 3.2 Boundary and load conditions for the pure bending load case.
For all nodes in both the journal and pin fillet von Mises equivalent stresses
extracted. The maximum value is used to calculate the SCF according to:equiv ,

BN
equiv ,

BN

equiv are

-8Nominal stressN

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

MWeqw

3.3. Bending with shear force (3-point bending)This load case is calculated to determine the SCF for pure transverse force (radialforce, Q ) for the journal fillet.
In analogy to the testing apparatus used for the investigations made by FVV, thestructure is loaded in 3-point bending. In the model, surface warp at the both endfaces is suppressed. All nodes are connected rigidly to the centre node; boundaryconditions 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 theconnecting 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 be modelled with one connecting rod force only. Using two connecting rod forces
will make no significant change in the SCF.

-9-Load:
Force F3p appliedat central node atconnecting rod centreline.

yx

Boundary Conditions:
Displacement in z direction
for master node isrestrained, uz = 0;uy, ux and(axial,vertical displacements androtations are free)zMulti-point
constraint:
All nodes ofcross section
are connected
to a central
node (= master)BoundaryConditions:
Displacements formaster node are
fully restrained
ux,y,z = 0;(rotationsare free)

BoundaryConditions:
Displacements in yand z directions formaster node arerestrained
u y,z = 0.
ux,(axialdisplacement androtations are free)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.
The maximum equivalent von Mises stress 3P in the journal fillet is evaluated.
The SCF in the journal fillet can be determined in two ways as shown below.

-103.3.1. Method 1
This method is analogue to the FVV investigation. The results from 3-point and 4point bending are combined as follows:
3PN 3PBQ3P

Q

where:3P
N3P

B
Q3P

as found by the FE calculation.
Nominal bending stress in the web centre due to the force F3P [N]applied to the centre-line of the actual connecting rod, see figure 3.4.
as determined in paragraph 3.2.
= Q3P/(B·W) where Q3P is the radial (shear) force in the web due to theforce F3P [N] applied to the centre-line of the actual connecting rod, seealso figures 3 and 4 in M53.

3.3.2. Method 2This method is not analogous to the FVV investigation. In a statically determinedsystem with one crank throw supported by two bearings, the bending moment andradial (shear) force are proportional. Therefore the journal fillet SCF can be founddirectly by the 3-point bending FE calculation.
The SCF is then calculated according to3P
BQ
N 3P

For 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 isthen evaluated:
BG

BQ

BFN

Note that the use of this method does not apply to the crankpin fillet and that thisSCF must not be used in connection with calculation methods other than thoseassuming a statically determined system as in M53.