SIMPACK News | September 2010 | 27

Stefan Dietz, SIMPACK AG; Wolfgang Erhardt, SAFE-FEM GmbH | SoftwAre

fatigue Analyses with fAt4feM in SIMPACK's PostProcessor

Fig. 1: Normal stress in the x-direction (axial) of the crank shaft.

Fig. 2: FAT4FEM — GUI for defining material properties to be used in fatigue analysis

Since the release of SIMPACK version 8900 in 2007, the computation and graphical representation of compo-nent stresses has been available in the SIMPACK PostProcessor. with the forthcoming SIMPACK version 8904 this feature is expanded with the ability to perform fatigue analyses. these may be configured and started in the PostProc-essor. After the computation, the results and safety factors may be displayed in the PostProcessor as a contour plot. the fatigue analyses are performed by fAt4feM which is an easy-to-use and easy-to-learn fatigue tool that is based on the critical plane approach.

tHe eXAMPLe MoDeLThe FEM model of the crankshaft, which was generated for the stress calculation, was created in NX NASTRAN. The model has approximately 3 million degrees-of-freedom that, in the interest of computational time, must be reduced to a lower number of degrees-of-freedom for a multi-body simu-

28 | SIMPACK News | September 2010

SoftwAre | Stefan Dietz, SIMPACK AG; Wolfgang Erhardt, SAFE-FEM GmbH

lation. The crankshaft in SIMPACK is defined by approx. 50 modal degrees of freedom and does not deviate by more than 1 per-cent from a static solution in NX NASTRAN. The reduced flexible crankshaft is coupled into the multi-body system at the main and large end bearings with the assistance of force elements in order to incorporate the stiffness and attenua-tion properties of the bearings. The connec-tions of the crankshaft with the flywheel and the torsion vibration damper are modeled with the help of joints and/or constraints (i.e. rigidly connected). In the multi-body model, the dynamics of the conrods, pistons and the engine with the engine mounts are all taken into consid-eration. Gas forces are applied as external loads. Consideration of the hydrodynamics in the main bearings and large end bearings, as well as the flexibility of the engine block, is also possible; however, the corresponding influences are not illustrated in this model.

StreSS CALCULAtIoNFor modal superposition of stress, unit stress vectors are needed in SIMPACK. These are the stresses of the eigen vectors as well as stresses of so-called "inertia relief modes". The eigen vectors are used to show stress as a result of free vibrations. In this model, only 40 eigen vectors are needed to illustrate vibration behavior in the relevant frequency range with sufficient accuracy. The stresses, caused by coupling forces in the bearings, are represented by "inertia relief modes". An inertia relief mode is the result of a static

Fig. 3: FAT4FEM — GUI for defining failure criteria for fatigue analysis

calculation in the FEM program. Here, the induced forces are compensated by inertia forces from the rigid body motion, i.e. the external load and the inertia forces form an equilibrium of forces and moments. Consis-tent with the mathematical formulation of linear elastic bodies, deformations are not considered in this equilibrium of forces. A

unit load (force and/or moment) is a load in the direction of the coordinate axes that is scaled to unity. Only the relevant unit forces

were considered for the bearings. These are the forces in x- (longitudinal direction) and y- and z-directions (radial) at the axial main bearing and at the interface points to the connecting rods. Forces in the y- and z-directions were considered at the main bearings, which do not transmit axial forces, and the forces and moments in all directions at the joints to the flywheel and the torsion vibration damper. In total, 35 inertia relief modes have been used in this case. This cor-responds to a total of 75 unit stress vectors. The modal coordinates of the eigen vectors considered in the SIMPACK model, as well as the forces in the coupling elements of the flexible crankshaft, are the result of a multi-body simulation that is required for superimposing the unit stress vectors. The stresses of the eigen vectors are scaled with their respective modal coordinates and the stresses of inertia relief modes with the corresponding forces. After the scaling of the unit stress vectors, their superposition and representation in the PostProcessor fol-lows; see Fig. 1. The combination of inertia

relief modes and eigenmodes can accurately represent the stresses due to static and dy-namic loading conditions. When simulating an engine running at constant speed (rpm), forces, modal coordinates, etc. are issued for approx. 720 communication points in time. With this modal superposition, results of static and time-dependent simulations can be efficiently and accurately reproduced in SIMPACK.

LIfeSPAN eStIMAtIoN wItH fAt4feMLifespan estimation is carried out with FAT4FEM ("Fatigue for FEM") available from Safe-FEM GmbH, www.safe-fem.de. This software has interfaces to Abaqus/CAE, ANSYS and FEMAP. FAT4FEM is integrated in to SIMPACK and can started from the PostProcessor. FAT4FEM is based on the critical plane approach. The critical plane approach looks for every comparison of two load cases and for the level at a node which yields the most damaging equivalent stress. This technology is suited particularly (but not solely) to problems concerning rotating principle stress directions (which is the case here). The critical plane approach is extremely computation-intensive and very precise in principle. Still, we can only speak of a fatigue estimation. Keep in mind that with today's technology, computer-aided fatigue prediction can always only be a fatigue estimation and cannot give absolute data, e.g. maximum number of years of lifetime, etc. Nevertheless, computer-aided fatigue prediction is a valuable tool for the engineer to quickly compare variants and to identify "weak points" of a mechanical design during the design process. During the development of FAT4FEM, primary focus was given to the user-friendliness of the graphical user interface. Operating the user interface of FAT4FEM is something you can learn in a matter of hours, which makes the program very suitable for non-experts, see Fig. 2 and 3.

LIfeSPAN eStIMAtIoN —tHe MoSt IMPortANt ISSUeSroughness effect: The crankshaft is made of cast iron (GGG-60). Therefore, roughness effect does not necessarily apply because GGG-60 is a material with internal notches, and surface is smoothed at critical places so no surface effect is taken into account. temperature effect: At oil temperatures up to 140 °C, the temperature effect must not be considered for GGG-60. The follow-ing factors are of importance for the correct assessment of the crankshaft with regard to lifespan:

“FAT4FEM is an easy-to-use and easy-to-learn fatigue tool

that is based on the critical plane approach.”

SIMPACK News | September 2010 | 29

Stefan Dietz, SIMPACK AG; Wolfgang Erhardt, SAFE-FEM GmbH | SoftwAre

Fig. 4: FAT4FEM results in the SIMPACK PostProcessor — Equivalent stress amplitude (red corresponds to large stresses)

Fig. 5: FAT4FEM results in the SIMPACK PostProcessor — Safety factor (green indicates critical spots)

1. Correctly determined stresses via MBS and feM It is assumed that the stresses calculated with SIMPACK and NX Nastran are suf-ficiently accurate. 2. Correctly defined S/N curve The material properties for GGG-60 were taken from the publicly accessible website of the TU Darmstadt. These properties are based on data pools of Ch. Boller and T. Seeger and are publicly accessible on the internet: www.wm.bauing.tu-darmstadt.de

3. Suitable equivalent stress hypothesisGGG-60 has a breaking strain A5 of 7 %. This means that the equivalent stress hypothesis according to Van Mises can be applied.

4. Mean stress correction Mean stress sensitivity is approx. 0.3 %, which indicates a ductile material.

5. Size effect This takes the size of the component into account. The size effect was not considered in the present study. There-fore, we get more conserva-tive values for safety. With comparative calculations, as is also customary for crankshafts, it is, of course, necessary to always use a specific method, either with or without notch sensitivity.

ILLUStrAtIoN of tHe reSULtSAfter the lifespan estimation, the results are automatically uploaded to the SIMPACK PostProcessor by FAT4FEM. Fig. 4 shows the mean stresses and Fig. 5 the factor of safety for the examined rpm.

SUMMArYThe SIMPACK FAT4FEM functionality de-scribed here is available as a licensed module in addition to the SIMPACK Stress module with version 8904. The seamless integration of MBS, FEM and Fatigue comes with clear time and cost advantages for the experi-

enced user. The process described here is available for automated calculations in batch operations. The fatigue estimation only causes minimal extra time

effort in the overall process chain. Defining the FAT4FEM project takes just a few min-utes. Regarding CPU times, the calculation of FAT4FEM for the areas shown in Fig. 4 and 5 and for 360 load steps is about one hour. If only every third load step is activated, one gets nearly the same results for a fatigue estimation, but evaluation time amounts to only about six minutes. This means that lifespan estimation for dynamically stressed components, even for a great number of operating modes, is possible in an extremely fast and simple manner.

“Operating the user interface of FAT4FEM is

something one can learn in a couple of hours.”