FEA Case Studies

Rack and Pinion Gear Set

Rack and Pinion Gear Set

Two steering rack and pinion designs were required to be analyzed for stress studies. Each design was required to withstand two load cases.

To determine the bending and contact stresses in the rack and pinion assemblies under the specified load cases.


  • Construct four finite element models using solid elements to represent two rack and pinion designs and two positions. Note that gear profiles differ in each model.
  • Portions of the rack and pinion where they contact are modeled. The rest of the rack and pinion is modeled with deformable beam elements.
  • Assign nonlinear material properties.
  • Define areas of contact between rack and pinion.
  • Apply loads and boundary conditions.
  • Perform nonlinear static stress analysis using HKS ABAQUS.
  • Observe results and compare between designs.
Loads & Boundary Conditions
The bearings on the rack and pinion were represented by specific translational and rotational constraints. Two axial moments of different magnitudes were applied to the pinion, one when the pinion was at the end of rack (in-corner), and when the pinion was on rack center (on-center).

Results - von Mises stresses
Von Mises stresses obtained from the analysis show that the stresses were below the yield strength of the material.

Results - Contact Stress Profile
The cutaway views illustrate the distribution of stresses within the rack and pinion at contact Stress continuity can be seen across the contact interfaces.

The stress levels were observed to be well below the critical limit and the rack and pinion gear sets are predicted to endure the loads defined in the analysis without failure.

Rear Axle

Rear Axle

Laboratory fatigue tests performed on the rear axle determined that the axle will not meet the stipulated durability requirements.

The low cycle fatigue life requirement defined by the customer was 200,000 cycles, while the high cycle fatigue life requirement was 1,000,000 cycles.

A low cycle fatigue laboratory test resulted in a fatigue life of 100,000 cycles, while a high cycle fatigue test resulted in a fatigue life of 500,000 cycles.

To simulate the high and low cycle loading conditions and correlate fatigue life predictions with laboratory results.

To conduct similar analyses on two design iterations (designs provided by the customer) and to compare the durability of the two designs with the baseline design.

Analysis Procedure

  • CConstruct Finite Element Model of the rear axle, wheel, bearing and nut, using 3D elements for the baseline design.
  • Define contact between the rear axle and bearing, and bearing and nut.
  • Apply loads and boundary conditions.
  • Perform a non-linear stress analysis using ABAQUS for two cases, high cycle loads and low cycle loads.
  • Perform a fatigue life analysis using MSC/Fatigue for each load case, yielding high and low cycle fatigue life predictions.
  • Correlate Finite Element results with laboratory tests.
  • Repeat steps 1 through 5 for design iterations.
  • Compare baseline with design iterations.
Results - Baseline Design
Crack location predicted from Stress Analysis.

Results - Iterations I & II
Iterations I and II consisted of a modification of the baseline design by increasing the radii as shown in the picture Iteration II exceeds the design target.
Design - Iteration I
FEA SimulationLaboratory TestDesign Target
Low Cycle Fatigue Life128,600   200,000
High Cycle Fatigue Life562,100   1,000,000

The Finite Element simulation correlated well with laboratory tests, both methods showing that the baseline design of the rear axle will not meet the required design criteria. The design used for Iteration II is the recommended design. The design exceeds the requirements stipulated by the customer.



(FMSS 207 / 210)
Federal Motor Vehicle Safety Standards have defined several test that evaluate automotive sub-systems for safety issues in a frontal crash. Two such standards are:

  • FMVSS 207: Evaluates the strength of the seat in a frontal crash
  • FMVSS 210: Evaluates the strength of the seat, with the effects of a person restrained by seat belts, in a frontal crash
To evaluate the strength of the baseline seat, and make design modifications to improve its strength, in frontal crash simulations.

  • Construct finite element model of the seat using shell elements, and assign material properties.
  • Define contact for components that interact with each other during deformation.
  • Apply loads and boundary conditions.
  • Perform a nonlinear crash analysis using LSDYNA.
  • Determine displacements and plastic strains.
  • Repeat steps 1 to 5 for design iterations.
  • Compare baseline results with design iterations
Loads & Boundary Conditions

Results - Baseline DesignThe outboard recliner bracket failed at 67 % of load

Recommended Design - Iteration I
A reinforcing bracket was welded to the outboard recliner bracket.

Results - Iteration I
The outboard tower bracket failed at 83% of load.

Recommended Design - Iteration II
A reinforcing bracket was welded to the outboard tower bracket.

Results - Iteration II
The outboard recliner and tower brackets pass at 100 % of load The other components of the seat also pass at 100% of load.

Baseline simulation results indicated that the seat would fail at 67 % of the FMVSS 207/210 load due to failure of the outboard recliner bracket.

Design Iteration 1 simulation results indicated that the seat, with the outboard recliner bracket reinforced, would fail at 83 % of the FMVSS 207/210 load due to failure of the outboard tower bracket.

Design Iteration 2 simulation results indicated that the seat, with both outboard recliner and tower brackets reinforced, will not fail under the FMVSS 207/210 loading conditions.

Test Correlation

Test Correlation

A steering column deformation was simulated through finite element analysis and was correlated with lab test results.

To simulate the collapse of a steering column under a displacement-controlled load.


  • A finite element model was constructed using solid, shell and 1D elements.
  • Material properties were defined and parts were connected with appropriate welds and springs.
  • Contact was defined for components that undergo surface interaction.
  • Boundary conditions were applied to the model. A displacement load was applied to the upper shaft along the column axis, corresponding to lab test procedures.
  • A nonlinear static analysis was conducted using HKS ABAQUS.
  • The analysis result was compared to lab test outcome.
Results & Conclusions
The top figure shows the displacement contours of the steering column components and its deformed shape.

The simulation result reflects the observed collapse condition during the impact test.

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