Efficient method for fatigue based shape optimization of the oil sump carrying a differential case in four wheel drive vehicles

This paper presents an efficient method to improve the minimum fatigue safety factor in a complicated mechanical system using fatigue based shape optimization. The effect of shape optimization on the probabilistic response of the minimum fatigue safety factor was studied as well. The example used for this purpose is the oil sump of a four wheel drive vehicle carrying a differential case by four bolt connections. The conventional method for such a design improvement problem is based on the stress analysis in ABAQUS and the fatigue analysis in FEMFAT. In the proposed method, a submodel of the original ABAQUS finite element model was built for OPTISTRUCT using a MATLAB script. Fatigue based shape optimization for the most critical differential case bolt connection region was performed in OPTISTRUCT. The optimum shape found using the submodel was tested by replacing it back into the original ABAQUS and FEMFAT models. The proposed method was successful in finding out efficiently the optimum shape that maximizes the fatigue life. Probabilistic analysis was performed for the minimum fatigue safety factor considering the statistical variation of the clamping forces of the four differential case bolts using Optimal Latin Hypercube design of experiment, response surface model and Monte Carlo simulation techniques in ISIGHT. The design with the optimized shape was found to be robust against the variation of the clamping forces of the four differential case bolts.