A crankshaft is often designed with a small fillet radius. The crankshaft fillet rolling process is one of the commonly adopted methods in engineering to improve fatigue life of the crankshaft. Compressive residual stresses on and below the fillet radius surface are induced through the fillet rolling operation. Consequently, fatigue life of the crankshaft is improved. An analytical technique is used to optimize the crankshaft rolling process to comply with a crankshaft design criterion for durability. A nonlinear finite element analysis is implemented to approximate the stress distributions induced by the crankshaft rolling process, and a crack modeling technique is developed to calculate the equivalent stress intensity factor ranges based on the combined residual and operational stress distributions along various crack growth planes. The threshold equivalent stress intensity factor range is obtained from previous staircase testing on crankshaft sections. The durability design criterion is met if the threshold equivalent stress intensity factor range exceeds the largest calculated equivalent stress intensity factor range. Due to the complexity of the modeling techniques in simulating the rolling process and calculating the equivalent stress intensity factors, a meta-model is generated based on the uniform design method for the choice of sample points and the quadratic polynomial fitting technique for a response surface generation.
In the meta-model optimization process, rolling force, rolling angle, and fillet radius are the control factors, while the variations of the threshold equivalent stress intensity factor range, rolling force, rolling angle, and fillet radius are considered as the noise factors. By using the Hooke-Jeeves direct pattern search method and the Monte Carlo simulation technique, the optimal design is obtained for the highest reliability and the smallest coefficient of variation (COV).