Size optimization of shoulder filleted shafts with relief grooves for improving their fatigue life

Although in scientific literature there are studies regarding the inclusion of relief grooves in order to diminish the amount of stress concentration in stepped shafts, the incorporation of optimization algorithms capable of parametrically determining their geometry remains unexplored. In this paper, an approach to the problem of size optimization of shoulder filleted shafts with relief grooves and subject to axial loads is presented. The objective of the optimization is to minimize the maximum value of stress at both, the root of the shoulder fillet, and the root of the groove, thus minimizing stress concentration and improving fatigue life of such elements. Under this methodology, different percentages of reduction of stress are achieved for the shafts with relief grooves, in comparison with the shafts without relief grooves. The novelty of this approach lies in the incorporation of an algorithm for the determination of the optimum geometry of the grooves.