Adaptive mixed differential evolution algorithm for bi-objective tooth profile spur gear optimization

Abstract

Nowadays, the increasing demand for high-strength, efficient, quiet, and high-precision gear design leads to the use of various optimization methods. In this study, a new evolutionary optimization algorithm, named adaptive mixed differential evolution (AMDE), based on a self-adaptive approach is introduced. The proposed method is applied to solve the problem of the optimal spur gear tooth profile, where the objectives are to equalize the maximum bending stresses and the specific sliding coefficients at extremes of contact path. The mathematical model of the maximum bending stresses is developed using a finite element analysis (FEA) calculation. The effectiveness of the proposed method is demonstrated by solving some well-known practical engineering problems. The optimization results for the test problems show that the AMDE algorithm provides very remarkable results compared to those reported recently in the literature. Moreover, for the spur gear used in this work, a significant improvement in balancing specific sliding coefficients and maximum bending stresses are found.