Pareto Front Exploration for Hypoid Gear Multi-Objective Optimization Model

Optimizing hypoid gear is crucial in modern gear design to meet the increasing demand for high durability, high efficiency, and low noise. The Pareto front is used to illustrate the trade-off between the conflicting objectives in multi-objective optimization models. However, exploring the Pareto front optimization space for hypoid gear is challenging due to its non-convex nature and non-linearity, primarily caused by the complex contact behavior. These complexities often result in larger computational costs and can lead to the convergence of optimization into a local solution rather than a global one. In this study, a multi-objective optimization model is established to optimize hypoid gear contact performance such as the peak-to-peak value of loaded transmission error and maximum contact pressure. The Pareto fronts of optimization objectives are obtained based on the Pattern Search method. To explore the optimizable space of the Pareto front, the various initial values and optimization objectives range are specified. Several Pareto front and corresponding solution distributions are obtained and analyzed. Also, the best trade-off optimization solutions are reported to demonstrate the effectiveness and correctness of optimization. The results show that the optimization space of the local Pareto front has been explored effectively and gives insight for gear designers to decision-making.