Multi Objective Topology Optimization of Gearbox Based on Combination Weighting and Variable Density

To address the issue of weight allocation in multi-objective topology optimization of planetary gearboxes relying on subjective experience, this paper proposes a combined weighting method integrating the Analytic Hierarchy Process (AHP) and Entropy Weight Method (EWM) to scientifically determine the optimization weights for static stiffness and multiple natural frequencies. Based on this, the Solid Isotropic Material with Penalization (SIMP) method is employed to perform multi-objective topology optimization on a cast aluminum gearbox housing with volume fraction as the constraint. The optimized structure achieves a 16.4% reduction in mass, while the maximum stress and deformation decrease by 24.4% and 26.8%, respectively. The first six natural frequencies remain stable (variation rate: 0.03% ~ 1.02%). This approach significantly enhances the static stiffness and lightweight performance of the housing while ensuring dynamic characteristics.