Optimization Methods for Controlling Stresses at Contacting Surfaces of Interference Fit Assemblies Under Axial and Torsional Loads

While the nonuniformity of the diameter of a shaft can be optimized to reduce damaging stress concentrations at the ends of the contact region that are typically found in interference fits between uniform diameter shafts and hubs, the resulting shape changes may adversely affect the joint strength. A more robust design may be achieved if the surface profile is optimized under both interference fit and functional loads. A novel gradientless structural shape optimization method is applied in this work with a unique multiobjective formulation that includes the contact interactions and their effects on the shaft. The method incorporates surface-averaged based optimization goals, which consider both local and global variations, so that the optimization of the entire contacting region can be readily achieved. The formulation has no system-dependent parameters, weighting factors, or stopping criterion, allowing for its broad application to design and compare systems of varying geometries, loads, and meshes. The method was used to attain design goals specific to contacting interfaces subjected to interference, axial, and torsional loads, achieving a 50% improvement in the stress state uniformity over the entire contract region in all cases. Through the presented method, the relative influence of each optimization goal on the resulting shape is demonstrated.