Effect of rotational symmetry order on topology optimization of gears

LIU Zhihua; DONG Rui; LI Hao

doi:10.16578/j.issn.1004.2539.2026.03.008

Abstract：[Objective]Because gears perform circumferential rotational motion,the topological optimization design of the gear body requires consideration of rotational symmetry.Different rotational symmetry orders may influence the results of the gear body's topological optimization design.However,no definitive conclusions have yet been established regarding which order of rotational symmetry produces the most optimal results in topological optimization.In this regard,the influence of rotational symmetry order on the results of the gear's topological optimization design was investigated.[Methods]The output shaft gear of a specified reducer was selected as the research object.Stress analysis and modal analysis were performed on the gear without topological optimization design using the finite element simulation software Abaqus,resulting in the stress state and the natural vibration characteristics during gear meshing.The gear was then subjected to topological optimization design by the variable density method.Subsequently,stress analysis and modal analysis were conducted on the topologically optimized gear.Additionally,the influence of different rotational symmetry orders on the results of the gear's topological optimization was systematically analyzed.[Results]The finite element simulation results indicate that the rotational symmetry order influences the distribution of the topology-optimized regions of the gear,but has a slight effect on the volume reduction fraction of topology optimization.For the gears designed with different rotational symmetry orders,no yielding occurs under meshing stress.However,modal analysis results reveal significant variations in the natural vibration characteristics.When the rotational symmetry order is set to 6,the topology-optimized gear not only avoids yielding under meshing stress,but also exhibits the largest frequency difference between its natural vibration frequency and the meshing frequency,which can effectively avoid resonance during gear meshing.