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<p>A&#xa0;non-circular gear (NCG) is characterised by&#xa0;smooth transmission, good rigidity and periodic movement at&#xa0;variable speed. The change in the pitch curve radius of the&#xa0;NCG affects its meshing characteristics, which makes the analytical calculation of the&#xa0;time-varying mesh stiffness (TVMS) difficult. According to the idea of NCG design by commuted tooth shape method, focusing on the equivalent cylindrical gear of it, the analytical model of TVMS of NCG is established using the energy method, and the eccentricity fluctuation rule affecting the degree of fluctuation of the TVMS is obtained. Taking the non-circular gear planetary gear system (NCPGS) as the research subject, the effects of crack depth along tooth thickness, crack propagation angle and crack length along tooth width on TVMS are studied. The results show that the TVMS of NCG decreases with the increase of crack parameters. The dynamic characteristics such as the&#xa0;load distribution ratio and transmission error in the&#xa0;crack state are obtained. Finally, the validity of the analytical model is verified by the finite element model, which provides a theoretical basis for the calculation of the TVMS of NCG.</p>

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An Analytical Calculation of Time-Varying Mesh Stiffness of Non-circular Planetary Gear System with Crack

  • 期刊论文

  • 发表日期：

    2025年2月24日

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  • Yongping Liu,
  • Juan Wang,
  • Changbin Dong,
  • Junhai Guo

摘要

A non-circular gear (NCG) is characterised by smooth transmission, good rigidity and periodic movement at variable speed. The change in the pitch curve radius of the NCG affects its meshing characteristics, which makes the analytical calculation of the time-varying mesh stiffness (TVMS) difficult. According to the idea of NCG design by commuted tooth shape method, focusing on the equivalent cylindrical gear of it, the analytical model of TVMS of NCG is established using the energy method, and the eccentricity fluctuation rule affecting the degree of fluctuation of the TVMS is obtained. Taking the non-circular gear planetary gear system (NCPGS) as the research subject, the effects of crack depth along tooth thickness, crack propagation angle and crack length along tooth width on TVMS are studied. The results show that the TVMS of NCG decreases with the increase of crack parameters. The dynamic characteristics such as the load distribution ratio and transmission error in the crack state are obtained. Finally, the validity of the analytical model is verified by the finite element model, which provides a theoretical basis for the calculation of the TVMS of NCG.