An accurate and numerically efficient time-varying mesh stiffness model for modified straight bevel gear under load

• Published in: Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Journal of mechanical engineering science, 2023-03, Vol.237 (5), p.1023-1039
• Main Authors: Chen, Siyu, Tan, Rulong, Guo, Xiaodong, Zhang, Weiqing, Shu, Ruizhi
• Format: Article
• Language: English
• Subjects: Accuracy; Bevel gears; Finite element method; Mathematical models; Principles; Stiffness
• ISSN: 0954-4062; 2041-2983
• DOI: 10.1177/09544062221123703

Gear time-varying mesh stiffness (TVMS) plays an important role in the analysis accuracy of a gear transmission mechanism. In previous research, the TVMS of a modified straight bevel gear (SBG) was mainly obtained by the finite element method (FEM), whose computation time is usually long to ensure computational accuracy. By contrast, this work proposes a fast calculation method with high accuracy for the TVMS of a modified SBG. First, B-spline surfaces are introduced to reconstruct a modified SBG using discrete tooth surface points. Next, based on the tooth contact analysis and loaded tooth contact analysis, combined with energy conservation principle and infinitesimal method, a semi-analytical instantaneous single mesh stiffness (SMS) model for the modified SBG is derived. Then, using the additional deformation compatibility condition and principle of force balance, the calculation method of the TVMS of the modified SBG is obtained. Finally, a comparison of the mesh stiffness calculation results between the method of this study and that of FEM is completed. The results show that the semi-analytical TVMS model used in this study can be accurately and quickly solved.