Tensor based approach for tooth contact analysis of planar and spatial gearing contact

Abstract

This paper presents a new method for analysing gear tooth contact, leveraging tensor notation and discrete differential geometry. Existing analytical and numerical methods often face challenges in convergence and computational efficiency. Our proposed approach involves defining a novel tensor notation and applying it to the gear tooth contact kinematics problem. By discretizing the tooth surfaces and using tensor operations, we can accurately determine the kinematics, path of contact, and transmission error of the gear pair. To validate our approach, we compared its results with those obtained from commercial software, KISSsoft and KiMOS. The results demonstrated high accuracy, with mean absolute errors below 0.08 for specific sliding, 0.003 for sliding factor, and $0.1\mu m$ for transmission error. Furthermore, we applied our method to analyse non-involute gear types, such as S-gears, pin gearing and cosine gears. Our findings revealed the kinematic performance and contact characteristics of these gear types, providing valuable insights for gear design and optimization. In conclusion, the proposed tensor-based approach offers a promising alternative for gear tooth contact analysis, providing accurate and efficient results for a wide range of gear types.