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A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs

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Abstract

This work developed an efficient model for calculating the mesh stiffness of spur/helical internal gear pairs by combining the finite element method (FEM) and analytical formula. The tooth global deformation is obtained by separation of the deformation of a full finite element model and a partial model, and the local contact deformation is derived by an analytical line contact formula based on Hertz contact theory. The transmission error and mesh stiffness of the gear pair can be acquired after solving the nonlinear contact equilibrium equations. Compared with the conventional FEM, the proposed method has much smaller computational consumption. Furthermore, it also overcomes the disadvantage that the analytical method is difficult to consider different ring gear structures. Then the influences of ring thicknesses and the number of support pins of the ring gear on the mesh stiffness are discussed. The results show that the ring flexibility will change the amplitude-frequency components of the mesh stiffness a lot.

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Acknowledgments

This paper is supported by the Natural Science Basic Research Program of Shaanxi (Grant No. 2019JQ-695, 2018JQ5059), National Natural Science Foundation of China (Grant No. 51605040), and the China Postdoctoral Science Foundation (Grant No. 2018M640943).

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Authors and Affiliations

  1. Key Laboratory of Road Construction Technology and Equipment of Ministry of Education, Chang’an University, Xi’an, 710064, China

    Shuo Feng, Lehao Chang & Zhaoxia He

  2. Shaanxi Hande Axle Company Limited, Xi’an, 710201, China

    Lehao Chang

Authors
  1. Shuo Feng
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  2. Lehao Chang
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  3. Zhaoxia He
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Corresponding author

Correspondence to Lehao Chang.

Additional information

Recommended by Editor Seungjae Min

Shuo Feng is a Lecturer at School of Construction Machinery, Chang'an University, Xi’an, China. He received his Ph.D. degree in Northwestern Polytechnical University (NWPU), China. His research interests include mechanical strength and reliability, mechanical system dynamics, robotics, artificial intelligence and others.

Lehao Chang is an Associate Professor at School of Construction Machinery, Chang'an University, Xi’an, China. He received his Ph.D. degree in Northwestern Polytechnical University (NWPU), China. His research interests include gear contact theory, geared rotor system dynamics, and others. He has published more than 20 journal and conference papers.

Zhaoxia He is an Associate Professor at Chang'an University, Xi’an, China, and now serves as Assistant Dean of the School of Construction Machinery. She received her Ph.D. degree in Northwestern Polytechnical University (NWPU), China. Her research interests include mechanical system dynamics, gear system dynamics modeling and simulation, virtual prototype technology, and so on. She has published more than 30 journal and conference papers.

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Feng, S., Chang, L. & He, Z. A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs. J Mech Sci Technol 34, 2477–2485 (2020). https://doi.org/10.1007/s12206-020-0523-7

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  • DOI: https://doi.org/10.1007/s12206-020-0523-7

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