Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing Factors
Time-varying mesh stiffness (TVMS) of the internal mesh transmission is a significant source of excitation that causes vibration and noise in planetary gear systems, and is also an important parameter in dynamics analysis. Currently, the calculation of mesh stiffness for internal gear pairs primaril...
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MDPI AG
2025-04-01
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| author | Jubo Li Hengbo Zhao Yanbo Ren Jianjun Yang |
| author_facet | Jubo Li Hengbo Zhao Yanbo Ren Jianjun Yang |
| author_sort | Jubo Li |
| collection | DOAJ |
| description | Time-varying mesh stiffness (TVMS) of the internal mesh transmission is a significant source of excitation that causes vibration and noise in planetary gear systems, and is also an important parameter in dynamics analysis. Currently, the calculation of mesh stiffness for internal gear pairs primarily relies on finite element simulation, and there still lacks a mesh stiffness analytical model that accounts for tooth surface nonlinear contact. Therefore, this paper proposes an analytical model for nonlinear contact mesh stiffness that comprehensively accounts for tooth surface modification and the flexibility of the ring gear. Firstly, a mesh stiffness calculation model for a sliced tooth pair was established using the potential energy method, which accounted for the influence of gear ring flexibility. Secondly, the tooth deviation ease-off diagram was derived from the modified tooth surface equations, which provided data support for the nonlinear contact analysis. On this basis, slicing element pairs that met the contact conditions were identified by combining elastic deformation with mesh clearance. The comprehensive mesh stiffness in nonlinear contact was calculated by integrating the deformation coordination equation with the principle of minimum potential energy. Finally, using a group of internal helical gear pairs as an example, the validity of the proposed method was verified through finite element simulation. The effects of load, modification amount, and face width on the TVMS and load transmission error (LTE) of an internal helical gear pair were investigated by the analytical model. The results show that the analytical model can provide a reference for the optimal design of internal gear transmission. |
| format | Article |
| id | doaj-art-2baa67eda84b4987a118db0b29278f47 |
| institution | DOAJ |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-2baa67eda84b4987a118db0b29278f472025-08-20T02:59:07ZengMDPI AGApplied Sciences2076-34172025-04-01159459910.3390/app15094599Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing FactorsJubo Li0Hengbo Zhao1Yanbo Ren2Jianjun Yang3School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471000, ChinaSchool of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471000, ChinaSchool of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471000, ChinaSchool of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471000, ChinaTime-varying mesh stiffness (TVMS) of the internal mesh transmission is a significant source of excitation that causes vibration and noise in planetary gear systems, and is also an important parameter in dynamics analysis. Currently, the calculation of mesh stiffness for internal gear pairs primarily relies on finite element simulation, and there still lacks a mesh stiffness analytical model that accounts for tooth surface nonlinear contact. Therefore, this paper proposes an analytical model for nonlinear contact mesh stiffness that comprehensively accounts for tooth surface modification and the flexibility of the ring gear. Firstly, a mesh stiffness calculation model for a sliced tooth pair was established using the potential energy method, which accounted for the influence of gear ring flexibility. Secondly, the tooth deviation ease-off diagram was derived from the modified tooth surface equations, which provided data support for the nonlinear contact analysis. On this basis, slicing element pairs that met the contact conditions were identified by combining elastic deformation with mesh clearance. The comprehensive mesh stiffness in nonlinear contact was calculated by integrating the deformation coordination equation with the principle of minimum potential energy. Finally, using a group of internal helical gear pairs as an example, the validity of the proposed method was verified through finite element simulation. The effects of load, modification amount, and face width on the TVMS and load transmission error (LTE) of an internal helical gear pair were investigated by the analytical model. The results show that the analytical model can provide a reference for the optimal design of internal gear transmission.https://www.mdpi.com/2076-3417/15/9/4599internal gearpotential energy methodtime-varying mesh stiffnesstransmission errortooth surface modification |
| spellingShingle | Jubo Li Hengbo Zhao Yanbo Ren Jianjun Yang Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing Factors Applied Sciences internal gear potential energy method time-varying mesh stiffness transmission error tooth surface modification |
| title | Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing Factors |
| title_full | Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing Factors |
| title_fullStr | Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing Factors |
| title_full_unstemmed | Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing Factors |
| title_short | Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing Factors |
| title_sort | calculation of time varying mesh stiffness of internal mesh transmission and analysis of influencing factors |
| topic | internal gear potential energy method time-varying mesh stiffness transmission error tooth surface modification |
| url | https://www.mdpi.com/2076-3417/15/9/4599 |
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