A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs
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DOI 10.1007/s12206-020-0523-7
Journal of Mechanical Science and Technology 34 (6) 2020 Original Article DOI 10.1007/s12206-020-0523-7 Keywords: · Internal gear pair · Mesh stiffness · Finite element method · Analytical contact theory
A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs Shuo Feng1, Lehao Chang1,2 and Zhaoxia He1 1
Correspondence to: Lehao Chang [email protected]
Citation: Feng, S., Chang, L., He, Z. (2020). A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs. Journal of Mechanical Science and Technology 34 (6) (2020) ?~?. http://doi.org/10.1007/s12206-020-0523-7
Received August 4th, 2019 Revised
February 14th, 2020
Accepted March 28th, 2020
Key Laboratory of Road Construction Technology and Equipment of Ministry of Education, Chang’an 2 University, Xi’an 710064, China, Shaanxi Hande Axle Company Limited, Xi’an 710201, China
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.
† Recommended by Editor Seungjae Min
1. Introduction
© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Planetary gear trains (PGT) are used in many industrial applications because of their compact structures, low vibration and noise, large power density and high transmission efficiency, especially in high-speed and heavy-duty situations. As an important part of PGT, accurate prediction of the mesh stiffness for external and internal gear pairs is essential for the strength checking and low vibration design. According to the frequently used formula recommended in ISO 6336, only the stiffness of a single tooth pair and the average mesh stiffness can be obtained. To predict the system vibration more accurately, the time varying mesh stiffness needs to be obtained both for external and internal gear pairs. The previous studies on gear mesh stiffness mainly focused on external gear pairs. The classical analytical methods (AM) in early studies included the widely used formulae proposed by Weber
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