A general contact stiffness model for elastic bodies and its application in time-varying mesh stiffness of gear drive

Abstract

As a critical element of time-varying mesh stiffness (TVMS), contact stiffness of a gear drive has been defined based on simplified Hertzian contact stiffness or semi-empirical nonlinear Hertzian contact stiffness in previous works. This study proposes a general contact stiffness model for elastic bodies through piecewise linear interpolation of contact pressure. The TVMS of a spur gear drive is determined through potential energy method and proposed contact stiffness model verified by Hertzian contact theory and finite-element method. Then, the influence of applied load on contact stiffness is studied, and the differences among proposed contact stiffness, simplified Hertzian contact stiffness, and nonlinear Hertzian contact stiffness are analyzed. Results show that contact stiffness increases with the applied load, and the TVMS based on the proposed contact stiffness model is the smallest among the three contact stiffness models. Effects of tooth width and input torque on the TVMS are further discussed. The TVMS becomes bigger with increased tooth width and input torque, but the increase rate decreases as tooth width or input torque increases. These findings indicate that reasonable matching of design parameters is beneficial for increasing load capacity and optimizing the dynamic performance of gear systems.

A time‐varying meshing stiffness model for gears with mixed elastohydrodynamic lubrication based on load‐sharing

“…Nonlinear contact forces give rise to nonlinear contact stiffness during gear meshing, which is addressed by utilizing the nonlinear Hertz contact model for calculating the contact stiffness. The contact stiffness 𝑘 c is approximated by the following formula 31 :…”

“…Nonlinear contact forces give rise to nonlinear contact stiffness during gear meshing, which is addressed by utilizing the nonlinear Hertz contact model for calculating the contact stiffness. The contact stiffness $${k}_{\mathrm{c}}$$ is approximated by the following formula 31 : $$$$\begin{equation}{k}_{\mathrm{c}} = \frac{{E_{{\mathrm{eq}}}^{0.8}{L}^{0.9}F_{\mathrm{n}}^{0.1}}}{{1.275}}\end{equation}$$$$where $${E}_{{\mathrm{eq}}}$$ is the equivalent Young's modulus of gear pairs, $${E}_{{\mathrm{eq}}} = \frac{1}{2}[ {\frac{{{E}_1}}{{( {1 - v_1^2} )}} + \frac{{{E}_2}}{{( {1 - v_2^2} )}}} ]$$, $${E}_1$$ and $${E}_2$$ represent the Young's modulus of gear‐1 and gear‐2, $${\nu }_1$$ and $${\nu }_2$$ denote the Poisson's ratio of gear‐1 and gear‐2, respectively. $$L$$ is the tooth face width.…”

Nonlinear dynamic modeling and analysis of mesh stiffness of the spur gear pair considering tooth tip modification

“…And further, by considering the flexibility effect of planet bearing and carrier, the author proposed an analytical method for calculating the mesh stiffness of the planetary gear system, and the validity was proved through a full FE model [13]. In addition to the above studies, some researchers also made varying degrees of improvements to the traditional analytical method for other gear examples, and the correctness of different methods in dealing with different problems were verified by FE method [14][15][16][17][18]. As far as the combination of FE method and analytical method is concerned, many scholars have also conducted some research.…”