Estimating Gear Mesh Stiffness Based on the Potential Energy Method Considering Load-dependent Tooth Deformation

Although gear mesh stiffness plays a critical role in predicting the dynamic behavior of gear systems, conventional analytical methods do not adequately reflect the load-dependent physical deformation of the teeth, which tends to appear more prominently in plastic gears. In this study, an improved approach based on potential energy is proposed, which incorporates elastic tooth deformation and nonlinear contact behavior to compute realistic, load-sensitive meshing stiffness. The magnitude of the contact stiffness is updated iteratively based on the applied load while maintaining the computational efficiency of the original potential energy method. Values for meshing stiffness obtained using the proposed approach closely matched the results of a finite element analysis, whereas conventional methods failed to reproduce the nonlinear variation under increasing load. The proposed stiffness function was implemented in a time-domain dynamic model of a gear system to evaluate its performance, and the results show that it was able to predict the dynamic transmission error and meshing force accurately. The predictions also agreed closely with values obtained using the finite element method. These findings demonstrate that the proposed method effectively captured the load-dependent behavior of gear mesh stiffness and can thus be applied as a reliable tool in the dynamic analysis and design of plastic gear systems.