Dynamics analysis of spur gears considering random surface roughness with improved gear body stiffness

In previous calculation of gear mesh stiffness, the gear body is typically treated as a deformable elastic ring, and the stiffness of the gear body is determined using Sainsot's empirical formula. In this paper, a new calculation method for determining the gear body stiffness based on the analytical finite element-potential energy method is proposed, and its feasibility is verified by the finite element method. A new nonlinear dynamic model for a spur gear system is established, taking into account the time-varying backlash and random surface roughness. This model aims to investigate the dynamical responses of the gear system under various parameters, including rotational speed, shaft hole radius and surface roughness. The results indicate that the proposed method for calculating the stiffness of the gear body is significantly more accurate than Sainsot's empirical formula, as it closely aligns with the finite element method. This leads to a more precise calculation of the time-varying mesh stiffness. The gear dynamics model incorporating random surface roughness exhibits a heightened degree of realism and complexity in its dynamic phenomena. This study provides a valuable reference for the future development of dynamic gear systems.