New deterministic model for calculating mesh stiffness and damping of rough-surface gears considering elastic–plastic contact and energy-dissipation mechanism

For a long time, meshing parameter calculations and dynamic modeling of gear systems have assumed smooth tooth surfaces, disregarding the impact of actual three-dimensional (3D) microscopic topography. Based on elastic–plastic contact and energy-dissipation mechanisms, this work developed a comprehensive deterministic model that integrates 3D rough surface modeling, reconstruction, and contact analysis, for calculating the time-varying mesh stiffness (TVMS) and mesh damping (TVMD) of deterministic rough-surface gears. Distinct from fractal and statistical models, the deterministic model analyzes deterministic, real 3D rough surfaces rather than simple surfaces defined by a few parameters. Utilizing stochastic process theory, different-topography surfaces are obtained using height and spatial features and reconstructed employing watershed algorithm and ellipsoidal asperity fitting. Subsequently, a deterministic elastic–plastic contact model based on equivalent rough curved-surface contact is constructed, emphasizing local contact states and energy dissipation for calculating contact stiffness (CS) and damping (CD) of gears. Accordingly, a meshing characteristics analysis model is established for calculating TVMS, TVMD, and load sharing ratio (LSR). Experimental validation and comparisons with several statistical and gear contact models demonstrate the effectiveness, reliability, and superiority of the proposed deterministic model. Multi-parameter impact analysis reveals small Sq (meaning low roughness Sa) and Ssk and high load correlate with increased CS and TVMS, while CD and TVMD depend on their interaction and hardness. Overall, by bridging the micro-surface topography and macro-meshing parameters, our model provides essential insights for the design and manufacturing of high-performance gear to reduce vibration and noise.