Contact characterization and time-varying meshing stiffness calculation of elliptical gears

The investigation of tooth contact characteristics in elliptical gears holds significant importance for gear transmission analysis. This study focuses on elliptical gear pairs, establishing precise tooth surface equations through gear hobbing principles to develop a digital model. A contact stress computational model was developed using Hertz contact theory with time-varying meshing forces. The equivalent tooth number method was employed to determine meshing stiffness, followed by parametric analysis of contact stress variation under different design parameters. Finite element analysis validated the stress distribution trends. To address computational challenges in time-varying meshing stiffness of elliptical gears, a novel approach integrating tooth surface grid node stiffness was proposed for calculating single/double-tooth meshing stiffness. Transmission errors were derived through angular displacement relationships, enabling systematic analysis of time-dependent and tooth-width-dependent variations in normal contact force, comprehensive elastic deformation, and meshing stiffness. Comparative results demonstrate the proposed method’s superior rationality and accuracy in computing time-varying meshing stiffness for elliptical gears.