Time-varying mesh stiffness calculation and dynamic analysis of the star gearing system based on loaded tooth contact analysis

This study proposes a time-varying mesh stiffness calculation approach for star gears with topological modifications. Employing loaded tooth contact analysis along with the slice and potential energy methods, the mesh stiffness accounting for tooth surface deviations under load is determined separately for both the internal and external gear pairs in a star gearing system, based on deformation compatibility conditions. A lumped-parameter dynamic model is established for the star and planetary gearing systems, incorporating nonlinearities such as time-varying mesh stiffness (TVMS) and phasing. The system’s dynamic response is obtained with the Runge-Kutta method. At an input speed of 12,500 r/min, the vibration acceleration of the planetary gearing system’s output component exceeds that of the star gear system. Theoretical analysis indicates that optimal vibration suppression for the ring gear is achieved with axial and profile modifications of 5 and 10 μm, respectively. Under operating conditions of 1570 r/min and 3200 N·m, the peak frequency-domain vibration amplitudes of the ring gear in the x, y, and z directions are reduced by 54.34%, 40.69%, and 37.45%. Experimental validation on a star gearing reducer shows maximum deviations in the root mean square vibration acceleration of 24.25%, 22.87%, and 20.09% along the three orthogonal directions. The proposed method offers improved stiffness modeling for more accurate dynamic characterization of star gearing systems.