An improved time-varying mesh stiffness calculation method and dynamic characteristic analysis for helical gears under variable torque conditions

Based on the slice theory and numerical calculation methods, the time varying meshing stiffness (TVMS) calculation method of the gear pair was constructed for the helical gear pair of a electric continuously variable transmission (ECVT), and the TVMS of the helical gear were calculated under different constant and time-varying torque in this study. The obtained stiffness values were introduced into the established dynamics model of helical gear system, and the influence of changed TVMS, resulting from the variable speed and torque, on the nonlinear dynamic characteristics of gear pair was analyzed using the Runge-Kutta method. The results show that the proposed TVMS calculation method is very effective in computing the TVMS of helical gear pair under time-varying condition. The TVMS and dynamic transmission error (DTE) increase as the torque increase, and vice versa. Meanwhile, the system exhibits a diverse range of periodic, sub-harmonic, and chaotic behaviors at high speed and at low speed when torque is low, whereas not appear at steady high torque under low speed range. This study offers a method for gaining the TVMS of helical gear pair to analyze the dynamic characteristics of gear pair under actual working condition, and the influence of torque that change with the speed ratio on the dynamic performance of a gear system should be considered in the industrial applications.