Modeling and Dynamic Analysis of Planetary Gear Transmission Joints with Backlash

As one of the core components, the joint plays an important role during the movement of space manipulator, and its performance will be influenced by the existence of the backlash, which can severely sacrifice the quality of the manipulator to perform a task. In order to have a comprehensive understanding of the influence of the backlash to the gear transmission joints, a dynamic model of planetary gear transmission joint with consideration of the time-varying mesh stiffness, mesh damping, gear backlash, and gear mesh error is established by the lumped parameter method, and the differential equations of motion are established by Newton-Euler method in this paper. In addition, a novel calculation method is proposed to solve the differential equation analytically using the precise integration algorithm under Hamiltonian system on the basis of a simplified treatment. The simulation results indicate that the backlash within a certain range has little effect on periodic solutions of the planetary gear transmission train, but with the enlargement of backlash, the dynamic response of the system is significantly changed.