Nonlinear dynamic analysis of a split path torque gear transmission system

A nonlinear time-varying dynamic model for a split-path gear train in which one gear meshes simultaneously with two gears, is proposed in this study. The dynamic model also includes the backlash and meshing phase difference between the two paths. The time-varying mesh stiffness is calculated with a three-dimensional finite element model. The dimensionless equations of motion are solved using the direct numerical integration. The Floquet theory is applied to determine the stability and bifurcation type of the model. The effects of excitation frequency and meshing phase on nonlinear dynamic behaviors are investigated. The results indicate that, as the excitation frequency increases, sub-harmonic resonance occurs in the high-frequency range. Moreover, variations in the meshing phase difference between two split paths significantly affect the amplitude of the two natural-resonance peaks. These findings provide valuable theoretical guidance for the optimization of relevant design parameters in practical engineering applications.