Abstract: A nonlinear pure torsional dynamic model of a planetary gear transmission system in a specific gear position of a heavy-duty hydraulic automatic transmission was developed. This gear mode demonstrates a fully compound relationship between the plantary rows. The dynamic model synthetically considers the internal excitation factors of the system, such as the time-varying meshing stiffness, the tooth side clearance and the meshing error amplitude. On the basis of which the dimensional-dynamic equation of the system in generalized coordinates was derived. The fourth-order Runge-Kutta method was used to solve the nonlinear differential equation system, and the nonlinear dynamic response of the system was obtained. A combination of time-domain response, frequency-domain response, phase-space trajectory, system bifurcation, and Poincare cross-section was used to investigate the relationship between the specific input speed and the system response, resulting in a reasonable speed for the gear. The response differences between the planetary rows at different levels caused by the composite structure were studied. It is found that a single planetary row can affect or even determine the response of the whole transmission system, which can be used to guide the production and reduce the production cost.

Key words: heavy-duty hydraulic automatic transmission, planetary row, nonlinear dynamics