Nonlinear dynamic analysis of power reflux hydraulic transmission system

Power reflux hydraulic transmission system (PRHTS), which is a recently introduced continuously variable transmission system, enables the improvement of fuel economy of construction vehicles. For investigating the nonlinear dynamic characteristics of PRHTS, its nonlinear dynamic model is established by merging the dynamic models of a planetary gear train and torque converter. A dynamical model of the planetary gear train reveals the parameters of mesh damping, time-varying mesh stiffness, and transmission error. The nonlinear dynamic equations of the PRHTS are solved using the fourth-order Runge-Kutta method. The dynamic orbits of the system are observed through bifurcation diagrams, which use the internal excitation frequency and meshing damping ratios, both of which are dimensionless, as control parameters. Numerical examples show the dynamic evolution mechanism involving one-period motion, multi-periodic motion, quasi-periodic motion, and chaotic motion. The onset of chaotic motion is identified from bifurcation diagrams, dynamic trajectories, phase plane diagram, and Poincaré maps of the PRHTS. The simulation results provide an understanding of the operating conditions under which undesirable dynamic motion occurs in PRHTS and serve as invaluable information for effective dynamic design of PRHTS.