The Research on Nonlinear Vibration Characteristic of Ravingneaux Compound Planetary Gear Sets

The nonlinear dynamic model of Ravingneaux compound planetary gear sets has been built. The model includes time-varying mesh stiffness of gears, backlash as well as comprehensive mesh errors nonlinearities. By introducing relative displacements of components as the new generalized coordinates, uniform nonlinear differential equations of compound planetary gear sets are built. Then the nondimensional dynamic differential equations are derived. The nonlinear differential equations have been solved utilizing ariable step size Gill method. By changing system nondimensional excitation frequency, monocycle anharmonic response, multiply periodic subharmonic response, quasi-periodic response and chaotic response are obtained. By means of time histories, phase-plane diagram, Poincare maps and power spectrum, various responses are compared and analyzed in detail.