Abstract: A purely rotational model of Ravigneaux compound planetary gear train sets including time-varying mesh stiffness, synthetic mesh errors and gear backlashes is developed to show the nonlinear dynamic behavior of the system with the action of multi-clearances. The gap function is expressed as describing function and harmonic balance method (HBM) is used to convert the differential equations to nonlinear algebraic equations, which is solved iteratively by single rank inverse Broyden method. The steady state response of fundamental frequency is obtained. The influences of gear backlashes, time-varying mesh stiffness and synthetic mesh errors are analyzed by changing the value of the parameter. It is showed from the research that multiple value and amplitude jump discontinuities are presented on the dynamic curves, there the impact phenomenon is reflected. Meanwhile the nonlinearity degree of the system is increased by the coupling of stiffness fluctuation, mesh errors and backlashes. The HBM based on describing function can be used for more complicated model to obtain the steady state response of fundamental frequency, which provides a method for deeply researching the dynamic behavior of compound planetary gear train sets.

Key words: Compound planetary gear sets, Harmonic balance method, Nonlinear characteristics, Transmission system