A purely rotational model of Ravigneaux compound planetary gear sets including time-varying mesh stiffness,synthetical mesh errors and backlashes was developed.Incremental harmonic balance method was applied to obtain the steady state response of fundamental frequency.The influences of the system parameters on dynamic characteristics were analized by changing the magnitudes of time-varying mesh stiffness,backlashes and external excitations.It is shown that multiple values and amplitude jump discontinuities are presented on the frequency-response curves due to the existence of backlashes.More abundant dynamic behaviors will appear in compound planetary gear sets by the coaction of system parameters.Incremental harmonic balance method can be used in more complex systems to obtain the approximate solutions of arbitrary-precision,which lay the foundation of controlling vibration and noise of the system to achieve the dynamic design of compound planetary gear sets.