Harmonic balance method implementation of nonlinear dynamic characteristics for compound planetary gear sets

In this paper, the harmonic balance method has been extended to investigate the nonlinear dynamics of a compound planetary gear sets. The lumped parameter dynamic model, incorporating parametric gear mesh stiffness fluctuations, transmission errors and gear backlash, is established. The responses of the system, mesh stiffness, transmission error, and gear backlash have all been represented by harmonic functions, which have been utilized to derive the algebraic equations via Galerkin process. The nonlinear dynamic characteristics of the gear sets are researched, and the effect of nonlinearities on the frequency response characteristic has been investigated by changing the value of the non-dimensional backlash, mesh stiffness, and amplitude of error excitations. The multiple value, jump and discontinuities phenomena have been revealed in the presented frequency response curves. The formulation derived here can also be extended to incorporate incremental harmonic balance method and parameter continuation scheme for further nonlinear dynamics investigation.