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. This study conducts an analytical investigation of thedynamic response characteristics of a two-stage series composite system(TsSCS) with a planetary transmission consisting of dual-power branches. Animproved incremental harmonic balance (IHB) method, which solves the closedsolution of incremental parameters passing through the singularity point ofthe analytical path, based on the arc length extension technique, isproposed. The results are compared with those of the numerical integrationmethod to verify the feasibility and effectiveness of the improved method.Following that, the multi-scale perturbation (MsP) method is applied to theTsSCS proposed in this subject to analyze the parameter excitation and gapnonlinear equations and then to obtain the analytical frequency responsefunctions including the fundamental, subharmonic, and superharmonic resonanceresponses. The frequency response equations of the primary resonance,subharmonic resonance, and superharmonic resonance are solved to generatethe frequency response characteristic curves of the planetary gearsystem (PGS) in this method. A comparison between the results obtained bythe MsP method and the numerical integration method proves that the formeris ideal and credible in most regions. Considering the parameters of TsSCSexcitation frequency and damping, the nonlinear response characteristics ofsteady-state motion are mutually converted. The effects of the time-varyingparameters and the nonlinear deenthing caused by the gear teeth clearance onthe amplitude–frequency characteristics of TsSCS components are studied inthis special topic.

mechanical sciences

Semi-numerical analysis of a two-stage series composite planetary transmission considering incremental harmonic balance and multi-scale perturbation methods