The nonlinear dynamic analysis of a multi-gear train with time-varying mesh stiffness on account of the modification coefficient effect is in vestigated in this paper. The proposed application of the modification coefficient will revise the center distance of the gear pair, avoid undercut and raise the mesh stiffness of the designed gear system. In this study, the gear profile is generated from the relationship between the rack cutter and the gear work piece by using the envelope theory. The rack cutter with the modification coefficient increases the mesh stiffness and thus enhances the strength of the gear tooth. Then the time-varying mesh stiffness at the contact position of the gear pair is calculated from the tooth deflection analysis using the generated gear profile. With the obtained time-varying mesh stiffness, the nonlinear dynamic behavior of multi-gear train is investigated by using Runge-Kutta integration method. The numerical results of the studied examples show the harmonic motion, sub-harmonic motion, chaotic motion and bifurcation phenomenon of the gear train.

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