A Nonlinear Torsional Dynamic Model of Multi-Mesh Gear Trains Having Flexible Shafts

A non-linear time-varying dynamic model is developed to study torsional dynamic behavior of a typical multi-mesh gear train. The physical system consists of M shafts (M ≥ 2 ) coupled to each other by M −1 gear pairs. The discrete dynamic model includes the gear backlash clearance, gear mesh stiffness fluctuations, and torsional flexibilities of the shafts. In addition, the gear tooth modifications and typical manufacturing errors are included in the form of periodically time-varying displacement functions applied at gear meshes. A multi-term Harmonic Balance formulation is used in conjunction with discrete Fourier Transforms and a Parametric Continuation technique to obtain the steady-state period-n motions. Direct numerical integration results are used to demonstrate the accuracy of the harmonic balance predictions. Effects of key system parameters are also studied.