Nonlinear, parametrically excited dynamics of two-stage spur gear trains with mesh stiffness fluctuation

Abstract

This work studies the nonlinear, parametrically excited dynamics of two spur gear pairs in a two-stage counter-shaft configuration. The dynamic model includes parametric excitations and contact loss of both tooth meshes with two different mesh frequencies. The time-varying mesh stiffnesses and nonlinear tooth separation functions are reformulated into forms suitable for perturbation analysis. The periodic steady-state solutions are obtained by the method of multiple scales and compared against a semi-analytical harmonic balance method as well as numerical integration for fundamental and subharmonic resonances for ranges of system parameters. The interaction of the two meshes is found to depend strongly on the relation of the two mesh periods. The dynamic influences of design parameters, such as shaft stiffness, mesh stiffness variations, contact ratios, and mesh phasing, are discussed. The closed-form solutions provide design guidelines in terms of the system parameters.