Non-linear dynamics of gear pair with dynamic backlash subjected to combined internal and external periodic excitations

In this paper, we theoretically investigate the nonlinear dynamic characteristics of a gear pair system with dynamic backlash subjected to internal and external periodic excitations. The dynamic model of a viscously damped single degree of freedom gear pair model with periodic time-varying stiffness, dynamic backlash, static transmission error and external periodic excitation is established. The incremental harmonic balance method (IHBM) is applied to analyze the frequency response characteristics as well as the effects of dynamic backlash, time-varying stiffness, excitation force amplitude and damping ratio on the dynamic characteristics of the gear pair system. The analysis results are compared with the numerical integration results to show accuracy and authority of the IHBM. The difference between the constant backlash and the dynamic backlash models is also discussed. The results show that the nonlinear dynamic characteristics such as parametric resonance, multi-valued properties and jump phenomena are strongly attributed to the interaction between time-varying stiffness and backlash. Significantly, under combined internal and external periodic excitations, the multi-valued properties and jump phenomena occur not only in primary resonance frequency but also in super harmonic frequency. The increase of the dynamic backlash and damping ratio could effectively control the nonlinear vibration of gear system; whereas the excitation force amplitude has less influence on the nonlinear dynamic characteristics and the increase of the excitation force amplitude could no longer control the nonlinear vibration of gear system, which is different from the dynamic characteristics under internal periodic excitations.