Dynamic Modeling and Stability Analysis for a Spur Gear System Considering Gear Backlash and Bearing Clearance

In practice, gear backlash and bearing clearance usually exist together in a gear system. They may induce complicated dynamic responses and degrade transmission performance. Up to now, although each of them has been researched, little attention has been paid to the coupling dynamic characteristics of gear backlash and bearing clearance. In a limited number of relevant studies, since the linear collision models they adopted are difficult to realistically depict actual collision behaviors caused by bearing clearance, these studies cannot accurately reveal the coupling dynamic characteristics of gear backlash and bearing clearance. Furthermore, system stability of the gear system considering gear backlash and bearing clearance has not been thoroughly investigated. In view of this, this paper contributes to the research on dynamic modeling and stability analysis for the spur gear system considering gear backlash and bearing clearance. A nonlinear collision model with time-varying contact stiffness/damping is suggested for describing the bearing collision behaviors. Based on the geometrical relationship of dynamic center distance, dynamic working pressure angle, and dynamic backlash, the coupling motion model of gear backlash and bearing clearance is developed. On this basis, the dynamic model of the spur gear system considering gear backlash and bearing clearance is established and verified by numerical simulations, virtual prototyping simulations and experiments. Afterwards, to thoroughly explore the complicated dynamic characteristics of the gear system considering gear backlash and bearing clearance, several important parameters, i.e., rotational speed, gear backlash and bearing clearance, are chosen as bifurcation parameters to study their influences on system stability via bifurcation diagrams, time-domain waveforms, FFT spectra, Poincaré maps, and phase diagrams. Various complicated nonlinear behaviors, such as hopping, multiple periodic motion, quasi-periodic motion, and chaotic motion, are revealed. This study can provide useful reference for the multi-clearance coupling research of the gear system in complicated working environments.