Nonlinear dynamics analysis of high contact ratio gears system with multiple clearances

A brief research status on high contact ratio gears (HCRG) is first conducted to obtain a basic understanding. Subsequently, a nonlinear dynamic model of HCRG with multiple clearances is established by the lumped mass method, in which time-varying mesh stiffness (TVMS), static transmission error, gear backlash, and bearing radial clearance are taken into consideration as well. The TVMS of HCRG is calculated based on an improved potential energy model and then fitted into a Fourier series form. After the dimensionless treatment, the system differential equations of motion are solved using Runge-Kutta numerical integration method. With the help of bifurcation diagrams, largest Lyapunov exponent charts, time-domain waveforms, FFT spectra, Poincare maps, and phase diagrams, the influence of excitation frequency, gear backlash, mesh damping ratio, error fluctuation, and bearing radial clearance on the nonlinear dynamic characteristics of the system is investigated in detail. The results show that with the changes of these analysis parameters, the system exhibits different types of nonlinear behaviors and dynamic evolution mechanism, including period-one, multi-periodic, quasi-periodic, chaotic motions, and jump discontinuity phenomenon. Meanwhile, three typical routes to chaos, namely period-doubling bifurcation to chaos, quasi-period to chaos, and crisis to chaos, are also demonstrated. Additionally, it is found that the bearing radial clearance produces a weaker nonlinear coupling effect when compared to gear backlash. The research results can provide a certain theoretical support for the dynamic design and vibration control of the HCRG.