Nonlinear Dynamic Response Of A Spur Gear Pair With Hertz Contact Damping

ABSTRACT:Gear transmission system is widely adopted in power and motion transmission equipments, such as the engineering fields of aviation and aircrafts, automobiles, ships, wind turbines and railways. The dynamic model of spur gear transmission system is established with nonlinear Hertz contact damping, where the nonlinear parameters such as backlash, time-varying stiffness, manufacturing errors are considered. The nonlinear dynamic responses of nonlinear spring and damping contact force model and Kelvin-Voigt contact force model are analyzed comparatively. Five kinds of hysteretic damping coefficients are adopted and the contact force lines and dissipation energy are deduced. Finally, the static transmission error is coupled with backlash equation to reveal the dynamic responses, which demonstrate with the experimental results. The main research content is as followings.(1) Based on the spur gear pair, the dynamic model of gear transmission system is proposed with real time-varying stiffness, real error excitation, backlash and nonlinear impact damping. Three kinds of situation according to the relative displacement and impact results are listed, and the contact force and dissipation energy are associated. The dynamic motion equations are converted with dimensionless parameters.(2)According to the established spur gear dynamic model with nonlinear Hertz contact damping, the Kelvin-Voigt contact force model is adopted with some assumptions and simplifications. With the Runge-Kutta simulation method, the time domain responses, frequency responses, bifurcation and chaotic responses are characterized. Under the heavy loaded situation, two systems are stable and single-period solutions come out. As the variation of control parameter, multiple period of bifurcation is obtained. With the decrease of load, chaotic motions are discovered. Under the low velocity situation, the responses of two models are similar. Contrarily, the period windows of Kelvin-Voigt are smaller than nonlinear spring and damping model at high velocity.(3)The energy dissipation is depicted as damping dissipation among the gear teeth contact. According to the nonlinear impact damping model, combining with five different hysteric damping coefficients, the contact force and energy dissipation during the nonlinear impact are exhibited. Then, the time domain responses, the frequencies responses are involved as well. Subsequently, the nonlinear dynamic responses are analyzed with the varying parameter of velocity. It is concluded that the path from periodic solution to chaotic are depicted.(4) The static transmission error is adopted as displacement excitation to conserve the shaft frequency. The research results show that the shaft frequency is the main part of dynamic response and double period responses are associated. Under the low velocity condition, rattling responses show up. With the increase of load, the amplitude of responses decreases on the contrary. The same tendency appears with velocity.(5) Based on the LMS test system, the dynamic transmission error curve and frequency curve deduced from the experimental data show a very good agreement with numerical results, which demonstrate the validation of theoretical analyses. Figure53, Table8, Reference64.