螺旋锥齿轮振动研齿系统的拍击响应

建立了位移激励下的螺旋锥齿轮振动研齿系统的扭转振动模型,推导出考虑摩擦的轮齿斜碰撞前后状态间的局部映射关系式,得到了螺旋锥齿轮振动研齿系统的Lyapunov指数计算方法.通过算例,运用相图、Poincare映射图、Lyapunov指数和系统分叉图,分析了研齿系统随激励参数变化的动态响应,结果表明,随激励幅值的增大,研齿系统由单边碰撞状态经倍周期分叉进入混沌,并在混沌状态中有周期窗口的出现.继续增大激励幅值,系统进入了双边碰撞状态.

Rattling response of vibration lapping of spiral bevel gear

The torsional vibration model of vibration lapping process for spiral bevel gear under displacement excitation was established. and the method of local maps between pre-impact state and post-impact one was introduced. The Poincaré map relation was deduced in consideration of the oblique-impact vibration between teeth under the influence of sliding friction. The calculation method for Lyapunov Exponent of vibration lapping system of spiral bevel gear was obtained. The dynamic response for a given gear lapping system with the change of excitation parameter was analyzed by employing phase plane plots, Poincaré map, Lyapunov Exponent and bifurcation plot compositely. The results show that with the increase of excitation amplitude, the gear lapping system exhibits a period doubling route to chaos in single-side tooth impact state, and period window can be found in chaotic region. With the continued increase of excitation amplitude, a double-side tooth impact phenomenon of the lapping system is appeared.