螺旋锥齿轮摆振系统动力学

Jianjun Yang, Kai Xu, Xiaozhong Deng, B. Wei
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引用次数: 1

摘要

考虑输入轴角激励和正常传动误差,建立了带间隙的非光滑螺旋锥齿轮卡嗒模型。基于泊松冲击定律,分析了考虑齿间摩擦的斜冲击过程,得到了冲击前状态与冲击后状态的关系。选取齿面作为poincar截面,构造poincar图,提出了一种利用局部图法计算Lyapunov指数的方法,避免了碰撞点处的雅可比矩阵计算。算例验证了上述计算方法的正确性。结果表明:随着受力幅值的增大,摇齿系统的运动状态由单面齿冲击转变为双面齿冲击;在很大的参数范围内计算了最大李雅普诺夫指数的谱。
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Dynamics of spiral bevel gear rattling system
A non-smooth spiral bevel gear rattling model with backlash was established by considering input shaft angle excitation and normal transmission error. Based on the Poisson's impact law, the oblique-impact process was analyzed in which friction was considered between gear teeth, and the relation between the pre-impact state and the post-impact one was obtained. Selecting the tooth face as the Poincaré section, the Poincaré map was constructed, and a calculation method of Lyapunov exponents presented by using the local map method to avoid calculating the Jacobian at the impact points. An example was given to validate the above calculation method. The results show that with increase in forcing amplitude, the motion state of the gear rattling system change from single-sided tooth impact to double-sided tooth impact. The spectrums of the largest Lyapunov exponents are calculated in a large range of parameters.
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