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含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究
引用本文:王三民,沈允文,董海军. 含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究[J]. 机械工程学报, 2003, 39(2): 28-32
作者姓名:王三民  沈允文  董海军
作者单位:西北工业大学机电工程学院,西安,710072
基金项目:国家自然科学基金(50075070),西北工业大学博士创新基金资助项目。
摘    要:齿面侧隙和时变啮合刚度等因素的存在,将导致弧齿锥齿轮传动系统在工作过程中呈现典型的非线性特性;置于转子上的弧齿锥齿轮传动系统被等效处理为8自由度动力学模型,借助动态相对传动误差,使两轮转动自由度合并,建立了7自由度的非线性振动方程。采用A算符算法获得了不同工况下弧齿锥齿轮系统的扭转、横向及轴向的振动位移和速度,发现随着啮合频率的变化,系统经倍周期分岔进入混沌,而随着支承刚度的变化,系统经拟周期分岔进入混沌振动,在啮合频率的变化过程中,系统存在跳跃现象。

关 键 词:非线性振动  弧齿锥齿轮  A算符算法  混沌振动
修稿时间:2002-01-09

NONLINEAR DYNAMICAL CHARACTERISTICS OF A SPIRAL BEVEL GEAR SYSTEM WITH BACKLASH AND TIME-VARYING STIFFNESS
Wang Sanmin Shen Yunwen Dong Haijun. NONLINEAR DYNAMICAL CHARACTERISTICS OF A SPIRAL BEVEL GEAR SYSTEM WITH BACKLASH AND TIME-VARYING STIFFNESS[J]. Chinese Journal of Mechanical Engineering, 2003, 39(2): 28-32
Authors:Wang Sanmin Shen Yunwen Dong Haijun
Affiliation:Northwestern Polytechnical University
Abstract:The spiral bevel gears supported by rotor exhibit emblematical phenomena of nonlinear dynamical system, such as bifurcation, chaos and quasi-periodic response etc, and the nonlinear frequency response characteristics of a spiral bevel gear system are numerically examined. An eight degree freedom dynamic model is developed which includes non-linearities associated with backlash and time-varying meshing stiffness. The equations of coupled torsional, lateral and longitudinal motion of the spiral bevel gear system are simplified by defining dynamic relative transmission error, and rewritten into state equations by introducing the state variables. With A-operator method, a numerical algorithm is put forward, and the dynamical responses of the geared system with harmonic internal excitation and parameter excitation are obtained.. Numerical results show that, the system goes through the period doubling route to chaos with change of the meshing frequency, and through Hopf bifurcation to chaos with change of bearing stiffness. Furthermore, the phenomena of jump always occur for different supporting system.
Keywords:Non-linear vibration Spiral bevel gear A-operator method Chaotic vibration
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