混合轮系扭转非线性振动建模与分岔特性分析  

Nonlinear torsional vibration modeling and bifurcation characteristic analysis of a mixed gear train

作　　者：田亚平[1] 褚衍东[1] 饶晓波[1] 

机构地区：[1]兰州交通大学机电工程学院,甘肃兰州730070

出　　处：《机械设计》2017年第3期36-42,共7页Journal of Machine Design

基　　金：国家自然科学基金资助项目(11262009);兰州市人才创新创业资助项目(2015-RC-3);高等学校博士学科点专项科研基金资助项目(20136204110001)

摘　　要：考虑齿轮副间的时变刚度、齿侧间隙及综合传递误差等因素,建立了风力发电机行星轮系-平行轴混合轮系的齿轮-转子系统扭转非线性振动模型;推导出了系统的量纲一化动力学方程,采用数值积分法对方程进行求解,得到了系统的非线性动态响应结果。综合运用分岔图、位移-映像图、功率谱线图研究了系统转速、啮合阻尼和齿侧间隙对系统分岔特性的影响。结果发现,系统在低速重载工况下具有复杂的非线性动力学特性;系统随转速的变化出现了单周期运动、拟周期运动和混沌等多种运动状态,系统通过Hopf分岔、阵发性激变途径进入混沌运动;阻尼过小将会导致系统的稳态运动由短周期运动向复杂的混沌运动转变。齿侧间隙是影响系统分岔特性的重要因素。A nonlinear gear-rotor system torsional vibration model of a planetary-parallel shaft mixed gear train in the wind turbine was established considering the time variation stiffness,gear backlashes and comprehensive transfer error.The normalized dynamic equations of the system were deduced.The nonlinear dynamic response of the system was carried out using the numerical integration method.The influence of system rotation speed,meshing damping and gear backlash on the system bifurcation was analyzed using bifurcation diagram,displacement-mapping diagram and power spectrum diagram.The results revealed that the system motion state was in complicated nonlinear dynamic characteristics under the condition of low speed and heavy loading.The dynamic system motion showed single periodic motion,quasi periodic motion and chaotic motion with the change of rotating speed.The system motion state would change into chaos through the hopf bifurcation and paroxysmal violent change with the increase of speed.A smaller damping would make the system stable periodic motion state change into complex state from short period.Gear backlashes had a strong impact on the system bifurcation characteristics.

关 键 词：混合轮系 非线性振动 HOPF分岔 激变 混沌 

分 类 号：TH132.4[机械工程—机械制造及自动化]