混合轮系扭转非线性振动建模与分岔特性研究  

Nonlinear Torsional Vibration Modeling and Bifurcation Characteristic Study 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：《兰州交通大学学报》2016年第3期125-131,共7页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(11262009);兰州市人才创新创业项目(2015-RC-3);高等学校博士学科点专项科研基金(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,推导了系统的无量纲非线性微分方程,采用数值积分法对其求解,得到了系统的非线性动态响应.综合运用分岔图和Pioncaré截面研究了系统转速、啮合阻尼和齿侧间隙对系统分岔特性的影响.研究表明:在低速重载工况下系统具有复杂的非线性动力学特性;随转速变化系统呈现单周期运动、长周期运动、拟周期运动和混沌等运动状态,系统经Hopf分岔、激变途径进入混沌;系统阻尼过小会导致其稳态运动由短周期运动向复杂运动转变.齿侧间隙是影响系统分岔特性的重要因素.A nonlinear torsional vibration model for a planetary-parallel mixed gear transmissionsystem of wind turbine with errors of transmission,time varying meshing stiffness and gear backlashesis established and dimensionless equations of the system are derived. The nonlinear dynamicresponse of the equations is carried out by using the method of numerical integration. By comparingwith Poincare maps and bifurcation diagrams, the bifurcation properties of the system arestudied. The influences of some bifurcation parameters such as rotational speed, damping coefficientproperties of the system are assessed. The study results reveal that the system7 s motionstate has complicated nonlinear dynamic characteristics under the condition of low speed and heavyloading. Along with the change of rotating speed,the system shows a variety of motions such assingle periodic motion,periodic motion,quasi periodic motion and chaotic and so on. The system7s motion state will change into chaos in the way of crisis and hopf bifurcation as the speed increases.A smaller damping coefficient will make the system^ periodic motion state change into complexstate. Gear backlashes have a strong impact on the system^ bifurcation characteristics.

关 键 词：混合轮系 非线性振动 分岔 激变 混沌 

分 类 号：O322[理学—一般力学与力学基础]