三自由度齿轮转子系统的周期运动及其稳定性  

Periodic Motion and Its Stability of 3 Degree-of-freedom Gear Rotor System

作　　者：田亚平[1] 褚衍东[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：《机械传动》2017年第1期6-10,共5页Journal of Mechanical Transmission

基　　金：国家自然科学基金(No.11262009;11161027);高等学校博士学科点专项科研基金(No.20136204110001);兰州市人才创新创业项目(2015-RC-3)

摘　　要：研究了含间隙三自由度的齿轮转子非线性系统的周期轨道及其稳定性。采用有限差分法近似代替非光滑系统的Jacobi矩阵,改善了CPNF法在求解非线性动力学时需要系统必须光滑的缺陷。改进后的CPNF法对算例的计算结果与数值积分结果比较验证了其有效性。在给定参数下采用改进后的CPNF法研究了齿轮转子系统的共存的周期运动,并判断了各周期的稳定性;通过延续追踪法判断了不同转速下系统周期轨道的稳定性;研究了齿轮转子系统随无量纲转速变化的分岔特性。结果发现,齿轮转子非线性系统在某些参数组合下多个稳定和不稳定周期轨道共存;转速在1.54~1.42变化时,齿轮转子系统通过倍周期分岔的形式最终通向混沌运动。The coexisting periodic trajectory and its stability of a single - stage gear rotor transmission sys- tern with 3 degree - of - freedom are studied by using the method of CPNF （ Continue - Poincare - Newton - Floquet）. The finite difference method is used to approximate instead of the Jacobi matrix of non - smooth sys- tem, and the defect that the nonlinear dynamic system must be smooth of the CPNF method is improved. Through calculation results of improved CPNF method comparing with the results of numerical calculation for ex- ample, the improved CPNF method is verified to be effective. The coexisting periodic motion of the gear rotor system is studied by using the method of improved CPNF, the stability of each periodic motion is determined at the same＂ time. Through the CPNF, the stability of the periodic trajectory under different speeds is determined, the bifurcation characteristic of the gear rotor system under certain dimensionless rotational speed is studied. The results show that a nonlinear gear rotor system with certain parameters may have several coexisting stable or unstable periodic trajectories. Moreover, the motion of the system could also evolve into chaos by way of period - doubling bifurcation as the speed decreases in 1.54 - 1.42.

关 键 词：齿轮转子传动系统 非线性动力学 共存周期轨道 稳定性 CPNF 

分 类 号：TH132.41[机械工程—机械制造及自动化]