双参变量下单级齿轮传动系统分岔/冲击特性分析  

Bifurcation & impact characteristics of a single-stage gear train in a two-parameter plane

作　　者：田亚平[1] 褚衍东[2] 饶晓波[1] TIAN Yaping;CHU Yandong;RAO Xiaobo(School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China;Gansu Provincial Key Lab of System Dynamics and Reliability of Rail Transport Equipment, Lanzhou Jiaotong University, Lanzhou 730070, China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070 [2]兰州交通大学甘肃省轨道交通装备系统动力学与可靠性重点实验室,兰州730070

出　　处：《振动与冲击》2018年第13期218-223,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(11262009;11462012);高等学校博士学科点专项科研基金(20136204110001);兰州市人才创新创业项目(2015-RC-3)

摘　　要：为分析多参数耦合对非线性齿轮系统分岔/冲击特性的影响,在时变刚度幅值系数与量纲一转速的双参平面内,采用PNF(Poincaré-Newton-Floquet)法和延续算法获得单级齿轮传动系统的分岔/冲击图,确定了周期、拟周期、混沌运动与啮合冲击类型的区域,找出了擦切、倍化、激变、幅值跳跃、Hopf等分岔行为及其分岔的转迁规律,用Rung-Kutta数值法仿真的三维/二维分岔图、Poincaré映射图和相图验证了其方法的有效性。在双参平面内找出了参数耦合匹配的单周期无冲击稳定运动区域,为齿轮系统结构设计优化提供了一定的数据参考。In order to analyze effects of multi-parameter coupling on bifurcation impact characteristics of a nonlinear gear system,in a plane with 2 parameters of time-varying stiffness amplitude coefficient and dimensionless rotating speed,the bifurcation/impact diagram of a single-stage gear train was obtained using Poincaré-Newton-Floquet（ PNF） method and the extended algorithm.The regions of periodic motion,quasi-periodic motion,chaotic motion and mesh impact type were determined in the diagram.The dynamic behaviors of graze bifurcation,double-period bifurcation,upheaval bifurcation,amplitude jump,Hopf bifurcation and the bifurcation transition law were found in the diagram.The validity of the proposed method was verified with 3D/2D bifurcation diagram,Poincaré map one and phase one simulated with Runge-Kutta numerical method.The stable region for single period motion with non-shock of parametric coupling and matching was found in the two-parameter plane.The results provided a reference for structural design and optimization of gear systems.

关 键 词：单级齿轮传动系统 非线性振动 分岔 PNF数值法 双参平面 

分 类 号：TH132.425[机械工程—机械制造及自动化] O322[理学—一般力学与力学基础]