双参变量下单级齿轮传动系统分岔/冲击特性分析

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (13) : 218-223.

论文

田亚平1，褚衍东2，饶晓波1

作者信息 +

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

TIAN Ya-ping1，Chu Yan-Dong2，Rao Xiao-Bo1

Author information +

文章历史 +

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。

Abstract

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.

导出引用

田亚平1，褚衍东2，饶晓波1. 双参变量下单级齿轮传动系统分岔/冲击特性分析[J]. 振动与冲击, 2018, 37(13): 218-223

TIAN Ya-ping1，Chu Yan-Dong2，Rao Xiao-Bo1. Bifurcation & impact characteristics of a single-stage gear train in a two-parameter plane[J]. Journal of Vibration and Shock, 2018, 37(13): 218-223

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