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

Tian Yaping; Chu Yandong

doi:10.16578/j.issn.1004.2539.2017.01.002

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

更新时间：2022-10-20

- Periodic Motion and Its Stability of 3 Degree-of-freedom Gear Rotor System
- Vol. 41, Issue 1, Pages: 6-10(2017)
- 作者机构：
  
  1. 兰州交通大学机电工程学院
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2017.01.002
  CLC：
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[1]田亚平,褚衍东.三自由度齿轮转子系统的周期运动及其稳定性[J].机械传动,2017,41(01):6-10.

Tian Yaping, Chu Yandong. Periodic Motion and Its Stability of 3 Degree-of-freedom Gear Rotor System. [J]. 41(1):6-10(2017)
[1]田亚平,褚衍东.三自由度齿轮转子系统的周期运动及其稳定性[J].机械传动,2017,41(01):6-10. DOI： 10.16578/j.issn.1004.2539.2017.01.002.

Tian Yaping, Chu Yandong. Periodic Motion and Its Stability of 3 Degree-of-freedom Gear Rotor System. [J]. 41(1):6-10(2017) DOI： 10.16578/j.issn.1004.2539.2017.01.002.

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。

Abstract

The coexisting periodic trajectory and its stability of a single- stage gear rotor transmission system 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 system,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 example,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

Keywords

Gear rotor transmission systemNonlinear dynamicsCoexisting periodic trajectoryStabilityCPNF

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