Study on Nonlinear Dynamics Characteristic of Two-stage Planetary Gear Train

Xiaolu Leng; Xiaosun Wang; Chongshan Lu; Shijing Wu

doi:10.16578/j.issn.1004.2539.2020.10.007

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Study on Nonlinear Dynamics Characteristic of Two-stage Planetary Gear Train

Theory·Reserach | 更新时间：2022-11-10

- Study on Nonlinear Dynamics Characteristic of Two-stage Planetary Gear Train
- Journal of Mechanical Transmission Vol. 44, Issue 10, Pages: 44-54(2020)
- 作者机构：
  
  1.武汉大学动力与机械学院，湖北武汉 430072
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2020.10.007
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冷晓鲁,王晓笋,陆崇山等.两级行星轮系非线性动力学特性研究[J].机械传动,2020,44(10):44-54.

Leng Xiaolu,Wang Xiaosun,Lu Chongshan,et al.Study on Nonlinear Dynamics Characteristic of Two-stage Planetary Gear Train[J].Journal of Mechanical Transmission,2020,44(10):44-54.
冷晓鲁,王晓笋,陆崇山等.两级行星轮系非线性动力学特性研究[J].机械传动,2020,44(10):44-54. DOI： 10.16578/j.issn.1004.2539.2020.10.007.

Leng Xiaolu,Wang Xiaosun,Lu Chongshan,et al.Study on Nonlinear Dynamics Characteristic of Two-stage Planetary Gear Train[J].Journal of Mechanical Transmission,2020,44(10):44-54. DOI： 10.16578/j.issn.1004.2539.2020.10.007.

摘要

建立了两级行星齿轮传动系统“平移-扭转”耦合强非线性动力学模型，引入时变啮合刚度、齿侧间隙与啮合误差等非线性因素，无量纲处理后，建立动力学方程组。采用数值积分的方法对方程组进行求解，得到了系统的非线性动态响应结果，并计算了系统不同齿侧间隙情况下随激励频率变化的分岔图。综合利用相轨线、Poincaré截面和Lyapunov指数谱，通过G-P算法得到系统关联维数。从定性和定量角度对两级行星系统进行非线性动力学特性研究，得到两级行星系统的混沌频率、进入混沌的途径和齿侧间隙对两级行星轮系非线性特性的影响，为两级行星齿轮系统的故障机理研究提供一定理论依据。

Abstract

The translation and torsion coupled strong nonlinear dynamics model of two-stage planetary gear transmission system is established， and the nonlinear factors such as time-varying meshing stiffness， tooth side clearance and meshing error are introduced， after dimensionless treatment， dynamics equations are established. By using the numerical integration method， system of equations are solved， the nonlinear dynamic response result of the system is obtained， and the bifurcation diagram of the system changing with excitation frequency in the case of different backlash is calculated. Through comprehensive use of phase trajectory， Poincare section and Lyapunov index spectrum， and the system correlation dimension is obtained by the G-P algorithm. The nonlinear dynamics characteristic of two-stage planetary system is studied from the perspective of qualitative and quantitative， the influence of chaotic frequency， into the way of chaos and backlash of two-stage planetary system on the nonlinear characteristics of two-stage planetary gear train is obtained. Some theoretical basis for the study of fault mechanism of two-stage planetary gear system is provided.

关键词

两级行星轮Lyapunov指数平移-扭转耦合非线性动力学分岔混沌

Keywords

Two-stage planetary gear systemLyapunov indexTranslation-torsion couplingNonlinear dynamicsBifurcationChaos

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