Nonlinear Dynamics of Helicopter Planetary Gear-rotor System Caused by Stiffness Variation

Lanlan Hou; Mingqiang Li; Guosheng Wang; Lingyun Lai; Hao Chen; Yuping Huang

doi:10.16578/j.issn.1004.2539.2021.09.022

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Nonlinear Dynamics of Helicopter Planetary Gear-rotor System Caused by Stiffness Variation

Test·Analysis | 更新时间：2022-11-10

- Nonlinear Dynamics of Helicopter Planetary Gear-rotor System Caused by Stiffness Variation
- Journal of Mechanical Transmission Vol. 45, Issue 9, Pages: 145-150(2021)
- 作者机构：
  
  1.中国直升机设计研究所，江西景德镇 333001
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2021.09.022
  CLC：
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侯兰兰,李明强,王国胜等.刚度变化下直升机行星齿轮-转子系统非线性动力学[J].机械传动,2021,45(09):145-150.

Hou Lanlan,Li Mingqiang,Wang Guosheng,et al.Nonlinear Dynamics of Helicopter Planetary Gear-rotor System Caused by Stiffness Variation[J].Journal of Mechanical Transmission,2021,45(09):145-150.
侯兰兰,李明强,王国胜等.刚度变化下直升机行星齿轮-转子系统非线性动力学[J].机械传动,2021,45(09):145-150. DOI： 10.16578/j.issn.1004.2539.2021.09.022.

Hou Lanlan,Li Mingqiang,Wang Guosheng,et al.Nonlinear Dynamics of Helicopter Planetary Gear-rotor System Caused by Stiffness Variation[J].Journal of Mechanical Transmission,2021,45(09):145-150. DOI： 10.16578/j.issn.1004.2539.2021.09.022.

摘要

建立了行星齿轮-转子系统的非线性动力学模型，系统模型将内啮合刚度嵌入齿圈刚度进行建模，考虑了转子扭转效应、齿侧间隙、时变啮合刚度和综合传动误差等因素。采用分岔图、最大李雅普诺夫指数（LLE）、庞加莱截面图和相图来分析响应特征。研究齿轮与转子间扭转振动位移响应，分析了旋翼轴与传动轴扭转刚度比变化影响规律。研究发现，系统具有非线性动力学特性，通过准周期分岔和倍周期分岔进入混沌运动，获得了系统避免失稳的刚度比阈值区间。研究为直升机主减速器行星齿轮-转子系统的动力学设计和扭转振动控制提供了参考。

Abstract

A nonlinear dynamics model of the planetary gears-rotor system is established with a developed internal mesh stiffness embedded with ring gear stiffness. The torsional effect of rotor and pivotal parameters from gears including gear backlash， time-varying mesh stiffness and comprehensive transmission error are incorporated. Responses characteristic are analyzed with bifurcation diagrams， the largest Lyapunov exponents （LLE）， Poincaré maps and phase diagrams. The torsional vibration displacement response between gear and rotor is studied， and the influence law of torsional stiffness ratio between rotor shaft and drive shaft is analyzed. It is found that the system exhibits nonlinear characteristic， enters into chaotic motion through quasi-periodic bifurcation and period-doubling bifurcation， threshold values for stiffness ratios to avoid bifurcation and chaos are obtained. The research provides a reference of undesirable torsional behaviors in dynamic designing and vibration controlling for planetary gears-rotor systems in helicopter main reducer transmission.

关键词

直升机主减速器行星齿轮-转子系统非线性动力学分岔混沌

Keywords

Helicopter main reducerPlanetary gears-rotor systemNonlinear dynamicsBifurcationChaos

references

KISHOR B，GUPTA S K.On the dynamic analysis of a rigid rotor-gear pair-hydrodynamic bearing system［J］.Journal of Vibration，Acoustics，Stress，and Reliability in Design，1989，111（3）：234-240.

WAN Z，CAO H，ZI Y，et al.An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack［J］.Engineering Failure Analysis，2014，42：157-177.

KAHRAMAN A.Planetary gear train dynamics［J］.Journal of Mechanical Design，1994，116（3）：713-720.

PARKER R G，AGASHE V，VIJAYAKAR S M.Dynamic response of a planetary gear system using a finite element/contact mechanics model［J］.Journal of Mechanical Design，2000，122（3）：304-310.

LEQUE N，KAHRAMAN A.A three-dimensional load sharing model of planetary gear sets having manufacturing errors［J］.Journal of Mechanical Design，2017，139（3）：033302.

CHEN Z，SHAO Y.Mesh stiffness of an internal spur gear pair with ring gear rim deformation［J］.Mechanical and Machine Theory，2013，69：1-12. （下转第169页）

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