具有分形特性的齿侧间隙对齿轮-轴承系统动态特性的影响

doi:10.3901/JME.2018.09.153

机械工程学报 ›› 2018, Vol. 54 ›› Issue (9): 153-160.doi: 10.3901/JME.2018.09.153

具有分形特性的齿侧间隙对齿轮-轴承系统动态特性的影响

李小彭, 牟佳信, 潘五九, 闻邦椿

东北大学机械工程与自动化学院沈阳 110819

收稿日期:2017-05-15 修回日期:2017-11-23 出版日期:2018-05-05 发布日期:2018-05-05
作者简介:李小彭,男,1976年出生,博士,教授,博士研究生导师。主要研究方向为机械综合设计理论方法及应用、结合面振动摩擦耦合动力学。E-mail:xpli@me.neu.edu.com;牟佳信,男,1992年出生,硕士研究生。主要研究方向为结合面动力学、齿轮-转子动力学。E-mail:jiaxinmu@foxmail.com
基金资助:
国家自然科学基金（51575091）和中央高校基本科研业务专项资金（N160306003）资助项目。

Influence of Fractal Backlash on Dynamic Behavior of Gear-bearing System

LI Xiaopeng, MU Jiaxin, PAN Wujiu, WEN Bangchun

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819

Received:2017-05-15 Revised:2017-11-23 Online:2018-05-05 Published:2018-05-05

摘要/Abstract

摘要： 主要研究具有分形特性的齿侧间隙对齿轮-轴承系统动态特性的影响。首先建立该系统的动力学模型，考虑转轴、轴承等重要部件对齿轮系统动态特性的影响。模型中计及滑动轴承非线性油膜力、综合传递误差及齿轮时变啮合刚度等非线性因素。在对系统的动力学分析中引入分形理论，讨论齿侧间隙表现出的分形行为，并使用W-M函数对其进行描述。通过Runge-Kutta法求解动力学方程并得到系统响应的相图，Poincaré截面图与分岔图。结果表明：当啮合刚度较大时，系统的分岔行为减少，1周期与混沌交替出现；当齿侧间隙在小范围内波动时，相比于固定齿侧间隙，使用具有分形特性的齿侧间隙时系统响应表现出了更多细节，可以更准确地描述系统的动态特性；随着啮合刚度的增大，系统可以在分形维数D较大的情况下依然保持准周期运动，即刚度较大时系统较稳定。

关键词: 齿侧间隙, 齿轮, 非线性, 分形特性

Abstract: The chief objective is to study the influence of the fractal backlash on the dynamic characteristics of the gear bearing system. Firstly, the dynamic model of the system is established, and the influence of the rotating shaft and bearing on the dynamic characteristics of the system is considered. The nonlinear factors such as the nonlinear oil film force of the journal bearing, the time-varying meshing stiffness of gear and the dynamic transmission error are analyzed. In this paper, the fractal theory is introduced into the dynamic analysis of the system, the fractal behavior of the backlash is discussed, and the W-M function is employed to describe this fractal behavior. Runge-Kutta method is used to solve the dynamic equation, and the phase diagram of the system response, Poincare section and bifurcation diagram are obtained. The results reveal that when the meshing stiffness is large, the bifurcation behavior of the system is reduced, 1 periodic motion and chaos appear alternately; when the backlash fluctuates in a small range when compared to the fixed backlash, there are more details of the system response when using the fractal backlash, and the dynamic characteristics of the system can be described more accurately; with the increase of meshing stiffness, the system can keep the 1 period motion when the fractal dimension D is large, which means the system is more stable when the stiffness is large.

Key words: backlash, fractal characteristics, gear, nonlinear

中图分类号:

TH132

李小彭, 牟佳信, 潘五九, 闻邦椿. 具有分形特性的齿侧间隙对齿轮-轴承系统动态特性的影响[J]. 机械工程学报, 2018, 54(9): 153-160.

LI Xiaopeng, MU Jiaxin, PAN Wujiu, WEN Bangchun. Influence of Fractal Backlash on Dynamic Behavior of Gear-bearing System[J]. Journal of Mechanical Engineering, 2018, 54(9): 153-160.

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具有分形特性的齿侧间隙对齿轮-轴承系统动态特性的影响

Influence of Fractal Backlash on Dynamic Behavior of Gear-bearing System

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