第一作者张慧博男，博士生，1985年生

通信作者赵阳男，博导， 教授，1968年生

考虑多间隙耦合关系的齿轮系统非线性动力学分析

张慧博，王然,陈子坤,魏承,赵阳,游斌弟

(哈尔滨工业大学航天工程系，哈尔滨150001)

摘要：建立了一种新的考虑径向间隙与动态齿侧间隙耦合的齿轮转子系统动力学模型,分析了径向间隙与齿侧间隙的耦合关系及其对系统动力学特性的影响。在系统动力学模型中，建立了考虑径向间隙的接触碰撞模型；通过推导齿轮中心距与齿侧间隙之间的函数关系，建立了考虑动态齿侧间隙的齿轮扭转振动模型。进而利用该模型对多间隙齿轮系统的动力学特性进行分析。给出了一对直齿轮副的数值仿真结果，分别分析了径向间隙大小和齿侧间隙大小对齿轮系统动力学特性的影响规律，分析结果对含间隙齿轮转子系统的研究具有重要的理论与工程价值。

关键词：动态齿侧间隙；径向间隙；多间隙耦合；齿轮转子系统；动力学特性

基金项目：国家重点基础研究发展计划(973计划)(2013CB733000);“十二五”装备预先研究项目(51320030201)

收稿日期：2014-09-01修改稿收到日期：2014-11-20

中图分类号:TH113文献标志码：A

Nonlinear dynamic analysis of a gear-rotor system with coupled multi-clearance

ZHANGHui-bo,WANGRan,CHENZi-kun,WEICheng,ZHAOYang,YOUBin-di(School of Astronautics, Harbin Institute of Technology, Harbin150001, China)

Abstract:The dynamic behavior and the coupling relationship between radial clearance and backlash of a gear-rotor system with multi-clearance were investigated here. A new dynamic model of the gear-rotor system with coupled multi-clearance was developed including nonlinearity associated with radial clearance and dynamic backlash. In the dynamic model, the contact impact model considering radial clearance was established using the nonlinear contact force model. And the torsional vibration model with dynamic backlash was established using the geometrical relationship between gear center distance and backlash. And then, the dynamic characteristics of the gear-rotor system were analyzed based on the new dynamic model with coupled multi-clearance. The numerical simulation results for a spur gear pair with multi-clearance were presented and discussed. The effects of radial clearance size and initial backlash size on the system dynamic characteristics were analyzed, respectively. The conclusions had important theoretical and engineering values for gear-rotor systems with clearances.

Key words:dynamic backlash; radial clearance; coupled multi-clearance; gear-rotor system; dynamic characteristics

对于齿轮系统的动力学建模一直是人们关注的焦点，也取得了大量的研究成果。早期，齿轮系统的动力学模型为线性模型。如Winter等[1]利用分段线性化的方法研究含齿侧间隙的齿轮系统。Galhoud[2]也利用同样的方法建立了考虑齿侧间隙的两自由度齿轮系统动力学模型，并发现了啮合力的谐波响应现象。……