星型齿轮传动系统的非线性动力学分析  

On Nonlinear Dynamic Behavior ofStar Gear System Due to Clearances

作　　者：孙智民[1] 沈允文[1] 王三民[1] 李华[1] 

机构地区：[1]西北工业大学机械系,陕西西安710072

出　　处：《西北工业大学学报》2002年第2期222-226,共5页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金重点项目(59835040);国家自然科学基金(50075070)

摘　　要：建立了星型齿轮传动系统的间隙型非线性动力学模型,考虑了齿轮副的啮合综合误差,齿轮的啮合间隙和时变啮合刚度。并用数值解法对系统的动力学微分方程进行求解,获得了星型齿轮传动在外扭矩作用下受齿轮副传动误差激励的非线性稳态强迫响应。以一个具有3个星轮的四自由度星型齿轮传动为例,对系统的非线性动态响应做了分析,利用时间历程、相平面、Poincar(?)映射以及 Fourier频谱阐述了多自由度间隙型非线性星型齿轮传动系统的简谐、非谐单周期、次谐波、准周期和混沌响应的动力学特性。To our best knowledge, there is no paper in the open literature on the nonlinear dynamic behavior of star gear system caused by the existence of clearances in it when excited by the static transmission error under a mean torque load. In section 1, we established a nonlinear dynamic model of such a star gear system that takes into consideration not only the usually considered time-varying gear meshing stiffness but also the clearances in it. In section 2, we derived equations needed for calculating the steady-state forced response to the internal sinusoidal excitation. In section 3, we used the Gill numerical method to obtain numerical values of response for a four-degree-of-freedom gear train consisting of three star gears. Data processing of these numerical results revealed time histories, phase plane plots, Poincaremaps and Fourier spectra, which helped us to discover five types of steady-state response: ( Ⅰ ) harmonic(Fig. 3); ( Ⅱ ) non-harmonic (Fig. 4); ( Ⅲ ) subharmonic (Fig. 5); ( Ⅳ ) quasi-periodic (Fig. 6); ( Ⅴ ) chaotic (Fig. 7).

关 键 词：非线性动力学 星型齿轮传动 非线性振动 动态特性 模型 

分 类 号：TH132.425[机械工程—机械制造及自动化]