【作者】 王立刚；

【导师】 刘习军；

【作者基本信息】 天津大学 ， 一般力学， 2004， 硕士

【摘要】 干摩擦引起的振动问题是工程界极为普遍的现象，本文针对机床切削加工过程中存在的颤振问题，利用非线性动力学，着重讨论了机床系统的内共振现象。对于非线性振动问题的研究，特别对于工程技术中出现的非线性问题，一般采用实验法和分析法，而分析法的主要研究内容，就是非线性动力学系统各种运动的定性和定量分析。本文的主要工作是对机床发生的颤振现象进行非线性动力学研究。主要包括以下几个方面：1．简述了目前国内外机床颤振问题的研究现状以及相关领域的发展方向，指出了本文的实际工程研究背景。2．讨论了干摩擦型颤振和机床自激振动的特点，结合非线性振动理论，针对机床的刀架弹性子系统和工件弹性子系统在非线性切削力耦合下的颤振现象，利用动力学理论和振型的正交性，建立了多自由度的非线性耦合方程。3．针对两个自由度方程，利用龙格－库塔方法分别讨论了系统发生1：1和1：2内共振时的数值解，初步确定了系统的动力学特性，如时间历程及幅频曲线等。利用近似方程讨论了系统平衡点的稳定性，并且根据庞加莱理论分析了系统的全局分叉特性。然后，采用平均法求出系统发生1：2内共振时的解析解，得到了工件和刀架发生颤振的稳态解以及振幅响应曲线，进一步对机床颤振系统的动力学特性作了相应的分析。4．利用多尺度法求出了方程组的解析解，得到了相应的分叉方程。根据奇异性理论，对系统的分岔方程进行了分岔行为的分析和讨论，得到多种转迁集和分岔图。5．最后，对本文的工作进行了总结，并且讨论了该课题中有待进一步研究的问题和今后的发展方向。更多还原

【Abstract】 The vibration induced by dry friction is a very prevalent phenomenon in the engineering fields. Emphases on the internal resonant activities, the chatter of a cutting machine is descussed in this thesis using the analyse method of nonlinear dynamics. The experimental and analysis methods are usually used to study non-linear vibration problems, especially the theme produced in the engineering and technology fields. Also one of the primary tasks of nonlinear dynamics is to analyze all kinds of the system′s movements qualitatively and quantitatively. The main work of this paper is to study the nonlinear dynamics activities of cutting chatter in a machine tools system, which includes the followings: 1. the research of the present situation and the future directions on cutting chatter from home and overseas are Intruduced briefly, from which, the practical engineering research background is derived. 2. The characteristic of dry friction and self-sustained oscillations are discussed .To investigate the phanomena of cutting chatter occurring on machine tools coupled system, multi-DOF nonlinear equations are acquired by using the theory of danamics and orthogonality of each mode. 3. Based on two- DOF equations, The internal resonance phenomenon is analysed by using numerical calculation ,and the curves of time histories and amplitude spectrum are obtained. the numerical solution of the coupled system′s equations .In order to analyze the stable nature of equilibrium point,the discontinuous friction forces are approximated by smooth function. And also the phenomenon of global bifurcation is exhibited according the theory of Poincare. The analytical solutions of 1:2 internal resonance are obtained by using the nonlinear vibration theory, the stable <WP=5>amplitude and resonance curves are obtained by using average method in established the coupled system′s vibration equations.4. Then, according to the method of multiple scales to work out the first approximately resolution, and analyze the coupled system′s nonlinear dynamics in detail. What′s more, the bifurcation behaviors are analyzed by means of singularity theory.the transition sets and bifurcation figures are got. 5. At the end of this dissertation, the main investigation results of this paper are summarized, and the problems which remained unsolved and prospective research topics in the future are presented.更多还原