Studies On Nonlinear Vibration Of Cutting Chatter Of Machine Tools

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 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.