Dynamics Of Mass-Spring-Belt Friction-Induced Vibration System

The friction-induced vibration phenomenon exists widely in the engineering field and daily life, and affect the performance of the mechanical system in various ways. The friction-induced vibration problems usually cause the mechanical parts wear, and then reduce the precision and quality of the workpiece, also can reduce the precision of the control system. The interaction between the friction and vibration in the low speed is relatively more apparent, showing strong nonlinear characteristics, whose impact on the system dynamics is very serious, thus also greatly reduces the performance of the system. Hence, the study on the vibration phenomenon caused by the friction and the friction model is becoming more and more important. While considering the friction of mechanical system dynamics research has a long history, but so far, the mechanism of the nonsmooth dynamics including the self-excited vibration has not yet been deeply understood, the research theory of the self-excited vibration lacks of systemic, no drawing a certain systemically law. Therefore, this paper takes the representative machine tool cutting system and feed system system as the research object, the dynamics and its bifurcation control of the friction self-excited vibration phenomena that exist in these mechanical system are carried on.This paper analyzes and summarizes the existing friction theory, the present situation of the friction model used commonly in engineering, the friction system dynamics, the bifurcation control of vibration, the system compensation methods, the friction chatter of the machine cutting chatter.Firstly, the paper analyzes the dynamics behavior of the plastid-spring-belt self-excited vibration system considering the Stribeck friction model. On the basis of the research on friction dynamical system, the friction self-excited vibration system model containing the Stribeck friction model is established, which is a nonlinear dynamical mass-spring-stiffness model; for the established model, the equilibrium stability of the system is analyzed by making use of an first approximate stability criterion of Lyapunov theory, and the critical instability speed of the system is determined, indeed, the stability of limit cycles are determined by the curvature coefficient obtained of the limit cycle parameters. Then the approximate analytical solution and the critical velocity between the stick-slip and the pure slip is obtained by using the method of average analysis method; Then, the system behavior of the friction self-excited vibration system under different parameters is analyzed by using the numerical simulation method, based on the phase diagram, the frequency spectrum diagram, time-domain diagram and the Poincare section diagram of the dynamic analysis methods, the complex phenomenon of the self-excited vibration system is analyzed; Finally, the system bifurcation and chaos characteristics under different parameters are obtained.Secondly, the paper analyzes the dynamics behavior of the plastid-spring-belt self-excited vibration system considering the LuGre friction model. The friction model is replaced by the LuGre friction model to study the friction self-excited vibration dynamic model; First of all, of the equilibrium stability of the system are analyzed by using the stability theory; a velocity threshold of the nonlinear friction self-excited vibration dynamical model is obtained with the varderpol method; Then, the system behavior of the friction self-excited vibration system under different parameters is analyzed with the numerical simulation method, through the use of the phase diagram, the frequency spectrum diagram, time-domain diagram and the Poincare section diagram of the dynamic analysis methods, the complex phenomenon of the self-excited vibration system is analyzed.Thirdly, the dynamic characteristics of the friction self-excited vibration system established in the second chapter under the action of the external excitation is studied, with the help of the theoretical method, we found the stick-slip phenomenon of the system will disappear in some high frequency excitation. In order to study the dynamic behaviors of the system under the external harmonic vibration, In order to study the system to the outside world under the simple harmonic vibration, the dynamic behavior of the system is studied under different damping and excitation frequency, and then the graphic of the displacement amplitude of excitation amplitude and excitation frequency with the bifurcation theory is obtained. Finally, the bifurcation characteristics under different parameters is analyzed.According to the nonlinear characteristics of the friction self-excited vibration, the Washout filter method which can control the bifurcation point of the friction self-excited vibration. How to using the Washout filter technology control the Hopf bifurcation phenomenon in a system is studyed. The control point is selected according to the Hopf bifurcation point of the prototype system, the linear gain coefficients and the nonlinear gain coefficient of the Washout filter are determined according to the Hopf bifurcation conditions, through the above measures, the subcritical Hopf bifurcation is controlled with the supercritical Hopf bifurcation of the self-excitation system, and thus the vibration amplitude of the friction self-excited system obtained is greatly reduced. Finally, the Washout filter control method is verified to be effective with a numerical simulation.Finally, the theoretical research and numerical simulation on the machine cutting chatter has been carried out, verifying the theory and the simulation results of friction self-excited vibration system derived in the above chapter.in order to prove the theory and simulation conclusion of the friction self-excited vibration system derived in the above chapters, the cutting chatter simulation of the machine tool is conducted. Through analyzing the change of the cutting force in cutting process conditions, a multidimensional nonlinear system model of the cutting chatter is established, which contains the subsystems of the workpiece and the tool; and then with the theory of mechanics and mechanical dynamics theory, the vibration equation of the whole system is established. Finally, based on the Poincare maps and bifurcation theory, the global bifurcation diagram about the system vary with the feed is obtained; the results of numerical simulation of the1:1internal resonance,1:2and1:3resonance in mechanical system are obtained with the help of the MATLAB software.In this paper, the research work of this paper has certain reference value on the dynamics characteristics of the friction self-excited vibration system.