Research On Nonlinear Dynamics Analysis Methods And Stablity Of Hysteresis Of The Contact System

In this paper, a model of bed lathe saddle-bed rail junction contact system as the research object, Using the method of nonlinear dynamics analysis to study the nonlinear dynamics characteristics and stability of hysteresis of the contact system. We shall first introduce the history of the contact problems and the development of the hysteretic system, the engineering background and the method of the subject. on the basis of them, describes the nonlinear dynamics of the contact system in chaos theory, bifurcation theory and the method of the nonlinear dynamic. Finally, using the method of the nonlinear dynamics to study the nonlinear dynamics characteristics of the contact system, and other corresponding problems, the main work as follows:To a certain type of bed lathe saddle-bed rail junction contact system as the research object, on the basesis of the previous studies, we established a single degree of freedom model with the hysteresis.According to the mechanical model, we analyzed this kind of hysteresis characteristics of the contact system, established the equations of the system, since this system has non-linear parts, so we applied the method of the equivalent linearization to analyse of the system.The fourth-order Runge-Kutta algorithm is used to analyze the contact system, and made use of the MATLAB software to study the system's nonlinear dynamics characteristics under the changes of the external excitation frequency, damping parameter, as well as external excitation amplitude.Making use of the bifurcation maps,time-history curve, phase diagrams and poincare sections of the system to analyze the convert and evolution of periodical response, double-periodical bifurcation,chaos of system response.from the analysis, we inclued that the system has chaos and bifurcation behaviors in some certain parameters.Using an approximation method of nonlinear systems to analyse the stability of the contact system, and obtained the movement state of the system is stable.Through studied the nonlinear dynamic characteristics of the machine tools, we attained some useful conclusions. For example, the contact system has the chaos and bifurcation behaviors in some certain parameters, which have a great influence for the machining accuracy and quality characteristics of the machine tools, so we must take into account of the impact when studied dynamic characteristics of machine tools, which have offerd theorical reference for the design of the future machine tools, and have a more practical significance.