Study On Bifurcations And Chaos Of Dynamic Contact Of Guideway Joint Of Machine Tools

With the development of science and technology, the nonlinear phenomenon in natural sciences and engineering dynamical problems is becoming prominent and hot research. In the field of mechanical engineering, there are large numbers of the hysteresis phenomenons. Thus, the research of chaotic characteristics of hysteresis systems has a broad application prospects. In this paper, theoretical analysis, numerical calcuation method and graphical method are utilized to analysis the dynamical behaviors of guideway joint of machine tools. The main contents include the following:Firstly, the important significance of studying on nonlinear vibration is shown, and the progress about researching of chaos is briefly reviewed, and the study background is shown. Some necessary theoretical knowledge of bifurcation and chaos is preliminary introduced. Poin-care mapping method and Lyapunov exponent method , which are mianly used in this paper, are descrided in detail.Secondly, taking into account hysteretic characteristics of guideway joint of machine tools, a bilinear hysteresis model is utilized to describe the dynamical behavior of system, and the equation is given.Thirdly, the asymptotic method, which is used to solve nonlinear equations, is briefly introduced, and the equivalent coefficients of damping and stiffness to the hysteresis can be deduced by means of this menthod.Fourthly, Matlab software is used to analysis the numerical solution of system. Range-Kutta method is used to iteretive calculate the equation, and Wolf method is utilized to calculate the time series of system. Different characteristics graphics are charted through the prepraration and operation of the program codes.Fifthly, the nonlinear dynamical behavior of guideway joint of machine tools in changing excitation frequency and damping is discussed. Nonlinear dynamics techniques, such as bifurcation diagrams, the largest Lyapunov exponents, phase diagram, and Poincare sections are employed to ascertain dynamics responses of the system. By analyzing the dynamical behavior of the model, the result is that under some special parameters, the system has chaotic behaviors.