Evolution Of Nonlinear Dynamical Responses With Parameters In Mechanical Vibro-impact System

There is a large class of engineering machinery such as vibrating shaping machines, Pavement compaction machines, vibrating screen machines, using vibro-impact to fulfill their engineering function. Meanwhile, vibro-impact system widely exists in other fields of engineering, for example gear drive, the train wheels and rail system. It is of great significance to discuss the vibro-impact system for utilizing its advantages or avoiding the negative effect like mechanical failure, structure damage and noise caused by the system.Whose nonlinear dynamics behaviors are extremely complex due to the vibrations and impacts. We usually discuss the dynamics responses under the qualitative and quantitative way with the nonlinear dynamics research methods such as phase diagrams, Poincare maps and bifurcation. In mechanical system, we particularly concern the relevance between mechanical behavior and parameters such as system’s restrain, clearance, frequency.In this paper, single-degree-of-freedom and double-degree-of-freedom vibro-impact system with clearance based on actual engineering machinery was established. The contacts collision course was defined by instantaneous impact method and the connect model of breaking spring and damping. With the help of four order Runge-Kutta method, differential equations were solved in Matlab calculating software. This thesis mainly covers the following four aspects.1. Single-degree-of-freedom free-oscillator vibro-impact system was established, kinetic equations were also put forward in this thesis. Simulate the dynamics responses with Matlab. Discuss the dynamic behavior under the method combining time response graph, phase diagrams, Poincare maps and bifurcation graph. Analyze the effect of system responses caused by different parameters.2. A dynamics analyzing method—Three-Dimensional Overall Bifurcation was innovatively provided on the basis of a case study on choosing parameters in vibrating shaping machines. System dynamics responses bifurcation graph controlled by two parameters was obtained. Based on the standard of real manufacturing process requirement, suitable range of parameters was selected as the research objects. All those are offered as a theoretical foundation for solving the practical problems.3. Double-degree-of-freedom vibro-impact system with unilateral constraint was established, kinetic equations were put forward and dimensionless quantity method was used to process the equations. Discuss the dynamic behavior and the stability of the system. Analyze the effect of system responses such as periodicity, bifurcation and chaos, caused by different parameters.4. The influences of nonlinear parameter elements on system responses in the nonlinear vibro-impact system were discussed in this paper. To be specific, in the system with single-degree-of-freedom, how the nonlinear spring with piecewise linearity affects its dynamics behavior; and in the double-degree-of-freedom system, how the nonlinear elements of air spring affect that.