Dynamics Research On Nonlinear Mechanical Vibration System

With the increasing complexity of modern mechanical structure and the increasing movement speed, the problems of nonlinear vibration caused by clearance and dry friction are widely existed. In this article, dynamics model of two kinds of common mechanical system is established which used the combination of theoretical analysis and numerical simulation and studied the motion law of the system under different parameters. The main contents of this article are as following:Firstly, research status of home and abroad and its significance of the nonlinear mechanical vibration system are summarized. Later, the main unsolved problems in this field are surveyed. Specific contents and the research steps adopted in this article are given, from the aspect of stability, bifurcations, chaos, attractors, Poincaré mapping and Floquet theory, thus formed theoretical basis of this article.Secondly, a simplified model of the three-degree-of-freedom linear screening system is established. Considering only nonlinear factor of the gap which can lead to the jump of the system movement speed, by using Floquet theory and Matlab programming simulation, explored the law of system with different parameters between codimension-one bifureation and codimension-two bifurcation, it is found that the system not only has a flip bifurcation and torus doubling bifurcation to chaos of the single path, but also has period doubling bifurcation, Neimark-Sacker bifurcation and torus doubling bifurcation between intersection and transition, and finally leads to chaotic road. In the system of codimension-two bifurcation, the Hopf-Hopf bifurcation is found, the dynamic behavior in the vicinity of the codimension-two bifurcation point is very complex, which showed quasi periodic attractors that are being similar with "eyes", "star shaped" quasi periodic attractors. Based on the analysis in the dynamic characteristics of the system under different parameters, the states of the system in different frequency are obtained, which can help people to choose more appropriate vibration parameters to some extent, such as, frequency, amplitude and vibration force, etc and help people improve the separation efficiency of the screen.At last, a simplified model of a two-degree-of-freedom of the disc brake system is established. At the same time, considered the two nonlinear factors of clearance and dry friction and the system's critical condition of sticking-slipping-collision is given, using the semi analytical method to derive the mathematical expression of the differential equations of motion of the system. The working out of Matlab procedural and numerical number simulates the system's partial braking function. Firstly, its influence on the friction force between the brake pad and brake disc is analyzed and its influence on braking systems' movement law. Secondly, when the braking system's resonance is happening, the parameter characteristics are analyzed. In the influence of the track's vertical excitation, the effect of braking speed on the vertical vibration of the system is analyzed, and in the situation of the combination between chatter and friction chatter caused by the vertical excitation are also analyzed. Through the analysis of the effect of the vehicle disc's braking system on different influential factors and also have a simulation analysis, it provides a reference for reducing the bad vibration and noise and improve the stability and traveling comfort of the train.