Dynamics Of Vibrating Systems Based On Hertz's Contact

In this paper, the dynamic characteristic of a nonlinear vibration system with clearance is simulated and analyzed, the influence of some changing main parameters on the system dynamic characteristic are studied, and parameter selection rules to make the system state stable are get. These are helpful to parameter optimization of general impact vibration system.Taking an double masses impact-forming machine as the study object, simplified it to be a dynamic model first, then list its dynamic equation based on Newton's second law, and give dimensionless processing to it. Then the classic fourth order Runge-Kutta methods with variable step are used to numerical simulation of system equations. The simulation results are displayed intuitively by bifurcation diagram, phase plan diagram and Poincaré section diagram. Give analysis and summary with the help of nonlinear research methods and other theories in the field. Mainly studied the periodic vibration and bifurcation characteristics of the system at the changing main parameters and exciting frequency, reveals the process from periodic motion to chaotic motion through quasi-periodic motion, and studied the influence of main parameters as restitution coefficient, Hertz contact stiffness ratio, Hertz contact damping ratio, system mass ratio, stiffness ratio, damping ratio, clearance and damping coefficient on impact and vibration characteristics of the system. Finally, the practical significance of the study is expounded.In general research, the contact form between the impact plane are act as rigid collision, but in order to get more accurate simulation data, this paper describes the collision force based on the Hertz's law mainly, act the contact form between the two masses as elastic collision. Moreover, give two kinds of elastic collision model, which one consider the influence of stiffness between the collision plane on Hertz contact force only, and another consider the influence of the stiffness and damping of the collision plane at the same time. Respectively study the dynamic response characteristics of the system under these two Hertz contact force, and compared them with the simulation results of rigid collision model, so as to select the research methods which satisfy the accuracy and efficiency at the same time.Simulation results showed that under most parameters, the system response experience transformation from periodic motion to quasi-periodic motion, and then to chaotic motion once or several times with the increase of vibration frequency, mixed many times doubling bifurcation, boundary crisis, multi periodic interval paroxysmal chaos and other complicated dynamic behaviors when system in poor stability. In order to make the system keep a relatively stable vibration state under various parameters, external excitation frequency must be kept in the middle and low frequency domain. In addition, the three models get similar results. Therefore, in similar study, rigid collision model can be directly used when qualitative analysis is needed only, and elastic collision model can be selected according to the accuracy requirement when quantitative analysis is needed, and then can get a higher simulation efficiency and accuracy simulation conclusion at the same time. The conclusions and methods can promotion in the field, for which have generality in the simulation study of similar impact vibration systems.