Dynamic Characteristics Of Impact Vibration System With Dynamic Friction And Its Engineering Application

Vibration systems with friction and clearance are often encountered in mechanical and vehicle engineering applications,such as cylindrical roller bearing rotation systems,train disc brake systems,etc.Such collision vibration systems are often affected by dynamic friction and random factors.Changes in some specific parameters of the system often cause essential changes of the response of the system,such as the phenomenon of bifurcation,which causes the dynamic instability of the system.If the instability is not controlled timely,it will lead significant damage to the dynamic structure.So we need to know more comprehensive understanding of the dynamic behavior about such systems.Therefore,this paper establishes several types of collision vibration system models of dynamic friction and clearance with certain progressive relationship by considering the dynamic friction,clearance,collision and other factors based on the simplified vibration system model of the train disc brake system.The differential equations of the system are obtained.The dynamic characteristics of the system and the system parameter influences on some dynamic behaviors are analyzed by numerical simulation.The application of such systems is studied by examples in practical engineering.The main contents and conclusions of this paper are as follows:Firstly,based on the classic friction-containing single-degree-of-freedom vibration system model simplified by the train disc brake system,considering the factors such as clearance,collision and random interference,Dankowicz dynamic friction,Lu Gre dynamic friction and improved Lu Gre dynamic friction are introduced.In the model,a single-degree-of-freedom rigid and elastic collision vibration system model with dynamic friction and clearance is established.The differential equations of the system are obtained and the system states of the motion are analyzed.Based on the system bifurcation diagram,phase diagram and time history diagram,the numerical simulations are used to analyze the various friction-induced vibration modes of the system under certain parameters,and the influence of specific parameters on the system dynamics behavior and the dynamics under random disturbance are analyzed.The results show that the rigid collision system presents friction-induced viscous chaotic vibration,viscous-slip-impact motion,special edge collision and flutter motion in different motion modes.The random excitation interference makes the system’s phase-track appear divergent trend,and its collision at the right constraint is greater.There are two different complex evolution processes in the elastic collision system:(1)slipcollision contact-contact separation slip-viscous-collision contact-contact separation slipviscosity;(2)slip-fluctuation-collision contact-contact separation slip-fluctuation-viscouscollision contact-contact separation slip-double viscous-collision contact-contact separation slip-collision contact-contact separation;random excitation interference makes the system’s phase rail also show divergence trend,and as the random excitation intensity increases,the system’s phase-track will have irregular divergence behavior.In engineering practice,most of the disc brake system and the cylindrical roller bearing rotation system are multi-degree of freedom vibration systems.The increase of the degree of freedom makes the system’s mechanical modeling,motion process analysis and numerical simulation more complicated.Dynamic characteristics will be more complicated too.Therefore,in order to facilitate the mechanical modeling and dynamic behavior analysis of the following engineering application examples,based on the previous single-degree-offreedom rigid and elastic collision vibration system modeling and dynamic analysis with dynamic friction and clearance,the dynamic friction with Dankowicz was established.The mechanical model of the two-degree of freedom one-sided rigid constraint and the double-sided rigid-constrained collisional vibration system with the clearance,the numerical simulation of the visco-slip flutter characteristics of the system is established.The two-degree-of-freedom elastic collision vibration system with Lu Gre dynamic friction and clearance is established.The mechanical model and numerical simulation analyze the effects of belt speed and clearance on the dynamic behavior and stability of the system.The results show that the two kinds of two-degree of freedom rigid collision systems have more obvious flutter at low frequencies,and there will be sliding-viscous-several collisions or flutter-slow-stay-sliding motions going back and forth,and as the frequency increases,fluttering and remain on the restraining surface is shortened until it disappears.The two-degree of freedom elastic collision system exhibits an adhesive motion before the elastic collision when the belt speed is low;when the belt speed is high,the relative velocity of the mass 1 and the belt changes between zero and greater than zero.When the gap of the two-degree of freedom elastic collision system is small,the adhesion motion occurs before the collision;when the gap is large,the adhesion motion occurs before and after the elastic collision.Finally,considering the actual impact vibration system of the project,based on the previous researches of dynamic friction and clearance collision systems,a model of single row cylindrical roller bearing system with Lu Gre dynamic friction and clearance is established.The numerical simulations of some key parameters of the system analyze the influences of dynamic behavior;a four-degree-of-freedom vehicle braking system model with Dankowicz dynamic friction and improved Lu Gre dynamic friction are established respectively.The differential equations of system are obtained.The eigenvalues according to the Jacobian matrix are solved to analyze the stability of the system.The numerical simulations concluded the vibration characteristics of the brake system in the longitudinal and vertical directions and the influence of some key parameters of the system on the dynamic behavior by phase diagram and time history diagram.The results show that the cylindrical roller bearing system has different motion periods when the excitation frequency is small.As the excitation frequency increases,the number of motion cycles of the system gradually decreases until it becomes the state of stable single-cycle;when the excitation frequency and the gap are small,the system evolves between chaos and period doubling bifurcation,and the system also exists multicycle state.In the four-degree of freedom vehicle braking system,the system is in an unstable state when we get some certain parameters.The longitudinal and vertical vibration displacement and velocity amplitude of the brake disc are increased by time,and the system will be destroyed finally.The longitudinal and vertical vibrations of the two brakes can be stabilized by adjusting the system parameters and the friction model parameters.