Dynamic Research On Vibro-impact System With Clearance

Vibro-impact system with clearance is the common nonlinear dynamic system, there arevaries of errors among different mechanical equipments in the process of producing,manufacturing and assembling, which leads to clearance in mechanical equipment; moreover,in the process of commissioning and operation, clearance takes place because of impact andfriction. In addition, take different factors of the mechanical equipment into consideration,some mechanical equipment reserves clearance in the process of designing, there is clearancein relating components of meshing gear and rolling bearing, these clearance cannot beeliminate and avoid, clearance cause variation of contact condition in contact area, componentof the mechanical equipments constantly have repeated impact, collision between impactleads to local deformation of the component structure, in the process of impact, transmit offorce wave have serious consequence on loading and dynamic character of the system. Hence,for vibro-impact system with clearance, how to take use of its advantages and get rid of thedisadvantages is of great significance in improving the reliability of the system. This papermakes specific study aiming at three vibration models of these vibro-impact systems.1. This paper study three typical vibro-impact system. By establishing mechanics modelof the vibro-impact system, then making force analysis for the system, afterwards, theoreticaldeduce the periodic motion using numerical analysis method. Decoupling the equations set bytransformation of coordinates, work out the via model matrix method; boundary conditions ofthe periodic motion combining general solution of the equations set periodic center fixedpoint, deduce a series of results such as the analytical solution of the three kinds of typicalmodel system, linearization matrix, then gets various of Poincaré mapping throughcalculating.2. Analyzing the complicated dynamic behavior of the system such as bifurcation andchaos, find out the stability of the system by matlab software programming using Poincarémapping theory. The veracity of result and bifurcation and chaos phenomenon are checked bynumerical simulation. In addition, the trend chart of the linearized matrix eigenvalues whichtransverse the unit circle is given. Proper system parameters are found during the process ofnumerical simulating, study the vibro-impact system of different models under differentcircumstances. And Poincaré section diagram in the process of the system leading to chaos isgot.3. We can draw some conclusions from the simulation process that: some parameters ofthe system such as excitation frequency, clearance, recovery coefficient, etc, the controllingfor the variation of the parameters has great influence on the motion of the system, thechoosing of the system parameters near the critical point is very vital in vibro-impact system, the parameters which is got from simulation offer theoretical reference to vibration systemcontrol and the optimization of the mechanical design.