Nonlinear Dynamics Study Of Fault Rolling Bearing System

Bearing is a kind of mechanical support widely used in various fields,especially in wheel and axle.Its performance is one of the important factors affecting the dynamic characteristics of rotating machinery.When the bearing fails,the ball will collide with the outer or inner ring during its movement.In mechanical equipment,clearance often exists in the parts of the equipment.Under the influence of external force,friction and bump will occur between the parts.More serious,it will lead to the damage of the equipment,which will threaten the operation safety of the staff,and even affect the durability of the equipment.Therefore,it is particularly important to study the collision problem so that the equipment can run in the most ideal state.In this paper,a three-degree-of-freedom impact vibration system and a three-degree-offreedom elastic impact vibration system model are established based on the engineering background of fault rolling bearings.The mechanical model is established according to the actual situation,and the differential equation of motion of the model can be obtained by analyzing the force exerted on the model.By analyzing the condition of boundary collision,we can get the periodic solution of the system and the condition of periodic motion.Based on the perturbation motion,the expression of Poincaré mapping and its Jacobi matrix are determined.The model is programmed with the software of Matlab,and then the dynamics simulation is carried out to analyze the bifurcation behavior of the two models and the way to chaos.Firstly establishes a kind of three-degree-of-freedom impact vibration system is established as an example with the fault rolling bearing model.By decoupling the whole system,modal analysis and reasoning,the corresponding Poincaré mapping expression and Jacobi matrix are obtained.The model is programmed and simulated by Matlab,and bifurcation diagram is obtained.Through image analysis,we can know that the system will undergo periodic doubling bifurcation,Hopf bifurcation and other bifurcation behavior under certain parameters,and finally lead to chaos.The bifurcation diagram is obtained by changing the mass ratio of plastids to analyze the effect of mass on the critical value of periodic bifurcation.In practical engineering,bearing motion should be kept in periodic motion range as far as possible to avoid serious consequences caused by instability.Then establishes its theoretical model according to the engineering practice of rolling bearing with inner ring fault.After the stress analysis of the model,the differential equation of the system is obtained,the periodic solution of the system is obtained by analyzing its boundary conditions,and the existence condition of the system bifurcation is analyzed by Floquet theory.The fourth-order Runge-Kutta method is used to program in Matlab.Then the system and performance dynamics simulation are carried out.By choosing appropriate parameters,the non-linear dynamic behavior of the system at low,medium and high frequencies is obtained.The path of the system to chaos is found through classical bifurcation(periodic doubling bifurcation,Hopf bifurcation,etc.)and non-classical bifurcation(jump,catastrophe,etc.).Then the dynamic behavior of the system is analyzed with the fault depth as a variable.It is concluded that the fault depth of the system should under the condition of rotating frequency.It provides a theoretical reference for the design and fault diagnosis of large rotary machinery.