Research On Nonlinear Dynamics Of Cracked Rolling Bearing

Under long-term high-speed and heavy-load operation of train bearings,bearing materials are prone to contact fatigue,cracks and peeling due to crack propagation,which are potential hazards to train operation.The purpose of this paper is to study the dynamic behavior of axle box bearings in the case of cracked faults,and to provide a reference for bearing detection and other technologies.By establishing a multi-degree-of-freedom bearing impact vibration model and introducing crack faults with time-varying stiffness and time-varying clearance characteristics,the nonlinear dynamics and complex characteristics of the bearing affected by crack impact excitation are analyzed.First,based on Hertzian contact theory,the bearing elastic deformation theory is introduced and with the help of Solidworks software simulation,the theoretical stiffness of the bearing under load is calculated,and the damping of the bearing is analyzed and calculated based on the bearing’s own damping characteristics.Secondly,the dynamic characteristics of the impact vibration between the roller and the inner ring under the crack impact excitation are analyzed,the crack function expression with time-varying stiffness and time-varying gap is introduced,and the differential equation established is solved with the help of matrix function theory,and analyzed Conditions for the existence of periodic motion of the system.The accuracy of the model is verified by analyzing the vibration simulation diagram of the faulty bearing in the radial displacement velocity.The Poincaré map was established by analyzing the velocity displacement before and after the collision,and the complex dynamic behavior of the bearing was analyzed using the periodic cross section,combined with phase diagram,time history diagram,bifurcation diagram,and frequency spectrum diagram.This paper analyzes a type of two-and three-degree-of-freedom roller inner ring collision vibration models,and analyzes the path of the system to chaos in different frequency bands.It is found that in the low frequency band,the system has the characteristics of cycle doubling into chaos,and it is in the analysis.Catastrophic behavior appears at the bifurcation point.In the high frequency range,the system simultaneously has the dynamic characteristics of period doubling leading to chaos,intermittent leading to chaos,and Hopf bifurcation leading to chaos.Finally,the collision vibration model of the roller and the inner and outer ring under the double crack excitation is established,the differential equation is established and solved through mechanical analysis,and the Matlab-simulink software is used for numerical analysis and simulation verification.Through the establishment of the Poincaré map of the collision cross-section combined with the velocity-displacement phase diagram,time history diagram,and frequency spectrum diagram,the evolution process of the system from stable periodic motion to chaos is explored.By simulating the dynamic response of the crack excitation frequency and the crack gap to the radial vibration of the bearing,the dynamic characteristics of the bearing under different operating conditions are obtained.Analysis of this model shows that bearings with gaps in multiple degrees of freedom are more prone to multiple periodic motions and chaotic motions,and the paths leading to chaotic motions such as period doubling bifurcation,toroidal bifurcation,and Hopf bifurcation are found.In this paper,through the analysis of the dynamic behavior of the crack-faulted bearing,the evolution mechanism of the crack-fault is obtained,which provides a certain theoretical basis for the safe operation of the bearing.