Dynamic Modeling And Vibration Analysis Of Ball Bearings With Local Defects Based On Variable Contact Area

Rolling bearing is one of the common parts of rotating machinery,once quality problems occur,it will directly lead to mechanical failure or even safety accidents.For bearings,after a long period of operation under normal conditions,the alternating load will cause cracks under the bearing surface,and the cracks will spread to the contact surface,resulting in a large area of spalling,which is fatigue spalling,which is the main reason for the failure of rolling bearings.The flaking pits caused by fatigue flaking will appear on the raceways and balls,and the flaking pits on the raceways are the most common.There are some progress in the research of vibration mechanism of fault bearing for the traditional bearing dynamic model,but some researches are still insufficient,which include the calculation model of the contact force in the defect zone,the effect of damping and clearance on vibration response of the bearing system.In this paper,a vibration model of deep groove ball bearing with a local defect is established based on Hertz contact theory.Firstly,an improved ball-defect contact force calculation model is established based on Hertz contact stress theory,and a vibration model of bearing system considering the mass of balls,inner and outer rings is established.Then,a vibration model of bearing system considering the effect of damping and non-uniform radial clearance of the bearing system is established.In order to solve the problem of calculating the ball-defect contact force on the raceway of the deep groove ball bearings,firstly,the problems existing in the traditional calculation method of ball-defect contact force and the effect of raceway curvature on the contact deformation between ball and raceway are analyzed;Secondly,a new method for calculating the ball-defect contact force considering the change of contact zone is proposed based on Hertz contact stress theory;Finally,the stress distribution and contact force curve of the ball passing through the defect are analyzed by finite element method,and the difference between the proposed algorithm and the traditional one is compared.In order to study the vibration mechanism of ball bearings with a local defect,the vibration model of ball bearings is established based on variable contact area,to analyze the effect of the local defect on the ball-raceway contact force and vibration characteristics of bearings.Considering the relative motion relationship among the inner ring,outer ring and balls,the fourth-order Runge-Kutta algorithm is used to solve the vibration model equations,and the vibration experiments of the bearing with a local defect under different loads are established.With the increase of applied load,the contact zone between the ball and raceway in the proposed model increases,the deformation of the ball passing through the defect increases,and the time span of the contact force changes is also increasing.The vibration experiment of the bearing with a local defect on the outer ring under different loads is established,the fault frequencies and vibration amplitudes of simulation signals are fully verified by comparing with the experimental measurement signals in time domain and frequency domain.At the same time,the differences between the proposed model and the traditional model are compared.The effect of non-uniform radial clearance on vibration mechanism of defective bearings is studied,the geometric model of the outer ring considering deformation is established,and the geometric expression of the deformed outer ring is given.The effects of non-uniform radial clearance on the ball-raceway contact force,the loading zone,the force acting on the outer ring and vibration characteristics of the bearing are analyzed.Time-frequency analysis of experimental and simulated signals is carried out.The results show that the non-uniform radial clearance has a significant effect on the vibration amplitude at the fault characteristic frequency.The effect of different dampings on the vibration mechanism of defective bearing is analyzed.The interaction forces between the inner ring,outer ring and balls are considered under different damping coefficients;The damping ratios of the defective bearing system with different viscous greases are measured experimentally,then the damping coefficients corresponding to different viscosities of greases are calculated.The vibration characteristic of the defective bearing system with different viscous greases is analyzed by the dynamic model.The results of experiment and numerical analysis show that different viscosities of grease can affect the vibration signal of defective bearing.In summary,the vibration model of deep groove ball bearing based on variable contact area proposed in this paper can better reflect the change of contact force when the ball passes through the defect zone of the raceway.At the same time,the effect of the damping and radial clearance on the vibration mechanism of the fault bearing is considered comprehensively.It is of great theoretical significance to study the vibration characteristics of the bearing with the local defect.