Characteristic Analysis Of Angular Contact Ball Bearing For Precision Machine Tool Spindle Under Multi-physical Field Coupling Condition

Angular contact ball bearing is one of the common bearings of precision machine tool spindle.There are many reasons for the decline of angular contact ball bearing’s accuracy,however at present,most of the research is focused on mechanics and elastohydrodynamic analysis,while theoretical calculations of bearings specially for wear or considering the effects of wear are relatively scarce.Therefore,this paper established the mechanical,elastohydrodynamic and wear analysis model of angular contact ball bearing for precision machine tool spindle under the coupling condition of displacement field,stress field and elastohydrodynamic field,and explored the relationship between the bearing’s load,deformation,wear and the bearing’s working condition,structural parameters,lubrication conditions.(1)The static theory has been firstly used to calculate the deformation of the spindle bearing system of the machine tool,and also to explore the relationship between the load and deformation.Then the bearing’s motion including the rolling element’s revolution speed,rotation speed and raceway speed were calculated by using raceway control theory.On this basis,considering the effects of centrifugal force and gyroscopic moment,the three-dimensional mechanical analysis model of angular contact ball bearing has been established using the pseudo statics method.Based on case study,the influence of bearing structure and working condition on its inner load,displacement and deformation were analyzed.(2)Based on the elastohydrodynamic lubrication theory,a two-dimensional elliptical contact isothermal elastohydrodynamic lubrication model of angular contact ball bearing has been established.The model was solved by multi grid method,Gauss seidel linear relaxation iteration method,Jacobi linear iteration method and the improved stiffness matrix method.The distribution in the contact area of elastohydrodynamic pressure,lubricant viscosity,lubricant density and film thickness have been calculated.The MATLAB program was used to verify the model and also to analyze the influence of structure parameters and load conditions on lubrication.(3)The distribution of friction coefficient,slip distance and wear coefficient toward to the direction that perpendicular to the motion in the contact area under both elastohydrodynamic lubrication and lean oil lubrication were calculated by Archard fatigue wear calculation theory,and were applied to angular contact ball bearing for establishing the bearing raceway fatigue wear calculation model.Taking 7006 C as an example to verify the model,the effects of different loads,speeds and structural parameters on bearing wear have been analyzed,and the effects of bearing wear on contact and elastohydrodynamic conditions including contact load,contact angle,elastohydrodynamic pressure and elastohydrodynamic film thickness were also studied.(4)Taking bearing wear depth as feedback parameter,a coupling model of mechanics,elastohydrodynamic and wear has been established,and the reliability of the model was verified by comparing with L-P life.At the same time,the structural parameters including curvature radius of inner and outer raceway and diameter of rolling element,the working conditions including external load and spindle speed,and the lubrication conditions including surface roughness and initial viscosity of the lubricating oil were all changed respectively to analyze their affections on shaft stiffness,radial stiffness and bearing’s wear life.The results show that the increase of bearing load will,on one hand,lead to the deterioration of lubrication and wear,and on the other hand,help to the rise of axial,radial and angular stiffness.The rotational speed has little effect on the bearing’s mechanical properties like displacement or deformation,however it will cause the expand of the oil film thickness and friction coefficient.Compared with the number of balls,the bearing’s characteristics are more sensitive to the change of inner and outer raceways’ curvature radius and the ball’s diameter.The growth of bearing surface roughness and the decline of lubricating oil viscosity will both lead to the rapid change of fatigue wear,but has tiny help to the elastohydrodynamic wear.At the same time,the wear of the bearing raceway will add the load on itself,and meanwhile cause the lubricating oil to increase in viscosity and also decrease in density.