Dynamic Modeling And Analysis Of Angular Contact Ball Bearing On Electric Spindle

Rolling bearings,as important components for carrying and supporting the operation of the main shaft,are widely used in electric main shafts due to their advantages of easy maintenance,high rigidity,and high-speed performance.Its operating condition greatly affects the tool vibration on the electric spindle,the dimensional accuracy of the workpiece being processed,the life of the machine tool and the noise.Therefore,a more in-depth study of the dynamic characteristics of bearing components and revealing their internal operating mechanism can provide theoretical support for the optimization design of electric spindle bearings,increase the speed and machining accuracy of electric spindles,and explore the mechanism of internal defect generation.This subject takes angular contact ball bearings as research objects,and constructs a quasi-static model based on Jones orbit control theory.Based on the Newton-Euler method,a 6-DOF complete dynamic model of the component is constructed.Through mathematical modeling,programming calculation,and numerical analysis,the static characteristic parameters and dynamic characteristic parameter changes of electric spindle angular contact ball bearings are analyzed.The main content and research conclusions of are summarized as follow:(1)The relationship between the internal geometry of the bearing was described.The development process of bearing simulation modeling research and the research progress of electro-spindle dynamics were introduced.The structure of the electro-spindle and the composition of the electro-spindle system were briefly described.The internal load change of the ball bearing under static load was considered.The change of the geometric contact relationship of the angular contact ball bearing under different load conditions was analyzed.(2)A quasi-static analysis model of ball bearings at high speed was constructed.The bearing revolution and rotation speeds under high-speed conditions were calculated.Using Jones' track control theory,the internal load distribution of the ball bearings was analyzed,and the influence of structural parameters on the static characteristics of the bearings was revealed.Studies have shown that the increase in the initial contact angle causes the axial center position of the ball to be closer to its initial position and improve the axial load-bearing capacity.The increase in the coefficient of curvature of the raceway groove leads to a reduction in the load on the ball,resulting in improved bearing performance.(3)A 6-degree-of-freedom dynamic analysis model for angular contact ball bearings is constructed.The geometric relationship and kinematic relationship between the bearing components are analyzed.By considering the geometric interaction of the rolling elements and the rings,the dynamic equation is established by the Newton-Euler method,solved by the fourth-order Runge-Kutta method,and calculated by programming,To obtain the motion parameters(displacement,velocity,acceleration parameters)within a working cycle,and verify this model through the calculation results of the classic Jones-Harris model.(4)The influence of the inner ring tilting conditions and different structural parameters on the dynamic characteristics of the bearing was studied.From the angles of contact load,contact angle,and the boundary distance between the ball and the ring,the reason for the unstable working performance of the bearing under the tilting condition of the ring is revealed.The study found that increasing the curvature coefficient of the raceway groove helps increase the boundary distance,keep the ball away from the raceway boundary,and improve the dynamic performance of the bearing.Increasing the initial contact angle makes the ball closer to the boundary of the raceway,and the dynamic performance of the bearing deteriorates.