Axial Static Stiffness Analysis Of Feed System With Ball Screw Considering Elastic Deformation Outside Contact Zone

Ball screw,with the characteristics of high transmission efficiency,reversibility,high precision and long service life,has become an important executive mechanism in the linear feed system of machine tool.Axial stiffness is the important performance of the linear feed system with ball screw,and modeling calculation of axial stiffness is an important research topic.The traditional model of the axial stiffness is established based on the Hertz point contact theory,which only takes into account the elastic deformation inside the contact zones of the screw-nut pair and bearing and the screw shaft.In fact,the elastic deformation of bearing mounting parts(end cover)and the elastic deformation outside the Hertz contact zone of the ball screw and bearing can also reduce the axial stiffness of the feed system.Therefore,considering the elastic deformation outside the Hertz contact zone,the flexible model of axial stiffness of machine tool linear feed system with ball screw is established,which is of important scientific significance and engineering value for the design of the machine tool feed system.In this paper,considering the elastic deformation outside the Hertz contact zone,the linear feed system of a typical grinding machine driven by ball screw is taken as the research object to conduct the modeling and analysis of the axial static stiffness of the feed system.The specific research work is as follows:1)The flexible model of machine tool linear feed system: Considering the elastic deformation of the bearing mountings and outside Hertz zones of the ball screw and bearing,and based on the stiffness of the screw shaft,screw-nut pair,bearing and end cover connected in series,the flexible model of the axial stiffness of the feed system is established.Considering the torsional deformation of the screw and based on the rod combination deformation theory,the axial stiffness of the screw is analyzed.2)The axial stiffness analysis of the ball screw: Considering the elastic deformation outside the Hertz contact zone of the balls and raceways and based on the Hertz point contact theory and the finite element method,the geometric relationship,the physical equation and the axial force balance equation are derived to establish the flexible model of the axial static stiffness of the ball screw.The flexible model is verified and the influence of elastic deformation outside the contact zone on the axial stiffness of the ball screw is analyzed.3)Analysis of the axial stiffness of the bearing and mountings: Considering the elastic deformation outside the Hertz contact zone of the rolling elements and the rings,based on the Hertz point contact theory and the finite element method,the geometric relationship,the physical equation and the axial force balance equation are derived to establish the flexible model of the axial static stiffness of the bearing is established.And then the model verification is conducted.Based on the finite element method,the axial stiffness of the bearing mountings is analyzed.4)Test study of axial static stiffness of feed system: A test method of axial static stiffness of the linear feed system with ball screw is proposed.The axial static stiffness of a grinding machine linear feed system with ball screw is tested to verify the accuracy of the flexible model.And then,the influence of each component on the axial stiffness of the feed system is analyzed.The results of study suggest:1)Compared with the traditional rigid model,the axial stiffness values of the ball-screw pair,bearing and linear feed system calculated by using the flexible model proposed in this paper are closer to the actual measured values.So the influence of the elastic deformation outside the Hertz contact zone of the screw-nut pair and rolling bearing on the axial stiffness of the feed system cannot be ignored.2)The elastic deformation outside the Hertz contact zone of the screw-nut pair and rolling bearing can be solved by the finite element method.The loading method that the rigid ball simulates contact force is proposed in this paper,which not only solves the loading problem of the contact force,but also can obtain the linear and angular displacements between the raceway and the ball resulting from the elastic deformation outside the Hertz contact zone.The calculation technique and boundary condition processing method are simple and feasible.3)For the example in this paper,the contribution to the feed system stiffness in descending order is: rolling bearing,screw-nut pair,screw shaft and bearing end cover.The rolling bearing is the weak link in the feeding system,so the axial stiffness of the feeding system can be significantly improved by improving the bearing stiffness.