Study On Aixal Contact Stiffness Of Ball Screws

Ball screw mechanisms have been widely used in feeding mechanism of precision mechanics, especially in the numerical control machine tools, due to its performance such as high accurate positioning, high stiffness, low friction, etc. The CNC's machining accuracy should be higher due to the development of modern manufaturing technique. In order to achieve this goal, the control of CNC's feeding machanism should be more precise. The axial contact stiffness of ball screw should be studied, because it is the weakest link of stiffness of CNC's feeding mechanism.The axial contact deformation and axial contact stiffness of ball screw have been studied in this paper, based on Hertz theory and force analysis of ball screw. The main cotent is as followed.1. The background of the task, the structure feature and working principle of ball screw are introduced. The present research situation and present production situation both in and out are summarized. The development trend of ball screw and the content of subject are presented.2. The factors that influence the axial contact stiffness of ball screw, e.g. shape of raceway, contact angle, ratio of raceway, are introduced. The theoretical model, which is used to calculated the the number of balls of ball screw is founded, the influence of helix angle is considered in this model. Circulating mode of balls, pre-loaded mode of ball screw and the working principal of pre-loaded ball screw are introduced, the determination of preload force is described. 3. Two hypothesis are proposed to establish theoretical model, which is used to solve the axial contact deformation and axial contact stiffness of ball screw. (1) The influence of ball screw's structure feature and manufacture error on load distribution is ignored. Consider that the load on every ball is equal. (2) The variation of contact angle is ignored, consider the contact angle is 45o unchanged. Hertz point contact theory is introduced, the method and process to solve Hertz point contact theory is discussed. The relations between axial force and normal force on ball, between axial deformation and normal deforamtion of ball are analyzed by establishing coordinate systerm. On this basis, the theoretical models which is used to solve axial contact deformation and axial contact stiffness of single-nut ball screw are established. Then, solve these models by numerical method, and draw the figures. The stiffness of single-nut ball screw becomes large as axial load and helix angle increased, which is derived from the analysis of axial contact stiffness model.4. The axial contact deformation of double-nut ball screw is analyzed and studied, when there is only preload on double-nut ball screw(axial load is zero). On this basis, the deformation of double-nut ball screw is studied, when the axial load acts on ball screw, force equation and compatibility equation of displacement are established. The theoretical model, which is used to solve axial contact deformation and axial contact stiffness of double-nut ball screw, is derived, by the analysis of force equation and compatibility equation of displacement which have been established. Solve the theoretical model by numerical method, according to related dimensions and parameters, the result of double-nut ball screw is compared with result of sing-nut ball screw, and draw the figures. The stiffness of double-nut ball screw will be decreased as load increases. But the stiffness of double-but ball is larger than the stiffness of single-nut ball screw, and the former is steadier than the latter. The stiffness of ball screw will become larger as the helix angle and the sitffness of spacing disc increase.5. The helix angle of ball screw if supposed to be zero, according to it's structure feature, in this way , the finite element model of ball screw can be established reasonably. On this basis, the simplified finite element model of ball screw is established. In order to ensure the precision of calculation and save the resources of calculation, finite element meshes are generated reasonably. In this way, the meshes beside the contact point are denseness, and the meshes far away from the contact point are sparse. The contact deformation of ball screw under different axial load is analyzed by the method of finite element analysis, and the result is compared with the result which is solved by theoretical model. In this way the theoretical model of contcat deformation of ball screw is verified.The study of this paper is helpful to the profound and system stduy on ball screw. According to this paper, the controlling parameter of CNC's feeding mechanism will be more precise, and this will be helpful to improve CNC's machining precision.