Analysis On The Contact Load And Stiffness Of The Single Nut Ball Screw

With the continuous improvement of machining accuracy,the demand for high-end CNC machine tools is becoming more and more important in China,and the high-end CNC machine tools have become an important factor restricting the modernization process and economic development of the country.As an important driving mechanism of NC machine tool,ball screw pair is widely used in the feed system.In the process of processing,the higher and higher requirements for the rotational speed of the ball screw,some vibration problems become more prominent,which seriously affect the positioning accuracy of the CNC machine feed system.Ball screw pair stiffness have important influence to the stability of the feed system,therefore,to establish precise ball screw pair stiffness model,analysis the influence factors of ball screw pair stiffness and law is of great significance.Based on the Hertz contact theory and deformation coordination conditions,the load distribution model based on the whole ball single nut ball screw was established.According to the differential coordinate transformation,the contact stiffness model of ball screw is deduced based on the load distribution model.Specific research contents are as follows:(1)Based on Hertz contact theory and differential geometry theory,deformation and coordination equation deformation was established.In order to characterize the relation of contact Angle with ball bearings,the nonlinear equations of the load distribution characteristics of ball screw are deduced,and the distribution model of ball screw is established.With New-Raphson numerical iteration method,developed the ball screw vice matlab numerical calculation of load distribution,the numerical calculation results with half lead load model computed results with reasonable characteristics,preliminary verified the ball screw nut pair model and the correctness of the numerical algorithm.(2)In order to further verify the ball screw pair of load distribution model is established,the accuracy of using ANSYS simulation platform,to establish finite element model of ball screw pair,explore the method of the model constraints,the constraints of ball contact calculation results,the finite element model of load distribution characteristics and distribution of load is obtained by theoretical model simulation feature comparison,further verify the validity of the theoretical model.(3)Based on the load distribution model of ball screw,the influence of axial load,guide path,rolling path curvature ratio and raceway effective winding number on the load distribution is discussed respectively.The results show that,with the increase of axial load,the increase of the screw lead,the increase of the effective winding number and the decrease of the curvature ratio,the load distribution is more and more remarkable.(4)According to the principle of load distribution model and differential coordinate transformation,the mathematical model of axial stiffness,lateral stiffness and swing stiffness of ball screw is deduced.Through numerical calculation,the influence and regularity of axial load,screw lead,effective winding number of ball bearing and roll curvature ratio of local stiffness and overall stiffness are analyzed.