Analysis on Dynamic Contact Characteristics and Dynamic Stiffness Estimating Method of Single Nut Ball Screw Pair Based on the Whole Rolling Elements Model  
[PERSON]  
1 College of Mechanical Engineering and Automation, Liaoning University of Technology, Jinzhou 121001, China; [EMAIL_ADDRESS]  
[PERSON]  
2 School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; [EMAIL_ADDRESS] (Z.L.); [EMAIL_ADDRESS] (Z.L.)  
[PERSON]  
2 School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; [EMAIL_ADDRESS] (Z.L.)  
[PERSON]  
2 School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; [EMAIL_ADDRESS] (Z.L.)
and the phenomenon could be found from the computational results that load distribution was uneven with the unit of half a lead. [PERSON] et al. [3] verified the ball screw nut pair's uneven distribution, through photoelasticity, tag tracking and the FEM numerical method based on the half lead model. However, the models proposed by the above scholars cannot describe the contact state of the whole ball-raceway pairs, and the research on the screw nut is still in the stage of static analysis. [PERSON] et al. [4] introduced the method of medial axis transform (MAT), and analyzed normal force, contact angle and contact stress of contact surface between the ball and the raceway. [PERSON] et al. [5] researched ball screw pair kinematic characteristics by using the Frenet-Serret coordinate system, and proved that a sliding state existed in the screw and nut raceway. At the same time, [PERSON] et al. [6] also proposed three methods to obtain ball screws' mechanical efficiency. Based on his theory, the optimization design of the ball screw pair mechanical structure was carried out. According to the literature [5], [PERSON] et al. [7] carried out further research, and analyzed the dynamic variation of the contact angle, frictional force and slip angle of the contact surface between the ball and the raceway. However, the above scholars' ball screw pair dynamic analysis was in view of the assumption that the loading force of all the ball-raceway contact pairs is evenly distributed, which is contrary to the research results of [PERSON] and [PERSON]. [PERSON] [8] investigated friction characteristics. The effect of creep parameters on the ball screw friction and friction distribution were analyzed. [PERSON] [9] researched rolling element bearing, creep in one lap of ball screw nut pair, but he did not analyze all laps of the pairs. The axial, torsional and bending dynamic models of the ball screw were built, and the stiffness, mass and damping matrix of the system were derived [9,10]. [PERSON] et al. [11] established the mathematical model of the axial and torsional stiffness of the ball screw based on the fixed constraint of the ball screw. By using Simulink, a simulation model of CNC machine tool feed system considering the stiffness was established. However, the contact stiffness model of ball screw pair is not accurate because all contact states of ball and raceway are not considered. Moreover, the extraction of dynamic contact stiffness of ball screw pair has not been applied to mass production CNC machine tools.  
In view of the above problems, a dynamic contact model of a single nut ball screw pair (SNBSP) was proposed. Dynamic contact characteristics of an SNBSP were analyzed. Then, the stiffness sensorless estimating method of SNBSP was carried out. This paper consists of the following parts: In Section 2, dynamic contact mechanics model of an SNBSP was proposed. In Section 3, the influence of dynamic factors on contact normal force, contact angle and contact stiffness distribution characteristics of contact pairs are analyzed. In Section 4, a stiffness sensorless estimating method of SNBSP was proposed. An experiment is carried out by which the model is verified. Finally, Section 5 contains the conclusions.