Design of the Ball Screw Mechanism for Optimal Efficiency

Abstract

This paper develops theories for evaluating the efficiency of the ball screw mechanism and additionally, for designing this mechanism. Initially, a quasi-static analysis, which is similar to that of the early work in this area, is employed to evaluate efficiency. Dynamic forces, which are neglected by the quasi-static analysis, will have an effect on efficiency. Thus, an exact theory based on the simultaneous solution of both the Newton-Euler equations of motion and the relevant kinematic equations is employed to determine mechanism efficiency, as well as the steady-state motion of all components within the ball screw. However, the development of design methods based on this exact theory is difficult due to the extensive computation necessary and thus, an approximate closed-form representation, that still accounts for the ball screw dynamics, is derived. The validity of this closed-form solution is proven and it is then used in developing an optimum design methodology for the ball screw mechanism based on efficiency. Additionally, the self-braking condition is examined, as are load capacity considerations.

Effect of contact angle and helix angle on slide-roll ratio under the uniform motion state of BSM

“…Wei [1][2][3] introduced the theory of differential geometry of curve to analyze the motion rules of a ball considering the effect of the elastic deformation of contact angle and found that the self-spin and rotational angular velocities of the ball have an approximately linear relationship with the rotational velocity of the screw. Lin et al [4][5] confirmed the existence of both the rolling and sliding motions relative to each other between the ball and raceway during the operation of BSM and proposed a calculation model to estimate the transmission efficiency. Gnanamoorthy and Govindarajan [6][7] identified the slide/roll ratio of the contact point as the key factor influencing the wear velocity of the contact area.…”

A new method to calculate the friction coefficient of ball screws based on the thermal equilibrium

“…Therefore, many studies have been conducted for the calculation of the friction torque and the coefficient of friction is usually considered as a fixed value in these studies. Lin et al 4 developed a theory to design the ball screw mechanism and evaluate the efficiency of the mechanism. A peak efficiency can be obtained when the coefficient of friction is equal to 0.075 based on their study.…”

A new model for predicting the mechanical efficiency of ball screws based on the empirical equations for the friction torque of rolling bearings

“…Lin et al 9,10 presented two studies of the kinematics of ball screws to describe the ball motion and mechanical efficiency, which contributes to achieve the optimum design of ball screws. Based on Lin's study, Wei et al 11 studied the kinematics of a singlenut double-cycle ball screw by considering the friction force produced by a ball moving in an oil lubricant, in which both of the mechanical efficiency with and without oil lubrication were compared and discussed.…”