Modeling of Thermal Contact Resistance of Ball Screws Considering the Load Distribution of Balls

Abstract

A new analytical method for the modeling of the thermal contact resistance of ball screws considering the load distribution of balls is proposed in this research. The load on balls is analyzed by the force analysis of ball screws, and then, the thermal contact resistance is obtained by the minimum excess principle and Majumdar–Bhushan (MB) fractal theory. The proposed method is validated by experimental results. The comparison with experimental and former results indicates that it is an effective method to evaluate the thermal contact resistance of ball screws. On that basis, effects of axial load, axial pretension, and geometry error of balls are discussed. It is concluded that the thermal contact resistance of ball screws increases along with axial load increase. The load on balls all decreases with axial pretension increase, and the thermal contact resistance of ball screws decreases with the axial pretension increase as well. When the axial load is applied on the nut in an axial-pretension ball screw, the load distribution in Nut A or B becomes less homogenized when the nut moves from nut position parameter ξ = 0 to 1. When the nut moves to ξ = 0.25, the thermal contact resistance will reach a minimum value, and it gets a maximum value at the nut position ξ = 1. The interval range of load and thermal contact resistance are obtained via uncertain analysis. It is concluded that the geometry error has much greater effects on the balls far away from the spacer.