考虑热弹流润滑作用的滚珠丝杠副摩擦力矩建模与分析

针对以往研究中滚珠丝杠副摩擦力矩计算方法中未考虑润滑作用对其影响,或未考虑接触弹性滞后效应以及滑移摩擦效应对其影响的情况。首先基于单个滚珠接触效应建立其热弹流润滑方程;然后在考虑润滑效应的基础上建立其黏性摩擦力、弹性滞后摩擦力及滑移摩擦力方程;最后提出一种基于全滚珠载荷分布与热弹流润滑耦合的滚珠丝杠副摩擦力矩计算模型,建立了预紧力、转速与摩擦力矩之间的耦合关系。试验结果表明,当预紧力从1 kN变化到6 kN,在滚珠丝杠低转速(100 r/min)时,摩擦因数变化范围为0.005 6～0.006 5。随转速的提髙摩擦因数升高且变化量逐渐增大,说明国际标准DIN ISO3408-3:2006中将滚珠丝杠副空载摩擦力矩测量速度定为100 r/min具有合理性,验证了所提出的摩擦力矩计算方法的准确性。

Modeling and Analysis of Friction Torque of Ball Screw Considering the Thermal Elastohydrodynamic Lubrication

In previous studies, the influence of lubrication on friction torque of ball screw is not considered, or the influence of contact elastic hysteresis effect and the sliding friction effect are not considered. The thermal elastohydrodynamic lubrication equation is established based on the contact effect of a single ball. The equations of viscous friction, elastic hysteresis friction and slip friction are established on the basis of considering the lubrication effect. A calculation model of friction torque for ball screw based on the coupling of full ball load distribution and the thermal elastohydrodynamic lubrication is proposed. The coupling relationship among preload, rotational speed and friction torque is established. The experimental results show that when the preload changes from 1 kN to 6 kN, the friction coefficient of the ball screw varies from 0.005 6 to 0.006 5 at low speed (100 r/min). The variation of the friction coefficient increases gradually with the increase of rotational speed, which indicates that it is reasonable to set the measurement speed of no-load friction torque of ball screw as 100 r/min in the international standard DIN ISO3408-3:2006. The accuracy of the friction torque calculation method is verified.