目的 为了对滚珠丝杠接触热导及磨损进行深入的研究,为滚珠丝杠的设计优化提供理论指导。方法 本文将建立考虑摩擦因数的滚珠丝杠接触面接触热导模型。以三维分形理论为基础,对滚珠丝杠粗糙接触表面进行建模,通过分析滚珠丝杠粗糙表面接触的变形状态与滚珠丝杠表面接触特征,建立了滚珠丝杠粗糙表面接触热导模型。通过球盘磨损等效实验得到了滚珠丝杠磨损系数与载荷以及转速的关系,修正了传统Archard模型。分析了分形参数,摩擦系数与实际接触面积之间的影响,探究了分形参数,摩擦系数与滚珠丝杠接触表面接触热导的关系,并获得了接触载荷对接触表面接触热导的影响规律。结果 分形维数与接触热导以及实际接触面积呈正相关关系,同时随着摩擦因数的增大,接触面间的接触热导减小。分形维数大于2.6时,可以看出,考虑摩擦时接触热导明显大于没有考虑摩擦接触的情况,分形维数约等于2.8附近图像出现拐点,接触面的接触热导开始减小。结论 分形维数的增加能够提高实际接触面积及界面传热能力,但摩擦效应会削弱界面有效热传导能力。摩擦因数对接触热导的影响呈现明显的非线性特征,在D≈2.8附近出现临界转折现象说明界面热传导能力并非随分形维数单调增强,而是在高分形维数区间受到摩擦-热耦合作用的显著影响。此外,工程实际中考虑摩擦时,会去除表面氧化膜等,使得丝杠本身的金属材料暴露,从而有高的导热率。
Abstract
To investigate the thermal contact conductance and wear behavior of ball screws and provide theoretical guidance for design optimization, the work aims to establish a thermal contact conductance model for ball screw interfaces with friction effects considered. Based on three-dimensional fractal theory, a rough contact surface model of ball screws was developed. By analyzing the deformation state and contact characteristics of the rough surface, a thermal contact conductance model for the rough surface of ball screws was established. The effect of fractal parameters, friction coefficient, and actual contact area was analyzed. Meanwhile, their relationship with the thermal contact conductance of the ball screw interface was investigated. The effect of contact load on thermal contact conductance was also investigated. The analysis revealed that the fractal dimension was positively correlated with thermal contact conductance and actual contact area. In contrast, thermal contact conductance decreased with an increasing friction coefficient. When the fractal dimension exceeded 2.6, thermal contact conductance considering friction became significantly higher than that without friction consideration. Near a fractal dimension of approximately 2.8, an inflection point appeared in the curve, and thermal contact conductance began to decrease.
Furthermore, considering that the working contact pair of a ball screw involved point contact between the balls and the raceway, a ball-on-disc wear test was employed for equivalent simulation. In the experiments, a ball and a disc made of the same material were processed with identical methods and subjected to the same surface heat treatment as the ball screw pair. The ball had a diameter of 6 mm, and tests were conducted with a fixed rotational radius of 8 mm under various rotational speeds and loads. The mass difference before and after wear was measured, and the wear volume was calculated based on the material density. This volume was then substituted into the traditional Archard model to derive the wear coefficient. Experimental results indicated that the wear coefficient was not a fixed value but varied with changes in rotational speed and load. The findings reflected the relationship between the wear coefficient of the ball screw and variations in load and rotational speed. With this relationship, the traditional Archard model was modified, and a ball screw wear model incorporating a variable wear coefficient was established. The new model was employed to investigate the effects of fractal dimension and fractal scale coefficient on the wear rate. The effect of rotational speed on the wear rate was also examined. The wear rate curve exhibited a shape similar to a bathtub curve, indicating that the wear rate was relatively low at moderate fractal dimension levels.
Therefore, in the design of ball screws, the friction coefficient and fractal scale coefficient should be minimized as much as possible. The design must simultaneously meet operational requirements and precision tolerances. This approach helps prevent localized overheating caused by frictional heat during high-speed operation. Such overheating could otherwise lead to uneven thermal expansion. In practical engineering applications, the surface oxide layers may be removed due to friction, thereby exposing the base metal of the screw. This process contributes to an improvement in thermal conductivity.
关键词
分形理论 /
接触热导 /
摩擦因数 /
滚珠丝杠
Key words
fractal theory /
thermal contact conductance /
friction factor /
ball screw
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基金
国家自然科学基金项目（52475124）; 陕西省秦创原“科学家+工程师”队伍建设项目（2025QCY-KXJ-165）; 西安市“科学家+工程师”队伍建设项目（24KGDW0026）
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