Precision double-nut ball screws are key functional parts in machine tools. The positioning accuracy of a ball screw can directly affect the machining accuracy of a machine tools. During actual use, the preload degradation and the large axial clearance of the double-nut ball screw are caused by the contact wear, which directly affects the transmission positioning accuracy. The contact wear is focused on the ball and the rough raceway surface of the ball screw. Therefore, a novel method is proposed in this paper to characterize the rough spherical morphology of raceways for ball screws based on fractal theory, and the fractal parameters of the screw and nut raceways are identified. A fractal contact model of the asperity on the raceway surface is established. By introducing contact parameters to modify the contact area, an area distribution function suitable for the coordinated contact is obtained. A mathematical model for calculating the normal contact load of the ball screw in three states is established by considering the friction factor. A precision loss model of the ball screw is established based on the full ball load distribution model and the multiscale contact load model, and the proposed model is verified by experiments. The surface contact coefficient of the inner and outer raceways is discussed. The influence of raceway fractal parameters on the wear rate is analyzed, and coupling research on precision loss and preload degradation for the ball screw is carried out. The initial wear rate under different axial load is discussed, and the change trend of wear rate with time is analyzed. The precision loss model of the preload double-nut ball screw based on fractal theory provides a new theoretical basis for accurately predicting the precision degradation and provides method support for establishing the wear life prediction of a ball screw.

精密双螺母滚珠丝杠是机床中的关键功能部件。滚珠丝杠的定位精度直接影响机床的加工精度。在实际使用过程中，双螺母滚珠丝杠的预紧力退化和轴向游隙较大是由于接触磨损造成的，直接影响传动定位精度。接触磨损集中在滚珠和滚珠丝杠的粗糙滚道表面。因此，本文提出了一种基于分形理论表征滚珠丝杠滚道粗糙球形形态的新方法，并确定了丝杠和螺母滚道的分形参数。建立了滚道表面粗糙度的分形接触模型。通过引入接触参数来修改接触面积，得到适合协调接触的面积分布函数。考虑摩擦系数，建立了计算滚珠丝杠三种状态下法向接触载荷的数学模型。基于全滚珠载荷分布模型和多尺度接触载荷模型建立了滚珠丝杠精度损失模型，并通过实验验证了所提出的模型。讨论了内外滚道的表面接触系数。分析了滚道分形参数对磨损率的影响，进行了滚珠丝杠精度损失与预紧退化的耦合研究。讨论了不同轴向载荷下的初始磨损率，分析了磨损率随时间的变化趋势。