Abstract: A calculation model of the axial static stiffness for a preloaded double-nut ball screw was improved by considering both the dimensional errors and radial loads. Firstly， based on Hertz theory， the ball load distribution and axial static stiffness model were improved considering the dimensional errors in the manufacturing processes and the radial loads caused by factors such as improper assembly. Secondly， the Newton-Raphson iterative method was used to calculate the axial static stiffnesses of the double-nut ball screws， and the loading deformation tests were carried out on the self-developed test bench to verify the correctness of the model. Finally， the influences of axial loads， radial loads and ball dimensional errors on the axial static stiffnesses of double-nut ball screws were studied by simulation analysis. The results show that the static stiffness model established has a good effect on describing the axial deformation displacements and axial static stiffnesses， which has a good reference significance for guiding the bearing capacity evaluation and precision design of the preloaded double-nut ball screw under static or low-speed conditions. 

Key words: ball screw, axial static stiffness, radial load, load distribution

摘要： 同时考虑尺寸误差和外部径向载荷，改进了一种预紧双螺母滚珠丝杠的轴向静刚度计算模型。首先，基于赫兹理论，考虑制造过程中的尺寸误差和因装配不当等因素引起的径向外部载荷，改进了滚珠载荷分布和轴向静刚度模型。其次，采用Newton-Raphson迭代法计算了双螺母滚珠丝杠的轴向静刚度，并在自行研制的加载试验台上进行了加载变形试验，验证了模型的正确性。最后，通过仿真分析，研究了外部轴向载荷、外部径向载荷和滚珠尺寸误差对双螺母滚珠丝杠轴向静刚度的影响。研究结果表明，所建立的双螺母滚珠丝杠静刚度模型对描述轴向变形位移和轴向静刚度有较好的效果，对指导预紧双螺母滚珠丝杠在静止或低速工况下的承载能力评估和精度设计有一定的参考意义。

关键词: 滚珠丝杠, 轴向静刚度, 径向载荷, 载荷分布