双螺母垫片预紧式滚珠丝杠副微分变化关系的推导与验证

为了推导出通用且符合滚珠丝杠副空间结构特点的微分变化关系,以双螺母垫片预紧式滚珠丝杠副为研究对象,建立了滚珠丝杠副中各坐标系间的齐次变换矩阵,在此基础上推导出了统一且直观的滚珠丝杠副中各坐标系间的微分变化式。通过该方法推导出滚动轴承的微分变化式,与权威滚动轴承文献中出现的微分变化式进行了对比,验证了该推导方法。并利用其他方法推导出滚珠丝杠副的微分变化式,与所使用方法推导出的滚珠丝杠副微分变化式进行对比,确保了所推导的滚珠丝杠副微分变化式表达式的可靠性。最后,根据所推导的滚珠丝杠副微分变化对比分析了不同的轴向静接触刚度建模,所建立的理论模型计算值较传统模型计算值与实验测量值更为接近。

Derivation and Validation of Differential Relationship of Double nut Pre tighten Ball Screw

In order to derive a general and proper transformed coordinate system according to the characteristics of ball screw mechanism, a double-nut pre-tighten ball screw was selected as an example of study.The homogeneous transformation matrix between the each coordinate system of the double-nut ball screw was first established.Then, based on it, the unified and intuitive relationship was derived of small displacement and rotation and force between the coordinate systems of the ball screw, by using differential transformation method.The differential relationship of the ball bearing was derived by the present method, and compared with the authority of differential relationship of ball bearing in the literature, to verify the derivation method.And the differential relationship of the double-nut ball screw was established by the other method, and compared with that of come from used method to ensure the reliability of the expression of relationship derived.Finally, according to the derived differential relationship of ball screws, compared and analyzed modeling of contact rigidity in different axial, the calculated value of theoretic model established is more closed to the measured value in experiment than that of a traditional model.