基于Hertz接触的滚珠丝杠副结合部刚度特性分析

摘要

滚珠丝杠副传动时，螺母滚道和丝杠滚道与滚珠的接触方式是一种典型的非线性接触。基于弹性力学中Hertz接触理论，分析计算双螺母预紧滚珠丝杠副的轴向接触刚度。以某型号预紧双螺母滚珠丝杠副为例，建立其所受载荷与轴向接触变形的函数映射关系，推导其结合部接触刚度计算方法。针对其空载与承载两种不同状态，计算其结合部轴向接触刚度，并着重讨论了载荷对接触刚度的影响规律。基于有限单元法，对接触刚度计算结果进行数值验证，结果表明所建立的结合部接触理论模型能快速、准确的计算双螺母滚珠丝杠副的接触刚度，具有一定的理论价值和工程意义。%The contact between balls and nut races or screw races is a kind of typical non-linear contact. The axial stiffness of a double-nut ball screw was analysed and calculated by using the Hertz Contact Theory of elastic mechanics. A double-nut ball screw is selected as an example, the function of the axial contact de-formation and the cutting load was built, and the contact stiffness model was developed . Under the situation with and without the cutting load, the axial stiffness of joint part was investigated, and the effect of cutting load was focused on. Finally, the finite element model was employed to verified the theoretical model. The analytical results show that it can not only calculate the contact stiffness quickly and exactly, but also offer theoretical support and engineering meaning.