基于Hertz接触的滚珠直线导轨副接触刚度建模与分析

为建立滚珠直线导轨副接触刚度模型,基于Hertz接触理论对滚珠和滚道的接触面进行了力学与变形分析.考虑了承载前后滚珠接触角的变化,得到了单个滚珠所受接触力与弹性变形之间的关系,在此基础上得到整个导轨所受外载荷同弹性变形的关系.以NSK滚珠直线导轨为研究对象,对所建立的模型进行仿真分析.计算了导轨在不同预紧力情况下的临界载荷,分析了外载荷在临界载荷前后导轨刚度变化情况,通过对比NSK官网相关资料验证了所建模型及理论分析的合理性.

Contact Stiffness Modeling and Analysis of Linear Ball Guides Based on Hertz Contact Theory

To construct contact stiffness of the ball linear guides model, mechanics and deformation of the contact surface between the ball and raceway based on Hertz contact theory were analyzed. The change of ball’s contact angle under loading was considered. The relationship of contact force and elastic deformation of the single ball was deduced. From this, The relationship of external load and elastic deformation of ball linear guides was deduced. Tooking the NSK ball linear guides as objects, the simulation of the proposed model was anylazed. The guide’s critical load under different preloads were calculated. The change of guide’s contact stiffness were analyzed when the external load was larger than the critical load and less than the critical load. By comparing the data on the NSK official website, the proposed model and the theoretical analysis are reasonable.