交叉滚柱直线导轨五自由度静刚度理论模型

Modeling and analysis on the static stiffness of cross roller guide under five degrees of freedom

交叉滚柱直线导轨广泛应用于机床等精密机械中,静刚度为交叉滚柱直线导轨的重要性能指标,然而到目前为止,尚未见到该导轨静刚度的理论模型的报道.本研究建立交叉滚柱直线导轨五自由度静刚度的理论模型.首先,基于Hertz线接触理论与弹性理论的Boussinesq解,采用分片法推导了滚柱-滚道接触力及接触力矩的函数表达式;在此基础上,建立直线导轨结合部变形协调方程、物理方程与静力平衡方程,迭代求解方程获得交叉滚柱直线导轨五自由度静刚度.其次,以一款交叉滚柱直线导轨为例,开展了导轨五自由度静刚度的实验测试,并与理论模型计算结果进行了对比,验证了本模型的正确性.最后,分析讨论了预紧力对交叉滚柱直线导轨各向位移及刚度的影响,为交叉滚柱直线导轨预紧力的调节奠定理论基础.

The cross roller guide has been widely used in precision machinery,such as machine tools,and contact stiffness is an important performance index of the cross roller guide.However,no report can be found on modeling about the contact stiffness of the cross roller guide.In this study,a theoretical model for the static stiffness of cross roller guide with five degrees of freedom was established.On the basis of the Hertzian line contact theory and the Boussinesq solution of elasticity theory,the function expressions of contact force and moment between the roller and the raceway were derived using the slicing method.On this basis,the guide deformation compatible equation,physical equation,and force equilibrium equation of the guide were established,and the static stiffness of the cross roller guide with degrees of freedom was obtained by iteratively solving the equations.Then,a test rig was developed to measure the static stiffness of the cross roller guide,and the proposed model was verified by comparing the experimental data with the theoretical results.Further analysis regarding the effect of preload on the displacement and stiffness of the cross roller guide was conducted,which lays a theoretical foundation for the preload adjustment of the cross roller guide.