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

Abstract

<p indent=0mm>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.