Abstract: Static stiffness is an important performance index of hydrostatic cylindrical guide. The static stiffness of the hydrostatic cylindrical guide with five degrees of freedom is modeled. Considering that the hydrostatic cylindrical guide is a series system consisting of guide column and hydrostatic linear bearing, firstly, geometric relationship between displacement of worktable and deformation of the guide column and displacement of the hydrostatic linear bearing was given,and the mathematical expressions of the stiffness coefficients under five degrees of freedom were derived according to definition of the static stiffness of the hydrostatic linear cylindrical guide. Secondly, the linear superposition principle was used to deduce deformation equation of the guide column under bearing force by using the theory of beam bending deformation. Thirdly,formula for bearing capacity considering the influence of guide column deflection was derived by using the Gaussian integral and hydrostatic lubrication theory, and the displacement of the bearing bush relative to guide column was obtained. Finally, a test rig for the cylindrical hydrostatic guide rail was developed,and the static stiffness under five degrees of freedom were measured to verify the theoretical model in this study. The results show that the model for the static stiffness of the hydrostatic linear cylindrical guide with five degrees of freedom has high precision, which can lay a theoretical foundation for analyzing the static characteristic of the hydrostatic linear cylindrical guide.

Key words: hydrostatic linear cylindrical guide, static stiffness, 5 degrees of freedom, beam bending deformation theory, hydrostatic lubrication theory