静压圆柱导轨系统静态刚度理论模型研究

静态刚度是静压圆柱导轨系统的重要性能指标，然而到目前为止尚未见到该类导轨静态刚度的理论模型。研究建立静压圆柱导轨五自由度静态刚度模型，考虑到静压圆柱导轨系统是由导柱与静压直线轴承的串联系统，首先，给出了工作台位移与导柱变形、静压直线轴承位移之间的几何关系，并根据静压圆柱导轨五自由度静态刚度的定义，推导了各刚度系数的数学表达式；其次，基于梁弯曲变形理论，采用线性叠加原理推导导柱在轴承油膜力作用下的变形方程；再次，基于静压理论，运用高斯积分推导了考虑导柱挠曲影响的轴承油膜承载能力模型，提出了轴瓦相对导柱的位移计算方法；最后，搭建了静压圆柱导轨刚度测试装置，完成了五自由度静态刚度的测试，验证了理论模型。结果表明：建立的静压圆柱导轨五自由度静态刚度模型精度高，可为静压圆柱导轨静态特性计算奠定理论基础。

Modeling on Static Siffness of Hydrostatic Linear Cylindrical Guide

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.