A new numerical calculation method for the characteristics of hydrostatic slide

In the design and manufacture of the ultra-precision machine tools, hydrostatic slides have been applied frequently, in the state-of-the-art technology. They can provide extremely smooth and accurate motion and positioning. At design stage, the carrying capacity and the stiffness of hydrostatic slide is an important value. But, the traditional calculation method of slide stiffness used in engineering is an approximate solution, the accuracy is low. In this paper, finding an accurate calculation method of slide stiffness is present, to improve modeling accuracy. Reynolds equation is the basic equation of calculating performance of hydrostatic slide, oil film pressure distribution can be obtained by solving the Reynolds equation. But Reynolds equation is a second-order partial differential equations, it is difficult to directly solve the equation using analytic methods. Therefore, a discrete model is developed to solve the problem. A method that has been widely used is finite element analysis (FEA). Matlab PDE Toolbox provides a convenient way to solving the partial differential equations based the FEA. But it can only directly solve the partial differential equations with standard form. It is discussed how to transform the Reynolds equation into elliptic partial differential equation with standard form. Then combined with the specific boundary conditions, obtain the oil film pressure distribution through Matlab PDE toolbox, and then write program to achieve high-precision calculation of carrying capacity and stiffness of the slide.