基于阻抗法的矩形截面均压槽气浮支承静态性能分析

针对CFD仿真方法效率低下的状况，提出利用阻抗法来提升气浮支承承载性能的计算速度. 以矩形截面均压槽气浮支承为研究对象，研究了当均压槽高度、角度、数量、半径和供气压力变化对气浮支承承载性能的影响. 结果表明:与CFD仿真方法相比，阻抗法在保证计算结果精度的前提下可提高气浮支承承载力的计算速度. 当均压槽高度、角度、数量、半径和供气压力增大时，阻抗比会增加，气浮支承的承载力和刚度峰值对应的阻抗比也会增加. 当气膜厚度增加时，阻抗比会增加，但承载力会相应地减小. 本文作者通过阻抗法推导了气浮支承承载力简化计算公式，解决了气浮支承在均压槽方向上简化计算的难点，并为阻抗法在均压槽中的研究与应用提供了理论依据. 

Rectangle Section Pressure Groove on Static Performance of Aerostatic Bearings with Impedance Method

In view of the low efficiency of CFD simulation method, and most of the existing simplified calculation methods can only simplify the two-dimensional direction of the aerostatic bearings, for the simplified calculation of the aerostatic bearings with pressure equalizing groove involves little. In order to better solve this problem, this paper proposed the impedance method to improve the calculation speed of the bearing capacity and stiffness of the aerostatic bearings. It was found that the impedance method solved the aforementioned problems. The difficulty of simplified calculation in the direction of equalizing groove made up for the deficiency of the existing simplified calculation method of aerostatic bearings. In this paper, the impedance of slot, pressure equalizing cavity, pressure equalizing slot and gas film were established respectively. Then the concept of impedance ratio was defined. Through the calculation formula, the mathematical relationship between impedance ratio and pressure of slot orifice of aerostatic bearings was established, and the mathematical relationship between impedance ratio and bearing capacity was established. The calculation formula of bearing capacity was simplified. In addition, this paper investigated the influence of the above variables and film thickness on the impedance ratio, as well as the influence of the impedance ratio on the bearing capacity and stiffness of the aerostatic bearing when the height, angle, number, radius of the equalizing groove and the gas supply pressure changed. Through the analysis of the corresponding curve results, it showed that compared to CFD simulation method, impedance method improved the calculation speed of the bearing capacity and stiffness of the aerostatic bearings under the premise of ensuring the accuracy of the calculation results, and greatly reduced the simulation consumption. When the height, angle, number, radius and gas supply pressure of equalizing groove increased, the impedance ratio, the bearing capacity of aerostatic bearings and the impedance ratio corresponding to the peak stiffness increased. When the film thickness increased, the impedance ratio increased, while the bearing capacity decreased accordingly. When the impedance ratio increased, the stiffness increased firstly and then decreased, while the bearing capacity decreased with slow decreasing rate. This paper established the impedance of each part of the aerostatic bearings, then established the corresponding connection between the impedance ratio and the bearing capacity formula of the aerostatic bearings. Moreover, this paper deduced the simplified calculation formula of the bearing capacity of the aerostatic bearings by using the impedance method, which greatly improved the calculation speed of the bearing capacity and stiffness of the aerostatic bearings, and solved the difficulty of the simplified calculation of the aerostatic bearings in the three-dimensional direction of the pressure equalizing groove. It provided a theoretical basis for the research and application of aerostatic bearings with pressure equalizing groove.