Abstract In this study, a novel analytical model considering practical oil pressure and a cantilever plate bending calculation method is proposed to calculate the deformation of a vertical hydrostatic guideway. Based on the governing equations of rectangular thin plates, the finite integral transformation theory and the series-by-item differential transformation theory are used to solve the bending deformation of the target guideway to avoid the errors caused by an artificially selected deflection function and Kirchhoff’s hypothesis. The deformation values obtained from finite element simulation and experiments are compared with those calculated from the model. The comparison results show that the proposed model is capable of providing deformation values that are in better agreement with the experimental values than simulation values and its computation time is much less than that of the finite element method. The quantitative relationship between the actual oil film thickness and the performance of the hydrostatic guideways considering the size effect of the oil film thickness is studied.

中文翻译：

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基于悬臂板弯曲计算法的静压导轨变形分析

摘要 在本研究中，提出了一种考虑实际油压的新型分析模型和悬臂板弯曲计算方法来计算垂直静压导轨的变形。基于矩形薄板的控制方程，利用有限积分变换理论和逐项微分变换理论求解目标导轨的弯曲变形，避免人为选择的挠度函数和基尔霍夫假设引起的误差. 将从有限元模拟和实验获得的变形值与从模型计算的变形值进行比较。对比结果表明，所提出的模型能够提供比模拟值更符合实验值的变形值，并且其计算时间远小于有限元方法的计算时间。研究了实际油膜厚度与考虑油膜厚度尺寸效应的静压导轨性能之间的定量关系。