為了在性能與壽命上有更好的表現，液靜壓軸承在超精密加工設備上經常扮演舉足輕重的角色。液靜壓軸承的工作原理為透過外部加壓使軸承面之間產生一層油膜，以避免軸承滑動面零件的直接接觸。此機構亦使液靜壓軸承具有下列特性：高剛性、低磨耗、低滑滯效應（stick-slip）、高阻尼、較長之使用壽命等。而液靜壓軸承中的重要零件－節流器，在整套系統中則扮演關鍵角色。許多文獻提到，薄膜式節流器能夠使液靜壓軸承達到高剛性的性能表現。然而，薄膜式節流器的結構與設計參數也相對其他節流器複雜許多。
根據本實驗室先前的研究成果顯示，薄膜節流器可由兩項設計參數進行設計，分別為：無因次薄膜剛性（Dimensionless membrane stiffness, K_r^*）與軸承系統的設計節流比（Design restriction ratio, λ），當K_r^*=1.33與λ=0.25時，軸承剛性在某段工作區間下趨近無限大，此組最佳解可適用於單向墊與對向墊之軸承設計。
本研究將此概念應用於實際案例，將一組液靜壓線性滑軌作為分析對象，該組滑軌由一組搭配薄膜式節流器之上墊，與四組搭配毛細管節流器之下墊所組成。本文之研究目的在於利用數值方法分析該滑軌之性能表現，並透過實驗與模擬結果互相對照。

To pursue superior performance for quality and durability, hydrostatic bearings were frequently adopted in ultra-precision machining machine. With the mechanism of fluid-film lubrication, hydrostatic bearing has plenty of advantages such as low friction, high stiffness, no stick-slip effect, high damping capacity, long operation life, etc. Many studies reported that membrane-type restrictor might enable bearing systems to have great performance. However, the mechanism and design parameters of membrane restrictor are much more complicated than other restrictors.
Based on our previous study, high bearing stiffness may be attainable as two design parameters of membrane restrictor are properly determined. These two parameters are the dimensionless stiffness of membrane (K_r^*) and design restriction ratio of bearing system (λ). Theoretically, the bearing can operate with high stiffness when K_r^* equals 1.33 and λ equals 0.25. The optimum result is applicable for both single-pad and opposed-pad bearings.
In this study, it is of interest to manufacture a hydrostatic module, which is a hydrostatic linear guideway with a membrane restrictor for the upper pad and capillary restrictors for the lower pads. The purpose of this research is to analyze the performance of this device using numerical methods and to verify the simulation results through experiments.

[1] A. H. Slocum, Precision Machine Design, Englewood Cliffs, New Jersey: Prentice-Hall, 1992.
[2] Richard G. Budynas, J. Keith Nisbett, Shigley's Mechanical Engineering Design (9th Ed.), 2011.
[3] W. B. Rowe, Hydrostatic, Aerostatic and Hybrid Bearing Design, MA: Butterworth-Heinemann, 2012.
[4] J. G. C. DeGast, "A new type of controlled restrictor (MDR) for double film hydrostatic bearings and its application to high-precision machine tools," Proceedings of Advances in Machine Tool Design and Research, pp. 273-298, 1966.
[5] T. H. Lai, Parameters design of a membrane restrictor for single-pad and opposed-pad hydrostatic bearing to achieve high static stiffness, 2017.
[6] T. H. Lai, T. Y. Chang, Y. L. Yang and S. C. Lin, "Parameters design of a membrane-type restrictor with single-pad hydrostatic bearing to achieve high static stiffness," Tribology International, vol. 107, pp. 206-212, 2017.
[7] L.D. Girard, Noueau Systkme de Locomotion sur Chemin de Fer;, Paris, 1852.
[8] R. Bassani and B. Piccigallo , Hydrostatic Lubrication, Amsterdam, AE: Elsevier, 1992.
[9] B. Bhushan, Introduction to Tribology, New York: John Wiley and Sons, 2002.
[10] A. Harnoy, Bearing Design in Machinery: Engineering Tribology and Lubrication, New York: CRC Press, 2002.
[11] B. J. Hamrock, R. S. Steven and B. O. Jacobson, Fundamentals of Fluid Film Lubrication, 2 ed., New York, NY: Marcel Dekker, 2004.
[12] Y. Hori, Hydrodynamic Lubrication, Tokyo: Springer-Verlag, 2005.
[13] M. S. A. Kotilainen, "Design and Manufacturing of Modular Self-Compensating Hydrostatic," Massachusetts Institute of Technology, 2000.
[14] A. M. Loeb, H. C. Rippel, "Determination of Optimum Proportions for Hydrostatic Bearings," A S L E Transactions, pp. 241-247, 1958.
[15] N.R. Kane, J. Sihler, A.H. Slocum, A hydrostatic rotary bearing with angled surface self-compensation, Precision Engineering 5321 (2003) 1–15, 2003.
[16] N. R. Kane, "Surface Self-Compensated Hydrostatic Bearings," 1999.
[17] M. Mohsin, "The use of controlled restrictors for compensating hydrostatic bearing," in Advances in Machine Tool Design and Research, 1962.
[18] W. B. Rowe, J. P. O'Donoghue, "Diaphragm valves for controlling opposed pad bearings," in Proceedings of the Institution of Mechanical Engineers, London, 1969-70.
[19] C. Cusano, "Characteristics of externally pressurized journal bearings with membrance-type variable-flow restrictors as compensating elements," in Proceedings of the Institution of Mechanical Engineers, 1974.
[20] C. Cusano and T. Conry, "Design of multirecess hydrostatic journal bearing for minimum total power loss," ASME Journal of Lubrication Technology, vol. 94, no. 1, pp. 226-232, 1974.
[21] S. A. Morsi, "Passively and Actively Controlled Externall Pressurized Oil-Film Bearings," Journal of Tribology, pp. 56-63, 1972.
[22] Y. Kang, P. C. Shen, Y. P. Chang, H. H. Lee and C. P. Chiang, "Modified predictions of restriction coefficient and flow resistance for membrane-type restrictors in hydrostatic bearing by using regression," Tribology International, vol. 40, no. 9, pp. 1369-1380, 2007.
[23] Yuan Kang, Ping-Chen Shen, Cheng-Hsign Chen, Yeon-Pun Chang and Hsing-Han Lee, "Modified determination of fluid resistance for membrane-type restrictors," Industrial Lubrication and Tribology, No.122, pp. 123-131, 2007.
[24] T. Y. Chang, "Analysis on parameters and design of membrane-type restrictors," 2015.
[25] G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge: Cambridge University Press, 2000.
[26] B. C. Majumdar, "The numerical solution of hydrostatic oil journal bearings with several supply ports," Wear, pp. 389-396, 1969.
[27] B. Ghosh, "An exact analysis of a hydrostatic journal bearing with a large circumferential sill," Wear, 21(2), pp. 367-375, 1972.
[28] M. K. Ghosh and B. C. Majudar, "Design of multirecess hydrostatic oil journal bearings," Tribology, 96(1), pp. 226-232, 1980.
[29] J. P. O' Donoghue and W. B. Rowe, "Hydrostatic journal bearing (exact procedure)," Tribology, pp. 230-236, 1968.
[30] Jayachandra Prabhu, T. & Ganesan, N., "Behavior of multirecess plane hydrostatic thrust bearings under conditions of tilt and rotation," Wear, 92, pp. 243-254, 1983.
[31] Jayachandra Prabhu, T. & Ganesan, N., "Characteristics of multipad hydrostatic thrust bearings under rotation," Wear, 92, pp. 219-231, 1984.
[32] Jayachandra Prabhu, T. & Ganesan, N., "Effects of tilt on the characteristics of multirecess hydrostatic thrust bearings under conditions of no rotation," Wear,92, pp. 269-277, 1983.
[33] F. M. Stansfield, Hydrostatic bearings for machine tools and similar applications, Machinery Publishing, 1970.