Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2396
標題: 外部供壓多孔式氣體軸承氣動潤滑特性分析暨軸承最佳設計參數探討
Analysis of the Aerodynamic Lubricating Characteristics and the Determination of the Best Design Parameters for an Externally Pressurize Porous Gas Bearing
作者: 李基銓
Lee, Chih-Chuan
關鍵字: Permeability;滲透率;Geometrical Design;Externally Pressurized;Porous Gas Bearing;幾何設計;外部供壓;多孔式氣體軸承
出版社: 機械工程學系所
引用: [1] Reynolds, O., 1886, “On The Theory of Lubrication and Its Application to Mr. Beauchamp Tower’s Experiments Including an Experimental Determination of the Viscosity of Olive Oil,” Philos. Trans. R. Soc. London, Ser. A, 177, pp.157-234. [2] Sneck, H. J. and Yen, K. T., 1964, “The Externally Pressurized, Porous Wall, Gas-Lubricated Journal Bearing – I,” ASLE Trans., 7, pp. 288-298. [3] Sneck, H. J. and Elwell, R. C., 1965, “The Externally Pressurized, Porous Wall, Gas-Lubricated Journal Bearing – II,” ASLE Trans., 8, pp. 339-345. [4] Sneck, H. J. and Yen, K. T., 1967, “The Externally Pressurized, Porous Wall, Gas-Lubricated Journal Bearing – III,” ASLE Trans., 10, pp. 339-347. [5] Sneck, H. J., 1968, “A Survey of Gas-Lubricated Porous Bearings,” ASME Jour. of Lubr. Tech., 90, 4, pp. 804-809. [6] Mori, H., Yabe, H. and Yamakage, H., 1968, “Theoretical Analysis of Externally Pressurized Porous Journal Gas Bearings (1st report),” Bull. of JSME, 11, 45, pp. 527-532. [7] Mori, H., Yabe, H. and Yamakage, H., 1969, “Theoretical Analysis of Externally Pressurized Porous Journal Gas Bearings (2nd Report, Journal Bearing with Solid Sleeve Parts),” Bull. of JSME, 12, 54, pp. 1512-1518. [8] Heller, S., Shapiro, W. and Decker, O., 1971, “A Porous Hydrostatic Gas Bearing for Use in Miniature Turbomachinery,” ASLE Trans., 14, pp. 144-155. [9] Stout, K. J. and Rowe, W. B., 1974, “Externally Pressurized Bearings – Design for Manufacture (Part 2 – Design of Gas Bearings for Manufacture Including a Tolerancing Procedure),” Trib. Int., 7, pp.169-180. [10] Majumdar, B. C., 1975, “Analysis of Externally Pressurized Porous Gas Journal Bearings – I,” Wear, 33, pp. 25-35. [11] Sun, D. C., 1975, “Analysis of the Steady State Characteristics of Gas-Lubricated, Porous Journal Bearings,” ASME Jour. of Lubr. Tech., 97, pp. 44-51. [12] Sun, D. C., 1975, “Stability of Gas-Lubricated, Externally Pressurized Porous Journal Bearings,” ASME Jour. of Lubr. Tech., 97, pp. 494-505. [13] Wu, E. R. and Castelli, V., 1976, “Gas-Lubricated Porous Bearings- Infinitely Long Journal Bearings, Steady-State Solution,” ASME Jour. of Lubr. Tech., 98, pp. 453-462. [14] Majumdar, B. C., 1976, “Gas-Lubricated Porous Bearings: A Bibliography,” Wear, 36, pp. 269-273. [15] Majumdar, B. C., 1976, “Design of Externally Pressurised Gas-Lubricated Porous Journal Bearings,” Trib. Int., 9, 2, pp. 71-74. [16] Rao, N. S., 1982, “Analysis of Aerostatic Porous Journal Bearings Using the Slip Velocity Boundary Conditions,” Wear, 76, pp. 35-47. [17] Koshal, D. and Rowe, W. B., 1981, “Fluid-Film Journal Bearings Operating in a Hybrid Mode: Part 1 - Theoretical Analysis and Design,” ASME Jour. of Lubr. Tech., 103, pp. 55 8-565. [18] Koshal, D. and Rowe, W. B., 1981, “Fluid-Film Journal Bearings Operating in a Hybrid Mode: Part 2 – Experimental Investigation,” ASME Jour. of Lubr. Tech., 103, pp. 566-572. [19] Lin, J. R. and Hwang, C. C., 1993, “Lubrication of Short Porous Journal Bearings – Use of the Brinkman-Extended Darcy Model,” Wear, 161, pp. 93-104. [20] Prakash, J. and Gururajan, K., 1999, “Effect of Velocity Slip in an Infinitely Long Rough Porous Journal Bearing,” Tribol. Trans., 42, 3, pp. 661-667. [21] Naduvinamani, N. B., Hiremath, P. S. and Gurubasavaraj, G., 2001, “Squeeze Film Lubrication of a Short Porous Journal Bearing with Couple Stress Fluids,” Trib. Int., 34, pp. 739-747. [22] Naduvinamani, N. B., Hiremath, P. S. and Gurubasavaraj, G. (2002), “Surface Roughness Effects in a Short Porous Journal Bearing with a Couple Stress Fluid,” Fluid Dynamic Research, 31, pp. 333-354. [23] Saha, H. and Majumdar, B. C., 2002, “Study of Externally-Pressurized Gas-Lubricated Two-Layered Porous Journal Bearings: a Steady State Analysis,” Proc. Instn. Mech. Engrs., Part J: Jour. of Engg. Trib., 216, pp. 151-158. [24] Elsharkawy, A. A., 2003, “Effects of Misalignment on the Performance of Flexible Porous Journal Bearings,” Tribol. Trans., 46, 1, pp. 119-127. [25] Su, C. T. and Lie, K. N., 2003, “Rotation Effects on Hybrid Air Journal Bearings,” Trib. Int., 36, pp. 717-726. [26] Cheng, K. and Rowe, W. B., 1995, “A Selection Strategy for the Design of Externally Pressurized Journal Bearings,” Trib. Int., 28, 7, pp. 465-474. [27] Scheidegger, A. E., 1974, The physics of Flow through Porous Media, 3rd Edition, University of Toronto Press, ISBN 0-8020-1849-1. [28] You, H. I. and Chang, C. H., 1997, “Determination of Flow Properties in Non-Darcian Flow,” ASME Jour. of Heat Transfer, 119, pp. 190-192. [29] 劉敦、劉育華、陳世杰, 1990, 靜壓氣體潤滑, 哈爾濱工業大學出版社. [30] 十合晉一, 1985, 氣體軸承-從設計到製造, 復漢出版社 [31] Hamrock, B. J., 1994, Fundamentals of Fluid Film Lubrication, International Editions, McGraw-Hill, Inc., ISBN 0-07-113356-9. [32] Cameron, A., 1983, Basic Lubrication Theory, 3rd Edition, Ellis Horwood Ltd., ISBN 0-47-027554-5. [33] Currie, I. G., 1993, Fundamental Mechanics of Fluids, 2nd Edition, McGraw-Hill, Inc., ISBN 0-07-015000-1. [34] Pao, Richard H. F., 1966, Fluid Dynamics, C. E. Merrill Books, ASIN: B0006BOKSQ.
摘要: 
本論文針對外部供壓多孔式氣體軸承的穩態性能進行了數值分析與探討,其中軸承氣膜壓力的統御方程式為非線性雷諾方程式,多孔式軸襯的氣體壓力統御方程式為三維達西方程式,此二方程式構成一組相互耦合的非線性偏微分方程組。本研究採用了Gauss-Seidel疊代法以及點鬆弛法(point successive over-relaxation method, PSOR)發展出求解此非線性偏微分方程組的準線性數值方法(quasi-linear numerical scheme)。本論文主要考慮軸承設計參數對穩態性能的影響,其中包括傳統之軸承數Λ、與多孔質材料有關之供給參數Λp以及與3個與軸承幾何比例有關之參數:寬徑比L/D、厚度比H/D、及間隙比。
當軸承外型固定時,供給參數Λp代表了多孔質軸襯的滲透率,而滲透率與多孔質結構之孔隙度具有強烈相關性。分析的結果顯示,當Λp值小時,軸承間隙內氣體的潤滑效應主要來自於氣動潤滑效應(aerodynamic lubricating effect),反之,當Λp值大時,氣靜潤滑效應(aerostatic lubricating effect)則成為軸承支撐負荷的重要因素。研究亦顯示,當軸承供給參數Λp值小時,重負荷操作狀態會增強軸承氣膜厚度最薄處的氣動潤滑效應。另一方面,相較於適中的供給參數(如Λp=1),過低的Λp值 (如Λp=0.1)會使轉軸碰觸到軸襯的風險提高。為了兼顧軸承操作安全性以及軸承負荷能力,本研究建議Λp的設計值應介於0.5與1之間。
就軸承的設計實務而言,軸承的外形幾何比例,如軸承寬度、直徑、潤滑間隙甚至軸襯的厚度皆會影響多孔式軸承的性能。分析的結果顯示,當L/D≧1、H/D≧0.1及0.0005≦C/R≦0.001時,軸承將呈現明顯的氣動潤滑行為。在考慮軸承負荷性能以及遭遇暈旋不穩定(whirl instability)狀況的前提下,研究結論認為L/D=1及C/R=0.001可分別作為軸承寬徑比與間隙比設計準則的最佳建議值。由於過度增加軸襯厚度比對提高負荷能力並無顯著效果,故本研究建議H/D=0.1為適當之設計值。

This thesis analyzes numerically the bearing performance of a finite length porous journal bearing fed by externally pressurized air. The nonlinear Reynolds equation coupled with the three dimensional Darcian equation are solved for the air pressure solutions of the bearing film and the porous air, respectively. A quasi-linear numerical scheme associated with an under-relaxation factor is developed to solve the pressure solutions of the nonlinear coupled partial differential equations (PDE). The characteristic parameters, including the conventional bearing number Λ, the feeding parameter Λp, and the three geometrical parameters, L/D, H/D, and C/R, are considered as the main influence factors for the bearing solutions.
For a fixed bearing geometry, the feeding parameter Λp represents the permeability of porous bushing and is strongly related to the size effect of structure porosity. The numerical results show that the aerodynamic lubricating effect is significant for the porous bearing having a small Λp number, whereas the aerostatic effect prevails inside the bearing space as the Λp number is large. When the permeability parameter Λp is small, the aerodynamic effect is further promoted for the bearing operating at a heavy load; herein the minimum film thickness becomes relatively small. It is found that a bearing with a small Λp will have a higher risk for the journal shaft to touch the bearing wall than a bearing with large Λp. Therefore, as the bearing safety and loading capacity are concerned, a porous journal bearing with Λp ranging between 0.5 and 1 is recommended in practical use.
For practical design considerations, geometrical dimensions such as bearing length, diameter, lubricated clearance, and even the thickness of the porous structure all have important influences on the performance of porous journal bearings. The numerical results show that the porous journal bearing exhibits a significant aerodynamic lubrication action when L/D≧1, H/D≧0.1 and 0.0005≦C/R≦0.001. This study recommends L/D=1, and C/R=0.001 as the optimum design criteria for the bearing aspect ratio and clearance ratio respectively, as the bearing load and whirling instability are concerned. Since a greater porous thickness does not improve the bearing load capacity, this study suggests H/D=0.1 as a proper porous thickness.
URI: http://hdl.handle.net/11455/2396
其他識別: U0005-3112200918121500
Appears in Collections:機械工程學系所

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