本篇論文主旨在於建立液壓臥式旋轉軸系統之動態模型與模擬分析。對於液壓軸承系統而言，其動態模型與主軸之運動方程式相關，本文的內容主要是參考兩種不同理論推導背景下之數學模型，建立適合代表液壓臥式旋轉軸系統之數學模型，並利用電腦輔助軟體模擬與分析不同控制變因下之主軸運動行為。
在理論推導部分，首先會推導液壓軸承之基本動態模型，接著將運動方程式之形式應用在液壓臥式旋轉軸系統上，在適當條件下，運動方程式中的係數可化簡，並將這些係數定義為油膜之靜態剛性、靜態剛性與阻尼。在基本動態模型推導中，會先推導油膜的雷諾方程式，接著代入液壓軸承運作時的邊界條件，以利推導油膜壓力場之方程式；再來將壓力場對主軸表面積分，可得到油膜對主軸之作用力，因此可建立主軸之運動模型。最後利用數學的解析方法建立運動方程式與係數之關係式。在液壓臥式旋轉軸之動態模型推導中，考慮動壓、靜壓和油膜流動與擠壓之特性。文獻為了化簡推導過程，代入了某些假設並推出一種動態模型，由於部分假設條件過於嚴格，不符合臥式旋轉軸在運作時之狀態，因此本文修改某些假設並推導出可控式主軸運動方程式。
本文利用電腦軟體MATLAB/Simulink建置動態模型與模擬。首先根據液壓軸承之基本動態模型，模擬運動方程式之係數與主軸偏心率之關係，並且根據此模擬結果，說明驗證液壓臥式旋轉軸系統的模型推導中，係數可化簡之合理性。接著利用可控式主軸運動方程式，模擬主軸受外力時之運動軌跡，並藉由改變控制變因，例如供油壓力與主軸轉速，根據模擬結果說明模擬結論。

Dynamic modeling, simulation and analysis of hydraulic recessed journal bearings are proposed in this work, including simulation and analysis. For hydraulic journal bearing systems, the dynamic model can be represented as the equation of motion of the shaft. The mathematical model is appropriately built for hydraulic recessed journal bearings and shaft motion behavior is simulated under different controllable factors by using MATLAB/Simulink.
In the dynamics derivation, basic model of hydraulic journal bearings will be introduced and applied to the modeling of recessed journal bearing systems. In the basic model derivation, firstly Reynolds equation for oil film will be derived, and secondly boundary conditions are substituted to derived oil film pressure field equation. Thirdly, the integral of oil film pressure field with respect to the shaft surface can obtain the oil film force acting on the shaft, and finally the equation of motion can be derived. In addition, the coefficients relations in the equation of motion can be received. In the derivation of recessed journal bearing dynamic model, the coefficients in the equation of motion can be simplified and defined as hydrostatic stiffness, hydrodynamic stiffness and squeeze damping considering static and dynamic properties of oil film. In the literature, a dynamic model will be derived based on several assumptions but that are only for ideal cases. Therefore, some of the assumptions must be revised and a controllable dynamic model will be proposed in order to meet the real operation conditions of recessed journal bearings.
In the simulation works, the relations between coefficients and eccentricity are illustrated and the shaft motion trajectories are presented. The coefficients and eccentricity plot can be used to explain the reason why the coefficients in the equation of motion can be simplified. Besides, use controllable dynamic model to simulate the shaft motion trajectories at different rotational speeds and supply pressure while applying an external force on the shaft. Simulation results show the shaft motion behavior and the system stability situations of recessed journal bearings.

1. D. W. Parkins, Theoretical and Experimental Determination of the Dynamic Characteristics of a Hydrodynamic Journal Bearing. ASME, 1979. 101: p. 129-137.
2. F. K. Choy, M. J. Braun, Y. Hu, Nonlinear Transient and Frequency Response Analysis of a Hydrodynamic Journal Bearing. ASME, 1992. 114: p. 448-454.
3. G. H. Jang, Y. J. Kim, Calculation of Dynamic Coefficients in a Hydrodynamic Bearing Considering Five Degree of Freedom for a General Rotor-Bearing System. ASME, 1999. 121: p. 499-505.
4. L. S. Andres, Hydrodynamic Fluid Film Bearings and Their Effect on the Statbility of Rotating Machinery. In Design and Analysis of High Speed Pumps, 2006.
5. 鐘洪, 張冠坤, 液體靜壓動靜壓軸承設計使用手冊. 2007.
6. B. M. Stanley, M. L. Alfred, The Effect of the Method of Compensation on Hydrostatic Bearing Stiffness. Journal of Basic Engineering, 1961: p. 179-187.
7. T. S. Ling, On the optimization of the stiffness of externally pressurized bearings. ASME, 1962. 84: p. 119-122.
8. S. C. Sharma, S. C. Jain, R. Sinhasan, R. Shalia, Comparative study of the performance of six-pocket and four-pocket hydrostatic-hybrid flexible journal bearings. Tribology International, 1995. 28: p. 531-539.
9. S. C. Sharma, R. Sinhasan, S. C. Jain, N. Singh, S. K. Singh, Performance of hydrostatic/hybrid journal bearings with unconventional recess geometries. Tribology Transactions, 1998. 41: p. 375-381.
10. Y. Kang, P. C. Shen, C. H. Chen, Y. P. Chang, H. H. Lee, Modified determination of fluid resistance for membrane-type restrictors. Industrial Lubrication and Tribology, 2007: p. 123-131.
11. M. E. Mohsin, The Use of Controlled Restrictors for Compensating Hydrostatic Bearing. Third International Conference on Machine Tool Design Research, 1963: p. 129-424.
12. W. B. Rowe, J. P. O'Donoghue, Diaphragm Valves for Controlling Opposed Pad Hydrostatic Bearing. Proc. I. E. Tribology, 1970.
13. S. A. Moris, Passively and Actively Controlled Externally Pressurized Oil-film Bearing. Trans. ASME, Ser. F, 1972. 94.
14. T. Osumi, H. Mori, K. Ikeuchi, Effects of stabilizer on initial response of self controlled externally pressurized bearings. Trans. JSLE, 1985. 20: p. 651-657.
15. N. Tully, Static and Dynamic Performance of an Infinite Stiffness Hydrostatic Thrust Bearing. Trans. of ASME, 1977. 99: p. 106-112.
16. N. D. Vaughan, J. B. Gamble, The modeling and simulation of a proportional solenoid valve. Transactions of the ASME. Journal of Dynamic Systems, Measurement and Control, 1996. 118(1): p. 120-5.
17. N. C. Cheung, K. W. Lim, M. F. Rahman, Modelling a Linear and Limited Travel Solenoid. IEEE, 1993.
18. Bernard J. Hamrock, Steven R. Schmid, Bo O. Jacobson, Fundamentals of Fluid Film Lubrication. Marcel Dekker, Inc., 2004.
19. Hguyen-Schafer Hung, Rotordynamics of Automotive Turbochargers. Springer International Publishing, 2015.
20. Dara W. Childs, Turbomachinery Rotordynamics: phenomena, modeling, and analysis. John Wiley & Sons, Inc., 1993.
21. W. B. Rowe, Dynamic and Static Properties of Recessed Hydrostatic Journal Bearings by small Displacement Analysis. ASME, 1980. 102: p. 71-79.
22. W. B. Rowe, Hydrostatic, Aerostatic, and Hybrid Bearing Design. ELSEVIER, 2012.