# 臺灣博碩士論文加值系統

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 摘 要 本論文主要研究目的為：(1) 探討具配流槽與未具配流槽氣靜壓軸承之靜、動態特性。(2) 探討具彈簧補償氣靜壓軸承之暫態響應特性。(3) 分析氣靜壓軸承在高速驅動進給下之相關特性。(4) 探討氣靜壓導軌系統之動態響應行為。 首先，利用Resistance Network Method (RNM) 解析靜態流量連續方程式，探討氣靜壓軸之承載能力、剛性與體積流量等靜態相關特性，並以實驗印證理論分析之結果。其次，利用RNM解析具擠壓膜效應與動壓效應之流量連續方程式，配合Newmark 數值積分法求解氣靜壓軸承與導軌系統運動方程式，兩者聯立以分析具配流槽補償、彈簧補償氣體軸承之動態特性與氣靜壓軸承在高速驅動進給下之動態行為，並配合氣體軸承動態實驗印證理論分析結果。最後，本研究變化相關參數設計氣靜壓軸承並應用於氣靜壓導軌系統，利用上述之理論分析模式，探討氣靜壓導軌系統之相關特性。 研究結果顯示： 1、具配流槽氣體軸承之靜態特性比未具配流槽者佳。 2、具彈簧補償氣體軸承比僅具配流槽補償軸承有較佳之動態特性，可明顯改善軸承與導軌系統之暫態響應特性。 3、氣體軸承靜、動態實驗結果與理論分析結果趨勢相近，印證RNM可應用於氣體軸承分析。 4、氣體軸承在高速驅動進給下，其靜、動態特性明顯受動壓效應之影響。 5、氣靜壓導軌系統動態特性與氣體軸承設計參數、導軌設計型式有關。 關鍵詞：氣靜壓軸承、Resistance Network Method、Newmark 數值積分法、擠壓膜效應、彈簧補償、暫態響應、高速進給、動壓效應、氣靜壓導軌系統。
 Abstract The objectives of this thesis are as follows, (1) Static behaviors and dynamic stability analysis of grooved rectangular aerostatic thrust bearings; (2) Dynamic analysis of the X-shaped grooved aerostatic bearings with disk-spring compensator; (3) Aerodynamic analysis of grooved rectangular aerostatic bearing on a slideway; (4) Dynamic analysis of aerostatic guideway systems. Firstly, the static characteristics of aerostatic bearings include nothing more than load capacity, stiffness and mass flow rate are investigated by the resistance network method (RNM). Further, a static experiment was carried out in order to verify the numerical analysis. Secondly, the Newmark integration method and the modified RNM, which takes into account the equilibrium of the mass flow rate, the squeeze film effect and the aerodynamic effect, are used to analyze the dynamic behaviors of aerostatic bearings and aerostatic guideway systems at each time step. Moreover, the dynamic experiments of aerostatic bearings were performed to verify the theory derived in this thesis. Finally, the optimum design parameters of aerostatic bearings are used to design the aerostatic guideway systems, and the analytical models mentioned as above are applied to investigate the dynamic performances of aerostatic guideway systems. From the research on the aerostatic bearings and aerostatic guideway systems, one can draw the following conclusions: (1).The grooved bearing provides greater stiffness and load capacity, but it may cause pneumatic hammer instability with too large width or depth. (2).After impulse, the bearing with disk-spring compensator can reduce the system vibration and the working table can maintain a small vibration or keep its balance around the equilibrium position. The superior dynamics of bearing with disk-spring compensator are demonstrated in comparison with bearing without compensator. (3).Good agreements between RNM analyses and experimental results are demonstrated. Hence, RNM is suitable for similar aerostatic bearing design and analysis. (4).When sliding begins, the static and dynamic characteristics of aerostatic bearing on a slideway are influenced by aerodynamic effect. (5).The dynamic characteristics of guideway systems depend very much on the bearing design parameters and guideway forms. Keywords: Aerostatic bearing, Resistance network method, Newmark integration method, Squeeze film effect, Disk-spring compensator, Impulse response, High feed rate, Aerodynamic effect, Aerostatic guideway system
 Contents Contents.............................................................................................................Ⅰ Table Captions....................................................................................................Ⅲ Figure Captions..................................................................................................Ⅳ Nomenclature.....................................................................................................XI Chapter 1 Introduction.........................................................................................1 1-1 Background.................................................................................................. 1 1-2 Purposes and Steps of this Research............................................................ 5 1-3 Literature Review......................................................................................... 8 Chapter 2 Analytical Model of the Aerostatic Thrust Bearings.......................... 13 2-1 Theory and Governing Equation.................................................................. 13 2-2 The Dynamic Model of the Aerostatic Table................................................23 2-3 Simulation Results and Discussion............................................................. 26 2-4 Experimental Verifications.......................................................................... 46 2-5 Summary.....................................................................................................56 Chapter 3 Dynamic analysis of Aerostatic Thrust Bearings with Passive Disk-Spring Compensator................................................................................. 58 3-1 Theoretical Analysis and Dynamic Simulation............................................ 58 3-2 Simulation Results and Discussion.............................................................. 63 3-3 Summary..................................................................................................... 79 Chapter 4 Aerodynamic Analysis of Grooved Aerostatic Bearing on a Slideway..................................................................................................... 80 4-1 Theory and Governing Equation...................................................................80 4-2 The Dynamic Model of Motion................................................................... 84 4-3 Simulation Results and Discussion.............................................................. 86 4-4 Summary......................................................................................................100 Chapter 5 Dynamic Analysis of Aerostatic Guideway System...........................101 5-1The Dynamic Model of Typical Guideway.................................................... 101 5-2 Results and Discussion................................................................................. 104 5-3 The Dynamic Model of Guideway Preload by Aerostatic Bearings............. 112 5-4 Results and Discussion................................................................................. 114 5-5 Experimental Verifications............................................................................ 122 5-6 Summary...................................................................................................... 126 Chapter 6 Conclusions and Recommendations................................................... 127 6-1 Conclusions.................................................................................................. 127 6-2 Recommendations........................................................................................ 129 Reference............................................................................................................. 130
 Reference[1]Powell, J. W., Design of Aerostatic Bearing, Machinery Publishing Co.Ltd.,1970[2]Wang, J., Design of Gas Bearing Systems for Precision Applications, Eindhoven University of Technology, Ph. D Dissertation, 1993[3]Kogure, K., Kaneko, R., and Ohtani, K., A Study on Characteristics of Surface Restriction Compensated Gas Bearing with T-shaped Grooves. Bulltin, JSME, Vol. 25, No. 210, pp. 2039-2045, 1982[4]Nakamura, T., and Yoshimoto, S., Static Tilt Characteristics of Aerostatic Retangular Double-Compound Restrictors. Tribology International, Vol. 29, No. 2, pp.145-152, 1996[5]Boffey, D.A., Barrow, A.A., and Deardent, J.K., Experimental Investigation into the Performance of an Aerostatic Industrial Thrust Bearings, Tribology International. Vol. 18, No. 4, pp.245-253, 1985[6]Chen, M.F., and Lin, Y.T., The Analysis and Application of the Aerostatic Bearing with X- shaped Grooves. The 17th National conference on mechanical engineering (in Chinese), Taiwan, 2000[7]White, J.W., and Nigam, A., A Factored Implicit Scheme for the Numerical Solution of the Reynolds Equation at Very Low Spacing, Journal of Lubrication technology, ASME, Vol. 102, No. 1, pp.80-85, 1980[8]Lin, G., Tojiro A., and Ichiro, I., A Computer Simulation Method for Dynamic and Stability Analysis of Air Bearing, Wear, Vol. 126, pp.307-319, 1988[9]Kinouch, K., Tanaka, K., Yoshimura, S., and Yagawa, G., Finite Element Analysis of Gas-Lubricated Grooved Journal Bearings. Series C, JSME, Vol. 39, pp.123-129, 1996[10]Takuji, K., Numerical Analysis of Herringbone-Grooved Gas-Lubricated Journal Bearings Using a Multigrid Technique. Transactions of the ASME, Vol.121, pp.148-159, 1999[11]Mohamed, F., Yong, T., and Marc, B., Prediction of the Stability of Air Thrust Bearing by Numerical, Analytical and Experiment Methods. Wear, Vol. 198, pp.1-6, 1996[12]Arakere, N. K., and Ravichhandar, B. C., Dynamic Response and Stability of Pressurized Gas Squeeze-Film Dampers. Journal of Lubrication technology, ASME, Vol. 84, pp.277-297, 1995[13]Yamamoto, H., Ono, K., Cui, C., and Tsuzuki, M., Vibration Analysis of Hydrostatic Gas Bearing Spindle Considering the Elastic Deformation of Rotor. Series C, JSME, Vol. 62, pp.4294-4301, 1996[14]Yoshimoto, S., Tamura, J., and Nakamura, T., Dynamic Tilt Characteristics of Aeroststic Rectangular Double-pad Thrust Bearings with Compound Restrictors. Tribology International, Vol. 32, pp.731-738, 1999[15]Matsumoto, H., Yamaguchi, J., and Aoyama, H., An Ultra Precision Straight Motion System-Five Degrees of Freedom Control of Motion, JSPE, Vol. 54, No. 10, pp.1945-1950, 1998[16]Miyajt, R., and Harada, M., The Transient Response Characteristics of Actively Controlled Hydrostatic Thrust Gas Bearing, JSPE, Vol. 56, No. 6, pp.1111-1116, 1990[17]Yoshimoto, S., Anno, Y., Sato, Y., and Hamanaka, K., Float Characteristics of Squeeze-Film Gas Bearing with Elastic Hinges for Linear Motion Guide. Series C, JSME, Vol. 40, pp.353-359, 1997[18]Oswaldo, H., Yasuhara, K., Osada, H., and Shimokohbe, A., Dynamic Stiffness Control of Active Air Bearing. Series C, JSME, Vol. 25, pp.45-50, 1991[19]Kanaoka, A., and Yoshimoto, S., Hydrostatic Thrust Bearing with an Actively Controlled Restrictor Using a Voice Coil Motor. Series C, JSME, Vol. 63, pp.2099-2104, 1997[20]Rodkiewicz, C.M., On the Significance of the Inlet Pressure Built-up in the Design of Tilting-pad Bearing, Journal of Lubrication technology, ASME, Vol. 112, No. 1, pp. 104-111, 1990[21]Stout, K.J, Barrans, S.M., The Design of Aerostatic Bearings for Application to Nanometer Resolution Manufacturing Machine Systems. Tribology International Vol. 33, pp.803-809, 2000[22]Bernard, J., Hamrock, B., Jacobson, R., Fundamentals of Machine Elements, WCB/Mcgraw-Hill, pp.768-769, 1999
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