氣靜壓軸承之特性分析及最佳化

Characteristics Analysis and Optimization for Aerostatic Bearings

陸芷琪(Chih-Chi Lu)

指導教授 ： 康淵 ； 張永鵬

中原大學/工學院/機械工程學系/碩士(2006年)

https://doi.org/10.6840/CYCU.2006.00485

摘要

本文以分析方法探討設計參數影響氣靜壓軸承之承載及剛度，以提升負載及加大剛度為目的。運用最佳分析方法，在已知設計條件以及達到預期承載的目標下，實現最大剛度，除了探討實際設計範例，並針對使用單排及雙排多孔數以及使用小孔及環面兩種節流，在軸承設計參數範圍，比較軸承最大值的最佳化設計參數。
本文根據氣體狀態方程式，絕熱反應式以及可壓縮雷諾方程式建立各個氣區的流量守恆方程式，假設壓力為峯值及定值兩種形式，聯立這些方程式，以數值方法求解，求得各氣區的壓力值，進一步將上述聯立方程式對偏心位移取變異量，並且乘以面積，可以得到求解承載及剛度的聯立方程式。取最大剛度為目標函數，以基因演算法求軸承設計參數的最佳化。由於設計軸承之前，已知條件為軸頸直徑、軸承寬度、轉速、承載力及氣體黏度等，此外間隙受限於軸承表面粗糙度、加工精度，因此影響剛度的設計參數只剩下軸承節流面寬度比、周向節流面寬度比以及節流參數三個作為可變的設計參數。
本文分析設計參數的影響以及最佳化上述三個設計參數，探討氣靜壓頸軸承及止推軸承各兩種範例，以實際的原始設計，經過最佳化的設計，以及使用單排及雙排多孔，小孔及環面兩種節流，相較於原始設計比較，探討設計參數的最佳值，對於軸承負載能力及剛度之影響。
本文經由上述分析，探討兩種氣靜壓軸承的小孔及環面節流形式之比較，單排及雙排形式之比較，以及最佳的尺寸，據此建立氣靜壓頸軸承以及止推軸承的設計分析模式，有效提升氣靜壓軸承剛度及承載。
本文內容共分成八章，各章大綱說明如下：
第一章為導論，說明氣靜壓軸承之研究背景，國內外相關研究及產業發展的文獻回顧，市場產品的分析以及各國專利的介紹。第二章為理論分析，首先介紹氣靜壓軸承系統及構造，本文所使用的小孔及環面節流形式，比較其節流特性，其次根據氣流量守恆原理，及止推軸承的計算方程式及數值分析方法，並且對於多氣孔氣靜壓軸承作特性分析。第三章為氣靜壓頸軸承，針對頸軸承推導及數值分析方法，並且對於多氣孔氣靜壓軸承承載及剛度作特性分析設計。第四章為氣靜壓止推軸承，，針對止推軸承推導及數值分析方法，並且對於多氣孔氣靜壓軸承承載及剛度作特性分析設計第五章為設計參數最佳化分析，使用遺傳基因演算法，以最大剛度為目標函數，最佳化設計參數。第六章為氣靜壓頸軸承設計範例，分別探討小孔及環面兩種節流形式的影響，節流係數的影響，幾何尺寸的影響，並且以最大剛度為目標函數，軸承設計的最佳化參數，以及在最佳化參數條件下的軸承特性比較。第七章為氣靜壓止推軸承設計範例，，分別探討小孔及環面兩種節流形式的影響，節流係數的影響，幾何尺寸的影響，並且以最大剛度為目標函數，軸承設計的最佳化參數，以及在最佳化參數條件下的軸承特性比較。第八章為結論與未來研究方向。

關鍵字

基因演算法 ； 節流參數 ； 氣靜壓軸承 ； 環面節流 ； 設計參數 ； 剛度 ； 小孔節流

並列摘要

This thesis uses analysis method to study the influence of design parameters on load and stiffness of aerostatic bearings for the promoting the characteristics and performance. Furthermore, optimal design for maximum stiffness is addressed under known conditions and load goal. This thesis investigates aftual design cases for the influences of single and double arrays of orifices as well as the influence of both pocket and inherent kinds of throttles on optimal design which is restricted by practical range of design parameters.
This thesis formulates conservation of flow equation on the basis of state equation and isentropic process of gas as well as the Reynold equation of compressible fluid with the assumptions of peak-type and constant distribution of pressures. Those coupled equations are solved simultaneously to yield pressures of each pads. Furthermore, differentiating above mentioned equations with respect to eccentricity gives coupled equations of stiffness. Maximal stiffness is the objective function to determine optimal design parameters by using genetic algrithem. Before design bearing, some parameters including journal diameter, bearing width, rotational speed, load capacity and gas viscosity are known beforehand as well as bearing clearance is restricted to a limit by surface roughness and manwfacturing precision. Therefore, remained parameters which can influence bearing stiffness only include circumferential and axial land-width ratios, and restriction parameter which are three specifically addressing parameters in bearing design.
This thesis analyzes and discussed both aerostatic journal and thrust bearings with both the pocket and inherent compensations of the single and two arrays orifices. Which are compared with original design. The establishment of optimization for aerostatic bearings for the promotion in bearing stiffness and load capacity.
Eight chapters are presented in this thesis, which are described as follows： The first chapter is the introduce including background of aerostatic bearing, domestic and foreign researches and industrial development, literature review, produces as well as patents. The second chapter is the theoretical analysis. System and structure of aerostatic bearing, characteristics of the pocket and inherent compensations are described. Conservation of flow, equation formulations and the numerical analysis method of journal bearing and thrust bearing and are regarding, for single and double arrays. The third chapter and the fourth chapter are studies for aerostatic journal bearings and aerostatic thrust bearings, characteristics of the pocket and inherent compensations are described. Conservation of flow, equation formulations and the numerical analysis method of journal bearing and thrust bearing and are regarding, for single and double arrays.The fifth chapter presents optimization method of genetic algorithm to search optimal design parameters for maximal stiffness.The sixth chapter and the seventh chapter are case studies for aerostatic journal bearings and aerostatic thrust bearings, respectively. In both chapters the influence of different types restriction, geometry and size of bearing are analyzed and optimization results are compared with each others. The eighth chapter is conclusion and suggestions for future works.

並列關鍵字

Aerostatic Bearing ； Stiffness ； Genetic Algorithm ； Design Parameter ； Load Capacity ； Orifice Compensation ； Inherent Compensation

參考文獻

[1] Majumdar﹐B.C.,“On the General Solution of Externally Pressurized Gas Journal Bearings,”Journal of Lubrication Technology, pp. 291-296, 1972.

[2] Kazimierski, Z. and Trojnarski. J., “Investigations of Externally Pressurized Gas Bearings with Different Feeding System,” ASME Journal of Lubrication Technology, Vol. 102, 1980.

[3] Stout, K. J. and Barrans, S. M., “The Design of Aerostatic Bearings for Application to Nanometer Resolution Manufacturing Machine Systems,” Tribology International, Vol. 33, pp. 803-809, 2005.

[4] Lo, C. Y., Wang, C. C., and Lee, Y. H., “Performance Analysis of High-Speed Spindle Aerostatic Bearings,” Tribology International, Vol. 38, pp. 5-14, 2005.

[5] Blondeel, E., Snoeys, R., and Devrieze, L., “Dynamic Stability of Externally Pressurized Gas Bearings,” Journal Lubrication Technology, Vol. 102, pp. 511-519, 1980.