臺灣博碩士論文加值系統

本文以高速主軸為研究對象，目的在於研究斜角滾珠軸承於不同預壓，高速旋轉下之軸承動態剛性。本研究主要依據Harris之軸承負荷理論，並考慮滾珠在不同預壓及轉速下離心力及陀螺力矩之動態效應，以及滾珠與內、外環軌道之點接觸負荷下之變形，探討動態下軸承剛性之變化。
本研究之另一目的在於研究主軸高速切削的穩定性，並結合軸承之動態剛性。主要依據引用前人S. Smith與J. Tlusty所提出之切削穩定性理論，並考慮不同預壓下之軸承動態剛性，建立一電腦程式，利用電腦模擬主軸進行切削加工，從而建立切削之穩定性圖（stability lobes）預知其加工之最佳切削轉速。並進而探討不同預壓下之軸承動態剛性對高速主軸切削穩定性的影響。

The purpose of this work is to study the dynamic characteristics and cutting stability of a high-speed ball bearing spindle. It is known that the bearing stiffness becomes smaller at high speed due to the centrifugal force and gyroscope moment of the rotating elements of the bearings. Based on the model developed by Harris, we are able to analyze the dynamic characteristics of the ball bearings such as deformation, contact angle and stiffness under different preload conditions and rotating speed.
Another objective of this work is to study the high speed cutting stability of the spindle. It is known that the natural frequency of the spindle is an important factor of the high speed cutting stability. However, most works related to cutting stability analysis are based on the natural frequency of the spindle tested at the static conditions. We follow the cutting stability theory developed by Smith and Tlusty, but consider the dynamic characteristics of the bearings at high rotating spindle. Through the computer simulation, we are able to analyze the high speed cutting stability under different bearing preloads. The simulation result has shown a significant change of the cutting stability at high rotation speed.

目錄
中文摘要…………………..…………………………………..………Ⅰ
英文摘要…………………..…………………………………..………Ⅱ
目 錄…………….…………………………………Ⅲ
圖 目 錄………………………………………………………………Ⅴ
表 目 錄………………………………………………………………Ⅶ
第 一 章 緒 論……………………………………………………1
1.1 前 言……………………….………………………………1
1.2 文獻回顧..……………………………………………………1
1.3 研究動機與目標.………………………………………………4
1.3.1 研究動機………………………………………………4
1.3.2 研究目標……………………………………………….5
第 二 章 高速主軸之轉子動力方程式………………………………6
2.1 主軸之運動方程式…………………………………………..…6
2.2 模擬結果與討論………………………………………………10
2.2.1 主軸之臨界轉速………………………………………10
2.2.2 刀尖位移響應…………………………………………12
第 三 章 滾珠軸承之動態特性……………………………………14
3.1 斜角滾珠軸承之幾何分析……………………………………14
3.2 斜角滾珠軸承之動態分析……………………………………16
3.2.1 離心力…………………………………………………17
3.2.2 陀螺力矩……………………………………………….18
3.2.3 動態滾珠軸承之轉速分析…………………………….19
3.2.4 接觸點之負荷與撓曲關係…………………………….21
3.3斜角滾珠軸承動態負荷之推導………………………………26
3.3.1 第一組非線性方程組…………………………………28
3.3.2 第二組線性方程組…………………………………….32
3.3.3 電腦模擬計算之流程…………………………………32
3.4 斜角滾珠軸承動態剛性的推導………………………………35
3.4.1 斜角滾珠軸承軸向動剛性之分析……………………35
3.4.2 斜角滾珠軸承徑向動剛性之分析……………………37
3.5 電腦模擬之結果與討論………………………………………39
3.5.1 預壓及轉速對軸承之影響……………………………40
3.5.2 不同滾珠材質之滾珠軸承之討論…………………….45
第 四 章 高速主軸之切削穩定性分析……………………………46
4.1 切削穩定性之分析……………………………………………46
4.1.1 切削力方程式…………………………………………47
4.1.2 結構方程式…………………………………………….49
4.1.3 穩定性分析…………….……………………………….50
4.2 模擬結果與討論………………………………………………53
4.2.1 剛性為定值…………….………………………………..54
4.2.2 剛性非定值…………….………………………………..56
第 五 章 結 論…………………………………………………59
5.1 結 論………………………………………………………59
5.2 未來工作項目………………………………………………….61
參考文獻………………………………………………………………62

參考文獻：
1.Bert R.Forgensen,Yung C.Shin,”Dynamic of Spindle-Bearing System at High Speeds Including Cutting Load Effects”,Transactions of the ASME, Journal of Manufacturing Science and Engineering,May 1998,vol.120,pp.387-394
2.FAG,”Super Precision Bearings”,handbook
3.H.E.Merritt,”Theory of Self-Excited Machine-Tool Chatter”, Transections of the ASME,Journal of Engineering for Industry, 1965,vol.87,pp.447-454
4.Horst Voll,Paul Ramer,Herbert Schulz,Dietmar Schall,”ON the Way to a New Generation of Spindles”,1999 Sino-German Joint Symposium on High-Speed and High Precision Machining,March 15-16,1999,pp.45-53
5.K.W.Wang,Y.C.Shin,CH.Chen,”On the natural frequencies of high_speed spindles with angular contact bearings”,Proc.Instn.Mech. Engrs.1991,vol.205,147-154
6.J.Tlusty,”High-Sped Machining”,Annals of CIRP,vol.42/2/1993, pp.773-738
7.Subhajit Chatterjee,”Spindle Deflections in High-speed Machine Tools-Modelling and Simulation”,Int J Adv Manuf Technol,1996, vol.11,pp232-239
8.S.Smith,J.Tlusty,”Update on High-Sped Milling Dynamics”, Transections of the ASME,Journal of Engineering for Industry,May 1990,vol.112,pp.142-149
9.S.Smith,W.R.Winfough,J.Halley,”The Effect of Tool Length on Stable Metal Removal Rate in High Speed Milling”,Annals of the CIRP, vol.47/1/1998,pp.307-310
10.S.Smith,J.Tlusty,”Stabilizing Chatter by Automatic Spindle Speed Regulation”, Annals of the CIRP,vol.41/1/1992,pp.433-436
11.S.Smith,J.Tlusty,”Current Trends in High-Sped Machining”, Transections of the ASME,Journal of Manufacturing Science and Engineering, Novermber 1997,vol.119,pp.664-666
12.S.Smith,J.Tlusty,”Efficient Simulation Programs for Chatter in Milling”, Annals of the CIRP,vol.42/1/1993,pp.463-466
13.T.A.Harris,”Rolling Bearing Analysis”,John Wiley & Sons,Inc.,New York,1991
14.Oswald Bayer,”New Development of High Speed Bearings”,1999 Sino-German Joint Symposium on High-Speed and High Precision Machining,March 15-16,1999,pp.45-53
15.S.Smith,W.R.Winfough,H.J.Borchers,”Power Stability Limits in Milling”, CIRP Annals - Manufacturing Technology,vol.49/1/2000, pp309-312
16.Y.Altintas,E.Budak,”Analytical Prediction of Stability Lobes in Milling”, Annals of the CIRP,vol.44/1/1995,pp.357-362
17.Y.Altinaes,E.Shamoto,P.Lee and E.Budak,”Analytical Prediction of Stability Lobes in Ball EndMilling”,Transactions of the ASME, Journal of Manufacturing Science and Engineering,November,1999, vol.121,pp.586-592
18.Y.Altintas,P.Lee,”A General Mechanics and Dynamics and Dynamics Model for Helical End Mills”,Annals of the CIRP,vol.45/1/1996, pp.59-64
19.Y.C.Shin,”Bearing Nonlinerity and Stability Analysis in High Speed Machining”,Transaction of the ASME,Journal of Engineering for Industry,February 1992,vol.114,pp23-30
20.王健璋,”高速球軸承之負荷、壽命與溫昇之特性研究”, 國立中正大學機械工程研究所碩士論文,1996
21.楊益群,”CNC銑床之顫振控制”,國立台灣大學機械工程研究所碩士論文,1994
22.顏承偉,”高速主軸動平衡之研究”,國立中正大學機械工程研究所碩士論文,2000