臺灣博碩士論文加值系統

金屬切削用工具機主軸，必須滿足使用上的功能需求，軸承型式、跨距、預壓及拉刀力的設定，都會影響主軸的動、靜態性能，這些因素間的複雜關係是急待釐清的課題。
軸承是主軸的關鍵零件之一，主軸設計者必須選擇適當的參數。很明顯的，較高的軸承預壓可以提高剛性，但會限制主軸的最高轉速；而較低的預壓量卻會導致主軸軸鼻端的嚴重變形，甚至在加工中產生振動及噪音。針對二軸承支撐主軸的最佳跨距有許多研究，雖然現代的主軸構造不只有二個軸承，有的研究者提出在分析主軸靜剛性時可以將其簡化為二軸承系統，但我們如何確定這種簡化模型的適用性?
本研究的目的是希望分辨真實主軸與簡化模型間的差異，具有四個角接觸滾珠軸承的主軸，是本文的研究標的。在不同直徑的7/24刀把，與不同大小的拉刀力設定條件下，測試主軸的靜剛性，並利用套裝的有限元素分析軟體－“I-DEAS”，建構主軸的有限元素模型，在不同的邊界條件下，模擬主軸的靜態與動態特性，比較實驗數據及模擬結果，以確定有限元素模型的正確性。同時本文發現，簡化模型的主要弱點，是未考慮主軸襯套的變形量。希望本研究的結論，能對提升工具機業的主軸設計能力有所助益。

A spindle of a machine tool must be designed to provide the required performance features. Some factors, such as bearing’s type, bearing span, bearing preload and level of tool holder’s pull-in force will affect the spindle’s static and dynamic characteristics. The complicated relationships between these factors are urgent topics to be studied.
Bearing is one critical component of spindle. Several design parameters must be properly selected by the designer. It is evident that higher preload will provide higher stiffness. However, this will limit the maximum rotational speed. In other words, low preload will result in an unacceptable deflection of spindle, or will cause chattering and noise when machining. Numerous studies have been published regarding to the determination of the optimum bearing span of machine tool spindles with two bearings. However, most of the spindles of machine tools are equipped with more than two bearings. Can simplified two-bearings model be used to determine the optimum span of the far more complicated three or four-bearing system?
The purpose of this research is to determine the difference between the static performance of a real spindle mounted with four angular contact bearings and that of the simplified model. Several different 7/24 tool holders and different pull-in force of drawbar system are selected to exam the spindle’s static stiffness. The finite element(FE) analysis software package “I-DEAS” is utilized to build the spindle’s finite element model. The spindle’s static and dynamics characteristics were simulated with several different boundary conditions. The experimental and simulation results were then compared to ensure the FE model’s accuracy. Results showed that the deflection of the spindle housing is significant. The simplified model that did not consider the deflection of the spindle housing can not predict the static stiffness of the spindle accurately. I wish that the conclusions found in this research is helpful to the machine tool industry.

第一章　序論 1
1.1 前言　　　　　　　　　　　　　　　　 　 1
1.2 研究動機　　　　　　　　　　　　　　 　 3
1.3 文獻回顧　　　　　　　　 　　 　　　　　 5
1.4 研究方法與內容　　　　　　　 　　　　　 12
第二章　主軸的構造與靜剛性試驗 13
2.1 主軸的構造 13
2.2 斜角滾珠軸承的特性 14
2.2.1 軸承的接觸角 15
2.2.2 軸承的排列方式 17
2.2.3 軸承的預壓 17
2.2.4 軸承的潤滑方式 19
2.2.5 軸承的靜剛性特性 20
2.2.6 軸承的靜剛性值 25
2.3 軸-軸承系統的靜剛性 33
2.4 7/24刀把介面靜剛性 39
2.4.1 主軸拉刀力設定對軸-刀把介面剛性的影響 42
2.4.2 製造公差對軸-刀把介面剛性的影響 44
2.5 主軸系統靜剛性試驗架構 48
第三章 主軸系統脈衝試驗與分析 55
3.1 脈衝試驗(Impulse Testing) 56
3.1.1 衝擊槌與脈衝輸入訊號 58
3.1.2 加速規的安裝方式 62
3.1.3 訊號處理與訊號品質確認 64
3.2 實驗設備與架構 67
第四章 主軸有限元素模型 73
4.1 主軸有限元素模型靜剛性分析 73
4.1.1 選用元素種類與收斂性 74
4.1.2 主軸靜剛性模型的建構與分析 77
4.1.3 錯估軸承靜剛性的原因 92
4.2 襯套變形量的影響 94
4.3 軸承剛性及跨距對主軸靜剛性的影響 97
4.4 自然頻率分析 100
第五章 結論 103
參考文獻 105
附錄 主軸靜剛性試驗數據 A-1

[1]. 黃俊宏, “綜合加工機用各種7/24刀把介紹”, 機械工業雜誌, 三月號, 168期, 中華民國86年。
[2]. 黃俊宏, “綜合加工機的刀把”, 機械工業雜誌, 四月號, 中華民國82年, pp. 301~314。
[3]. J. Agapiou, E. Rivin, “Toolholder/Spindle Interfaces for CNC Machine Tools”, Annals of the CIRP, 44, 1, 1995, pp. 383~387。
[4]. M. Weck, I. Schubert, “New Interface Machine/Tool: Hollow Shank”, Annals of the CIRP, 43, 1, 1994, pp. 345~348。
[5]. 王文瑞, “主軸性能檢測方法”, 機械工業雜誌, 三月號, 中華民國86年, pp.223~233。
[6]. N. Urmaze, “Chatter-Free Milling and Optimized Material Removal Rates: Analysis of Chatter in Milling”, http://www.mmsonline/articles/。
[7]. 台中精機集團, “工具機主軸靜剛性分析與測試之整合”, http://www.or.com.tw/mz。
[8]. S. Smith, T. P. Jacobs, J. Halley, “The Effect of Drawbar Force on Metal Removal Rate in Milling”, Annals of the CIRP, 48, 1, 1999, pp. 293~296。
[9]. J. A. Brandon, K. J. H. Al-Shareef, “Optimization Strategies for Machine Tool Spindle-Bearing Systems: a Critical Review”, Journal of Engineering for Industry, Vol. 114, 1992, pp. 244~253。
[10]. T. Terman, J. G. Bollinger, “Graphical Method for Finding Optimum Bearing Span”, Machine Design, May, 27, 1965, pp. 159~162。
[11]. H. R. El-Sayed, “Bearing Stiffness and the Optimum Design of Machine Tool Spindles”, Machinery and Production Engineering, November, 6, 1974, pp. 519~524。
[12]. H. R. El-Sayed, “Dynamic Behaviour of Machine Tool Spindles Mounted in Three Bearings”, Machinery and Production Engineering, February, 6, 1974, pp. 139~144。
[13]. W. Popoli, “High Speed Spindle Design and Construction”, http://www.mmsonline/articles/。
[14]. 陳威廉, “工具機主軸軸承的預壓”, 機械月刊, 一月號, 2001, pp. 234~241。
[15]. M. Weck, “Spindle-Bearing Systems for Hogh-Speed Applications in Machine Tools”, Annals of the CIRP, 42, 1, 1993, pp. 445~448。
[16]. 黃俊弘, “工具機主軸的專利回顧”, 機械工業雜誌, 四月號, 中華民國83年, pp.197~206。
[17]. 唯薰, “可變預壓以實現高轉速及高剛性的主軸用軸承組”, 機械技術, 106, 1993, pp. 65~72。
[18]. F. P. Wardle, S. J. Lacey, S. Y. Poon, “Dynamic and Static Characteristics of a Wide Speed Range Machine Tool Spindle”, Precision Engineering, Vol. 5, No. 4, 1983, pp. 175~183。
[19]. J. A. Brandon, K. J. H. Al-Shareef, “On the Validity of Several Common Assumptions in the Design of Machine Tool Spindle-Bearing Systems”, International Journal of Machine Tools and Manufacture, vol. 31, no. 2, 1991, pp. 235~248。
[20]. S. Yang, “A Study of the Static Stiffness of Machine Tool Spindles”, International Journal of Machine Tool Design and Research, Vol. 21, no. 1, 1981, pp. 23~40。
[21]. M. Weck, “Handbook of Machine Tools- Vol. 2- Construction and Mathematical Analysis”, John Wiley & Sons, 1984, pp.193~194。
[22]. 徐國慶, “CNC綜合加工機整機規格分析”, PMC圖書室, 002049, pp. 107~163。
[23]. 日本規格協會, “JIS工作機械”, 1996, pp. 6230。
[24]. J. Tlusty, R. Livingston IV, Y. B. Teng, “Non-linearities in Spindle Bearings and Their Effects”, Annals of the CIRP, 35, 1, 1986, pp. 269~273。
[25]. 周麟恩, 蘇耀藤, “高速主軸軸承系統之運動與動態特性分析”, 碩士論文, 中山大學機械工程研究所, 中華民國90年6月。
[26]. N. Lynagh, H. Rahnejat, M. Ebrahimi, R. Aini, “Bearing Induced Vibration in Precision High Speed Routing Spindles”, International Journal of Machine Tools and Manufacture, vol. 40, 2000, pp. 561~577。
[27]. N. T. Liao, J. F. Lin, “A New Method for the Analysis of Deformation and Load in a Ball Bearing with Variable Contact Angle”, Journal of Mechanical Design, Vol. 123, 2001, pp. 304~312。
[28]. T. A. Harris, “Rolling Bearing Analysis-3rd ed.”, John Wiley & Sons, 1991。
[29]. T. L. H. Walford, B. J. Stone, “The Measurement of the Radial Stiffness of Rolling Element Bearings Under Oscillating Conditions”, Journal of Mechanical Engineering Science, Vol. 22, no. 4, 1980, pp. 175~181。
[30]. B. J. Stone, “The State of Art in the Measurement of the Stiffness and Damping of Rolling Element Bearings”, Annals of the CIRP, Vol. 31, no. 2, 1982, pp. 529~538。
[31]. M. F. While, “Rolling Element Bearing Vibration Transfer Characteristics: Effect of Stiffness”, Journal of Applied Mechanics, Vol. 46, 1979, pp. 677~684。
[32]. V. R. Reddy, A. M. Sharan, “The Finite Element Modelled Design of Lathe Spindles: the Static and Dynamic Analysis”, Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 109, 1987, pp. 407~415。
[33]. Y. Kang, Y. P. Chang, J. W. Tsai, S. C. Chen, L. K. Yang, “Integrated “CAE” Strategies for the Design of Machine Tool Spindle-Bearing Systems”, Finite Elements in Analysis and Design, Vol. 37, 2001, pp. 485~511。
[34]. 郭慶祥, 吳政憲, “工具機高速主軸之性能測試與分析”, 碩士論文, 大葉大學機械工程研究所, 中華民國89年7月。
[35]. T. Aoyama, I. Inasaki, “Performaces of HSK Tool Interfaces Under High Rotational Speed”, Annals of the CIRP, Vol. 50, no. 1, 2001, pp. 281~284。
[36]. Z. M. Levina, “Stiffness Calculations for Cylindrical and Taper Joints”, Machines & Tooling, Vol. 41, no. 3, 1970, pp. 5~11
[37]. Z. M. Levina, “Taper-Connexion Stiffness”, Machines and Tooling, Vol. 44, no. 10, 1973, pp. 21~26。
[38]. T. R. Kim, S. M. Wu, K. F. Eman, “Identification of Joint Parameters for a Taper Joint”, Journal of Engineering for Industry, Vol. 111, 1989, pp. 282~287。
[39]. I. L. Fadyushin, A. R. Maslov, “Accuracy of Taper-Spindle Bores and its Effect on Tool Clamping”, Machines & Tooling, Vol. 43, no. 5, 1972, pp.59~60。
[40]. J. H. Wang, “Investigation of the Tool Holder System with a Taper Angle 7:24”, International Journal of Machine Tools and Manufacture, Vol. 34, no. 8, 1994, pp. 1163~1176。
[41]. 林呈彰, 蕭庭郎, “主軸拉刀力動態量測及探討”, 中國機械工程學會第15屆全國學術研討會論文集, 中華民國87年11月, pp. 567~573。
[42]. D. J. Ewins, “Modal Testing-Theory , Practice and Application 2nd ed.”, Research Studies Press, 2000。
[43]. R. J. Allemang, “Vibrations: Analysis and Experimental Modal Analysis”, Course Notes: UC-SDRL-CN-20-263-662, University of Cincinnati, February, 1999。
[44]. D. J. Inman, “Engineering Vibration”, Prentice Hall, 1994。
[45]. HP, “The Fundamentals of Modal Testing-Application Note 243-3”, http://www.agilent.com。
[46]. P. Avitabile, “Experimental Modal Analysis-A Simple Non-Mathematical Presentation”, www.sandvmag.com。
[47]. PCB, “Introduction to Piezoelectric Accelerometers”, http://www.pcb.com/tech_accel.html。
[48]. M. Xu, J. R. Birchmeier, “Dynamic Stiffness Testing and its Applications in Machine Tools”, Sound and Vibration, June,1997, pp. 14~23。
[49]. J. Mathews, “Guide to Adhesively Mounting Accelerometers”, ENDEVCO, Technical paper 312, http://www.endevco.com/test/literature_tech.htm。
[50]. R. D. Sill, “Minimizing Measurement Uncertainty in Calibration and Use of Accelerometers”, ENDEVCO, Technical paper 299, http://www.endevco.com/test/literature_tech.htm。
[51]. E. I. Rivin, “Trends in Tooling for CNC Machine Tools: Tool-Spindle Interfaces”, Manufacturing Review, Vol. 4, no. 4, 1991, pp. 264~274。
[52]. SKF, “Precision Bearings”, SKF, 1987。
[53]. J. Brandlein, P. Eschmann, L. Hasbargen and K. Weigand, “Ball and Roller Bearings: Theory, Design and Application 3rd”, John Wiley & Sons, 2000。
[54]. 黃俊弘, “高速主軸之技術發展與應用”, 機械工業雜誌, no. 204, 三月號, 中華民國89年。
[55]. 王敬勝, “氣浮高速主軸拉刀機構之拉刀力有限元素分析”, 碩士論文, 高雄第一科技大學機械與自動化工程所, 中華民國90年7月。
[56]. K. G. McConnell, “Vibration Testing: Theory and Pratice”, John Wiley & Sons, 1995。
[57]. MTS Systems Corporation, “Siblab User Guide, V. 3.2.4”。
[58]. V. Adams, A. Askenazi, “Building Better Products with Finite Element Analysis”, Onword Press, 1999。
[59]. 詹子奇, 吳政憲, “高速化工具機動態特性分析與改善”, 碩士論文, 大葉大學機械工程研究所, 中華民國88年6月。
[60]. Structural Dynamics Research Corporation, “I-DEAS online help library”, MTS Systems Corporation。
[61]. R. Zeillinger, H. Kottritsch, “Damping in a Rolling Bearing Arrangement”, SKF, http://evolution.skf.com。