臺灣博碩士論文加值系統

本文從運動學的原理，闡明旋轉運動及其偏差，並以幾何精度的概念建立旋轉精度的數學模型，用以測量工具機主軸旋轉運動的誤差，如以圓度誤差的概念，檢測及評定單點切削工具機主軸旋轉的徑向、軸向及傾角誤差；以圓柱度誤差的概念評定多點切削工具機主軸旋轉的精度。
在工具機各運動機構的誤差分離技術上，係利用三點法分離滑軌的直線度運動誤差，再根據三測點的圓度誤差分離方法，運用光電感測及微電腦技術，控制及改變測量基準點，使檢測的裝置最適於三點法的假設條件，求得主軸旋轉的圓度誤差。
對圓柱度誤差的測量，係將每個斷面圓度誤差投影至底面，求出圓柱度誤差，以圖形及數據來表示工具機主軸旋轉的幾何精度。對圓錐及球度誤差的精度分析，以最小外接圓錐的概念，利用最小平方法及殘差定理，建立測量的幾何模型。
最後利用測試標準棒、感測器、信號轉換器、運算放大器、控制介面與微處理機等進行主軸旋轉的徑向、軸向及傾角運動誤差的測量驗證，得到良好的成果。

This paper elaborates the deviation of rotation based on dynamic mechanics, establishes the mathematical model of rotation through the concept of geometric accuracy, and constructs the measurement principle of spindle rotation for machine tools. For instance, the radial, axial and tilt errors are used to evaluate the accuracy of spindle rotation of single-point cutting machine tools; the concept of cylindrical error is used to evaluate the accuracy of spindle rotation of multi-point cutting machine tools.
To separate motion errors of machine tool parts, the three-point measuring method is used. This method can separate the errors of the straight-line motion of the slide track from those of the motional parts of the machine tools. The method is modified to separate the roundness errors of the rotational parts of spindle by changing its initial measuring point. The cylindrical error of the rotational spindle is the extension of roundness error. It can be obtained by evaluating the roundness error of each cross section projected onto the perpendicular basal plane according to the measurement of straight-line error.
The mathematical model of the cone and the sphere can be constructed by using the concept of the minimum circumscribed cone, the least-square method, and residual-error principle. This measurement principle has proved effective through the use of standard bar, sensor, transducer, amplify, control interface and computer to measure the radial, axial and tilt errors of spindle rotation of single-point cutting machine tools.

封面
授權書
考試合格證明
中文摘要
英文摘要
誌謝
總目錄
表目錄
圖目錄
符號說明
第一章 前言
1.1 研究目的及其背景
1.2 文獻回顧
1.3 本文架構
第二章 旋轉運動幾何精度的定義
2.1 工具機積貯主軸旋轉運動誤差的來源
2.1.1 軸承滾圓的偏心
2.1.2 工具機主軸及相關零件的配合誤差
2.1.3 工具積主軸旋轉的動態特性
2.1.4 工具機主軸旋轉精度檢測的重要性
2.2 幾何精度的定義
2.2.1 直線度
2.2.2 平面度
2.2.3 平行度
2.2.4 垂直度
2.2.5 球度
2.2.6 表面粗糙度
2.3 旋轉精度的定義
2.3.1 旋轉主軸的徑向、軸向及傾角誤差
2.3.2 旋轉運動座標系的定義
2.3.3 旋轉主軸圓度誤差的定義
2.3.4 旋轉主軸圓柱度誤差的定義
第三章 真圓度的精度分析與測量原理
3.1 旋轉主軸徑向、軸向及傾角誤差的測量原理
3.2 旋轉主軸圓度誤差的測量原理
3.2.1 反向法
3.2.2 多步法
3.2.3 三測點法
3.2.4 四測點法
3.3 主軸旋轉運動誤差的評定
3.3.1 最小外切圓法(M.C.C)
3.3.2 最大內接圓法(M.I.C)
3.3.3 最小平方圓法(L.S.C)
3.3.4 最小領域法(M.Z.C)
第四章 圓柱度的精度分析與測量原理
4.1 旋轉主軸圓柱度誤差的測量原理
4.2 主軸旋轉的圓柱度誤差評定
4.3 求圓柱度誤差的包容圓柱方法
4.3.1 包容圓柱的概念
4.3.2 包容圓柱的幾何模型
4.3.3 包容圓柱模型的求解方法
第五章 圓錐及圓球的精度分析
5.1 圓錐的精度分析
5.1.1 最小外接與最大內切圓錐的定義
5.1.2 最小外接圓錐的幾何模型
5.1.3 最大內切圓錐的幾何模型
5.1.4 圓錐幾何模型的求解過程
5.1.5 例題
5.2 圓球的精度分析
5.2.1 球度誤差的定義
5.2.2 球度誤差的評定方法
5.3 球度誤差的測量方法
第六章 測量系統動態數據的處理
6.1 動態量測數據的分類
6.1.1 確定性數據
6.1.2 隨機性數據
6.2 隨機過程理論
6.2.1 隨機過程的基本概念
6.2.2 隨機過程的特徵量
6.3 隨機過程的待徵量的求法
6.3.1 平穩隨機過程及其特徵量
6.3.2 非平穩隨機過程及其特徵量
6.4 動態數據的處理步驟
6.4.1 數據的獲得
6.4.2 數據的預處理
6.4.3 數據性質的檢驗
6.4.4 數據分析
第七章 工具機主軸旋轉運動襄差檢測元件
7.1 測試標準棒
7.2 感測器
7.3 運算放大器
7.4 信號轉換器
7.5 光電檢出器
7.6 取樣控制界面
7.7 微處理機
7.8 其他實驗設備
第八章 工具機主軸旋轉運動誤差的檢測程式
8.1 類比/數位轉換器的測試程式
8.2 取樣與準確度測試程式
8.3 取樣速度測試程
8.4 轉軸徑向誤差檢測試程式
8.5 車床主軸旋轉精度檢測試程式
8.6 主軸旋轉圓度誤差檢測試程式
第九章 工具機主軸旋轉運動檢測的誤差分析
9.1 測量誤差的來源與分類
9.2 測試標準棒幾何形狀引起的測量誤差
9.3 類比/數位轉換器的誤差
9.4 取樣數與系統準確性
9.5 取樣控制及其準確性
9.6 檢測系統的精度
9.7 旋轉工件案裝不完善引起的誤差
9.8 取樣延遲及檢測注意事項
第十章 結論
10.1 測量原理的探討
10.2 測量元件及程式的撰寫
10.3 測量數據統計分析的建議
10.4 測量方法的限制
10.5 未來研究的方向
參考文獻
附錄一 類比/數位轉換器校正程式
附錄二 取樣數與準確度測試程式
附錄三 取樣速度測試程式
附錄四 轉軸徑向誤差檢測程式
附錄五 實驗設備

[1] A.N. Poo, J.G. Bollinger, and G.W. Younkin, “Dynamic Errors in Type 1 Contouring systems”, IEEE Transactions on Industry Application, 8/4, p477~484, 1972.
[2] ANSI/ASME B89.3.4M “Axes of rotation methods for specifying and testing”, New York, The American Society of Mechanical Engineers, 1985.
[3] A.B Forbes, “Robust circle and sphere fitting by least squares”, National physical laboratory, p153~189, 1989.
[4] A.Halmal, A.Huba and L.Molnar, “Mechatronical equipment for measuring form defect by miniature shafts”, Mechatronics, 3/2, p139~147, 1993.
[5] ANSI/ASME Y14.5M, “Dimensioning and Tolerancing”, The American Society of Mechanical Engineers, New York, 1994.
[6] C.K. Taft, F.N. Lutz and M. Mazoh, “Dynamic accuracy in numerical control systems Part 1”, Manufacturing Engineering. P16~27, 1967.
[7] C.K. Taft, F. N. Lutz and M. Mazoh, “Dynamic accuracy in numerical control systems Part 2”, Manufacturing Engineering. P80~83, 1967.
[8] C. Mallanna, T.S. Murthy and M. E. Vis, “Influence of error in wheel and work of axes rotation on the work-piece in cylindrical grinding”, Annals of the CIRP, 29/1, p373~375,1980.
[9] C.K.Chen, J.Tan and Y.Tang, “An investigation on enveloping spheres and their correlative problems”, Proceeding of APSI Huangshan City China, p197~200, 1997.
[10] C.K. Chen and S.C.Wu, “Computer aided measuring for rotating accuracy of high speed lathe”, Proceeding of the fourth international symposium on measurement technology and intelligent instruments, p67~72, 1998.
[11] C.Goutam and R.Bernard “Chebychev approximation methods for evaluating conicity”, Measurement 23, p63-76, 1998.
[12] C.Y. Lo and S.C.Wu, “Evaluation of cylindrical error about the rotating spindle of machine tool”, Proceeding of the fourth international symposium on measurement technology and intelligent instruments, p89~94, 1998.
[13] C.K.Chen and S.C.Wu, “A method for measuring and separating cylindrical and spindle errors in machine tool rotational parts”, Measurement Science and Technology, 10/2, p76~83, 1999.
[14] D.J Whitehouse, “A best fit reference line for use in partial arcs”, Scientific Instruments, 6, p921~924, 1973.
[15] D.G. Lee, H.C. Sin. “Manufacturing of a graphite epoxy composite spindle for a michine tool”, Annals of the CIRP, 34/1, p365~369,1985.
[16] Dean and J.W. Dawson, “Cylindricity and its measurement”, Int. J. Machine Tools Manufacture, 32, p247-253, 1992.
[17] F.J. Ellert, “Feedback in contouring control systems”, AIEE Trans. 74, p345~354, 1956.
[18] F.P. Wardle, S.J. Lacey and S.Y. Poon, “Dynamic and static characteristics of a wide speed range machine tool spindle”, Precision Engineering, 5/4, p175~183, 1983.
[19] F.T. Jay, B. Bossmanns, and C.C. Hung, “Modeling and error analysis for assessing spindle radial error motions”, Precision Engineering, p90~107, 1997.
[20] G.T.Anthony, “Reference software for finding chebyshev best-fit geometric elements”, Precision Engineering, 19, p28~36, 1996.
[21] G.X. Zhang, “Four-point method of roundness and spindle error measurements”, CIRP annals, 42/1, 593~596, 1993.
[22] H.E. Vigon, “Effect of servo system characteristics on the accuracy of contouring around a corner”, AIEE Proc., p62~250, 1962.
[23] H.Yan, X.Q. Huang and C.H.Ku, “A method of on-line measuring the error motion of rotating spindle of machine tools-theory and application”, Proceedings of the 25rd International MTDR, p113~119, 1985.
[24] H.J.Hansen, “A new dynamic spindle analyzer”, Proceeding of the international conference on machinery moving accuracy, p472~475, 1989.
[25] H.Zhang, H.Yun and J.Li, “An on-line measuring method of work-piece diameter based on the principle of three-sensor error separation”, Proc. IEEE, 3, p1308~312,1990.
[26] ISO 230-1 Test code for machine tools Part 1 “Geometric accuracy of machines operating under no-load or finishing conditions”, International Standard, 1996.
[27] J.B.Bryan, P.Vanherck, “Unification of terminology concerning the error motion of axes of rotation”, Ann CIRP, 24/2, 1975.
[28] J.B.Bryan, “A simple method for testing measuring machines and machine tools Part 1: Principle and application”, Precision Engineering, 4/2, p61~69, 1982.
[29] J.B.Bryan, “A simple method for testing measuring machines and machine tools Part 2: Construction details”, Precision Engineering, 4/3, p125~138, 1982.
[30] J.M. Kaiser, “The geometry of the minimum radial separation functional: the planar case”, Measurement science and technology, p1442-1450, 1995.
[31] K. Mitsui, “Development of a new measuring method for spindle rotation accuracy by three-points method”, Proceedings of the 23rd International MTDR, p115~121, 1982.
[32] K.Iizuka and Mitsuo, “A new precision measuring system of roundness and cylindricity with self-calibration capability”, Nation research laboratory of metrology, p451~456, 1983.
[33] K.Busch, H.Kunzmann and F.Waldele, “Calibration of coordinate measuring machines”, Precision Engineering, 7/3, p139~144, 1985.
[34] L. Cao, “The measuring accuracy of the multi-step method in the error separation technique”, J Phys, E: Sci Instrum, 22, p903~6, 1988.
[35] M.Sawabe, N.Fujimuma, “Influence of radial motion on form error of work-piece in turning”, Annals of the CIRP, 27, p505~509, 1978.
[36] M. Szafarczyk and M. Misiewski, “Automatic measurement and correction of work-piece diameter on NC center lathe”, Annals of the CIRP, 32/1, p305~307, 1983.
[37] M.A.Donmez, D.S.Blomquist and R.J.Hocken, “A general methodology for machine tool accuracy enhancement by error compensation”, Precision Engineering, 4/8, p187~195, 1986.
[38] M.Weck and M.Schmidt, “A new method for determining geometric accuracy in the axis of movement of machine tools”, Precision Engineering, 8/2, p97~103, 1986.
[39] M.S.Shunmugam, ”Comparison of linear and normal deviations of forms of engineering surfaces”, Precision Engineering, p96~102, 1987.
[40] M.Burdekin and N.J.Lloyd, “A system for assessing the accuracy performance of machine tool spindles under load”, Proceedings of the 27rd International MTDR, p209~214, 1987.
[41] M.Burdekin & W.Jywe, “Application of contisure for the verification of the contouring performance of precision machines”, 6th international precision engineering conference, Germany, 1991.
[42] P.Vanherck and J.Peters, “An axis of rotation analyzer”, Proceedings of the 14rd International MTDR, p299~305, 1973.
[43] P.Vanherck and J.Peters, “Digital axis of rotation measurement”, Annals of the CIRP, 22/1, p135~136, 1973.
[44] P.D.Chapman, “A capacitance based ultra-precision spindle error analyzer”, Precision Engineering, 7/3, p129~136, 1985.
[45] R.Donaldson, “A simple method for separating spindle error from test ball roundness error”, Ann CIRP, 21, p125~126, 1972.
[46] R.Taylor and H.Limited, ”Analysis and Measurement of Surface Geometry”, Precision Engineering, pp138~147, 1987.
[47] S.T.Huang, K.C.Fan and J.H.Wu, “A new minimum zone method for evaluating straightness errors”, July, p158~165, 1993.
[48] S.H.Cheraghi, “Straightness and flatness tolerance evaluation: an optimization approach”, Precision Engineering, 18, p30~37, 1996.
[49] S. Tong, “Two-step method without harmonics suppression in error separation”, Measurement Science and Technology, 7, p1563~68, 1996.
[50] S. Tong, J. Tan & F. Li, “Compensating harmonics in multi-step error separation with comprehensive method”, Journal of the Chinese society of mechanical engineers, 1996.
[51] T.Tsuada, ”Minimum Zone evaluation of cylindricity deviation by some optimization techniques”, Precision Engineering, pp18~23, 1985.
[52] T.Tsukuda, T.kanada, and S.Liu, “Method for the evaluation of form errors of conical taped parts”, Precision Engineering 22, p8-12, 1988.
[53] T.Hatsuzawa, “A cylindrical envelope projection model for estimation of secondary electron intensity distribution at micro-steps”, Measurement Science and Technology, 4, p842~845, 1993.
[54] Unification document me, “Axes of rotation”, Annals of the CIRP Vol. 25. 1976.
[55] W.Gao, S.Kiyono and Takamitu, “High-accuracy roundness measurement by a new error separation method”, Precision Engineering, 21, p123~133,1977.
[56] W.Knapp, “Circular test for three-coordinate measuring machines and machine tools”, Precision Engineering, 5/3, p115~124, 1983.
[57] W. Gao & Tadatoshi. “A new multi-probe method of roundness measurements”, Precision Engineering, 19/1, p37~44, 1996.
[58] W.F. Chen, S.W.Lin and S.C.Wu, “Computer aided measuring of rotating error for high speed machine tool”, Proceeding of the fourth international symposium on measurement technology and intelligent instruments, p73~78, 1998.
[59] Y.Kakino, Y.Yamamoto & N.Ishii, “New measuring method of rotating accuracy of spindle”, annals of the CIRP Vol.25.1977.
[60] Y.Kakino, and J.Kitazawa, “In situ measurement of cylindricity”, Ann CIRP, 27, p371~375, 1978.
[61] Y.L.Xiong, ”Computer Aided Measurement of Profile Error of Complex surface and curves”, Tools Manufacture, pp339~357, 1990.
[62] Y.S. Sysoev, “Coordinate methods of determining average circle parameters in actual surface profile analysis”, Measurement Techniques, 38, p1108~114, 1995.