臺灣博碩士論文加值系統

在離散量測方面，圓形零件的幾何特徵測量是依據一群離散的資料點，取樣的不確定性會導致與真圓度的誤差；樣本數量是決定量測的不確定的關鍵因子。樣本數量的增加能提供完全的資訊和改進評估值的準確性，然而也會導致較高的費用。在最小區域(Minimum zone)標準下只需要四個在關鍵區域內的點即可決定真圓度，但樣本數量的增加亦會增加多餘樣本點數量。
本文以樣本點模擬輪廓零件外形，進而分析兩種策略下真圓度之準確性。在本文裡提供一套數學模型，用以建立樣本與評估圓準確性之間的關係。這個模型提供一個有效率的工具；能降低在量測過程的費用，亦能提供在決定適當的樣本量同時亦給予評估圓較高準確性。

For discrete measurement, circularity is calculated upon a set of discrete data points, which represent a sample of the measured part. The sampling uncertainty causes deviation from the true circularity. The sample size is the critical factor to determine the uncertainty of the measurement. The increment of sample size offers more comprehensive information of the measured part and improves the accuracy of the evaluated value, however, that causes a higher cost in the measurement. The increment of sample size also increases the number of redundant point since circularity under minimum zone criterion is determined by four critical points only.
A mathematical model created in this research is to establish the relationship between the sample size and the accuracy of the evaluated circularity. This model offers an effective tool to determine the proper sample size giving the required accuracy of the evaluated circularity with less cost in the measurement. Finally, a simulation of circularity measurement based on two different sampling strategies is given in this research to verify the effectiveness of the proposed model.

摘 要 i
ABSTRACT ii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
1.1. 研究背景 1
1.2. 研究動機 2
1.3. 研究目的 2
1.4. 論文架構 3
第二章 文獻探討 5
2.1. 幾何公差及定義 5
2.1.1. 真直度 7
2.1.2. 真圓度 7
2.1.3. 真平度 8
2.1.4. 圓柱度 9
2.2. 真圓度介紹 9
2.3. 相關文獻之探討 12
2.3.1. 量測方法方面 12
2.3.2. 量測儀器方面 14
第三章 研究方法 16
3.1. Voronoi diagram概述 16
3.2. 計算真圓度 19
3.3. 樣本點的分析 22
第四章 模擬及分析 26
4.1. 探討關鍵點 26
4.1.1. 評估真圓度 27
4.2. 探討機率值 34
4.3. u值的評估 36
4.4. 評估精確度 39
4.5. 驗證 41
4.6 未來研究建議 41
第五章 結論 42
5.1. 結論 42
參考文獻 43
附錄一 46

1.中國機械工業教育協會(2001)，幾何量精度設計與檢測，第一版，機械工業出版社，北京。
2.王滄吉(2006)，經濟可靠之真圓度量測與分析方法，義守大學，工業工程與管理系，碩士論文。
3.王遐(1993)，精密量測，四版，東大圖書發行，台北。
4.林詩偉(2002)，運用幾何特徵描述詮釋資料特性之研究，國立台灣科技大學，工業管理系，碩士論文。
5.林榮慶，林宸生，徐碧生(1993)，精密量具及機件檢驗，二版修訂，高立圖書發行，台北。
6.姜俊賢(2004)，精密量具及機件檢驗，十二版修訂，(陳長成等編者)，新文京開發出版，台北。
7.范光照，張郭益(2005)，精密量測，四版修訂，高立圖書發行，台北。

8.孫德萱(1998)，以類神經網路建立區間迴歸分析求解最小區間問題，國立中央大學，機械工程研究所，博士論文。
9.張達元，羅仕鵬(1999)，精密量具及機件檢驗實習，初版，全威圖書發行，台北。
10.許裕隆(2001)，基因演算法應用於三次元座標量測儀之量測路徑選擇規劃，朝陽科技大學，工業工程與管理系，碩士論文。
11.陳志龍(2001)，智慧型高速真圓度測定儀，國立台灣大學，電機工程研究所，碩士論文。
12.陳建宏(1995)，三度空間中之真圓度評估，國立台灣科技大學，管理技術研究所，碩士論文。
13.葉志雄(2001)，無順序性3D資料網格化及其應用，國立中正大學，機械系，碩士論文。
14.廖尉植(2004)，台中市鄰里公園可及性與服務水準之研究，逢甲大學，建築與都市計畫研究所，碩士論文。
15.劉建宏(2000)，數控加工機與銑刀誤差檢測之數模研究，國立成功大學，機械工程學系，博士論文。
16.蔡宗翰(2006)，應用粒子群最佳化演算法於真圓度量測，國立台北科技大學，工業工程與管理系，碩士論文。
17.蘇志盛(2003)，以有權重的質心范諾圖作漸進式三維模型重新網格化，國立成功大學，資訊工程學系，碩士論文。
18.鐘振周，葉賜旭，梁瑞芳(2002)，精密機械空間誤差量測與補償，初版，全華科技圖書發行，台北。
19.ANSI/ASME Y14.5M (1994).National Standard on Dimensioning and Tolerancing. American Society of mechanical Engineers, New York. (1994)
20.Chen, M.C.、Tsai, D.M.、Tseng, H.U.(1999). “A stochastic optimization approach for roundness measurements”, Pattern Recognition Letters, Vol.20, pp.707-719.
21.Cho, N.、Tu, J.(2001). “Roundness modeling of machined parts of tolerance analysis”, Precision Engineering, Vol.25, pp.34-47.
22.Choi, W.、Kurfess, T.R.、Cagan, J. (1998). “Sampling uncertainty in coordinate measurement data analysis”, Precision Engineering, Vol.22, pp.153-163.
23.Edgeworh, R.、Wilhelm, R.(1999). “Adaptive sampling for coordinate metrology”, Precision Engineering, Vol.23, pp.144-154.
24.Etrsami, F.、Qiao, H.(1990). “Analysis of two-dimensional measurement data for automated inspection”, Journal of Manufacturing System, Vol.9, pp.21-34.
25.Gleason, E.、Schwenke, H. (1998). “A spindleless instrument for the roundness measurement of precision spheres”, Precision Engineering, Vol.22, pp.37-42.
26.Haitjema, H. (1996). “Dynamic probe calibration in the μ m region with nanometric accuracy”, Precision Engineering, Vol.19, pp.98-104.
27.Horikawa, O.、Maruyama, N.、Shimada M. (2001). “A low cost, high accuracy roundness measuring system”,Precision Engineering, Vol.25, pp.200-205.
28.Huang, J.(1999). “An exact minimum zone solution for sphericity evaluation”, Computer Aided Design, Vol.31, pp.845-853.
29.Huang, J.(1999). “An exact solution for the roundness evaluation problems”, Precision Engineering, Vol.23, pp.2-8.
30.ISO/R1001 (1983). Technical Drawing-Geometrical Tolerancing.
31.Kim, W.S.、Raman, S.(2000). “On the selection of flatness measurement points in coordinate measuring machine inspection”, International Journal of Machine Tools and Manufacture, Vol.4, pp.427-443.
32.Lai, K.、Wang, J.(1988). “A computational geometry approach to geometric tolerancing”, 16th North American Manufacturing Research Conference, University of Illinois, pp.376-379.
33.Le, Van-Ban、Lee, D.T.(1991). “Out-of-Roundness Problem Revisited”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.13, pp.217-223.
34.Murthy, T.S.R. (1986). “A comparison of different algorithms for circularity evaluation”, Precision Engineering, Vol.8, pp.9-23.
35.Murthy, T.S.R.、Abdin, S.Z. (1980). “Minimum zone evaluation of surfaces”, International Journal of Machine Tool Design and Research, Vol.20, pp.23-136.
36.Nielsen, H.S.、Malburg, M.C. (1996). “Traceability and correlation in roundness measurement”, Precision Engineering, Vol.19, pp.175-179.
37.Philips, S.D.、Borchardt, W.T.、Estler, W.T,、Buttress, J.(1998). “The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines”, Precision Engineering, Vol.22, pp.87-97.
38.Roy, U. and Zhang, X.(1992). “Establishment of a pair of concentric circles with the minimal radial separation for assessing roundness error”, Computer-Aided Design, Vol.24, pp.161-168.
39.Swanson, K.、Lee, D.T.、Wu, V.L.(1995). “An optimal algorithm for roundness determination on convex polygons”, Computational Geometry, Vol.5, pp.225-235.
40.Ventura, J.A.、Yeralan, S.(1989). “The Minimax Center Estimation Problem for Automated Roundness Inspection”, European Journal of Operation Research, Vol.41, pp.64-72.
41.Wei, G.、Kiyono, S.、Nomura, T. (1996). ”A new multiprobe method of roundness measurements”, Precision Engineering, Vol.19, pp.37-45.
42.Yau, H.T.(1997). “Evaluation and uncertainty analysis of vectorial tolerances”, Precision Engineering, Vol.20, pp.123-137.
43.Yearlan, S.、Ventura, J.A.(1988). “Computerized roundness inspection”, International Journal of Production Researches, Vol.26, pp.1921-1935.