臺灣博碩士論文加值系統

本論文為微型三次元量測儀體積誤差補償之研究，希望藉由本實驗室自行開發
的各種系統，回授補償各種誤差，以達體積誤差修正而能提升量測能力之目的，
其中包含將量測儀組裝時的各項幾何誤差補償，如垂直度誤差與角度所造成的阿
貝誤差以及多自由度量測系統(MDFMS)的波長量測補償模組與量測光面鏡之形
貌誤差補。
文中將介紹微型三次元量測儀之各硬體部分，包括共平面平台、Z 軸、探頭、
波長補償模組及感測器，感測器包含作為位置回授的線性繞射光柵干涉儀
(LDGI)以及多自由度量測系統(MDFMS)。
本研究中利用穿透式光柵與自動視準儀結合成波長補償模組，並以市售 SIOS
雷射干涉儀比對校正出感測器之絕對波長，提高平台定位的準確度。另外就體積
誤差補償部分，整合面鏡誤差、光程差、阿貝誤差、垂直度誤差與平坦度誤差，
推導出一套完整體積誤差模型，在誤差模型下實現體積誤差自校正之功能。
而在探頭球頭部分，則以商用光纖熔接機搭配各項機構，設計出一套低成本
快速生產之製程，組裝後的探頭達到直徑< 50 μm，真圓度< 1 μm，偏心量< 1 μm之需求，將可應用於高深寬比等傳統不易量測之工件。
最後結合接觸式掃描探頭做量測應用，可以觸發功能量測出實際點，利用後
處理方式運算，計算出階高與組裝配合誤差。配合掃描程式量測綠點科技微透鏡，
推廣了微型三次元量測儀於小型複雜工件之量測應用。

In the modern metrological technology, traditional coordinate measuring
machines (CMM) is not able to satisfy the required precision and accuracy in
micro/nano scale. Therefore, NTU Metrology Lab developed a Micro coordinate
measuring machine (Micro-CMM) with high precision.
This research presents the combination of industrial techniques, including an
Abbe free XY Co-planar stage, Z-axis ram, scanning probe and high-resolution
sensors. Based on these parts, the goal of this research is to improve Micro-CMM,
which contains Laser wavelength error and volumetric error.
For the wavelength part, this research designs a wavelength compensator by
transmission grating and temperature sensor, and calibrates the real wavelength under
temperature variation.
Besides, this research builds a volumetric model, verified by experiments of
Abbe error, perpendicular error, flatness error and mirror error. By this volumetric
error model, the performance of Micro-CMM will be promoted well.
This research also improves the method of the fabrication process of optical fiber
tip ball. By this method, the fiber is heated to melting point and extruded before
forming the tip ball. The result tip ball diameter is around 50μm, and it’s much better
than commercial products.
Finally, apply the Micro-CMM to measure different parts with various functions,
such as small lens and commercial camera model.

CONTENTS
摘要 1
ABSTRACT 3
LIST OF FIGURES 7
LIST OF TABLES 11
Chapter 1 緒論 12
1.1 研究動機與目的 12
1.2 文獻回顧 14
1.2.1 各國三次元量測儀簡介 14
1.2.2 三次元體積誤差補償 29
1.2.3 探球製作 33
1.3 研究內容概要 34
Chapter 2 微型三次元量測儀之整體架構 35
2.1 共平面平台 36
2.2 寶塔式橋架配重主軸 38
2.2.1 寶塔式橋架結構 38
2.2.2 配重式主軸 40
2.3 線性繞射光柵干涉儀 42
2.3.1 量測原理 42
2.3.2 光柵繞射與督都卜勒頻移 43
2.3.3 線性光柵尺 46
2.4 多自由度量測系統 47
2.4.1 干涉儀量測原理 48
2.4.2 自動視準儀補償原理 51
2.4.3 波長補償原理 52
2.5 超音波馬達 53
2.5.1 超音波馬達結構及特性 53
2.5.2 Nanomotion超音波馬達 55
2.5.3 超音波馬達驅動器AB2 driver 介紹 58
2.5.4 超音波馬達運動控制 61
2.6 接觸式掃描探頭 62
Chapter 3 波長量測補償模組 65
3.1 波長補償光路 65
3.2 波長補償模組實驗架設 66
3.2.1 四象限光感測器 66
3.2.2 實驗架設光軸校準 67
3.3 波長模組校正補償實驗 68
Chapter 4 微型三次元量測儀體積誤差 73
4.1 面鏡誤差 76
4.2 光程差 78
4.3 阿貝誤差 79
4.3.1 定位誤差找阿貝臂 80
4.3.2 探頭與光軸校準 82
4.3.3 更換探針時求阿貝臂 84
4.4 垂直度 84
4.5 平坦度 88
4.6 三次元體積誤差求實際座標 91
4.6.1 XY共平面平台分析 91
4.6.2 X-Y-Z三次元座標量測儀運作時 91
Chapter 5 接觸式探頭 93
5.1 探頭矩陣校正 93
5.1.1 探頭矩陣定義 93
5.1.2 矩陣參數校正 95
5.2 探頭探球製作 99
5.2.1 製作流程 102
5.2.2 探球組裝 107
5.3 探頭觸發量測 110
5.3.1 階高塊量測 112
5.3.2 實驗用玻片厚度量測 113
5.3.3 CCD模組量測 114
5.4 探頭掃描量測 117
5.4.1 透鏡掃描 118
Chapter 6 結論與未來展望 120
6.1 結論 120
6.2 未來展望 120
REFERENCE 122

[1] Taniguchi N. Current Status in, and Future Trends of, Ultraprecision Machining and Ultrafine Materials Processing. CIRP Annals - Manufacturing Technology. 1983;32:573-82.
[2] Hansen HN, Carneiro K, Haitjema H, De Chiffre L. Dimensional micro and nano metrology. Cirp Ann-Manuf Techn. 2006;55:721-43.
[3] Takamasu K, Ozawa S, Asano T, Suzuki A, Furutani R, Ozono S. Basic concepts of nano-CMM (coordinate measuring machine with nanometer resolution). Jpn-China Bilateral Symp on Advanced Manufacturing Eng. 1996;155.
[4] Takamasu K, Hiraki M, Enami K, Ozono S. Development of Nano-CMM and Parallel-CMM—CMM in the 21th Century—. International Dimensional Metrology Workshop. 1999:10-3.
[5] Takamasu K, Fujiwara M, Naoi H, Ozono S. Friction drive system for nano-CMM. Proc Mechatronics, Poland. 2000:565-8.
[6] Fujiwara M, Takamasu K, Ozono S. Evaluation of Properties of Nano-CMM by Thermal Drift and Tilt Angle. Proc XVII IMEKO World Congress (June, Dobrovnik, Croatia). 2003;1797.
[7] Peggs GN, Lewis AJ, Oldfield S. Design for a Compact High-Accuracy CMM. CIRP Annals - Manufacturing Technology. 1999;48:417-20.
[8] Richard L, Jane H, Keith J, Andrew L, Simon O, Andrew Y. Advances in traceable nanometrology at the National Physical Laboratory. Nanotechnology. 2001;12:R1.
[9] Vermeulen MMPA, Rosielle PCJN, Schellekens PHJ. Design of a High-Precision 3D-Coordinate Measuring Machine. CIRP Annals - Manufacturing Technology. 1998;47:447-50.
[10] Theo A.M. Ruijl JvE. Novel Ultra Precision CMM based on Fundamental Design Principle. American Society for Precision Engineering. 2003.
[11] Uwe Brand TK-B, Heinrich Schwenke. Development of a special CMM for dimensional metrology on microsystem components. Proc of the 2000 Annual Meetimg of the ASPE, Scottsdale. 2000.
[12] Schwenke H, Waldele F, Weiskirch C, Kunzmann H. Opto-tactile Sensor for 2D and 3D Measurement of Small Structures on Coordinate Measuring Machines. CIRP Annals - Manufacturing Technology. 2001;50:361-4.
[13] Schmidt I, Hausotte T, Gerhardt U, Manske E, Jager G. Investigations and calculations into decreasing the uncertainty of a nanopositioning and nanomeasuring machine (NPM-Machine). Measurement Science and Technology. 2007;18:482.
[14] Jager G, Manske E, Hausotte T, Buchner HJ. The Metrological Basis and Operation of Nanopositioning and Nanomeasuring Machine NMM-1Metrologische Grundlagen und Wirkungsweise der Nanopositionier- und Messmaschine NMM-1. tm - Technisches Messen Plattform fur Methoden, Systeme und Anwendungen der Messtechnik2009. p. 227.
[15] Teague EC. The National Institute of Standards and Technology molecular measuring machine project: Metrology and precision engineering design. Journal of Vacuum Science &; Technology B. 1989;7:1898-902.
[16] J. Kramar JJ, W. Penzes , F. Scire , C. Teague , J. Villarrubia , E. Amatucci , D. Gilsinn. THE MOLECULAR MEASURING MACHINE. Proceedings of the 1998 International Conference on Mechatronic Technology. 1998.
[17] John AK. Nanometre resolution metrology with the Molecular Measuring Machine. Measurement Science and Technology. 2005;16:2121.
[18] Hocken RJ, Trumper DL, Wang C. Dynamics and Control of the UNCC/MIT Sub-Atomic Measuring Machine. CIRP Annals - Manufacturing Technology. 2001;50:373-6.
[19] Kung A, Meli F, Thalmann R. Ultraprecision micro-CMM using a low force 3D touch probe. Measurement Science and Technology. 2007;18:319.
[20] ZEISS. http://www.zeiss.com. 2010.
[21] Mitutiyo. http://www.mitutoyo.com. 2010.
[22] Panasonic. http://industrial.panasonic.com.
[23] Yang P, Takamura T, Takahashi S, Takamasu K, Sato O, Osawa S, et al. Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of XY linear stage. Precision Engineering. 2011;35:424-30.
[24] Sawano H, Gokan T, Yoshioka H, Shinno H. A newly developed STM-based coordinate measuring machine. Precision Engineering. 2012;36:538-45.
[25] Zhang G, Veale R, Charlton T, Borchardt B, Hocken R. Error Compensation of Coordinate Measuring Machines. CIRP Annals - Manufacturing Technology. 1985;34:445-8.
[26] Zhu S, Ding G, Qin S, Lei J, Zhuang L, Yan K. Integrated geometric error modeling, identification and compensation of CNC machine tools. International Journal of Machine Tools and Manufacture. 2012;52:24-9.
[27] Weekers WG, Schellekens PHJ. Compensation for dynamic errors of coordinate measuring machines. Measurement. 1997;20:197-209.
[28] Fan K-C, Chen M-J. A 6-degree-of-freedom measurement system for the accuracy of XY stages. Precision Engineering. 2000;24:15-23.
[29] Brand U, Kirchhoff J. A micro-CMM with metrology frame for low uncertainty measurements. Measurement Science and Technology. 2005;16:2489.
[30] Kim D, Lee DY, Gweon DG. A new nano-accuracy AFM system for minimizing Abbe errors and the evaluation of its measuring uncertainty. Ultramicroscopy. 2007;107:322-8.
[31] Sheu D-Y. Multi-spherical probe machining by EDM: Combining WEDG technology with one-pulse electro-discharge. Journal of materials processing technology. 2004;149:597-603.
[32] Sheu D-Y. Micro-spherical probes machining by EDM. Journal of Micromechanics and Microengineering. 2005;15:185.
[33] Fan K-C, Hsu H-Y, Hung P-Y, Wang W. Experimental study of fabricating a microball tip on an optical fibre. Journal of Optics A: Pure and Applied Optics. 2006;8:782.
[34] Tung C-H. Design and Research for High Precision Coplanar Stage: NTU, 2004.
[35] Wu P-T. The Development of a Precision Abbe-free Three-axis Moving Stage: NTU, 2007.
[36] Ke Z-Y. Design and assembly methodology of the structure of high precision 3-axis linear stage in nanometer accuracy: NTU, 2010.
[37] Ruiji T. Ultra Precision Coordinate Measuring Machine - Design, Calibration and Error Compensation. The Netherlands: Delft University of Technology,, 2001.
[38] Spaan H, Donker R, Widdershoven I. ISARA 400: enabling ultra-precision coordinate metrology for large parts. Proc of 10th Int’l Symposium on Measurement and Quality Control2010.
[39] F. L. Petrotti LSP. Introduction to Optics. 2nd ed: Prentice-Hall,Englewood Cliffs, 1996.
[40] 范光照, 張郭益. 精密量測: 高立圖書有限公司, 2003.
[41] Loewen E. Diffraction Grating Handbook2005

[42] Uchino K. Piezoelectric ultrasonic motors: overview. Smart Materials and Structures. 1998;7:273.
[43] Nanomotion AB2 Driver User Manual.
[44] Huang C-M. Fabrication of a tactile Scanning Probe fr Micro/Nano CMM: NTU, 2012.
[45] Liao B-S. Development of Michelson Interferometer with Wavelength Compensator and Dual Angle Measurements: NTU, 2012.
[46] Matlab. fmincon,http://www.mathworks.com/help/optim/ug/fmincon.html. http://www.mathworks.com/help/optim/ug/fmincon.html.
[47] Tsou M-C. Research on the Accuracy Improvement of
Micro Coordinate Measuring Machine: NTU, 2013.
[48] Williamson R, Miles M. Melt&;#8208;drawn scanning near&;#8208;field optical microscopy probe profiles. J Appl Phys. 1996;80:4804-12.
[49] Lin C-Y. The Analysis and Fabrications of a Contact Type Measuring
Probe for Micro/Nano CMM with an Observing Unit 2008.