因應未來電子機械產業的發展需要充分整合測試技術與設計分析，需要提升機械結構特性，以實現設計分析和測試技術的充分整合，才能夠實現高效率、高精度、高客製化、智慧化以及整廠整線整合，同時提升機電整體性能。其中機電設計整合是機械動態特性的核心基礎，而在機械高速運動中，動態特性的變化和精確控制將成為關鍵因素。
本研究對XY移動平台進行靜、動態特性分析、根據拓樸分析結果進行結構最佳化設計與結構運動模擬分析。靜、動態分析是在探討機械結構的靜態特性與動態特性。靜態特性可以得知機台不受外力時的變形、應力等情況，確認設計是否有重大缺失;動態特性可以得知機台的自然頻率與振型等，後續透過頻譜分析可以驗證模態分析的正確性，以便作為提高結構的自然頻率或降低共振情況來提高機械精度之參考，模態敲擊實驗是驗證機械實際之自然頻率與模態振型，藉此比對分析的精準度，其分析結果前三階主模態誤差百分比分別為10.9%、6.1%、1.4%，拓樸分析是對結構進行減少重量或是增加自然頻率以提升結構強度，進而提升機械性能的分析方式，由於有限元素分析主要用於分析結構的靜態特性，對於機構運動時的動態特性與定位精度確認是有限元素分析軟體較難達到的，因此將有限元素分析與多體動力學分析進行整合比對，並將相關兩者分析技術應用於機台軟硬體設備的改善，藉由拓樸分析結果進行最佳化設計，機構結構頻率前三階主模態提升了0.1%、4.1%、3.6%，機構運動分析定位時間減少5 ms，後續使用6D雷射干涉儀進行量測，並透過CCD檢測驗證後，建立XY平台的誤差預算表。

The development needs of the future electronic machinery industry, it is crucial to achieve seamless integration of testing technology and design analysis, whilst enhancing the mechanical characteristics. This is essential to achieving high efficiency, precision, customization, intelligence, and integration of the entire factory and production line, as well as improving overall electromechanical performance. Among these, the integration of electromechanical design is the foundation of dynamic mechanical properties. In high-speed mechanical motion, variations in dynamic characteristics and precise control will become critical factors.
This study analyzes the static and dynamic characteristics of an XY motion platform and investigates its structural optimization design based on the topological analysis results, and perform structural motion simulation analysis. Static and dynamic analysis investigates the static and dynamic characteristics of the mechanical structure. Static characteristics provides information on the deformation and stress of the machine when not subjected to external forces, helping to establish for any significant flaws in its design. Dynamic characteristics provide information about the natural frequency and mode shapes of the machine, whist spectral analysis helps in verify the accuracy of modal analysis and serves as references for enhancing the mechanical precision by increasing the natural frequency or reducing resonance. Modal impact testing validates the actual natural frequencies and mode shapes of the machine, comparing them to the analytical results. The percentage errors of the first three dominant mode shapes were 10.9%, 6.1%, and 1.4% respectively. Topological analysis is utilized to enhance structural strength and improve mechanical performance by reducing weight or increasing the natural frequency. While finite element analysis is primarily used to analyze the static characteristics of structures, accurately capturing dynamic characteristics and positioning accuracy during mechanical motion can be challenging for the software. Therefore, this study integrates and compares finite element analysis with multibody dynamics analysis, applying relevant techniques to improve the hardware and software of the machine. Using the results of topological analysis for optimization design, the first three dominant mode shapes of the mechanism structure were improved by 0.1%, 4.1%, and 3.6% respectively, and the positioning time in the mechanism motion analysis was reduced by 5 ms. Subsequent measurements were performed using a 6D laser interferometer, and validation was carried out using CCD detection, followed by the planning of an error budget.

摘要...i
Abstract...ii
誌謝...iv
目錄...v
表目錄...viii
圖目錄...x
第一章 緒論...1
1.1 研究背景...1
1.2 研究目的...1
1.3文獻回顧...2
1.4 論文大綱...5
第二章 理論與實驗設備...7
2.1 有限元素法原理...7
2.1.1有限元素法名詞...8
2.1.2有限元素類型...9
2.1.3有限元素靜態平衡方程式...11
2.2 振動基礎理論與模態實驗...13
2.2.1 單自由度系統...13
2.2.2 單自由度模態分析原理...15
2.2.3 模態測試實驗介紹...16
2.2.4 模態分析重要名詞...17
2.3 有限元求解器原理基礎...18
2.3.1 LU分解法...19
2.3.2 模態提取方法...20
2.4 多體動力學原理...21
2.4.1 多體動力學建模與求解方法...21
2.5 誤差預算原理...22
2.5.1 齊次座標轉換...22
2.5.2 誤差預算原理...24
2.6 實驗設備與軟體...26
2.6.1 半導體檢測機台...26
2.6.2 有限元素分析軟體...28
2.6.3 衝擊錘...29
2.6.4 加速規...30
2.6.5 頻譜分析儀...31
2.6.6 曲線擬合軟體ME’scope...32
2.6.7 多體動力學軟體...33
2.6.8 雷射位移計...33
2.6.9 API 6D雷射干涉儀...35
第三章 有限元素分析與結構運動分析...37
3.1 有限元素分析...37
3.1.1 建立有限元素分析模型...37
3.1.2 材料性質...38
3.1.3 網格設定...40
3.1.4 網格收斂性...40
3.1.5 網格結果...41
3.1.6 邊界條件設定...42
3.1.7 靜態分析...44
3.1.8 模態分析...45
3.1.9 頻譜分析(Harmonic)...46
3.2 結構運動分析...48
3.2.1 建立結構運動分析模型...48
3.2.2 結構運動分析參數設定...49
3.2.3 結構運動分析結果...53
3.3 拓樸分析與結構最佳化設計...55
3.3.1 結構改善目標...55
3.3.2 拓樸分析邊界條件...56
3.3.3 拓樸分析結果...58
3.3.4 結構最佳化設計比較...59
第四章 實驗測試與驗證...64
4.1 模態敲擊實驗...64
4.1.1 模態敲擊實驗量測點規劃...64
4.1.2 模態敲擊實驗設定...66
4.1.3 曲線擬合結果...69
4.1.4 模態分析結果與模態敲擊實驗結果對比...71
4.2 定位量測實驗...73
4.2.1定位量測規劃...73
4.2.2定位量測結果...74
4.2.3結構運動分析與定位量測實驗比較結果...75
第五章 誤差預算...77
5.1 體積誤差...77
5.1.1體積誤差公式...77
5.1.2誤差預算公式...79
5.2 6D雷射干涉儀量測實驗...82
5.2.1上方量測實驗...84
5.2.2下方量測實驗...90
5.3 體積誤差實驗比對...95
5.3.1上方量測結果比較...95
5.4 誤差預算表...100
第六章 結論與未來展望...101
6.1 結論...101
6.2 未來展望...102
參考文獻...104
Extend Abstract...107

[1]Aditya Sharma, Sashank Thapa, Bhaskar Goel, Raj Kumar, Tej Singh,” Structural analysis and optimization of machine structure for the measurement of cutting force for wood”, Alexandria Engineering Journal Volume 64, 1 February 2023, Pages 833-846.
[2]G. Lakshmi Srinivas, Arshad Javed,” Topology Optimization Of Industrial Manipulator-Link Considering Dynamic Loading”, Materials Today：Proceedings Volume 18, Part 7, 2019, Pages 3717-3725.
[3]Li Shengqin, Feng Xinyuan, “Study of structural optimization design on a certain vehicle body-in-white based on static performance and modal analysis”, Mechanical Systems and Signal Processing Volume 135, 1 January 2020, 106405.
[4]Aisha Muhammad, Mohammed A. H. Ali Ibrahim Haruna Shanono, “Design optimization of a diesel connecting rod”, Materials Today：Proceedings Volume 66, Part 3, 2022, Pages 829-833.
[5]G. Shanmugasundar, R. Sivaramakrishnan, S. Meganathan, S. Balasubramani, “Structural Optimization of an Five Degrees of Freedom (T-3R-T) Robot Manipultor Using Finite Element Analysis”, Materials Today：Proceedings Volume 16, Part 2, 2019, Pages 1325-1332.
[6]K. Satyanarayana, T.V. Hanumantha Rao, I . Niranjan Kumar, P.V. J Mohan Rao, V.V.S. Prasad, “Response optimization of four stroke variable compression ratio diesel engine cylinder head with stress analysis”, Materials Today：Proceedings Volume 5, Issue 9, Part 3, 2018, Pages 19497-19506.
[7]Ankit Bhamdare, Ashok Atulkar, Rajkumar Porwal, “Design, static structural analysis and topology optimization of a four wheeler connecting rod”, Materials Today：Proceedings Volume 66, Part 3, 2022, Pages 829-833.
[8]Zhu, J.-H., Zhang, W.-H., Xia, L, “Topology Optimization in Aircraft and Aerospace Structures Design”, Archives of Computational Methods in Engineering Volume 23, Issue 4, 1 December 2016, Pages 595-622.
[9]Kajal Chourasia, Sharnappa Joladarashi, “Modelling, static and dynamic analysis of offset bearing using ANSYS”, Materials Today：Proceedings Volume 66, Part 4, 2022, Pages 2124-2132.
[10]Chen Zhao, Ziming Chen, Jingke Song, Xu Wang, Huafeng Ding, “Deformation analysis of a novel 3-DOF parallel spindle head in gravitational field”, Mechanism and Machine Theory Volume 154, December 2020, 104036.
[11]Kaiji Sato, Ryouhei Hisamatsu, Kaoru Akamatsu, “Controller design for high-speed, ultra-precision positioning of a linear motion stage on a vibrating machine base stage control on a vibrating base”, Precision Engineering Volume 80, March 2023, Pages 10-19.
[12]Haojin Yang, Zihao Wang, Tao Zhang & Fuxin Du, “A review on vibration analysis and control of machine tool feed drive systems”, The International Journal of Advanced Manufacturing Technology volume 107, pages503–525 (2020).
[13]H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, F. Delbressine, “Geometric error measurement and compensation of machines—An update”, CIRP Annals Volume 57, Issue 2, 2008, Pages 660-675.
[14]L.C. Díaz-Pérez, M. Torralba, L. Muro, J.A. Albajez, J.A. Yagüe-Fabra, “Uncertainty budget of a large-range nanopositioning platform based on Monte Carlo simulation”, Measurement Volume 208, 28 February 2023, 112469.
[15]Seth Osei, Wei Wang, Qicheng Ding, “A new method to identify the position-independent geometric errors in the rotary axes of five-axis machine tools”, Journal of Manufacturing Processes Volume 87, 3 February 2023, Pages 46-53.
[16]Y.B. Huang, K.C. Fan, Z.F. Lou, W. Sun, “A novel modeling of volumetric errors of three-axis machine tools based on Abbe and Bryan principles”, International Journal of Machine Tools and Manufacture Volume 151, April 2020, 103527.
[17]Mehrdad Vahebi, Behrooz Arezoo, “Accuracy improvement of volumetric error modeling in CNC machine tools”, The International Journal of Advanced Manufacturing Technology volume 95, pages2243–2257 (2018).
[18]Shisong Wang, Huiling Feng, Zhifei Du, Xingqiao Deng, “Study and failure analysis of Zero-Backlash high precision roller Enveloping reducer”, Engineering Failure Analysis Volume 134, April 2022, 106090.
[19]Jinxing Yang, Zengming Feng, Xiaoguang Wang, “Oil injection lubrication analysis of a silent chain drive system”, Advances in Engineering Software Volume 172, October 2022, 103210.
[20]Xiangqian Zhu, Longye Pan, Zizheng Sun, Yi Wan, Yajun Huang, Jin-Hwan Choi, “Simulation tool for dozer data acquisition”, Automation in Construction Volume 142, October 2022, 104522.
[21]Kuang-Chao FAN, Han-Ming YEN, Kun-Ying LI, “A New Concept of Volumetric Error Analysis of Machine Tools Based on Abbé Principle”, The 3rd International Conference on Design Engineering and Science, ICDES 2014 Pilsen, Czech Republic, August 31 – September 3, 2014.
[22]J. Eguia, A. Lamikiz, L. Uriarte, “Error budget and uncertainty analysis of portable machines by mixed experimental and virtual techniques”, Precision Engineering Volume 47, January 2017, Pages 19-32.
[23]R.G. Grimes, J.G. Lewis, and H.D. Simon. “A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems”. SIAM Journal Matrix Analysis Applications. Vol. 15 No. 1. 228-272 . 1996.
[24] Kuang-Chao Fan, Hao-Wei Yang, Kun-Ying Li, “A Design Methodology of Volumetric Error Analysis and Error Budget”, The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015
[25]林漢暉，2022，「微小晶粒設備之機電設計與虛實整合系統開發」，國立虎尾科技大學機械與電腦輔助工程系，碩士論文。
[26]張家銓，2022，「工具機虛實整合設計與性能研究」，國立虎尾科技大學機械與電腦輔助工程系，碩士論文。
[27]李俊德，2022，「大型車銑複合工具機設計分析與健康診斷研究」，國立虎尾科技大學機械與電腦輔助工程系，碩士論文。
[28]高耀东、郭喜平、张宝琴，《ANSYS 18.2有限元分析》，电子工业出版社，2019，北京。
[29]曹树谦, 张文德, 萧龙翔，《振动结构模态分析：理论、实验与应用》，天津大学出版社，2014，天津。
[30]王栢村，《振動噪音科普專欄》，振動噪音產學技術聯盟。
[31]范光照、王志雄、溫光溥， “AOI機台精度檢測與調校”, 第12屆全國AOI論壇與展覽大會手冊。
[32]劉義，2013，RecurDyn多體動力學仿真基礎應用與提高，電子工業出版社，北京。