本研究旨在探討高精密平面磨床的靜動態特性，使用有限元素分析法(Finite Element Analysis, FEA)對整機進行靜剛性與動剛性分析，再透過實驗模態分析(Experimental Modal Analysis, EMA)與操作變形振型(Operational Deflection Shapes, ODS)量測實際振動特性並且加以驗證。本研究亦搭配拓撲最佳化進行結構剛性強化，避免機台產生共振現象導致精度損失，以滿足現代工業製造的需求。
透過模態分析和實際量測結果，觀察高精密平面磨床的前兩階自然頻率分別為68.2Hz和73.0Hz。進一步利用EMA與ODS進行量測加以驗證，於前六階模態中，對比誤差皆低於10%。這強化了分析結果的可信度和準確性。為了輕量化整體結構，利用ANSYS Workbench針對底座、立柱和主軸外殼進行拓撲分析與結構優化，使整機的總體質量減少了6.2kg，主軸的位移量降低了1.7%。同時，整體結構的前六階自然頻率分別提升了3.7%、2.5%、5.3%、0.7%、2.1%和4.1%。並且第一階模態提升至70.8Hz，成功避免了在3600rpm下的頻率區間（60Hz至70Hz）內的共振，達成了結構的輕量化與提升剛性之目標。利用RecurDyn對高精密平面磨床的主軸座與工作床台進行了有緩衝與無緩衝控制的運動模擬。透過模擬運動控制的差異，確保了機台運行的穩定性，更進一步掌握機台之實際運動特性。

This study aims to investigate the static and dynamic characteristics of a high-precision surface grinding machine. Finite Element Analysis (FEA) is employed to perform both static and dynamic stiffness analyses on the entire machine. Experimental Modal Analysis (EMA) and Operational Deflection Shapes (ODS) measurements are carried out to validate the actual vibration characteristics. Topology optimization is employed to enhance the structural stiffness in this study, thereby reducing the risk of resonance-induced accuracy loss and ensuring compliance with the exacting demands of contemporary manufacturing standards.
The initial two natural frequencies of the high-precision surface grinding machine were determined to be 68.2 Hz and 73.0 Hz through modal analysis and experimental testing. Utilizing ODS and EMA measurements for the initial six modes, further validation produced ensures with less than 10% error. Topological analysis and structural optimization with ANSYS Workbench led to a significant 6.2 kg reduction in mass and a 1.7% decrease in spindle displacement. The structure demonstrated improvements of 3.7%, 2.5%, 5.3%, 0.7%, 2.1%, and 4.1% across the initial six natural frequencies. Elevating the initial modal frequency to 70.8 Hz effectively averted resonance in the 60 Hz to 70 Hz range at 3600 rpm, highlighting enhanced weight efficiency and increased stiffness. RecurDyn simulated spindle seat and worktable motion control, with and without buffering, the stability of machine operation is ensured, providing a deeper understanding of the actual motion characteristics of the machine.

摘要...i
Abstract...ii
誌謝...iii
目錄...iv
表目錄...vii
圖目錄...viii
符號說明...xi
第一章 緒論...1
1.1 前言...1
1.2 研究動機及目的...2
1.3 文獻回顧...2
1.4 論文架構...8
第二章 基礎理論與研究設備...9
2.1 有限元素法介紹...9
2.1.1有限元素種類介紹...11
2.1.2有限元素法之平衡方程式...12
2.1.3軟體ANSYS介紹...14
2.2 模態與振動分析原理...16
2.2.1振動系統模型與理論...16
2.2.2模態分析重要名詞介紹...18
2.2.3模態試驗原理介紹...20
2.3 拓撲最佳化介紹...21
2.3.1拓撲最佳化理論...22
2.4 多體動力學(Multibody Dynamics, MBD)理論...23
2.5 磨床切削阻力計算...24
2.6 實驗設備介紹...26
2.6.1高精密平面磨床-ESG818CNC...26
2.6.2衝擊錘介紹...28
2.6.3頻譜分析儀...29
2.6.4三軸加速規...30
2.6.5模態擬合軟體ME’scope...31
2.6.6多體動力學RecurDyn介紹...32
第三章 有限元素分析與拓撲最佳化...34
3.1 有限元素分析...34
3.1.1建立有限元素分析模型...35
3.1.2材料性質設定...37
3.2 網格化設定...37
3.2.1網格收斂性分析...39
3.3 靜、動態分析...40
3.3.1接觸與邊界條件設定...40
3.3.2靜剛性分析...42
3.3.3模態分析...43
3.3.4簡諧響應分析...46
3.3.5振動收斂分析...49
3.4 空間精度分析...51
3.4.1靜態特性分析...52
3.4.2模態特性分析...60
3.4.3振動收斂特性分析...83
3.4.4簡諧響應特性分析...86
3.5 結構拓撲分析與優化...89
3.5.1拓撲優化目標...89
3.5.2拓撲分析邊界條件設定...91
3.5.3拓撲分析之優化建議...95
3.5.4拓撲優化結果...96
3.5.5整機拓撲優化前後對比...105
第四章 模態實驗與驗證...109
4.1 模態實驗方法...109
4.1.1實驗模態分析(EMA)...109
4.1.2操作變形振型(ODS)...110
4.1.3量測點位規劃...110
4.2 Novian量測軟體設定...112
4.3 結構模態量測結果...115
4.3.1實驗模態分析(EMA)量測結果...115
4.3.2操作變形振型(ODS)量測結果...116
4.4 模態分析與實驗結果對比...119
4.4.1 EMA與FEA對比...119
4.4.2 ODS與FEA對比...121
第五章 結構運動模擬與結果分析...126
5.1 建立分析結構模型...126
5.2 動力條件設定...130
5.3 運動模擬結果...133
5.3.1主軸座沿Z軸移動之分析探討...133
5.3.2工作床台沿Y軸移動之分析探討...136
5.3.3工作床台沿X軸移動之分析探討...139
第六章 結論與未來展望...141
6.1 結論...141
6.2 未來展望...142
參考文獻...143
Extended Abstract...147
Abstract...147
1. Introduction 148
2. Finite element analysis compared with EMA and ODS...148
3. Topology optimization analysis...149
4. Structural motion simulation and result analysis...151
5. Conclusions...152
Reference...154

[1]Myers, A., Ford, D. G., & Xu, Q. 2003. “Finite element analysis of the structural dynamics of a vertical milling machine.” WIT Transactions on Engineering Sciences, Vol. 44.
[2]Aurich, J. C., Biermann, D., Blum, H., Brecher, C., Carstensen, C., Denkena, B., & Weinert, K. 2009. “Modelling and simulation of process: machine interaction in grinding.” Production Engineering, Vol. 3, pp. 111-120.
[3]Chen, D., Fan, J., & Zhang, F. 2012. “Dynamic and static characteristics of a hydrostatic spindle for machine tools.” Journal of Manufacturing Systems, Vol. 31. No. 1, pp. 26–33.
[4]Pakzad, S., Rajab, A. K. S., Mahboubkhah, M., Ettefagh, M. M., & Masoudi, O. 2012. “Modal analysis of the surface grinding machine structure through FEM and experimental test.” Advanced Materials Research, Vol. 566, pp. 353-356.
[5]Chen, D. C., Chen, M. F., Kang, J. H., & Lai, C. C. 2017. “Vibration characteristics and modal analysis of a grinding machine.” Journal of Vibroengineering, Vol. 19, No. 8, pp. 6288-6300.
[6]Er, P. V., & Tan, K. K. 2018. “Machine vibration analysis based on experimental modal analysis with radial basis functions.” Measurement, Vol. 128, pp. 45-54.
[7]Zheng, D., Zhang, Q., Zhang, J., Yao, H., & Yin, S. 2020. “Finite element analysis and testing on the vibration mode of small grinding carriage in high-efficiency CNC grinding machine.” In Journal of Physics: Conference Series, Vol. 1653, No. 1, p. 012068, IOP Publishing.
[8]Saint Martin, L. B., Gusmao, L. L., Machado, T. H., Okabe, E. P., & Cavalca, K. L. 2021. “Operational modal analysis application to support structure identification under rotating machinery unbalance.” Engineering Structures, Vol. 249, 113344.
[9]Chan, T. C., Chang, K. C., Chang, S. L., & Chiang, P. H. 2022. “Simulation, modeling, and experimental verification of moving column precision grinding machine.” Journal of the Chinese Institute of Engineers, Vol. 45, No. 1, pp. 54-64.
[10]Sun, Y., Zhang, Z., Zhang, J., Jin, X., Xu, B., Deng, Y., & Zhao, G. 2015. “Effects of transient slamming and harmonic swings on the Marine Compound NC Machine Tool.” Ocean Engineering, Vol. 108, pp. 606–619.
[11]Masutage, V. S., & Kavade, M. V. 2018. “A Review Vibrating Screen and Vibrating Box: Modal and Harmonic Analysis.” International Research Journal of Engineering and Technology, Vol. 5, No. 1, pp. 401-403.
[12]Bendsoe, M. P., & Kikuchi, N. 1988. “Generating optimal topologies in structural design using a homogenization method.” Computer methods in applied mechanics and engineering, Vol. 71, No. 2, pp. 197-224.
[13]Cheng, D., Lu, X., & Sun, X. 2018. “Multi-objective topology optimization of column structure for Vertical Machining Center.” Procedia CIRP, Vol. 78, pp. 279–284.
[14]Srinivas, G. L., Javed, A. 2019. “Topology optimization of industrial manipulator-link considering dynamic loading.” Materials Today: Proceedings, Vol. 18, pp. 3717-3725.
[15]Muhammad, A., Ali, M. A., Shanono, I. H. 2020. “Design optimization of a diesel connecting rod.” Materials Today: Proceedings, Vol. 22, pp. 1600-1609.
[16]Teimouri, M., Mahbod, M., & Asgari, M. 2021. “Topology-optimized hybrid solid-lattice structures for efficient mechanical performance.” In Structures Vol. 29, pp. 549-560, Elsevier.
[17]Rong, Y., Zhao, Z. L., Feng, X. Q., & Xie, Y. M. 2022. “Structural topology optimization with an adaptive design domain.” Computer Methods in Applied Mechanics and Engineering, Vol. 389, 114382.
[18]Chan, T. C., Hong, Y. P., & Yu, J. H. 2021. “Effect of moving structure on the spatial accuracy and compensation of the coordinate measuring machine.” International Journal of Precision Engineering and Manufacturing, Vol. 22, pp. 1551-1561.
[19]Li, Y., Dai, S., Zheng, Y., Tian, F., & Yan, X. 2018. “Modeling and kinematics simulation of a Mecanum wheel platform in RecurDyn.” Journal of Robotics, Vol. 2018, Article ID 9373580.
[20]Zhang, C., Liu, W., Wang, S., Liu, Z., Morgan, M., & Liu, X. 2020. “Dynamic modeling and trajectory measurement on vibratory finishing.” The International Journal of Advanced Manufacturing Technology, Vol. 106, pp. 253-263.
[21]江柏輝，2019，「動柱式高精密平面磨床結構分析與實驗驗證」，國立虎尾科技大學動力機械工程系，碩士論文。
[22]余尚宸，2021，「高精密平面磨床結構分析與優化」，國立虎尾科技大學動力機械工程系，碩士論文。
[23]范光儀，2012，「CNC工具機動態結構特性分析測試與結構改良設計」，國立虎尾科技大學機械設計工程系碩士論文。
[24]邵先佑，2023，「大型龍門五軸工具機空間運動結構設計與精度分析」，國立虎尾科技大學機械與電腦輔助工程系碩士論文。
[25]蘇逸凡，2023，「高速高精XY移動平台定位精度改良設計」，國立虎尾科技大學機械與電腦輔助工程系碩士論文。
[26]周志忠、張浮明，「磨床振動之研究」，修平學報，Vol. 21，pp. 267-282.
[27]王柏村，2008，「振動學」，全華圖書出版，台灣。
[28]黃運琳，2019，「基於RecurDyn V9之多體動力學分析與應用」，五南圖書出版，台灣。
[29]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。
[30]唐文聰，2004，「精密機械加工原理」，全華圖書出版，台灣。
[31]王栢村，《振動噪音科普專欄》，振動噪音產學技術聯盟。
[32]Moaveni, S. 2011. “Finite Element Analysis Theory and Application with ANSYS, 4/e.” Pearson Education India.
[33]Budapesti Muszaki es Gazdasagtudomanyi Egyetem.
https://www.mm.bme.hu/~gyebro/files/ans_help_v182/ans_elem/
[34]衆程科技股份有限公司
https://www.equiptop.com.tw/tw/products/high-precision-surface-grinder/esg-818-cnc-new/esg818cnc.html