臺灣博碩士論文加值系統

熱變形引起的熱誤差是影響高速精密工具機之精度最重要的關鍵之一。本文將提出以有限元素分析方法(finite element method) 發展出熱-固模型去模擬並預測整個高速主軸系統中的暫態溫度場及熱結構變形場。此有限元素法的預測將參照監測點溫度與刀尖點熱變位數據來驗證此熱-固模型的有效性。為了獲得高品質且高精度的加工產品，高速主軸系統之誤差必須被預測，本研究引入實驗設計法(Design of Experiment) 的方式來預測加工誤差，根據變異性分析 (ANOVA) 的結果呈現出對於刀尖點的誤差之分析，尋找出確切的監測點將比其他監測點的影響更為顯著，並利用MATLAB軟體建立出二階迴歸數學模型去預測該響應值(即熱誤差值)。本論文利用有效的熱-固模型實施此方法，本研究將在指定的加工條件下搭配不同的轉速，預期地對高速主軸系統生成的熱誤差降低89%。

Thermal error caused by the thermal deformation is one of the most important concerns influencing the accuracy of machine tools. In this investigation, a thermal-structure model is developed by the finite element method (FEM) to effectively simulate thermal characteristics for predicting the transient temperature field and thermal deformation of a high speed spindle system. Since the machining error must be estimated to achieve high quality and precision of machining products, this study applied the design of experiment (DOE) method to predict machining errors. The ANOVA demonstrated that the temperatures measured from certain detection points were more significant factors than those from other points on the machining errors. The second-order regression model was adequate to forecast the response variables generated by MATLAB. The implementation of this model in the machine tool under study is expected to reduce its thermally induced deformation by 80% in specified working conditions at varied speeds for a spindle system.

摘要 I
ABSTRACT II
誌謝 III
目錄 IV
圖目錄 VI
表目錄 VII
第一章　緒論 1
1.1研究背景及動機 1
1.2文獻回顧 2
1.3工具機主軸之熱誤差補償發展[25] 4
第二章　有限元素分析 6
2.1有限元素原理 6
2.2問題描述 6
2.3建構模型 8
2.4網格生成 10
2.4.1 網格特性檢核 12
2.4.1.1網格收斂性分析 12
2.4.1.2網格獨立性分析 13
2.5基本假設 14
2.5.1熱行為之經驗方程式 14
2.5.1.1主要熱生成 14
2.5.1.2熱傳遞經驗方程式 15
2.5.2定義邊界條件 16
第三章　實驗與模擬驗證 19
3.1實驗架構 19
3.2模擬分析 21
第四章　模擬驗證結果與討論 24
第五章　實驗設計法(DESIGN OF EXPERIMENT) 28
5.1實驗設計之目的 28
5.2實驗設計之方法 28
5.2.1參數相關性分析(Parameter Correlation Analysis) 30
5.2.2響應曲面法(Response Surface Methodology) 35
5.2.2.1實驗設計法(Design of Experiment) 35
5.2.2.2響應曲面(Response Surface) 36
5.2.2.3最佳化尋優(Optimization) 41
5.2.2.4最佳組合之驗證結果 42
5.3實驗設計之結論 42
第六章　熱變形預測與補償機制 44
6.1熱變形預測/補償之目的 44
6.2熱變形預測/補償之方法 44
6.2.1多元迴歸與變異性 (Multiple Regression and ANOVA) 44
6.2.2檢驗預測模型 46
第七章　結論 52
參考文獻 53
符號彙編 56

[1]W. S. Yun, S. K. Kim, and D. W. Cho, "Thermal error analysis for a CNC lathe feed drive system," International Journal of Machine Tools and Manufacture, vol. 39, pp. 1087-1101, 7// 1999.
[2]J. Y. Ahn and S. C. Chung, "Real-time estimation of the temperature distribution and expansion of a ball screw system using an observer," Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture, vol. 218, pp. 1667-1681, 2004.
[3]M. A. Donmez, D. S. Blomquist, R. J. Hocken, C. R. Liu, and M. M. Barash, "A general methodology for machine tool accuracy enhancement by error compensation," Precision Engineering, vol. 8, pp. 187-196, 10// 1986.
[4]J. S. Chen, J. X. Yuan, J. Ni, and S. M. Wu, "Real-time Compensation for Time-variant Volumetric Errors on a Machining Center," Journal of Manufacturing Science and Engineering, vol. 115, pp. 472-479, 1993.
[5]Y. Li, W. Zhao, W. Wu, B. Lu, and Y. Chen, "Thermal error modeling of the spindle based on multiple variables for the precision machine tool," The International Journal of Advanced Manufacturing Technology, vol. 72, pp. 1415-1427, 2014/06/01 2014.
[6]J.-H. Lee and S.-H. Yang, "Statistical optimization and assessment of a thermal error model for CNC machine tools," International Journal of Machine Tools and Manufacture, vol. 42, pp. 147-155, 1// 2002.
[7]Z. Yang, M. Sun, W. Li, and W. Liang, "Modified Elman network for thermal deformation compensation modeling in machine tools," The International Journal of Advanced Manufacturing Technology, vol. 54, pp. 669-676, 2011/05/01 2011.
[8]E. Creighton, A. Honegger, A. Tulsian, and D. Mukhopadhyay, "Analysis of thermal errors in a high-speed micro-milling spindle," International Journal of Machine Tools and Manufacture, vol. 50, pp. 386-393, 4// 2010.
[9]J. Jedrzejewski, Z. Kowal, W. Kwaśny, and W. Modrzycki, "Hybrid Model of High Speed Machining Centre Headstock," CIRP Annals - Manufacturing Technology, vol. 53, pp. 285-288, // 2004.
[10]K. C. Fan, "An intelligent thermal error compensation system for CNC machining Centers," Journal of the Chinese Society of Mechanical Engineers, vol. 28, pp. 91-97, Feb 2007.
[11]H. J. Pahk and S. W. Lee, "Thermal error measurement and real time compensation system for the CNC machine tools incorporating the spindle thermal error and the feed axis thermal error," International Journal of Advanced Manufacturing Technology, vol. 20, pp. 487-494, 2002.
[12]J. Vyroubal, "Compensation of machine tool thermal deformation in spindle axis direction based on decomposition method," Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, vol. 36, pp. 121-127, Jan 2012.
[13]R. Ramesh et al, Error compensation in machine tools—a review: Part II: thermal errors, Int. J. Mach. Tools Manuf 40 (2000) 1257–1284. Xu Z.Z., Liu X.J., Kim H.K., Shin J.H., Lyu S.K., Int. J. Mach. Tools Manuf., vol.39 , p.1087-1101, 1999
[14]Holkup, T. H., Cao, P. Kola´rˇ , Y. Altintas , J. Zeleny´,” Thermo-mechanical model of spindles” CIRP Annals - Manufacturing Technology59 (2010) 365–368
[15]Uhlmann, E., Hu, J. “Thermal modeling of a high speed motor spindle” 5 th CIRP Conference on High Performance Cutting. Procedia CIRP 1 ( 2012 ) 313 – 318
[16]B. Bossmanns, J.F. Tu, A thermal model for high speed motorized spindles, Int.J. Mach. Tools Manuf. 39 (1999) 1345-1366.
[17]H. Li, Y.C. Shin, Analysis of bearing configuration effects on high speed spindles using an integrated dynamic thermo-mechanical spindle model, Int. J. Mach. Tools Manuf. 44 (4) (2004) 347-364.
[18]A. Zahedi, M.R. Movahhedy, Thermo-mechanical modeling of high speed spindles, Sci. Iran. 19 (2) (2012) 282-293.
[19]X.A. Chen, J.F. Liu, Thermal properties of high speed motorized spindle and their effects, J. Mech. Eng. 49 (11) (2013) 135-142.
[20]Zah MF, Maier T (2010) Thermal simulation of machine tools. Zeitschrift fur Wirtschaftlichen Fabrikbetrieb 105(7 – 8):655 – 659.
[21]Se-Ho Chun, Tae Jo Ko, Study on the Response Surface Model of Machining Error in Internal Lathe Boring, International Journal of precision Engineering and Manufacturing, Vol. 12, No. 2, pp. 177-182, 2011
[22]C. Brecher, P. Hirsch and M. Weck, “Compensation of thermo-elastic machine tooldeformation based on control internal data,” CIRP Annals - ManufacturingTechnology, Vol. 53, No. 1, 2004, pp. 299-304.
[23]Zhao HT, Yang JG, Shen JH (2007) Simulation of thermal behavior of a CNC machine tool spindle. Int J Mach Tool Manuf 47(6):1003 – 1010.
[24]Cui LY, Zhang DW, Gao WG, Qi XY, Shen Y (2011) Thermal errors simulation and modeling of motorized spindle. Adv Mater Res 154 – 155:1305 – 1309.
[25]Yang Li, Wanhua Zhao, Shuhuai Lan, Jun Ni, Wenwu Wu, Bingheng Lu (2015) A review on spindle thermal error compensation in machine tools,International Journal of Machine Tools & Manufacture 95 (2015) 20–38
[26]許進峰, ANSYS Workbench 15.0完全自學一本通, 電子工業出版社, ISBN13：9787121240959
[27]ANSYS Help Viewer
[28]Harris, T.A., Rolling Bearing Analysis. Wiley Sons, New York, 1991,pp. 540—560
[29]Stein JL, Tu JF (1994) A State-Space Model for Monitoring ThermallyInduced Preload in Anti-Friction Spindle Bearings of High-Speed MachineTools. Journal of Dynamic Systems Measurement and Control 116(3):372–386.
[30]Xu Min, Jiang Shuyun, Cai Ying, “An improved thermal model for machine tool bearings” International Journal of Machine Tools & Manufacture 47 (2007) 53–62
[31]Holman, J.P., Heat transfer, ninth ed, McGraw-Hill, New York,2002
[32]K.M. Becker, J. Kaye, Measurements of diabatic flow in an annulus with an inner rotating cylinder, Journal of Heat Transfer 84 (1962) 97-105.
[33]J. Bryan. International Status of Thermal Error Research (1990) Lawrence Livermore National Laboratory (retired), Pleasanton, CA/USA
[34]ANSYS DesignXplorer 訓練手冊
[35]李易庭, ” 運用實驗設計法探討製程因子—以CNC加工機為例”,國立成功大學工程管理碩士論文,2014
[36]張家勤, ” 結合反應曲面法、類神經網路與基因演算法 於觸控面板雷射切割製程參數最佳化”, 國立清華大學工業工程與工程管理學系碩士論文,2009
[37]機械資訊2月刊,”看工具機熱補償發展趨勢”, JIMTOF 2014