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系統識別號 U0026-0201201721050400
論文名稱(中文) 銑削製程之特徵分析及含製程阻尼之臨界切深預測
論文名稱(英文) An Eigen-analysis of Milling Process and Prediction of Critical Depth with Process Damping
校院名稱 成功大學
系所名稱(中) 機械工程學系
系所名稱(英) Department of Mechanical Engineering
學年度 105
學期 1
出版年 105
研究生(中文) 宋麒豐
研究生(英文) Chi-Feng Sung
學號 N18981288
學位類別 博士
語文別 中文
論文頁數 99頁
口試委員 召集委員-陳朝光
指導教授-王俊志
口試委員-李榮顯
口試委員-王世明
口試委員-盧銘詮
中文關鍵字 銑削  特徵分析  顫振  銑削力軌跡  臨界切深  製程阻尼 
英文關鍵字 milling  eigen-analysis  chatter  milling forces trajectory  critical depth of cut  process damping 
學科別分類
中文摘要 本文經由二維動態銑削系統之特徵值及特徵向量探討穩定與不穩定切削狀態下銑削力及振動之二維軌跡特性,並提出預測臨界切深公式及判別製程阻尼常數之方法。首先分析零階方向矩陣與結構動態所構成之定向轉移函數矩陣並推導系統特徵方程,據以獲得顯示極限軸深與轉速關係之穩定葉瓣圖。分析發現逆銑型態之顫振頻率取決於刀具運動方向x之模態自然頻率,而順銑之顫振頻率則由垂直刀具運動方向y之模態所決定。接著針對具有對稱結構之銑削製程,利用方向矩陣之特徵向量呈現顫振時銑削力和刀尖振動之軌跡。其提供包含軌跡形狀特徵、定向角和繞行方向等資訊,使能更明確地判別顫振發生。研究發現顫振之動態力軌跡在低徑深時呈線性,而高徑深時呈逆時針橢圓狀,接近槽銑則近似為圓形。此外,順和逆銑型態之振型方向分別指向刀具進給方向的左和右側。然而在穩定銑削情況,其穩態銑削力軌跡則顯示為順時針方向之橢圓。接著利用系統特徵值之解析式推導出具穩定加工之最佳、最差主軸轉速及其臨界軸深之公式。使無需經由穩定葉瓣圖得以快速獲得最佳與最差主軸轉速,方便進行趨穩避振之線上製程規劃。最後考慮刀腹犁切機制所產生製程阻尼效應對系統穩定性之影響。從包含切向與徑向犁切常數之局部動態切削力模式推導出製程阻尼係數矩陣,經解耦合獲得等效製程阻尼比,再與結構阻尼比結合得出含製程阻尼效應之系統特徵方程及不同轉速下之臨界切深曲線公式。應用在一般實務系統無需預知結構模態及切削參數等前置作業限制下,經由穩定性實驗獲得之兩組轉速與臨界切深即可建立此曲線公式。經此曲線公式可進一步提供理論上具無限穩定切深之漸進轉速及判別徑向犁切常數之方法。本文在穩定及不穩定製程下之銑削力和刀具振動軌跡分析及臨界切深預測與犁切常數之判別,均經實驗驗證解析模式之有效性。
英文摘要 In this thesis, the stability analysis for a 2D milling process with general asymmetric dynamics is reduced to a 1D scalar problem by an eigen-analysis approach. Through decomposing the oriented transfer function matrix, the scalar oriented frequency response functions for a regenerative milling chatter is defined and obtained in a closed form expression. The scalar modal characteristic equation is derived to obtain closed form expressions for the stability limit and spindle speed at each possible chatter frequency. This thesis further presents analytical models for determining the forces and tool tip displacement during stable and unstable milling with axis-symmetrical structural dynamics. The trajectory of nominal, static milling forces under both stable and unstable cutting conditions was demonstrated to run clockwise in an elliptical path, with the dynamic forces during chatter running counterclockwise. Both the static and dynamic forces had similar modal directions, pointing to the right and left sides of the x axis for up and down-millings, respectively. Moreover, the oriented FRF concept is adapted to determine the worst spindle speeds and the critical limiting axial depth of cut in explicit, analytic expressions. Finally, formulas for determining the critical depths of cut and asymptotic spindle speed for stable milling processes with process damping are presented. The asymptotic spindle speed of a theoretically infinite stable depth of cut is shown to be proportional to the modal natural frequency, radial ploughing constant and radial immersion angle, but inversely proportional to the shearing related cutting constant and tool diameter. These formulas enable identifying the asymptotic speed, absolute stability limit, and in-process radial ploughing constant from two sets of experimental stability limits without requiring modal parameters. The presented analytical models for the force and displacement trajectories, critical depth of cut and identification of process damping constants are verified by experiments.
論文目次 摘要 I
Abstract II
誌 謝 VIII
目錄 IX
表目錄 XII
圖目錄 XIII
符號表 XVI
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.2.1 銑削穩定性分析 2
1.2.2 製程阻尼 4
1.3 論文架構 5
第二章 銑削製程穩定性之特徵分析 7
2.1 系統特徵方程式 7
2.1.1 總銑削力 7
2.1.2 零階方向矩陣特徵值 14
2.1.3 系統特徵方程式 16
2.2 模態座標之系統特徵方程 18
2.2.1 系統特徵方程與穩定圖 18
2.2.2 結構動態不含耦合項之特徵 21
2.2.3 對稱結構之特徵 21
2.3 模式驗證 22
2.4 結論 28
第三章 穩定與不穩定狀態之銑削力和位移軌跡 29
3.1銑削顫振軌跡 29
3.1.1 低徑深之線性振型 30
3.1.2 高徑深之橢圓振型 32
3.1.3 顫振軌跡之幾何特徵 36
3.2 源於穩態進給之銑削力和振動軌跡 38
3.2.1 穩態銑削力軌跡 38
3.2.2 穩態位移軌跡 42
3.3模式驗證 43
3.3.1 實驗設置 43
3.3.2 實驗結果與討論 46
3.4 結論 53
第四章 最佳、最差主軸轉速和絕對穩定軸深之解析預測 54
4.1 絕對穩定軸深公式 54
4.2 最差與最佳主軸轉速 58
4.3 與平均切刃角法之比較 59
4.4模擬與實驗驗證 61
4.4.1 模擬之穩定葉瓣圖為基礎驗證比較解析模式 61
4.4.2 預測最差主軸轉速與臨界軸向切深 63
4.4.3 最佳主軸轉速 66
4.4.4 實驗結果與討論 68
4.5 結論 70
第五章 銑削製程阻尼之臨界切深與漸近轉速 71
5.1 動態總銑削力模式 71
5.2 含製程阻尼之系統動態方程 72
5.3 絕對穩定軸深與漸近轉速 78
5.4 模式驗證 81
5.4.1 參考文獻之實驗結果 81
5.4.2 銑削實驗驗證 86
5.4.3 驗證結果與討論 91
5.5 結論 92
第六章 總結與建議 93
6.1 總結 93
6.2 建議 94
參考文獻 95
參考文獻 Afazov, S.M., Ratchev, S.M., Segal, J., and Popov, A.A., “Chatter modeling in micro-milling by considering process nonlinearities,” International Journal of Machine Tools and Manufacture, Vol. 56, pp. 28-38, (2012).
Ahmadi, K., and Ismail, F., “Analytical stability lobes including nonlinear process damping effect on machining chatter,” International Journal of Machine Tools and Manufacture, Vol. 51(4), pp. 296–308, (2011).
Ahmadi, K., and Ismail, F., “Stability lobes in milling including process damping and utilizing Multi-Frequency and Semi-Discretization Methods,” International Journal of Machine Tools and Manufacture, Vol. 54-55, pp. 46-54, (2012).
Ahmadi, K., and Altintas, Y., “Identification of Machining Process Damping Using Output-Only Modal Analysis,” ASME Journal of Manufacturing Science and Engineering, Vol. 136(5), pp. 051017-1-13, (2014).
Altintas, Y., and Budak, E., “Analytical prediction of stability lobes in milling,” CIRP Annals, Vol. 44(1), pp. 357-362, (1995).
Altintas, Y., and Weck, M., “Chatter stability of metal cutting and grinding,” CIRP Annals, Manufacturing Technology, Vol. 53(2), pp. 619-642, (2004).
Altintas, Y., Stepan, G., Merdol, D., and Dombovari, Z., “Chatter stability of milling in frequency and discrete time domain,” CIRP Journal of Manufacturing Science and Technology, Vol. 1(1), pp. 35-44, (2008).
Arizmendi, M., Campa, F.J., Fernández, J., López, de Lacalle L.N., Gil, A., Bilbao, E., Veiga, F. and Lamikiz, A., “Model for surface topography prediction in peripheral milling considering tool vibration,” CIRP Annals, Manufacturing Technology, Vol. 58(1), pp. 93–96, (2009).
Bayly, P.V., Halley, J.E., Mann, B.P., and Davies, M.A., “Stability of Interrupted Cutting by Temporal Finite Element Analysis,” ASME Journal of Manufacturing Science and Engineering, Vol. 125(2), pp.220-225, (2003).
Bediaga, I., Muñoa, J., Hernández, J., and López de Lacalle, L.N., “An automatic spindle speed selection strategy to obtain stability in high-speed milling,” International Journal of Machine Tools and Manufacture, Vol. 49(5), pp. 384-394, (2009).
Biermann, D., Kersting, P., and Surmann, T., “A general approach to simulating workpiece vibrations during five-axis milling of turbine blades,” CIRP Annals - Manufacturing Technology, Vol. 59(1), pp. 125-128, (2010).
Biermann, D., and Baschin, A. “Influence of cutting edge geometry and cutting edge radius on the stability of micromilling processes,” Production Engineering Research and Development, Vol. 3, pp. 375-380, (2009).
Budak, E. and Altintas, Y., “Analytical Prediction of Chatter Stability in Milling-Part I: General Formulation,” ASME Journal of Dynamic System, Measurement and Control, Vol. 120(1), pp. 22-30, (1998).
Budak, E. and Tunc, L.T., “Identification and modeling of process damping in turning and milling using a new approach,” CIRP Annals - Manufacturing Technology, Vol. 59(1), pp. 403-408, (2010).
Chiou, R.Y., and Liang, S.Y., “Chatter stability of a slender cutting tool in turning with wear effect,” International Journal of Machine Tools and Manufacture, Vol. 38(4), pp. 315–327, (1998).
Costes, J.P., and Moreau, V., “Surface roughness prediction in milling based on tool displacements,” Journal of Manufacturing Processes, Vol. 13(2), pp. 133-140, (2011).
Davies, M.A., Pratt, J.R., Dutterer, B., and Burns, T.J., “Stability Prediction for Low Radial Immersion Milling,” ASME Journal of Manufacturing Science and Engineering, Vol. 124(2), pp. 217-225, (2002).
Delio T., Tlusty J., and Smith S., “Use of Audio Signals for Chatter Detection and Control,” ASME Journal of Engineering for Industry, Vol. 114(2), pp. 146-157, (1992).
Ding, Y., Zhu, L.M., Zhang, X.J., and Ding, H., “Numerical Integration Method for Prediction of Milling Stability,” ASME Journal of Manufacturing Science and Engineering, Vol. 133(3), pp. 031005-1-9, (2011).
Eksioglu C., Kilic Z. M. and Altintas Y., “Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems,” ASME Journal of Manufacturing Science and Engineering, Vol. 134(6), pp. 1-6, (2012).
Gasparetto, A., “A System Theory Approach to Mode Coupling Chatter in Machining,” ASME Journal of Dynamic Systems, Measurement and Control, Vol. 120(4), pp. 545-547, (1998).
Huang, C.Y., and Wang, J.J.J., “Mechanistic Modeling of Process Damping in Peripheral Milling,” ASME Journal of Manufacturing Science and Engineering, Vol. 129(1), pp. 12-20, (2007).
Huang, C.Y., and Wang, J.J.J., Effects of Cutting Conditions on Dynamic Cutting Factor and Process Damping in Milling, International Journal of Machine Tools and Manufacture, Vol. 51(4), pp.320–330, (2011).
Insperger, T., and Stépán, G., “Updated semi-discretization method for periodic delay-differential equations with discrete delay,” International Journal for Numerical Methods in Engineering, Vol. 61(1), pp. 117-141, (2004).
Insperger, T., Stépán, G., Bayly, P.V., and Mann, B.P., “Multiple chatter frequencies in milling processes,” Journal of Sound and Vibration, Vol. 262(2), pp. 333-345 (2003).
Jin, X., and Altintas, Y., “Chatter Stability Model of Micro-Milling with Process Damping,” ASME Journal of Manufacturing Science and Engineering, Vol. 135(3), pp. 031011-1-9, (2013).
Jun, M.B., DeVor, R.E., and Kapoor S.G., “Investigation of the Dynamics of Microend Milling-Part II: Model Validation and Interpretation,” ASME Journal of Manufacturing Science and Engineering, Vol. 128(4), pp. 901-912, (2006).
Koenigsberger, F., and Tlusty, J., Machine Tool Structures, section 2: Stability Against Chatter, Pergamon Press, (1970).
Kurata, Y., Merdol, S.D., Altintas, Y., Suzuki, N., Shamoto, E., “Chatter Stability in Turning and Milling with In Process Identified Process Damping,” Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol. 4(6), pp.1107-1118, (2010).
Lee, A.C., and Liu, C.S., “Analysis of chatter vibration in the end milling process,” International Journal of Machine Tools and Manufacture, Vol. 31(4), pp. 471-479, (1991).
Lee, B.Y., Tarng, Y.S., Ma, S.C., “Modeling of the Process Damping Force in Chatter Vibration,” International Journal of Machine Tools and Manufacture, Vol. 35(7), pp.951-962, (1995).
Liao, Y.S., and Young, Y.C., “A new on-line spindle speed regulation strategy for chatter control,” International Journal of Machine Tools and Manufacture, Vol. 36(5), pp. 651-660, (1996).
Merdol, S.D., and Altintas, Y., “Multi Frequency Solution of Chatter Stability for Low Immersion Milling,” ASME Journal of Manufacturing Science and Engineering, Vol. 126(3), pp.459-466, (2004).
Minis, I., and Yanushevsky, R., “A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling,” ASME Journal of Engineering for Industry, Vol. 115(1), pp.1-8, (1993).
Munoa, J., Beudaert, X., Dombovari, Z., Altintas, Y., Budak, E., Brecher, C., and Stepan, G., “Chatter suppression techniques in metal cutting,” CIRP Annals-Manufacturing Technology, Vol. 65(2), pp.785-808, (2016).
Opitz, H., and Bernardi, F., “Investigation and calculation of the chatter behavior of lathes and milling machines,” CIRP Annals 18, pp. 335-343, (1970).
Quintana, G., and Ciurana, J., “Chatter in machining processes: A review,” International Journal of Machine Tools and Manufacture, Vol. 51(5), pp. 363-376, (2011).
Rahnama, R., Sajjadi, M., and Park, S.S., “Chatter Suppression in Micro End Milling with Process Damping,” Journal of Materials Processing Technology, Vol. 209(17), pp. 5766-5776, (2009).
Schmitz, T.L., and Smith, K.S., Machining Dynamics_ Frequency Response to Improved Productivity, Springer Publishing Co., New York, (2009).
Shi, Y., Mahr, F., von Wagner, U., Uhlmann, E., “Chatter frequencies of micromilling processes: Influencing factors and online detection via Piezo-actuators,” International Journal of Machine Tools and Manufacture, Vol. 56, pp. 10–16, (2012).
Smith, S., and Tlusty, J., “Stabilizing Chatter by Automatic Spindle Speed Regulation,” CIRP Annals - Manufacturing Technology, Vol. 41(1), pp. 433-436, (1992).
Smith, S., and Tlusty, J., “An Overview of Modeling and Simulation of the Milling Process,” ASME Journal of Engineering for Industry, Vol. 113(2), pp.169-175, (1991).
Sun, C., and Altintas, Y., “Chatter free tool orientations in 5-axis ball-end milling,” International Journal of Machine Tools and Manufacture, Vol. 106, pp.89-97, (2016).
Tarng, Y.S., and Li, T.C., “The change of spindle speed for the avoidance of chatter in end milling,” International Journal of Materials Processing Technology, Vol. 41(2), pp. 227-236, (1994).
Tlusty, J., and Polacek, M., Beispiele der behandlung der selbsterregten Schwingung der Werkzeugmaschinen, FoKoMa, Hanser Verlag, Munchen, (1957).
Tlusty, J., and Ismail, F., “Basic Non-Linearity in Machining Chatter,” CIRP Annals-Manufacturing Technology, Vol. 30(1), pp. 299-304 , (1981).
Tlusty, J., Manufacturing Processes and Equipment, Prentice Hall, Upper Saddle River, New Jersey, (2000).
Tlusty, J., Zaton, W., and Ismail, F., “Stability Lobes in Milling,” CIRP Annals-Manufacturing Technlogy, Vol. 32(1), pp. 309-313, (1983).
Tlusty, J., and Ismail, F., “Special Aspects of Chatter in Milling,” ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 105(1), pp. 24-32, (1983).
Tobias, S.A., and Fishwick, W., Theory of Regenerative Machine Tool Chatter, The Engineer, London, Vol. 205(7), pp. 199-203, (1958).
Tunc, L.T., and Budak, E., “Effect of cutting conditions and tool geometry on process damping in machining,” International Journal of Machine Tools and Manufacture, Vol. 57, pp. 10-19, (2012).
Tunc, L.T., and Budak, E., “Identification and Modeling of Process Damping in Milling,” ASME Journal of Manufacturing Science and Engineering, Vol. 135(2), pp. 021001-1-12, (2013).
Tyler, C.T., Schmitz, T.L., “Analytical Process Damping Stability Prediction,” Journal of Manufacturing Processes, Vol. 15(1), pp. 69-76, (2013).
Uhlmann, E., and Mahr, F., “A Time Domain Simulation Approach for Micro Milling Processes,” 3rd CIRP Conference on Process Machine Interactions, Procedia CIRP, Vol. 4, pp. 22-28, (2012).
Uhlmann, E., Mahr, F., Shi, Y., and von Wagner, U., Chapter 12: Process Machine Interactions in Micro Milling, Process Machine Interactions, Springer-Verlag, Berlin Heidelberg, (2013).
Wang, J.J.J., Liang, S.Y., and Book, W.J., “Convolution Analysis of Milling Force Pulsation,” ASME Journal of Engineering for Industry, Vol. 116(1), pp. 17-25, (1994).
Wang, J.J.J. and Zheng, C.M., An analytical force model with shearing and ploughing mechanisms for end milling,” International Journal of Machine Tools and Manufacture, Vol. 42(7), pp. 761-771, (2002).
Wang, J.J.J., Zheng, C.M., and Huang C.Y., “The Effect of Harmonic Force Components on Regenerative Stability in End Milling,” ASME International Mechanical Engineering Congress and Exposition, IMECE 2003-42367, pp. 103-112, (2003).
Weck, M., Machine Tools-Metrological Analysis and Performance Tests, Springer-Verlag, Berlin•Heidelberg•New York, (1977).
Weck, M. and Teipel K., Dynamisches Verhalten spanender Werkzeugmaschinen, Vol. 4, Wiley Heyden Ltd., (1984).
Zatarain, M., Bediaga, I., Muñoa, J., Insperger, T., “Analysis of directional factors in milling: importance of multi-frequency calculation and of the inclusion of the effect of the helix angle,” International Journal of Advanced Manufacturing Technology, Vol. 47(5), pp. 535-542, (2010).
Zheng, C.M., and Wang, J.J., “Stability prediction in radial immersion for milling with symmetric structure”, International Journal of Machine Tools and Manufacture, Vol. 75, pp. 72-81, (2013).
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