臺灣博碩士論文加值系統

本論文主要對鋁合金端銑削加工面之尺寸精度與表面粗糙度作理論性與實驗性分析。在端銑過程中，螺旋端銑刀一端固定於主軸，另一端加工，容易受切削力作用使端銑刀產生偏斜，造成工件加工面之尺寸誤差。由於端銑刀以側刃負擔主要金屬移除工作，切削力作用於刀具周緣，理論分析假設端銑刀偏斜包括彎曲、扭轉與銑刀齒變形三部分。
為分析變截面刀具偏斜，將端銑刀和切屑沿刀具軸心小段切割，由旋轉銑刀小段截面建構動態彎曲剛度，並以Kline切削力理論計算偏心端銑刀對AL6061-T6切屑小斷之單位切削力。依截斷面性質分成均勻與非均勻扭轉兩部分分析銑刀扭曲偏斜，由於銑刀刃凸緣具有較大彎曲剛性，對於非均勻截斷面扭轉產生彎翹也加以推導。另以有限元素法模擬端銑刀刀刃變形，並由輔助試驗數據驗證端銑削尺寸精度模式適當性。結果顯示理論曲線很接近實驗值。
在實際加工中可能用到多種鋁合金，因此假定實驗模式包括工件硬度、切削速度、進給、軸向切深、徑向切寬等因子，利用中央合成設計與表面反應法建構模式，變異分析檢驗顯著因子並證明模式的近似值。結果顯示，尺寸精度隨工件硬度、進給、軸向切深、徑向切寬增加而減低，但切削速度100m/min以上時，尺度精度隨切削速度增加而增加。
另以切削速度、進給、切深、端銑刀底刃凹角、讓角為因子，利用表面反應法推導AL2014-T4乾切與使用冷卻液之加工面表面粗糙度模式，並和理論模式作比較，結果顯示，使用切削液對面粗度有很大改善，影響乾切面粗度顯著因子為切削速度、進給、端銑刀底刃凹角、讓角，使用冷卻液之表面粗糙度顯著因子為進給、端銑刀底刃凹角。當端銑刀底刃凹角2.5O以上，面粗度隨進給、端銑刀底刃凹角增加而增加。

This dissertation presents the theoretical and experimental analyses of the dimensional accuracy and surface roughness in the end milling of aluminum alloys. In the end milling operation, the helical end mill supports one end with the spindle and drive on the other, hence it is easily deflected by the cutting force and results in dimensional errors on the machined surface. Due to the side cutting edges taking the major work of metal removal and the cutting forces acting on the circumference of the tool, the theoretical analyses of the tool deflection including the bending, torsion and the teeth deformation are assumed.
In order to analyze the deflection of the nonprismatic tool, the mill and the cutting chips are sliced into small segments along the tool axis. The dynamic flexural rigidity is built from rotating the true cross-sections of the segments. The unit cutting forces on the chip segments of Aluminum 6061-T6, including the effect of tool run-out, are calculated by Kline’s cutting force model. According to the properties of the cross-sections, the analyses of tool deflection by torsion are divided into uniform and non-uniform portions. Since the teeth-flanges on the mill have a larger sidewise bending stiffness, the warp on cross-sections by torsion is also derived. To compute the tooth deformation, the finite element method using the ANSYS software is applied. An auxiliary experiments and measurements of data are used to verify the adequacy of the theoretical model. The results show the theoretical model with closed shapes to the experimental measurements.
For the more aluminum alloys may be used in the practical process, the experimental model including the factors such as the hardness of workpiece, cutting speed, feed, axial and radial depths of cuts is supposed. The central composite design with the Response Surface Methodology is adopted to build the experimental model. Variance analysis is then used to test the significant factors and verify the appropriation of this model. The results indicate that the dimensional accuracy is reduced with the increasing values of workpiece hardness, feed, radial and axial depths of cut, but it increases with greater cutting speed when the cutting speed is above 100 m/min.
The practical roughness models with dry cutting and coolant conditions are developed and compared with the theoretical model. Factors included in the developed models are, the cutting speed, feed, depth of cut, concavity and axial relief angles on end cutting edge by Response Surface Methodology for Aluminum 2014-T6. The adequacy and prediction of the machined surface accuracy models were verified with variance analyses and concluded well. The results show that the surface roughness greatly improves when the cutting fluid is applied. The significant factors affecting the finished surface with dry conditions are the cutting speed, feed, concavity and axial relief angles; respectively, the feed and concavity angles are for coolant conditions. For a given concavity angle more than 2.5o, surface roughness increases with the growths of feed, concavity and axial relief angles.

CHAPTER 1 INTRODUCTION……………………………………..………………..1
1.1 Problem Statement and Motivation………………….……………….1
1.2 Literature Survey………………………………….………………….5
1.3 Purpose of this Study………………………………..………………..8
CHAPTER 2 THEORETICAL ANALYSIS…………………………………………10
2.1 The Geometric Model of End Milling Process……………… ...…..10
2.2 The Stiffness of Cutter………………………………………………11
2.3 The Cutting Force Model……………………………………..…….14
2.4 The Deflection by Bending…………………………………………16
2.5. The Deflection by Torsion………… ………...…………………….18
2.6 The Teeth Deformation……………………………………………...24
2.7 The statistical model and experimental design for machined surface accuracy…………………………………………………………………25
CHAPTER 3 THE MODELING OF THE MACHINED SURFACE ACCURACY...27
3.1 The Modeling of Dimensional Accuracy for Machined Surface…....27
3.1.1 The Theoretical Model of Dimensional Accuracy………………..27
3.1.2 The Experimental Model of Dimensional Accuracy………….…..29
3.2 The Modeling of Surface Roughness for Machined Surface….……31
3.2.1 The Theoretical Model of Ideal Surface Roughness…………..….31
3.2.2 The Experimental Model of Surface Roughness………………….33
CHAPTER 4 THE EXPERIMENTAL APPARATUS……………………....…….…35
4.1 Introduction…………………………………………………………35
4.2 The Experiments for Modeling of Dimensional Accuracy…...….…36
4.2.1 The Experiments for the Theoretical Model of Dimensional Accuracy…………………...……………………………………………36
4.2.2The Experiments for the Experimental Model of Dimensional Accuracy.………………………………………..………………………38
4.3 The Experiments for the Experimental Model of Surface Roughness………………………………………..……………………..39
CHAPTER 5 RESULTS AND DISCUSSION……………….………………………40
5.1 The Results Concerning the Dimensional Accuracy………………..40
5.1.1 The Cutting Forces Model for Al6061-T6………….....……….....40
5.1.2 The Theoretical Analyses of Dimensional Accuracy……….…….42
5.1.3 The Factors Analyses of Dimensional Accuracy……….……...…44
5.2 The Results Concerning Surface Roughness………………………..47
5.2.1 The Experimental Model of Surface Roughness………………….47
5.2.2 The Factors Analyses of Surface Roughness…………....….….....49
5.3 Summary……………………………………………………………51
CHAPTER 6 CONCLUSION………………………………….……...……………..53

[1] L. Kops and D.T. Vo, “Determination of the Equivalent Diameter of an End Mill Base on its Compliance”, Annals of the CIRP, Vol. 39, No. 1, pp. 93-96, 1990.
[2] A.C. Lee, S.T. Chiang, and C.S. Liu, “Analysis of Cutting Forces and Shape Error in End Milling”, Journal of the Chinese Society of Mechanical Engineer, Vol.12, No. 4, pp. 412-426, 1991.
[3] T. Matsubara, H. Yamamoto and H. Mizumoto, “Study on Accuracy in End Mill Operations (1st Report)---Stiffness of End Mill and Machining Accuracy in Side Cutting”, Bulletin of the Japan Society of Precision Engineering, Vol. 21, No. 2, pp. 95-100, 1987.
[4] T. Matsubara, H. Yamamoto and H. Mizumoto, “Study on Accuracy in End Mill Operations (2nd Report)--- Machining Accuracy in Side Cutting Tests”, Journal of Japan Society for Precision Engineering, Vol. 25, No. 4, pp. 291-296, 1991.
[5] J.S.Tsai, J.S. Liao and C.L. Liao, “ Dynamic finite element modeling of surface errors in peripheral milling of thin-walled workpieces”, Journal of the Chinese Society of Mechanical Engineers, Transactions of the Chinese Institute of Engineers, Series C, Vol. 21, No. 3, pp. 265-282, 2000.
[6] J.S. Tsai and C.L. Liao, “Finite-element modeling of static surface errors in the peripheral milling of thin-walled workpieces”, Journal of Materials Processing Technology, Vol. 94, pp. 235-246, 1999.
[7] C.L. Liao and J.S. Tsai, “Dynamic response analysis in end milling using pretwisted beam finite element”, Journal of Vibration and Acoustics, Transactions of the ASME, Vol. 117, No. 1, pp. 1-10, 1995.
[8] F. Koenigsberger, A.J.P. Sabberwal, “An investigation into the cutting force pulsations during milling operations”, International Journal of Machine Tool Design and Research, Vol. 1, pp. 15—33, 1961.
[9] W.A. Kline and R.E. DeVor, “The Effect of Runout on Cutting Geometry and Forces in End Milling”, International Journal of Machine Tool Design and Research, Vol. 23, No. 2, pp. 123-140, 1983.
[10] W.A. Kline, R.E. DeVor and J.R. Lindberg, “The prediction of cutting forces in end milling with application to cornering cuts”, International Journal of Machine Tool Design and Research, Vol.22, pp. 7—22, 1982.
[11] J. W. Sutherland and R. E. DeVor, “An Improve Method for Cutting Force and Surface Error Prediction in Flexible End Milling Systems”, ASME Journal of Engineering for Industry, Vol. 108, pp. 269-279, 1986.
[12] A.E. Bayoumi, G. Yucesan, and L.A. Kendall, “Analytic mechanistic cutting force model for milling operations: A case study of helical milling operation” Journal of Engineering for Industry, Transactions of the ASME, Vol. 116, No. 3, pp. 331-339, 1994.
[13] S. Engin and Y. Altintas, “Mechanics and dynamics of general milling cutters. Part I: Helical end mills”, International Journal of Machine Tools and Manufacture, Vol. 41, No. 15, pp. 2195-2212, 2001.
[14] S. Engin and Y. Altintas, “ Mechanics and dynamics of general milling cutters. Part II: Inserted cutters”, International Journal of Machine Tools and Manufacture, Vol. 41, No. 15, pp. 2213-2231, 2001.
[15] Y. Altintas and S. Engin, “Generalized modeling of mechanics and dynamics of milling cutters”, CIRP Annals - Manufacturing Technology, Vol. 50, No. 1, pp. 25-30, 2001.
[16] H.J. Fu, R.E. DeVor and S.G. Kapoor, “A mechanistic model for the prediction of the force system in face milling operations”, ASME Journal of Engineering for Industry, Vol. 106, pp. 81—88, 1984.
[17] B.K. Fussel and K. Srinivasan, “An investigation of the end milling process under varying machining conditions”, ASME Journal of Engineering for Industry Vol. 111, pp. 27—36,1989.
[18] Y. Altintas and A. Spence, “End milling force algorithms for CAD Systems”, Annals of the CIRP, 40, pp. 31—34,1991.
[19] J.J. Wang, S.Y. Liang and W.J. Book, “Convolution analysis of milling force pulsation”, ASME Journal of Engineering for Industry, Vol. 116, pp. 17—251994.
[20] S.Y. Liang and J.J. Wang, “Milling force convolution modeling for identification of cutter axis offset”, Int. J. Machine Tools and Manufacture Vol. 34, pp. 1177—1190,1994.
[21] H.Z.Li, W.B. Zhang and X.P. Li, “Modeling of cutting forces in helical end milling using a predictive machining theory”, International Journal of Machine Tools & Manufacture, Vol. 42, pp. 761—771, 2002.
[22] A.P. Xu, Y.X. Qu, D.W. Zhang and T. Huang, Simulation and experimental investigation of the end milling process considering the cutter flexibility International Journal of Machine Tools & Manufacture, Vol. 43, pp. 283—292, 2003.
[23] J. Tlusty and P. MacNeil, “Dynamics of cutting forces in end milling”, Annals of the CIRP, Vol. 24, pp. 21—25, 1975.
[24] Alauddin, M.; El Baradie, M.A.; Hashmi and M.S.J. Hashmi, “Modeling of cutting force in end milling Inconel 718”, Journal of Materials Processing Technology, Vol. 58, No. 1, pp. 100-108, 1996.
[25] M. Alauddin, M.A. Mazid, M.A.El Baradi and M.S.J. Hashmi, “Cutting forces in the end milling of Inconel 718”, Journal of Materials Processing Technology, Vol. 77, No. 1, pp. 153-159, 1998.
[26] Y. Fujii and H. Iwabe, “INFLUENCE OF CUTTING FORCE ON PROFILE ERROR OF CONTOURING - ACCURACY OF CONTOURING BY NUMERICALLY CONTROLLED MACHINE TOOLS”, Bulletin of the Japan Society of Precision Engineering, Vol. 11, No. 4, pp.188-194, 1977.
[27] Y. Fujii, H. Iwabe and M. Suzuki, “Effect of dynamic behavior of end mill in machining on work accuracy (1st Report)*-Mechanism of Generating Shape Errors”, Bulletin of the Japan Society of Precision Engineering, Vol. 13, No. 1, pp. 20-26, 1979.
[28] Y. Fujii, and H. Iwabe, “EFFECT OF DYNAMIC BEHAVIOR OF END MILLING ON WORKING ACCURACY: MECHANISM OF GENERATING SHAPE ERROR OF BOTTOM SURFACE”, Bulletin of the Japan Society of Precision Engineering, Vol. 19, No. 4, pp. 297-299, 1985.
[29] W. A. Kline, R. E. DeVor and I. A. SHAREEF, “The Prediction of Surface Accuracy in End Milling”, ASME Journal of Engineering for Industry, Vol. 104, pp. 272-278, 1982.
[30] S.N. Melkote, W.J. Endres, “The importance of including size effect when modeling slot milling”, ASME Journal of Manufacturing Science and Engineering, Vol. 120, pp. 69—75, 1998.
[31] W.S. Yun, J. H. Ko, D.W. Cho and K. F. Ehmann, “Development of a virtual machining system, part 2: prediction and analysis of a machined surface error”, International Journal of Machine Tools & Manufacture, Vol. 42, pp. 1607—1615, 2002.
[32] K.M.Y. Law and A. Geddam, “Prediction of contour accuracy in the end milling of pockets”, Journal of Materials Processing Technology, Vol. 113, No. 1, pp. 399-405, 2001.
[33] J.G. Choi and M.Y. Yang, In-process prediction of cutting depths in end milling International Journal of Machine Tools & Manufacture, Vol. 39, No. 5, pp. 705-721, 1999.
[34] M.C. Leu, F. Lu and D. Blackmore, “Simulation of NC machining with cutter deflection by modeling deformed swept volumes”, CIRP Annals - Manufacturing Technology, Vol. 47, No. 1, pp. 441-446, 1998.
[35] K. Shirase and Y. Altintas, “Cutting force and dimensional surface error generation in peripheral milling with variable pitch helical end mills”, International Journal of Machine Tools & Manufacture, Vol. 36, No. 5, pp. 567-584, 1996.
[36] M.A. Elbestawi and R. Sagherian, “Dynamic modeling for the prediction of surface errors in the milling of thin-walled sections”, Journal of Materials Processing Technology, Vol. 25, No. 2, pp. 215-228, 1991.
[37] M.Y. Yang, and J.G. Choi, “Tool deflection compensation system for end milling accuracy improvement”, Journal of Manufacturing Science and Engineering, Transactions of the ASME, Vol. 120, No. 2, pp. 222-229, 1998.
[38] Y. Fujii and H. Iwabe, “IMPROVEMENT OF PROFILE ERROR BY DWELL FUNCTION OF CONTROLLER. ON ACCURACY OF CONTOURING BY NUMERICALLY CONTROLLED MACHINE TOOLS (2ND REPORT)”, Bulletin of the Japan Society of Precision Engineering, Vol. 18, No. 4, pp. 305-311, 1984.
[39] T. Watanabe and S. Iwai, CONTROL SYSTEM TO IMPROVE THE ACCURACY OF FINISHED SURFACES IN MILLING.
Journal of Dynamic Systems, Measurement and Control, Transactions ASME, Vol. 105, No. 3, pp. 192-199, 1983.
[40] R. Sagherian and A.M. Elbestawi, “Simulation system for improving machining accuracy in milling”, Computers in Industry, Vol. 14, No. 4, pp. 293-305, 1990.
[41] E. Budak and Y. Altintas, “Peripheral milling conditions for improved dimensional accuracy”, International Journal of Machine Tools & Manufacture, Vol. 34, No. 7, pp. 907-918, 1994.
[42] S.N. Melkote, A.R. Thangaraj, “An Enhanced End Milling Surface Texture Model Including the Effect of Radial Rake and Primary Relief Angles”, Journal of Engineering for Industry, Transactions of the ASME, Vol. 116, pp. 166-174, 1994.
[43] T. S. Babin, J. M. Lee, J. W. Sutherland and S. G. Kapoor, “MODEL FOR END MILLED SURFACE TOPOGRAPHY”, Manufacturing Engineering Transactions, pp. 362-368, 1985.
[44] K.H. Fuh and C.F. Wu, “A Proposed Statistical Model for Surface Quality Prediction in End-milling of Al Alloy”, International Journal of Machine Tools & Manufacture, Vol. 35, No. 8, pp. 1187-1200, 1995.
[45] H. Iwabe, T. Oseto and T. Goto, “Improvement of surface roughness for end milling using cutting edge with high-accurate flank surface”, Transactions of the Japan Society of Mechanical Engineers, Part C, Vol. 68, No. 2, pp. 650-656, 2002.
[46] M. Alauddin, M.A. El Baradie and M.S.J. Hashmi, “Computer-aided analysis of a surface-roughness model for end milling”, Journal of Materials Processing Technology, Vol. 55, pp. 123-127, 1995.
[47] M. Alauddin, M.A El Baradie and M.S.J. Hashmi, “Optimization of Surface Finish in End Milling Inconel 718”, Journal of Materials Processing Technology, Vol. 56, pp. 54-65, 1996.
[48] K.Y.Lee, M.C. Kang, Y.H.Jeong, D.W. Lee and J.S.Kim, “Simulation of surface roughness and profile in high-speed end milling,” Journal of Materials Processing Technology, Vol. 113, pp. 410-415, 2001.
[49] B. Huang and J.C. Chen, “An in-process neural network-based surface roughness prediction (INN-SRP) system using a dynamometer in end milling operations”, International Journal of Advanced Manufacturing Technology, Vol. 21, No. 5, pp. 339-347, 2003.
[50] A. Chukwujekwu Okafor, M. Marcus and R. Tipirneni, “Multiple sensor integration via neural networks for estimating surface roughness and bore tolerance in circular end milling. Part 1. Time domain”, Condition Monitoring & Diagnostic Technology, Vol. 2, No. 2, pp. 49-57, 1991.
[51] S.J. Lou and J.C. Chen, “In-process surface roughness recognition (ISRR) system in end-milling operations”, International Journal of Advanced Manufacturing Technology, Vol. 15, No. 3, pp. 200-209, 1999.
[52] J.C. Chen and S.J. Lou, “Statistical and fuzzy-logic approaches in on-line surface roughness recognition systems for end-milling operations”, International Journal of Flexible Automation and Integrated Manufacturing, Vol. 6, No. 1, pp. 53-78, 1998.
[53] M.E. Martellotti, An analysis of the milling process, Transaction of the ASME, Vol. 63, pp. 677—700, 1941.
[54] M.E. Martellotti, An analysis of the milling process, Part 2: down Milling, Transaction of the ASME, Vol. 67, pp. 233—251, 1945.
[55] A. Louis and J. Hill, Fundamental of Structural design: steel concrete, and timber, Thomas Y. Crowell 1975.
[56] S.P. Timoshenko and J.M. Gere, Theory of Elastic Stability, McGraw-Hill, 1961.
[57] W.F. Chen, Theory of Beam-Columns, Volume 2: Space Behavior and Design, McGraw-Hill, 1977.
[58] D.C. Montgomery, Design and Analysis of Experiments, John Wiley, New York, 1984.
[59] Metals Handbook Ninth Edition Volume 16 Machining, ASM INTERNATIONAL, 1989.
[60] K.G. Budinski, Engineering Materials Properities and Selection, Prentice Hall, 1992.
[61] M. Kronenberg, Machining Science and Application, Perganmon Press, 1966.
[62] P. Mathew and P.L.B. Oxley, “Predicting the Effects of Very High Cutting Speeds on Cutting Forces, etc.”, Annals of the CIRP, Vol. 31, No. 1, pp. 49—52, 1982.
[63] P.L.B. Oxley, The Mechanics of Machining: An Analytical Approach to Accessing Machinability, Wiley, New York, 1989.
[64] W.R. DeVries, Analysis of Material Removal Process, Springer-Verlag, New York, 1991.
[65] M.C. Shaw, Metal cutting principles, New York, 1984.
[66] R.F. Avila and A.M. Abrao, “The effect of cutting fluids on the machining of hardened AISI 4340 steel”, Journal of Materials Processing Technology, Vol. 119, pp. 21-26, 2001.
[67] J.M. Vieria, A.R. Machado and E.O. Ezugwu, “Performance of cutting fluids during face milling of steels”, Journal of Materials Processing Technology, Vol. 116, pp. 244-251, 2001.
[68] P.G. Benardos, G.C. Vosniakos, “Prediction of surface roughness in CNC face milling using neural networks and Taguchi’s design of experiments”, Robotics and Computer Integrated Manufacturing, Vol. 18, pp. 343-354, 2002.
[69] M.A. El Baradie, “CUTTING FLUIDS: PART I. CHARACTERISATION”, Journal of Materials Processing Technology, Vol. 56, pp. 786-797, 1996.