Abstract
The paper proposes a unified analytical cutting force model based on a predictive machining theory for variable helix end mill considering cutter runout. The variable helix end mill is divided into a set of differential oblique elements along the axial direction. The cutting process of oblique element is based on the non-equidistant shear zone model and the equivalent plane method. The cutting forces of oblique element are modeled by shearing force components due to shearing at the shear zone and edge force components due to rubbing in the tertiary zone. In the primary shear zone, a modified Johnson-Cook model is introduced to account for the material size effect affected by varying instantaneous uncut chip thickness (IUCT) during milling process. In the tertiary zone, edge radius and the partial effective rake angle are included in the analytical model in order to take into account the rubbing effect precisely. The total instantaneous cutting forces are obtained by summing up the cutting forces acting oblique elements on all flutes. The unified analytical cutting force model is verified by experimental data using four different types of end mills, and a good agreement of the predicted and measured cutting forces shows that the proposed model is valid for variable helix end mills.
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Arrazola PJ, Özel T, Umbrello D, Davies M, Jawahir IS (2013) Recent advances in modelling of metal machining processes. Cirp Ann-Manuf Techn 62(2):695–718
Tlusty J, MacNeil P (1975) Dynamics of cutting forces in end milling. Ann CIRP 24(1):21–25
Kline WA, DeVor RE (1983) The effect of runout on cutting geometry and forces in end milling. Int J Mach Tools Manuf 23(2):123–140
Gradišek J, Kalveram M, Weinert K (2004) Mechanistic identification of specific force coefficients for a general end mill. Int J Mach Tools Manuf 44(4):401–414
Wan M, Zhang WH, Qin GH, Tan G (2007) Efficient calibration of instantaneous cutting force coefficients and runout parameters for general end mills. Int J Mach Tools Manuf 47(11):1767–1776
Gonzalo O, Jauregi H, Uriarte LG, López De Lacalle LN (2009) Prediction of specific force coefficients from a FEM cutting model. Int J Adv Manuf Technol 43(3–4):348–356
Adetoro OB, Wen PH (2010) Prediction of mechanistic cutting force coefficients using ALE formulation. Int J Adv Manuf Technol 46(1–4):79–90
Adem KAM, Fales R, El-Gizawy AS (2015) Identification of cutting force coefficients for the linear and nonlinear force models in end milling process using average forces and optimization technique methods. Int J Adv Manuf Technol 79(9–12):1671–1687
Budak E, Altintas Y, Armarego E (1996) Prediction of milling force coefficients from orthogonal cutting data. J Manuf Sci Eng 118(2):216–224
Oxley PLB, Young H (1989) The mechanics of machining: an analytical approach to assessing machinability. Ellis Horwood Publisher:136–182
Li HZ, Zhang WB, Li XP (2001) Modelling of cutting forces in helical end milling using a predictive machining theory. Int J Mech Sci 43(8):1711–1730
Lalwani DI, Mehta NK, Jain PK (2009) Extension of Oxley’s predictive machining theory for Johnson and Cook flow stress model. J Mater Process Tech 209(12–13):5305–5312
Moufki A, Dudzinski D, Le Coz G (2015) Prediction of cutting forces from an analytical model of oblique cutting, application to peripheral milling of Ti 6Al 4V alloy. Int J Adv Manuf Technol 81(1–4):615–626
Fu Z, Yang W, Wang X, Leopold J (2015) An analytical force model for ball end milling based on a predictive machining theory considering cutter runout. Int J Adv Manuf Technol:1–12
Budak E, Kops L (2000) Improving productivity and part quality in milling of titanium based impellers by chatter suppression and force control. Cirp Ann-Manuf Techn 49(1):31–36
Budak E (2003) An analytical design method for milling cutters with nonconstant pitch to increase stability, part I: theory. J Manuf Sci Eng 125(1):29–34
Wan M, Zhang W, Dang J, Yang Y (2009) New procedures for calibration of instantaneous cutting force coefficients and cutter runout parameters in peripheral milling. Int J Mach Tools Manuf 49(14):1144–1151
Li B, Hu Y, Wang X, Li C, Li X (2011) An analytical model of oblique cutting with application to end milling. Mach Sci Technol 15(4):453–484
Moufki A, Dudzinski D, Molinari A, Rausch M (2000) Thermoviscoplastic modelling of oblique cutting: forces and chip flow predictions. Int J Mech Sci 42(6):1205–1232
Leopold J. Mechanical and physical models of machining: Proceedings of the 2th CIRP international workshop on modeling of machining operations, Nantes, France, 1999[C].
Li B, Wang X, Hu Y, Li C (2011) Analytical prediction of cutting forces in orthogonal cutting using unequal division shear zone model. Int J Adv Manuf Technol 54(5–8):431–443
Budak E, Ozlu E (2008) Development of a thermomechanical cutting process model for machining process simulations. Cirp Ann-Manuf Techn 57(1):97–100
Ozlu E, Budak E, Molinari A (2009) Analytical and experimental investigation of rake contact and friction behavior in metal cutting. Int J Mach Tools Manuf 49(11):865–875
Joshi SS, Melkote SN (2004) An explanation for the size effect in machining using strain gradient plasticity. J Manuf Sci Eng 126(4):679–684
Ding H, Shen N, Shin YC (2011) Modeling of grain refinement in aluminum and copper subjected to cutting. Comput Mater Sci 50(10):3016–3025
Bissacco G, Hansen HN, Slunsky J (2008) Modelling the cutting edge radius size effect for force prediction in micro milling. CIRP Ann Manuf Technol 57(1):113–116
Abdelmoneim ME, Scrutton R (1974) Tool edge roundness and stable build-up formation in finish machining. J Manuf Sci Eng 96(4):1258–1267
Waldorf DJ, DeVor RE, Kapoor SG (1998) A slip-line field for ploughing during orthogonal cutting. Journal of Manufacturing Science and Engineering, Transactions of the ASME 120(4):693–699
Armarego E, Deshpande N (1993) Force prediction models and CAD/CAM software for helical tooth milling processes. II Peripheral milling operations Int J Prod Res 31(10):2319–2336
Zhang X, Xiong C, Ding Y.(2012) Dynamic cutter runout measurement with laser sensor. In:Intelligent Robotics and Applications. Springer Berlin Heidelberg, 264–272
Srinivasa YV, Shunmugam MS (2013) Mechanistic model for prediction of cutting forces in micro end-milling and experimental comparison. Int J Mach Tools Manuf 67:18–27
Diez Cifuentes E, Pérez García H, Guzmán Villaseñor M, Vizán Idoipe A (2010) Dynamic analysis of runout correction in milling. Int J Mach Tools Manuf 50(8):709–717
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Chen, D., Zhang, X., Xie, Y. et al. A unified analytical cutting force model for variable helix end mills. Int J Adv Manuf Technol 92, 3167–3185 (2017). https://doi.org/10.1007/s00170-017-0357-3
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DOI: https://doi.org/10.1007/s00170-017-0357-3