Abstract
Accurate cutting force prediction is essential to precision machining operations as cutting force is a process variable that directly relates to machining quality and efficiency. This paper presents an improved mechanistic cutting force model for multi-axis ball-end milling. Multi-axis ball-end milling is mainly used for sculptured surface machining where non-horizontal (upward and downward) and rotational cutting tool motions are common. Unlike the existing research studies, the present work attempts to explicitly consider the effect of the 3D cutting motions of the ball-end mill on the cutting forces. The main feature of the present work is thus the proposed generalized concept of characterizing the undeformed chip thickness for 3D cutter movements. The proposed concept evaluates the undeformed chip thickness of an engaged cutting element in the principal normal direction of its 3D trochoidal trajectory. This concept is unique and it leads to the first cutting force model that specifically applies to non-horizontal and rotational cutting tool motions. The resulting cutting force model has been validated experimentally with extensive verification test cuts consisting of horizontal, non-horizontal, and rotational cutting motions of a ball-end mill.
Article PDF
Similar content being viewed by others
References
Martellotti ME (1941) An analysis of the milling process. Trans Am Soc Mech Eng 63:677–700
Kline WA, DeVor RE, Lindberg JR (1982) The prediction of cutting forces in end milling with application to cornering cuts. Int J Mach Tool Des Res 22:7–22
Kline WA, DeVor RE (1983) The effect of runout on cutting geometry and forces in end milling. Int J Mach Tool Des Res 23:123–140
Sutherland JW, DeVor RE (1986) An improved method for cutting force and surface error prediction in flexible end milling systems. ASME J Eng Ind 108:269–279
Li HZ, Liu K, Li XP (2001) A new method for determining the undeformed chip thickness in milling. J Mater Process Technol 113:378–384
Kumanchik LM, Schmitz TL (2007) Improved analytical chip thickness model for milling. Precis Eng 31:317–324
Sai L, Bouzid W, Zghal (2008) A chip thickness analysis for different tool motions for adaptive feed rate. J Mater Process Technol 204:213–220
Yucesan G, Altintas Y (1994) Improved modeling of cutting force coefficients in peripheral milling. Int J Mach Tool Manuf 34:473–487
Budak E, Altintas Y, Armarego EJA (1996) Prediction of milling force coefficients from orthogonal cutting data. ASME J Manuf Sci Eng 118:216–224
Yang M, Park H (1991) The prediction of cutting force in ball-end milling. Int J Mach Tool Manuf 31:45–54
Yucesan G, Altintas Y (1996) Prediction of ball-end milling forces. ASME J Eng Ind 118:95–103
Zhu R, Kapoor SG, DeVor RE (2001) Mechanistic modeling of the ball end milling process for multi-axis machining of free-form surfaces. ASME J Manuf Sci Eng 123:369–379
Fussell BK, Jerard RB, Hemmett JG (2003) Modeling of cutting geometry and forces for 5-axis sculptured surface machining. Comput Aided Des 35:333–346
Milfelner M, Cus F (2003) Simulation of cutting forces in ball-end milling. Robot Comput Integr Manuf 19:99–106
Gradisek J, Kalveram M, Weinert K (2004) Mechanistic identification of specific force coefficients for a general end mill. Int J Mach Tool Manuf 44:401–414
Feng HY, Menq CH (1994) The prediction of cutting forces in the ball-end milling process—I. Model formulation and model building procedure. Int J Mach Tool Manuf 34:697–710
Jung YH, Kim JS, Hwang SM (2001) Chip load prediction in ball-end milling. J Mater Process Technol 111:250–255
Lazoglu I (2003) Sculpture surface machining: a generalized model of ball-end milling force system. Int J Mach Tool Manuf 43:453–462
Ko JH, Cho DW (2005) 3D ball-end milling force model using instantaneous cutting force coefficients. ASME J Manuf Sci Eng 127:1–12
El-Mounayri H, Briceno JF, Gadallah M (2010) A new artificial neural network approach to modeling ball-end milling. Int J Adv Manuf Technol 47:527–534
Lopez de Lacalle LN, Lamikiz A, Sanchez JA, Salgado MA (2007) Toolpath selection based on the minimum deflection cutting forces in the programming of complex surfaces milling. Int J Mach Tool Manuf 47:388–400
Tsai CL, Liao YS (2010) Cutting force prediction in ball-end milling with inclined feed by means of geometrical analysis. Int J Adv Manuf Technol 46:529–541
Cao Q, Xue D, Zhao J, Li Y (2011) A cutting force model considering influence of radius of curvature for sculptured surface machining. Int J Adv Manuf Technol 54:821–835
Melkote SN, Endres WJ (1998) The importance of including size effect when modeling slot milling. ASME J Manuf Sci Eng 120:68–75
Lamikiz A, Lopez de Lacalle LN, Sanchez JA, Salgado MA (2004) Cutting force estimation in sculptured surface milling. Int J Mach Tool Manuf 44:1511–1526
Fontaine M, Devillez A, Moufki A, Dudzinski D (2006) Predictive force model for ball-end milling and experimental validation with a wavelike form machining test. Int J Mach Tool Manuf 46:367–380
Fontaine M, Moufki A, Devillez A, Dudzinski D (2007) Modelling of cutting forces in ball-end milling with tool–surface inclination. Part I: predictive force model and experimental validation. J Mater Process Technol 189:73–84
Fontaine M, Devillez A, Moufki A, Dudzinski D (2007) Modelling of cutting forces in ball-end milling with tool–surface inclination. Part II: influence of cutting conditions, run-out, ploughing and inclination angle. J Mater Process Technol 189:85–96
Feng HY, Menq CH (1996) A flexible ball-end milling system model for cutting force and machining error prediction. ASME J Manuf Sci Eng 118:461–469
Ikua BW, Tanaka H, Obata F, Sakamoto S (2001) Prediction of cutting forces and machining error in ball end milling of curved surfaces—I. Theoretical analysis. Precis Eng 25:266–273
Sun Y, Ren F, Guo D, Jia Z (2009) Estimation and experimental validation of cutting forces in ball-end milling of sculptured surfaces. Int J Mach Tool Manuf 49:1238–1244
Kim GM, Cho PJ, Chu CN (2000) Cutting force prediction of sculptured surface ball-end milling using Z-map. Int J Mach Tool Manuf 40:277–291
Ozturk E, Tunc LT, Budak E (2009) Investigation of lead and tilt angle effects in 5-axis ball-end milling processes. Int J Mach Tool Manuf 49:1053–1062
Ozturk E, Budak E (2010) Dynamics and stability of five-axis ball-end milling. ASME J Manuf Sci Eng 132(021003):1–13
Feng HY, Su N (2001) A mechanistic cutting force model for 3D ball-end milling. ASME J Manuf Sci Eng 123:23–29
Azeem A, Feng HY, Wang L (2004) Simplified and efficient calibration of a mechanistic cutting force model for ball-end milling. Int J Mach Tool Manuf 44:291–298
Zhang Z, Zheng L, Zhang L, Li Z, Liu D, Zhang B (2005) A study on calibration of coefficients in end milling forces model. Int J Adv Manuf Technol 25:652–662
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 Tool Manuf 47:1767–1776
Gonzalo O, Jauregi H, Uriarte LG, Lopez de Lacalle LN (2009) Prediction of specific force coefficients from a FEM cutting model. Int J Adv Manuf Technol 43:348–356
Riviere-Lorphevre E, Filippi E (2009) Mechanistic cutting force model parameters evaluation in milling taking cutter radial runout into account. Int J Adv Manuf Technol 45:8–15
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
About this article
Cite this article
Azeem, A., Feng, HY. Cutting force prediction for ball-end mills with non-horizontal and rotational cutting motions. Int J Adv Manuf Technol 67, 1833–1845 (2013). https://doi.org/10.1007/s00170-012-4612-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-012-4612-3