A separate-edge force coefficients’ calibration method using specific condition for cutters with variable helix and pitch angles combining the runout effect

  • Qiang Guo
  • Bo Zhao
  • MingYang Zhang
  • Yan Jiang
  • Yan Zhang


Classical ways of computing cutting force coefficients cannot be used by the cutters with non-uniform helix and pitch angles. So, this paper presents a novel separate-edge-forecast method to compute cutting force coefficients for any kind of flank-end cutter, especially for cutters with non-uniform helix and pitch angles. Using this method, the cutter runout can be combined into the cutting force coefficients without computing the cutter runout parameters. Simultaneously, the method predicts the cutting force coefficients for every cutter edge. Firstly, a series of three-axis machining experiments, which must satisfy the specific condition that only one cutter edge is removing materials at any time, is conducted. Then, the cutting force-curves are divided into N force lobes. Each lobe is assigned to the corresponding cutter edge using an algorithm. Subsequently, the cutter edge and the corresponding cutting force lobe are used to determine the cutting force coefficients. This means N cutter edges have N groups of cutting force coefficients, correspondingly. Finally, in order to verify the validity and correctness of the proposed method, a cutter with non-uniform helix and pitch angle is utilized to predict cutting force coefficients based on which the cutting forces are also computed. The results demonstrate that the cutting forces predicted agree well with the data measured. Simultaneously, it can be observed that the method can predict the coefficients considering the cutter runout effect.


Flank-end mill with variable helix and pitch angles Cutting force coefficients Cutter runout Separate-edge-forecast method 


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  1. 1.
    Sun YW, Guo Q (2011) Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out. Int J Mach Tools Manuf 51:806–815CrossRefGoogle Scholar
  2. 2.
    Wan M, Zhang WH, Tan G, Qin GH (2007) New algorithm for calibration of instantaneous cutting-force coefficients and radial run-out parameters in flat end milling. Proc Inst Mech Eng B J Eng Manuf 221:1007–1019CrossRefGoogle Scholar
  3. 3.
    Li ZL, Niu JB, Wang XZ, Zhu LM (2015) Mechanistic modeling of five-axis machining with a general end mill considering cutter runout. Int J Mach Tools Manuf 96:67–79CrossRefGoogle Scholar
  4. 4.
    Kline WA, Devor RE, Lindberg JR (1982) The prediction of cutting forces in end milling with application to cornering cuts. International Journal of Machine Tool Design Research 22:7–22CrossRefGoogle Scholar
  5. 5.
    Lin B, Wang L, Guo Y, Yao J (2016) Modeling of cutting forces in end milling based on oblique cutting analysis. Int J Adv Manuf Technol 84(1):727–736CrossRefGoogle Scholar
  6. 6.
    Przestacki D, Chwalczuk T, Wojciechowski S (2017) The study on minimum uncut chip thickness and cutting forces during laser-assisted turning of WC/NiCr clad layers. Int J Adv Manuf Technol. doi: 10.1007/s00170-017-0035-5
  7. 7.
    Chinchanikar S, Choudhury SK (2016) Cutting force modeling considering tool wear effect during turning of hardened AISI 4340 alloy steel using multi-layer TiCN/Al2O3 /TiN-coated carbide tools. Int J Adv Manuf Technol 83(9):1749–1762CrossRefGoogle Scholar
  8. 8.
    Chen L, Zhang K, Cheng H, Qi Z, Meng Q (2016) A cutting force predicting model in orthogonal machining of unidirectional CFRP for entire range of fiber orientation. Int J Adv Manuf Technol DOI. doi: 10.1007/s00170-016-9059-5
  9. 9.
    Xu JT, Sun YW, Zhang L (2015) A mapping-based approach to eliminating self-intersection of offset paths on mesh surfaces for CNC machining. Comput Aided Des 62:131–142CrossRefGoogle Scholar
  10. 10.
    Xu JT, Zhang XK, Wang SKWJ (2013) Tool path generation for pattern sculpting on free-form surfaces. Int J Adv Manuf Technol 67(9–12):2469–2476CrossRefGoogle Scholar
  11. 11.
    Xu JT, Wang YJ, Zhang XK, Chang S (2013) Contour-parallel tool path generation for three-axis mesh surface machining based on one-step inverse forming. Proceedings of the IMechEs, Part B: Journal of Engineering Manufacture 227(12):1800–1807CrossRefGoogle Scholar
  12. 12.
    Shi X, Liu H, Li H, Liu C, Tan G (2016) Comprehensive error measurement and compensation method for equivalent cutting forces. Int J Adv Manuf Technol 85(1):149–156CrossRefGoogle Scholar
  13. 13.
    Wojciechowski S, Twardowski P, Pelic M (2014) Cutting forces and vibrations during ball end milling of inclined surfaces. Procedia CIRP 14:113–118CrossRefGoogle Scholar
  14. 14.
    Wojciechowski S, Twardowski P (2012) Tool life and process dynamics in high speed ball end milling of hardened steel. Procedia CIRP 1:289–294CrossRefGoogle Scholar
  15. 15.
    Wojciechowski S, Twardowski P, Pelic M, Maruda RW, Barrans S, Krolczyk GM (2016) Precision surface characterization for finish cylindrical milling with dynamic tool displacements model. Precis Eng 46:158–165CrossRefGoogle Scholar
  16. 16.
    Maruda RW, Krolczyk GM, Nieslony P, Wojciechowski S, Michalski M, Legutko S (2016) The influence of the cooling conditions on the cutting tool wear and the chip formation mechanism. J Manuf Process 24:107–115CrossRefGoogle Scholar
  17. 17.
    Tai CC, Fuh KH (1995) The prediction of cutting forces in the ball-end milling process. J Mater Process Technol 54(1):286–301CrossRefGoogle Scholar
  18. 18.
    Guo Q, Jiang Y, Zhao B, Ming PM (2016) Chatter modeling and stability lobes predicting for non-uniform helix tools. Int J Adv Manuf Technol 87(1–4):1–16Google Scholar
  19. 19.
    Kim SK, Lee SY (2001) Chatter prediction of end milling in a vertical machining center. Journal of Sound Vibration 241:567–586CrossRefGoogle Scholar
  20. 20.
    Wan M, Zhang WH, Qiu KP, Gao T, Yang Y (2005) Numerical prediction of static form errors in peripheral milling of thin-walled workpieces with irregular meshes. Transaction of ASME, Journal of Manufacturing Science and Engineering 127:13–22CrossRefGoogle Scholar
  21. 21.
    Guo DM, Ren F, Sun YW (2010) An approach to modeling cutting forces in five-axis ball-end milling of curved geometries based on tool motion analysis. J Manuf Sci Eng 132(4):041004CrossRefGoogle Scholar
  22. 22.
    Gu F, Kapoor SG, Devor RE, Bandyopadhyay P (1997) An enhanced cutting force model for face milling with variable cutter feed motion and complex workpiece geometry. J Manuf Sci Eng 119(4A):467–475CrossRefGoogle Scholar
  23. 23.
    Wu YM, Kanamori H, Allen RM, Hauksson E (2007) Modeling and prediction of cutting noise in the face-milling process. J Manuf Sci Eng 129(3):527–530CrossRefGoogle Scholar
  24. 24.
    Wang H, Qin X, Li H, Ren C (2008) Analysis of cutting forces in helical milling of carbon fiber-reinforced plastics. Proc Inst Mech Eng B J Eng Manuf 222(6):665–676CrossRefGoogle Scholar
  25. 25.
    Zhang X, Zhang J, Pang B, Zhao WH (2016) An accurate prediction method of cutting forces in 5-axis flank milling of sculptured surface. Int J Mach Tools Manuf 104:26–36CrossRefGoogle Scholar
  26. 26.
    Tsai MY, Chang SY, Hung JP (2016) Investigation of milling cutting forces and cutting coefficient for aluminum 6060-T6. Computers & Electrical Engineering 51:320–330CrossRefGoogle Scholar
  27. 27.
    Wan M, Zhang WH, Qin GH, Zhang ZP (2008) Consistency study on three cutting force modelling methods for peripheral milling. Proc Inst Mech Eng B J Eng Manuf 222(6):665–676CrossRefGoogle Scholar
  28. 28.
    Pwu HY, Hocheng H (1998) Chip formation model of cutting fiber-reinforced plastics perpendicular to fiber axis. J Manuf Sci Eng 120(1):192–196CrossRefGoogle Scholar
  29. 29.
    Budak E, Altintaş Y, Armarego EJA (1996) Prediction of milling force coefficients from orthogonal cutting data. J Manuf Sci Eng 118(2):216–224CrossRefGoogle Scholar
  30. 30.
    Lamikiz A, DLLN L, Sanchez JA, Salgado MA (2004) Cutting force estimation in sculptured surface milling. Int J Mach Tools Manuf 44:1511–1526CrossRefGoogle Scholar
  31. 31.
    Wojciechowski S, Maruda RW, Nieslony P, Krolczyk GM (2016) Investigation on the edge forces in ball end milling of inclined surfaces. Int J Mech Sci 119:360–369CrossRefGoogle Scholar
  32. 32.
    Wojciechowski S (2015) The estimation of cutting forces and specific force coefficients during finishing ball end milling of inclined surfaces. Int J Mach Tools Manuf 89:110–123CrossRefGoogle Scholar
  33. 33.
    Oliveira FBD, Rodrigues AR, Coelho RT, Souza AFD (2015) Size effect and minimum chip thickness in micromilling. Int J Mach Tools Manuf 89:39–54CrossRefGoogle Scholar
  34. 34.
    Qiu W, Liu Q, Ding J, Yuan S (2016) Cutting force prediction in orthogonal turn-milling by directly using engagement boundaries. Int J Adv Manuf Technol. doi: 10.1007/s00170-015-8173-0
  35. 35.
    Ghorbani H, Moetakef-Imani B (2016) Specific cutting force and cutting condition interaction modeling for round insert face milling operation. Int J Adv Manuf Technol 84(5):1705–1715Google Scholar
  36. 36.
    Grossi N, Sallese L, Scippa A, Campatelli G (2015) Speed-varying cutting force coefficient identification in milling. Precis Eng 42:321–334CrossRefGoogle Scholar
  37. 37.
    Gradisek J, Kalveram M, Weinert K (2004) Mechanistic identification of specific force coefficients for a general end mill. Int J Mach Tools Manuf 44:401–414CrossRefGoogle Scholar
  38. 38.
    Kline WA, DeVor RE (1983) The effect of runout on cutting geometry and forces in end milling. International Journal of Machine Tools Design and Research 23:123–140CrossRefGoogle Scholar
  39. 39.
    Wang JJJ, Liang SY (1996) Chip load kinematics in milling with radial cutter runout. Transaction of ASME, Journal of Engineering Industry 118:111–116CrossRefGoogle Scholar
  40. 40.
    Yao ZQ, Liang XG, Luo L, Hu J (2013) A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling. J Mater Process Technol 213(9):1575–1587CrossRefGoogle Scholar
  41. 41.
    Zhang DL, Mo R, Chang ZY, Sun H, Li C (2016) A study of computing accuracy of calibrating cutting force coefficients and run-out parameters in flat-end milling. Int J Adv Manuf Technol 84:621–630CrossRefGoogle Scholar
  42. 42.
    Guo Q, Sun YW, Guo M, Zhang CT (2012) New mathematical method for the determination of cutter runout parameters in flat-end milling. Chinese Journal of Mechanical Engineering 25(5):947–952CrossRefGoogle Scholar
  43. 43.
    Sun YW, Guo Q (2012) Analytical modeling and simulation of the envelope surface in five-axis flank milling with cutter runout. Transactions of the ASME, Journal of Manufacturing Science and Engineering 134(2):160–165CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  1. 1.School of Mechanical and Power EngineeringHenan Polytechnic UniversityJiaozuoChina
  2. 2.School of Survey & Land Information EngineeringHenan Polytechnic UniversityJiaozuoChina

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