Modeling machining errors for thin-walled parts according to chip thickness

  • Caixu YueEmail author
  • Zhitao Chen
  • Steven Y. Liang
  • Haining Gao
  • Xianli Liu


In the milling process of titanium alloy thin-walled parts, because of its low stiffness, processing deformation easily occurs, which results in in low-dimensional accuracy of machined surface and affecting the workpiece performance. Cutting force is the main factor that causes cutting deformation. Cutting deformation also affects cutting force. There is a coupling relationship between them. To solve the above problems, a method is proposed to predict the surface error by calculating the milling force by varying the chip thickness and by coupling the force with the elastic deformation of the workpiece. Firstly, the analytical model of bending elasticity deformation of thin-walled parts is established. Then, the micro-unit entrance angle and instantaneous chip thickness are calculated by the contact relationship of workpiece deformation and the chip boundary decision conditions. The cutting force and workpiece deformation at random rotating angle are obtained by iterative calculation method. Finally, the surface error is predicted by calculating the deformation matrix and the principle of surface generation mechanism. The simulation results are in good agreement with the experimental results, which verifies the accuracy of the proposed method. The results provide theoretical support for milling process optimization and profile accuracy control of titanium alloy thin-walled parts.


Titanium alloy milling Thin-walled parts Milling force Elastic deformation Chip thickness Error prediction 


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Funding information

This project is supported by Projects of International Cooperation and Exchanges NSFC (51720105009).


  1. 1.
    Wan M, Zhang WH, Qin G, Tan G (2007) Efficient calibration of instantaneous cutting force coefficients and runout parameters for general end mills. Int J Mach Tools Manuf 47(11):1767–1776CrossRefGoogle Scholar
  2. 2.
    Wan M, Zhang WH (2006) Efficient algorithms for calculations of static form errors in peripheral milling. J Mater Process Technol 171(1):156–165CrossRefGoogle Scholar
  3. 3.
    Ratchev S, Liu S, Huang W, Becker A (2004) Milling error prediction and compensation in machining of low-rigidity parts. Int J Mach Tools Manuf 44(15):1629–1641CrossRefGoogle Scholar
  4. 4.
    Chen D, Zhang XJ, Xie YK, Zhang XM, Ding H (2017) A unified analytical cutting force model for variable helix end mills. Int J Adv Manuf Technol 92(9–12):1–19Google Scholar
  5. 5.
    Gao YY, Ma JW, Jia ZY, Wang FJ, Si LK, Song DN (2016) Tool path planning and machining deformation compensation in high-speed milling for difficult-to-machine material thin-walled parts with curved surface. Int J Adv Manuf Technol 84(9–12):1757–1767CrossRefGoogle Scholar
  6. 6.
    Li ZL, Tuysuz O, Zhu LM, Altintas Y (2018) Surface form error prediction in five-axis flank milling of thin-walled parts. Int J Mach Tools Manuf 128:21–32CrossRefGoogle Scholar
  7. 7.
    Lin Z, Yang C, Peng F, Rong Y, Deng B, Ming L (2018) Prediction of flexible cutting forces and tool deflections for general micro end mill considering tool run-out and deflection feedback. Int J Adv Manuf Technol 96(1–4):1415–1428Google Scholar
  8. 8.
    Budak E, Tunç LT, Alan S, Özgüven HN (2012) Prediction of workpiece dynamics and its effects on chatter stability in milling. CIRP Ann Manuf Technol 61(1):339–342CrossRefGoogle Scholar
  9. 9.
    Budak E, Altintas Y (1995) Modeling and avoidance of static form errors in peripheral milling of plates. Int J Mach Tools Manuf 35(3):459–476CrossRefGoogle Scholar
  10. 10.
    Yang L, DeVor RE, Kapoor SG (2005) Analysis of force shape characteristics and detection of depth-of-cut variations in end milling. J Manuf Sci Eng 127(3):454–462CrossRefGoogle Scholar
  11. 11.
    Desai KA, Rao PVM (2012) On cutter deflection surface errors in peripheral milling. J Mater Process Technol 212(11):2443–2454CrossRefGoogle Scholar
  12. 12.
    Denkena B, Krüger M, Bachrathy D, Stepan G (2012) Model based reconstruction of milled surface topography from measured cutting forces. Int J Mach Tools Manuf 54:25–33CrossRefGoogle Scholar
  13. 13.
    Zheng L, Liang SY, Zhang B (1998) Modelling of end milling surface error with considering tool-machine-workpiece compliance. J Tsinghua Univ 38:76–79Google Scholar
  14. 14.
    Zhang Z, Zheng L, Li Z, Zhang B (2001) Analytical model for end milling surface geometrical error with considering cutting force/torque. Chin J Mech Eng 37(1):6–10CrossRefGoogle Scholar
  15. 15.
    Kline WA, DeVor RE, Shareef IA (1982) The prediction of surface accuracy in end milling. J Eng Ind 104(3):272–278CrossRefGoogle Scholar
  16. 16.
    Song G, Li JF, Sun J (2013) Analysis on prediction of surface error based on precision milling cutting force model. J Mech Eng 49(21):168–170CrossRefGoogle Scholar
  17. 17.
    Eksioglu C, Kilic ZM, Altintas Y (2012) Discrete-time prediction of chatter stability, cutting forces, and surface location errors in flexible milling systems. J Manuf Sci Eng 134(6):061006CrossRefGoogle Scholar
  18. 18.
    Yue CX, Gao HN, Liu XL, Liang SY, Wang LH (2019) A review of chatter vibration research in milling. Chin J Aeronaut.
  19. 19.
    Dépincé P, Hascoet JY (2006) Active integration of tool deflection effects in end milling. Part 1. Prediction of milled surfaces. Int J Mach Tools Manuf 46(9):937–944CrossRefGoogle Scholar
  20. 20.
    Wan M, Zhang WH (2006) Calculations of chip thickness and cutting forces in flexible end milling. Int J Adv Manuf Technol 29(7–8):637–647CrossRefGoogle Scholar
  21. 21.
    Altintaş Y, Lee P (1996) A general mechanics and dynamics model for helical end mills. CIRP Ann 45(1):59–64CrossRefGoogle Scholar
  22. 22.
    Qi HJ, Zhang DW, Cai YJ, Shen Y (2010) Modeling methodology of flexible milling force for low-rigidity processing system during high speed milling. J Tianjin Univ 43(2):143–148Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Caixu Yue
    • 1
    Email author
  • Zhitao Chen
    • 1
  • Steven Y. Liang
    • 2
  • Haining Gao
    • 1
  • Xianli Liu
    • 1
  1. 1.The Key Laboratory of National and Local United Engineering for “High-Efficiency Cutting & Tools”Harbin University of Science and TechnologyHarbinChina
  2. 2.George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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