Coupling Analytical and Numerical Models to Simulate Thermomechanical Interaction During the Milling Process of Thin-Walled Workpieces

  • S. WimmerEmail author
  • J. Loehe
  • M. F. Zaeh
Part of the Lecture Notes in Production Engineering book series (LNPE)


Lightweight design is continually gaining in importance within the engineering sector, thus leading to a wide array of low rigidity components that are very demanding regarding the milling process in case manufactured by cutting. Within this chapter a new approach to model thermomechanical effects that occur during the milling process of thin-walled structures is introduced. For this purpose, an empirical process heat model was developed, which is calibrated by deformation measurements. In conjunction with well-established analytical cutting force models, the proposed process heat model was coupled with a numerical model of the workpiece to predict process induced deformations. This allows for the design of counter measures in order to either reduce occurring workpiece deflections or to compensate the resulting geometrical error. It was shown in experiments that both, an optimization of process parameters as well as a tool path adaption, can be successfully applied to avoid the violation of tolerance specifications without affecting the productivity of the milling operation.



Area of active surfaces associated to the heat flux in vector \( \uplambda_{\Delta } \)

\( {\text{a}}_{\text{e}} \)

Cutting width

\( {\text{a}}_{\text{p}} \)

Cutting depth

\( {\text{b}}_{\text{w}} \)

Remaining wall thickness


Model constant


Tool diameter

\( {\text{f}}_{\text{z}} \)

Feed per tooth

i, j

Counter of independent parameters

\( {\text{J}}_{\text{T}} \)

Cost function of thermal regression models


Number of regression model

\( {\text{k}}_{\text{c}} \)

Specific cutting energy

\( {\text{m}}_{\text{k}} \)

Row size of vectors and matrices

\( {\text{n}}_{\text{k}} \)

Column size of matrices


Rotational speed of the tool



\( {\text{P}}_{\text{c}} \)

Cutting power

\( {\text{Q}}_{\text{w}} \)

Material removal rate

\( {\dot{\text{q}}} \)

Heat flux

\( {\text{R}}^{2} \)

Coefficient of determination



\( {\text{u}}_{\text{y}} \)

Total deformation of the workpiece (in y-direction)

\( {\text{u}}_{\text{T}} \)

Thermally induced deformation of the workpiece

\( {\text{u}}_{\text{dyn}} \)

Dynamic component of the deformation

\( {\text{u}}_{\text{stat}} \)

Static component of the deformation

\( {\text{u}}_{\text{plast}} \)

Plastic component of the deformation

\( {\text{v}}_{\text{c}} \)

Cutting speed

\( {\text{v}}_{\text{f}} \)



Independent parameter


Number of flutes

\( {\text{z}}_{\text{MP}} \)

Z-position of the measuring point (MP)

\( \beta \)

Helix angle of the tool

\( \Delta \)

Difference of two regression models (k)

\( \upgamma \)

Angular position of the leading cutting edge

\( {\varvec{\uplambda}} \)

Vector of independent parameters

\( {\boldsymbol{\varphi }} \)

Vector of linear model constants

\( {\varvec{\Omega}} \)

Matrix of quadratic and linear interacting model constants



This paper is based on the investigations and findings of the project Coupling analytical and numerical models to simulate thermomechanical interaction during the milling process of thin-walled workpieces (ZA 288/38-1) of the priority program SPP 1480 (CutSim), which was kindly supported by the German Research Foundation (DFG).


  1. 1.
    Weinert, K., Inasaki, I., Sutherland, J.W., Wakabayashi, T.: Dry machining and minimum quantity lubrication. CIRP Ann.—Manuf. Technol. 53(2), 511–537 (2004)Google Scholar
  2. 2.
    Sölter, J., Gulpak, M.: Heat partitioning in dry milling of steel. CIRP Ann.—Manuf. Technol. 61(1), 87–90 (2012)CrossRefGoogle Scholar
  3. 3.
    Loehe, J., Zaeh, M.F., Roesch, O.: In-process deformation measurement of thin-walled workpieces. In: Procedia CIRP 1, pp. 546–551 (2012)Google Scholar
  4. 4.
    Philippe, D., Hascoët, J.Y.: Active integration of tool deflection effects in end milling. Part 2. Compensation of tool deflection. Int. J. Mach. Tools Manuf. 46(9), 945–956 (2006)CrossRefGoogle Scholar
  5. 5.
    Arrazola, P.J., Özel, T., Umbrello, D., Davies, M., Jawahir, I.S.: Recent advances in modelling of metal machining processes. CIRP Ann.—Manuf. Technol. 62(2), 695–718 (2013)Google Scholar
  6. 6.
    Loehe, J., Zaeh, M.F.: A new approach to build a heat flux model of milling processes. Procedia CIRP 24, 7–12 (2014)CrossRefGoogle Scholar
  7. 7.
    Loehe, J., Wimmer, S., Hairer, M., Zaeh, M.F.: An experimental study on the deformation behavior of thin-walled workpieces. In: Proceedings of the 17th International Conference on Machine Design and Production, Bursa, 12–15 July 2016Google Scholar
  8. 8.
    Klocke, F., Lung, D., Puls, H.: FEM-Modelling of the thermal workpiece deformation in dry turning. Procedia CIRP 8, 240–245 (2013)CrossRefGoogle Scholar
  9. 9.
    Frąckowiak, A., Botkin, N.D., Ciałkowski, M., Hoffmann, K.H.: A fitting algorithm for solving inverse problems of heat conduction. Int. J. Heat Mass Transf. 53(9–10), 2123–2127 (2010)CrossRefzbMATHGoogle Scholar
  10. 10.
    Altintas, Y.: Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design. Cambridge University Press, Cambridge (2000)Google Scholar
  11. 11.
    Löhe, J., Zäh, M.F.: Fräsbearbeitung dünnwandiger Werkstücke—Simulation und Kompensation thermomechanischer Wechselwirkungen. ZWF 107(7–8), 528–532 (2012)CrossRefGoogle Scholar
  12. 12.
    Warnecke, G.: Fertigungstechnische Berichte—Band 2—Spanbildung bei metallischen Werkstoffen. Technischer Verlag Resch KG, Gräfelfing b. München (1974)Google Scholar
  13. 13.
    Dawson, P.R., Malkin, S.: Inclined moving heat source model for calculating metal cutting temperatures. J. Eng. Ind. 106, 179–186 (1984)CrossRefGoogle Scholar
  14. 14.
    Lazoglu, I., Ulutan, D., Dinc, C.: 3D temperature fields in machining. In: Procedings of the 3rd International CIRP HPC Conference. Dublin (2008)Google Scholar
  15. 15.
    Siebertz, K., Van Bebber, D., Hochkirchen, T.: Statistische Versuchsplanung—Design of Experiments (DoE). Springer, Berlin (2010)Google Scholar
  16. 16.
    Denkena, B., Tönshoff, H.K.: Spanen—Grundlagen, 3rd edn. Springer, Berling Heidelberg (2011)Google Scholar
  17. 17.
    König, W., Essel, K., Witte, L.: Spezifische Schnittkraftwerte für die Zerspanung metallischer Werkstoffe. Verlag Stahleisen MBH, Düsseldorf (1982)Google Scholar
  18. 18.
    Wan, X.J., Hua, L., Wang, X.F., Peng, Q.Z., Qin, X.P.: An error control approach to tool path adjustment conforming to the deformation of thin-walled workpiece. Int. J. Mach. Tools Manuf. 51(3), 221–229 (2008)CrossRefGoogle Scholar
  19. 19.
    Ratchev, S., Liu, S., Huang, W., Becker, A.: An advanced FEA based force induced error compensation strategy in milling. Int. J. Mach. Tools Manuf. 46, 542–551 (2006)CrossRefGoogle Scholar
  20. 20.
    Chen, W., Xue, J., Tang, D., Chen, H., Qu, S.: Deformation prediction and error compensation in multilayer milling processes for thin-walled parts. Int. J. Mach. Tools Manuf. 49, 859–864 (2009)CrossRefGoogle Scholar
  21. 21.
    Wimmer, S., Zäh, M.F.: Fräsbearbeitung dünnwandiger Werkstücke—Prognose und Kompensation von Formabweichungen. Werkstattstechnik online 2016(9), submitted and accepted (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute for Machine Tools and Industrial ManagementTechnical University of Munich (TUM)GarchingGermany

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