Modeling, Simulation and Compensation of Thermomechanically Induced Material Deformation in Dry NC Milling Processes

  • T. SiebrechtEmail author
  • P. Wiederkehr
  • A. Zabel
  • M. Schweinoch
  • A. Byfut
  • A. Schröder
Part of the Lecture Notes in Production Engineering book series (LNPE)


During machining processes, a significant amount of energy is converted into heat at the point of contact of the machining tool and the workpiece. Throughout the process, the workpiece is thermally loaded, resulting in a complex and transient temperature distribution. The latter induces material deformations, which, when not considered in the planning of the machining process, may result in rejects of the manufactured part due to shape deviations or tolerance violations. Compensating thermally induced deformations in machining processes is a challenge for several reasons: The workpiece geometry itself is constantly changing due to the material removal process, which influences the heat flow and dispersion within the semi-finished workpiece. Due to the relative tool-workpiece movement and varying engagement conditions, the heat source changes with respect to location and magnitude, while the change of the surface area affects the cooling of the workpiece. The induced complex and inhomogeneous temperature field within the workpiece leads to an equally complex material response, which may lead to an erroneous material removal when finishing the workpiece in a thermally loaded state. As a result of the transient nature of the thermal loading and the induced deformations, an accurate compensation approach must take into account the specific time-dependent state of the workpiece for a particular engagement condition. For any non-trivial geometry, this requires the use of a simulation system. This paper presents a hybrid simulation system comprised of a geometric physically-based (GP) process simulation and a variation of the fictitious domain method in combination with a (higher-order) finite element (FE) method. The resulting FE simulation is used to predict the thermomechanically induced material response, while the GP simulation provides the appropriate boundary conditions. The hybrid simulation system is able to provide a detailed analysis of the transient in-process state of the workpiece, which forms the basis for avoiding or compensating an erroneous material removal. The simulation system and the compensation procedure are validated with machining experiments.



This paper is based on the investigations and findings of the project Simulation of Thermomechanical Deformations in NC Milling (SCHR 1244/2-3) and (ZA 427/3-3) of the priority program SPP 1480 (CutSim), which is kindly supported by the German Research Foundation (DFG).


  1. 1.
    Abouridouane, M., Klocke, F., Döbbeler, B.: Analytical temperature prediction for cutting steel. Annals CIRP 65(1), 77–80 (2016)CrossRefGoogle Scholar
  2. 2.
    Altintas, Y., Kersting, P., Biermann, D., Budak, E., Denkena, B., Lazoglu, I.: Virtual process systems for part machining operations. CIRP Annals-Manuf. Technol. 63(2), 585–605 (2014)CrossRefGoogle Scholar
  3. 3.
    Arrazola, P.J., Özel, T., Umbrello, D., Davies, M., Jawahir, I.S.: Recent advances in modelling of metal machining processes. Annals CIRP 62(2), 695–718 (2013)CrossRefGoogle Scholar
  4. 4.
    Astrakhantsev, G.: Method of fictitious domains for a second-order elliptic equation with natural boundary conditions. USSR Comput. Math. Math. Phys. 18(1), 114–121 (1978). doi: 10.1016/0041-5553(78)90012-5 MathSciNetCrossRefGoogle Scholar
  5. 5.
    Boley, B., Weiner, J.: Theory of Thermal Stresses. Wiley Ltd., Inc. XVI, New York and London (1960)Google Scholar
  6. 6.
    Bollig, P., Köhler, D., Zanger, F., Schulze, V.: Effects of different levels of abstraction simulating heat sources in FEM considering drilling. Proc. CIRP 46, 115–119 (2016)CrossRefGoogle Scholar
  7. 7.
    Byfut, A., Schröder, A.: Unsymmetric multi-level hanging nodes and anisotropic polynomial degrees in \(H^1\)-conforming higher-order finite element methods. Comput. Math. Appl. 73(9), 2092–2150 (2017). doi: 10.1016/j.camwa.2017.02.029
  8. 8.
    Byfut, A., Schröder, A.: A fictitious domain method for the simulation of thermoelastic deformations in NC-milling processes. Int. J. Numer. Methods Eng. (submitted) (2017)Google Scholar
  9. 9.
    Byfut, A., Hellwig, F., Schröder, A.: Marching volume polytopes algorithm. Int. J. Numer. Methods Eng. (submitted) (2017)Google Scholar
  10. 10.
    Calvo, J., Novaga, M., Orlandi, G.: Parabolic equations in time dependent domains. J. Evol. Equ. (2016). doi: 10.1007/s00028-016-0336-4
  11. 11.
    Demkowicz, L.: Computing with \(hp\)-adaptive finite elements. Vol. 1: One- and two-dimensional elliptic and Maxwell problems. With CD-ROM. Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series (2007). doi: 10.1201/9781420011685
  12. 12.
    Demkowicz, L., Kurtz, J., Pardo, D., Paszyński, M., Rachowicz, W., Zdunek, A.: Computing with \(hp\)-adaptive finite elements. Vol. 2: frontiers: three-dimensional elliptic and Maxwell problems with applications. Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series (2008). doi: 10.1201/9781420011692
  13. 13.
    Denkena, B., Brüning, J., Niederwestberg, D., Grabowksi, R.: Influence of machining parameters on heat generation during milling of aluminium alloys. Proc. CIRP 46, 39–42 (2016)CrossRefGoogle Scholar
  14. 14.
    Düster, A., Parvizian, J., Yang, Z., Rank, E.: The finite cell method for three-dimensional problems of solid mechanics. Comput. Methods Appl. Mech. Eng. 197(45–48), 3768–3782 (2008). doi: 10.1016/j.cma.2008.02.036 MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Evans, L.: Partial Differential Equations. American Mathematical Society, Providence, RI (1998)zbMATHGoogle Scholar
  16. 16.
    Fluegge, S.: Encyclopedia of Physics. Vol. VIa/2: Mechanics of Solids. Springer, Berlin (1972)Google Scholar
  17. 17.
    Glänzel, J., Herzog, R., Ihlefeldt, S., Meyer, A., Unger, R.: Simulation-based correction approach for thermo-elastic workpiece deformations during milling processes. Proc. CIRP 46, 103–106 (2016)CrossRefGoogle Scholar
  18. 18.
    Glowinski, R., Pan, T.W., Periaux, J.: A fictitious domain method for dirichlet problem and applications. Comput. Methods Appl. Mech. Eng. 111(3–4), 283–303 (1994). doi: 10.1016/0045-7825(94)90135-X MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Green, A.: A note on linear thermoelasticity. Mathematika 19, 69–75 (1972)CrossRefzbMATHGoogle Scholar
  20. 20.
    Haupt, P.: Continuum Mechanics and Theory of Materials. Springer, Berlin (2002)CrossRefzbMATHGoogle Scholar
  21. 21.
    Hughes, J.F.: Computer Graphics: Principles and Practice (1995)Google Scholar
  22. 22.
    Hughes, T.: The Finite Element Method—Linear Static and Dynamic Finite Element Analysis. Dover Publications Inc (2000)Google Scholar
  23. 23.
    Jawahir, I.S., Brinksmeier, E., M’Saoubi, R., Aspinwall, D.K., Outeiro, J.C., Meyer, D., Umbrello, D., Jayal, A.D.: Surface integrity in material removal processes: recent advances. Annals CIRP 60(2), 603–626 (2011)CrossRefGoogle Scholar
  24. 24.
    Joliet, R., Byfut, A., Kersting, P., Schröder, A., Zabel, A.: Machining of lightweight frame structures. Proc. CIRP 8, 402–407 (2013). doi: 10.1016/j.procir.2013.06.124 CrossRefGoogle Scholar
  25. 25.
    Joliet, R., Byfut, A., Kersting, P., Schröder, A., Zabel, A.: Validation of a heat input model for the prediction of thermomechanical deformations during NC milling. In: 14th CIRP Conference on Modeling of Machining Operations (CIRP CMMO) (2013). doi: 10.1016/j.procir.2013.06.124
  26. 26.
    Karaguzel, U., Bakkal, M., Budak, E.: Modeling and measurement of cutting temperatures in milling. Proc. CIRP 46, 173–176 (2016)CrossRefGoogle Scholar
  27. 27.
    Karniadakis, G., Sherwin, S.: Spectral/\(hp\) Element Methods for CFD. Oxford University Press, USA (2005). doi: 10.1093/acprof:oso/9780198528692.001.0001
  28. 28.
    Kersting, P., Odendahl, S.: Capabilities of a process simulation for the analysis of five-axis milling processes in the aerospace industry. In: 18th International Seminar on High Technology (2013)Google Scholar
  29. 29.
    Kienzle, O.: Die Bestimmung von Kräften und Leistungen an spanenden Werkzeugen und Werkzeugmaschinen. VDI-Z 94 (1952)Google Scholar
  30. 30.
    Parvizian, J., Düster, A., Rank, E.: Finite cell method\(. h\)- and \(p\)-extension for embedded domain problems in solid mechanics. Comput. Mech. 41(1), 121–133 (2007). doi: 10.1007/s00466-007-0173-y MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Pavlicek, F., Beer, Y., Weikert, S., Mayr, J., Wegener, K.: Design of a measurement setup and first experiments on the influence of \(CO_2\)-cooling on the thermal displacement on a machine tool. Proc. CIRP 46, 23–26 (2016)CrossRefGoogle Scholar
  32. 32.
    Puls, H., Klocke, F., Döbbeler, B., Peng, B.: Multiscale modeling of thermoelastic workpiece deformation in dry cutting. Proc. CIRP 46, 27–30 (2016)CrossRefGoogle Scholar
  33. 33.
    Putz, M., Schmidt, G., Semmler, U., Oppermann, C., Bräunig, M., Karagüzel, U.: Modeling of heat fluxes during machining and their effects on thermal deformation of the cutting tool. Proc. CIRP 31, 611–614 (2015)CrossRefGoogle Scholar
  34. 34.
    Rossi, F., Baizeau, T., Moureaux, C.: Thermal finite difference modeling of machining operations in polymers. Proc. CIRP 46, 234–237 (2016)CrossRefGoogle Scholar
  35. 35.
    Salençon, J.: Handbook of Continuum Mechanics—General Concepts. Thermoelasticity, Springer, Berlin (2001)CrossRefzbMATHGoogle Scholar
  36. 36.
    Schulze, V. (ed.): 15th Conference on Modelling of Machining Operations—Sessions on Thermal Effects in Machining Processes, vol. 31, Procedia CIRP, Elsevier (2015)Google Scholar
  37. 37.
    Schulze, V., Uhlmann, E., Mahnken, R., Menzel, A., Biermann, D., Zabel, A., Bollig, P., Ivanov, I.M., Cheng, C., Holtermann, R., Bartel, T.: Evaluation of different approaches for modeling phase transformations in machining simulation. Prod. Eng.—Res. Dev. Annals Ger. Acad. Soc. Prod. Eng. 9(4), 437–449 (2015). doi: 10.1007/s11740-015-0618-7 Google Scholar
  38. 38.
    Schweinoch, M., Joliet, R., Kersting, P.: Predicting thermal loading in NC milling processes. Prod. Eng. 9(2), 179–186 (2015). doi: 10.1007/s11740-014-0598-z
  39. 39.
    Schweinoch, M., Joliet, R., Kersting, P., Zabel, A.: Heat input modeling and calibration in dry NC-milling processes. Prod. Eng.—Res. Dev. Annals Ger. Acad. Soc. Prod. Eng. 9(4), 495–504 (2015). doi: 10.1007/s11740-015-0621-z
  40. 40.
    Schweinoch, M., Joliet, R., Kersting, P., Zabel, A.: Heat input modeling and calibration in dry NC-milling processes. Prod. Eng. Res. Dev. 9(4), 495–504 (2015c). doi: 10.1007/s11740-015-0621-z CrossRefGoogle Scholar
  41. 41.
    Surmann, T., Ungemach, E., Zabel, A., Joliet, R., Schröder, A.: Simulation of the temperature distribution in NC-milled workpieces. Adv. Mater. Res. 223, 222–230 (2011). doi: 10.4028/ CrossRefGoogle Scholar
  42. 42.
    Vos, P., van Loon, R., Sherwin, S.: A comparison of fictitious domain methods appropriate for spectral/\(hp\) element discretisations. Comput. Methods Appl. Mech. Eng. 197(25–28), 2275–2289 (2008). doi: 10.1016/j.cma.2007.11.023 MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Šolín, P., Segeth, K., Doležel, I.: Higher-Order Finite Element Methods. Chapman & Hall/CRC Press, London/Boca Raton (2003)Google Scholar
  44. 44.
    Wanigarathne, P.C., Kardekar, A.D., Dillon, O.W., Poulachon, G., Jawahir, I.S.: Progressive tool-wear in machining with coated grooved tools and its correlation with cutting temperature. Wear 259(7), 1215–1224 (2005)CrossRefGoogle Scholar
  45. 45.
    Wiederkehr, P., Siebrecht T.: Virtual machining: capabilities and challenges of process simulations in the aerospace industry. Proc. Manuf. 6, 80–87 (2016). doi: 10.1016/j.promfg.2016.11.011. 16th Machining Innovations Conference for Aerospace Industry - MIC
  46. 46.
    Wilmanski, K.: Continuum Thermodynamics—Part I: Foundations (Series on Advances in Mathematics for Applied Sciences). World Scientific Publishing Company (2008)Google Scholar
  47. 47.
    Young, D., Melvin, R., Bieterman, M., Johnson, F., Samant, S., Bussoletti, J.: A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics. J. Comput. Phys. 92(1), 1–66 (1991). doi: 10.1016/0021-9991(91)90291-R MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Zabel, A.: Prozesssimulation in der Zerspanung - Modellierung von Dreh- und Fräsprozessen. Habilitation, TU Dortmund (2010)Google Scholar
  49. 49.
    Zimmermann, M., Schindler, S., Steinmann, P., Aurich, J.C.: Compensation of thermo-mechanically induced workpiece and tool deformations during dry turning. Proc. CIRP 46, 31–34 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • T. Siebrecht
    • 1
    Email author
  • P. Wiederkehr
    • 1
  • A. Zabel
    • 1
  • M. Schweinoch
    • 1
  • A. Byfut
    • 2
  • A. Schröder
    • 2
  1. 1.Institute of Machining TechnologyTU Dortmund UniversityDortmundGermany
  2. 2.Department of MathematicsParis Lodron University of SalzburgSalzburgAustria

Personalised recommendations