Extended bisection method for parameter identification of the transient heat conduction equation for thermo-elastic deformations during drilling

  • Janine GlänzelEmail author
  • Arnd Meyer
  • Roman Unger
  • Michael Bräunig
  • Volker Wittstock
  • Steffen Ihlenfeldt


A new interdisciplinary approach is discribed to identifying unknown parameters using an extended version of the known interval bisection method. This developed method is based on the use of finite elements for calibrating the simulation calculation. The resulting thermo-elastic deformations which occur in drilling processes with impaired cooling lubrication are to be used as correction values for tool positioning in the NC control. Based on the strong impact on workpiece temperature of machining, a simulation approach is presented for calculating the temperature fields and their thermo-elastic consequences. In addition, methods are presented to correct these effects. This paper particularly deals with the temperature fields of drilling operations. Special attention is paid to the technique employed for iterative numerical determination of the unknown heat flux η w and heat transfer coefficient \(\bar {\gamma }\) values. Finally, the data obtained from experiments are compared with those achieved by numerical simulation in order to verify the efficiency of simulation and determination of parameters.


Adaptive FE simulation Thermo-elasticity Parameter approximation Temperature simulation in nc-drilled workpieces 




Specific heat capacity


Volume force


Boundary temperature for Γ D


Explicit displacement for Γ D


Force density for Γ N


Surface normal




Temperature field


Ambient temperature


Reference of temperature


Deformation field


Coefficient of thermal expansion


Heat transfer coefficient

\(\bar {\gamma }_{l}\), \(\bar {\gamma }_{r}\)

Interval limits for heat transfer


Boundary of Ω


Periphery Γ of Dirichlet b. c.


Periphery Γ of Neumann b. c.


Periphery Γ of Robin b. c.


Green’s strain tensor


Heat flux

\(\eta _{\omega _{l}}\), \(\eta _{\omega _{r}}\)

Interval limits for heat flux


Thermal conductivity

μ, λ

Lamé constant




Cauchy’s stress tensor


Scalar test function H 1(Ω)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dix M, Wertheim R, Schmidt G, Hochmuth C (2014) Modelling of drilling assisted by cryogenic cooling for higher efficiency. CIRP Ann Manuf Technol 63:73–76CrossRefGoogle Scholar
  2. 2.
    Weinert K, Inasaki I, Sutherland JW, Wakabayashi T (2004) Dry machining and minimum quantity lubrication. CIRP Ann 53(2):511–537CrossRefGoogle Scholar
  3. 3.
    Hanke M (1999) Methodik zur Bewertung des thermo-mechanischen Verhaltens von komplexen kubischen Aluminiumwerkstücken bei der Trockenbearbeitung. Ph.D.-Thesis, TU ChemnitzGoogle Scholar
  4. 4.
    Papst R (2008) Mathematische Modellierung der Wärmestromdichte zur Simulation des thermischen Bauteilverhaltens bei der Trockenbearbeitung. Dissertationsschrift, Universität KarlsruheGoogle Scholar
  5. 5.
    Surmann T, Ungemach E, Zabel A, Joliet R, Schröder A (2011) Simulation of the temperature distribution in nc-milled workspieces. In: Proceedings of the 13th CIRP conference on modelling of machining operations, pp 222–230Google Scholar
  6. 6.
    Kuznetsov AP, Kosarev MV (2014) Standard types of temperature deformation in metal-cutting machines. Russ Eng Res 34 :330–333CrossRefGoogle Scholar
  7. 7.
    Kuznetsov AP, Kosarev MV (2015) Classification of temperature strains in metal-cutting machines. Russ Eng Res 34 :250–256CrossRefGoogle Scholar
  8. 8.
    Bryan J (1990) International status of thermal error research. CIRP Ann 645–656Google Scholar
  9. 9.
    Ciarlet P (1988) Mathematical elasticity. Elsevier Science Publishers B.V., AmsterdamzbMATHGoogle Scholar
  10. 10.
    Jung M, Langer U (2001) Methode der finiten Elemente für Ingenieure. B. G. TeubnerGoogle Scholar
  11. 11.
    Glänzel J, Meyer A, Wittstock V (2013) A-posteriori fehlergesteuerte adaptive Finite-Elemente-Netzverfeinerung. Konstruktion Ausgabe 11/12:88–90Google Scholar
  12. 12.
    Grossmann C, Roos H-G, Styles M (2007) Numerical treatment of partial differential equations. Springer-Verlag , BerlinCrossRefGoogle Scholar
  13. 13.
    Verfürth R (1996) A review of a posteriori error estimation and adaptive mesh-refinement techniques. B. G. Teubner , StuttgartzbMATHGoogle Scholar
  14. 14.
    Beuchler S, Meyer A, Pester M (2003) SPC-PM3AdH v1.0 - programmer’s manual. Preprint SFB393 01-08 TU ChemnitzGoogle Scholar
  15. 15.
    Glänzel J (2009) Kurzvorstellung der 3D-FEM Software SPC-PM3AdH-XX. Preprint CSC 09-03 TU ChemnitzGoogle Scholar
  16. 16.
    Meyer A (1999) Projected PCGM for handling hanging nodes in adaptive finite element procedures. Preprint SFB393 99-25 TU ChemnitzGoogle Scholar
  17. 17.
    Meyer A (2001) Programmer’s manual for adaptive finite element code SPC-PM 2Ad. Preprint SFB393 01-18 TU ChemnitzGoogle Scholar
  18. 18.
    Meyer A (2014) Programmbeschreibung SPC-PM3-AdH-XX Teil 1. Preprint CSC/14-01 TU ChemnitzGoogle Scholar
  19. 19.
    Datenblatt. DIN EN 60751Google Scholar
  20. 20.
    Drossel WG, Wittstock V, Bräunig M, Schmidt G (2013) Untersuchung der thermischen Werkzeugverformung. wt-Werkstatttechnik online 103(11/12):882–887Google Scholar
  21. 21.
    Faires JD, Burden RL (2013) Numerical methods. Books/Cole, BostonzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • Janine Glänzel
    • 1
    Email author
  • Arnd Meyer
    • 2
  • Roman Unger
    • 2
  • Michael Bräunig
    • 2
  • Volker Wittstock
    • 2
  • Steffen Ihlenfeldt
    • 1
    • 3
  1. 1.Fraunhofer Institute for Machine Tools and Forming Technology IWUChemnitzGermany
  2. 2.Technische Universität ChemnitzChemnitzGermany
  3. 3.Technische Universität DresdenDresdenGermany

Personalised recommendations