Skip to main content
SpringerLink
Log in

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

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

Symbol :

Description

c :

Specific heat capacity

f T (x,t):

Volume force

\(g_{T_{D}}\) :

Boundary temperature for Γ D

g D :

Explicit displacement for Γ D

g N :

Force density for Γ N

n :

Surface normal

t :

Time

T(x,y):

Temperature field

T a :

Ambient temperature

T r e f :

Reference of temperature

u(x,t):

Deformation field

α :

Coefficient of thermal expansion

γ :

Heat transfer coefficient

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

Interval limits for heat transfer

Γ:

Boundary of Ω

Γ D :

Periphery Γ of Dirichlet b. c.

Γ N :

Periphery Γ of Neumann b. c.

Γ R :

Periphery Γ of Robin b. c.

𝜖 :

Green’s strain tensor

η w :

Heat flux

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

Interval limits for heat flux

κ :

Thermal conductivity

μ, λ :

Lamé constant

ρ :

Density

σ :

Cauchy’s stress tensor

ψ :

Scalar test function H 1(Ω)

References

  1. Dix M, Wertheim R, Schmidt G, Hochmuth C (2014) Modelling of drilling assisted by cryogenic cooling for higher efficiency. CIRP Ann Manuf Technol 63:73–76

    Article  Google Scholar 

  2. Weinert K, Inasaki I, Sutherland JW, Wakabayashi T (2004) Dry machining and minimum quantity lubrication. CIRP Ann 53(2):511–537

    Article  Google Scholar 

  3. Hanke M (1999) Methodik zur Bewertung des thermo-mechanischen Verhaltens von komplexen kubischen Aluminiumwerkstücken bei der Trockenbearbeitung. Ph.D.-Thesis, TU Chemnitz

  4. Papst R (2008) Mathematische Modellierung der Wärmestromdichte zur Simulation des thermischen Bauteilverhaltens bei der Trockenbearbeitung. Dissertationsschrift, Universität Karlsruhe

  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 222–230

  6. Kuznetsov AP, Kosarev MV (2014) Standard types of temperature deformation in metal-cutting machines. Russ Eng Res 34 :330–333

    Article  Google Scholar 

  7. Kuznetsov AP, Kosarev MV (2015) Classification of temperature strains in metal-cutting machines. Russ Eng Res 34 :250–256

    Article  Google Scholar 

  8. Bryan J (1990) International status of thermal error research. CIRP Ann 645–656

  9. Ciarlet P (1988) Mathematical elasticity. Elsevier Science Publishers B.V., Amsterdam

    MATH  Google Scholar 

  10. Jung M, Langer U (2001) Methode der finiten Elemente für Ingenieure. B. G. Teubner

  11. Glänzel J, Meyer A, Wittstock V (2013) A-posteriori fehlergesteuerte adaptive Finite-Elemente-Netzverfeinerung. Konstruktion Ausgabe 11/12:88–90

    Google Scholar 

  12. Grossmann C, Roos H-G, Styles M (2007) Numerical treatment of partial differential equations. Springer-Verlag , Berlin

    Book  Google Scholar 

  13. Verfürth R (1996) A review of a posteriori error estimation and adaptive mesh-refinement techniques. B. G. Teubner , Stuttgart

    MATH  Google Scholar 

  14. Beuchler S, Meyer A, Pester M (2003) SPC-PM3AdH v1.0 - programmer’s manual. Preprint SFB393 01-08 TU Chemnitz

  15. Glänzel J (2009) Kurzvorstellung der 3D-FEM Software SPC-PM3AdH-XX. Preprint CSC 09-03 TU Chemnitz

  16. Meyer A (1999) Projected PCGM for handling hanging nodes in adaptive finite element procedures. Preprint SFB393 99-25 TU Chemnitz

  17. Meyer A (2001) Programmer’s manual for adaptive finite element code SPC-PM 2Ad. Preprint SFB393 01-18 TU Chemnitz

  18. Meyer A (2014) Programmbeschreibung SPC-PM3-AdH-XX Teil 1. Preprint CSC/14-01 TU Chemnitz

  19. Datenblatt. DIN EN 60751

  20. Drossel WG, Wittstock V, Bräunig M, Schmidt G (2013) Untersuchung der thermischen Werkzeugverformung. wt-Werkstatttechnik online 103(11/12):882–887

  21. Faires JD, Burden RL (2013) Numerical methods. Books/Cole, Boston

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fraunhofer Institute for Machine Tools and Forming Technology IWU, Chemnitz, Germany

    Janine Glänzel & Steffen Ihlenfeldt

  2. Technische Universität Chemnitz, Chemnitz, Germany

    Arnd Meyer, Roman Unger, Michael Bräunig & Volker Wittstock

  3. Technische Universität Dresden, Dresden, Germany

    Steffen Ihlenfeldt

Authors
  1. Janine Glänzel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arnd Meyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roman Unger
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michael Bräunig
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Volker Wittstock
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Steffen Ihlenfeldt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Janine Glänzel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Glänzel, J., Meyer, A., Unger, R. et al. Extended bisection method for parameter identification of the transient heat conduction equation for thermo-elastic deformations during drilling. Int J Adv Manuf Technol 88, 1279–1288 (2017). https://doi.org/10.1007/s00170-016-8661-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-016-8661-x

Keywords

Search

Navigation