FE-analysis and in situ visualization of pressure-, slip-rate-, and temperature-dependent coefficients of friction for advanced sheet metal forming: development of a novel coupled user subroutine for shell and continuum discretization

  • F. Klocke
  • D. TrauthEmail author
  • A. Shirobokov
  • P. Mattfeld


In sheet metal forming simulations using finite element method, the coefficient of friction according to Coulomb is normally assumed to be constant for the whole tool region. Recent research has demonstrated that under contact conditions typical for sheet metal forming, the coefficient of friction is strongly dependent on the contact pressure and the slip-rate between the interacting partners as well as on the contact temperature. A friction law based on the approach of Filzek is proposed in this research paper and implemented as a user subroutine in Abaqus. Moreover, a novel user subroutine coupling is developed which enables the visualization of local coefficients of friction for every contact node. For the very first time, this enables the in situ visualization of local coefficients of friction in sheet metal forming simulations using the FE system Abaqus. Multiple evaluation algorithms are presented as well. The presented friction model and the user subroutine coupling are validated using experimental data of an industrial deep drawing process. The proposed combination of the friction modeling and the in situ visualization of coefficients of friction enables the identification of friction hot spots. Based on such analysis, the tool and die making industry can realize tribologically optimized tools either by applying special coatings in areas of low or high friction, or by choosing different materials for tooling inserts, or by changing the type as well as the amount of the lubricant. Whereas the presented friction model is tailored to sheet metal forming and developed using the commercial code of Abaqus, the visualization coupling methodology is transferable to any manufacturing process and various FE systems supporting Fortran programming language.


Sheet metal forming Coefficient of friction Visualization User subroutine Friction hot spots Tool design 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kessler L, Gerlach J (2008) Industrial aspects of material modeling for steel grades in the past, present and future. In: Proceedings of Numisheet 2008 - 7th international conference on numerical simulation of 3d sheet metal forming processes - Part A, InterlakenGoogle Scholar
  2. 2.
    Keum Y, Wagoner R, Lee J (2004) Friction model for FEM simulation of sheet metal forming operations. In: Proceeding of Numiform 2004 - 8th international conference on materials processing and design: modeling, simulation and applications , OhioGoogle Scholar
  3. 3.
    Roll K, Wiegand K (2008) Möglichkeiten der simulation von Umformvorgängen in der Blechumformung. In: Neuere Entwicklungen in der Blechumformung, pp 53–74Google Scholar
  4. 4.
    Banabic D (2010) Sheet metal forming processes—constitutive modeling and numerical simulation. Springer, BerlinGoogle Scholar
  5. 5.
    Hu Z, Schulze Niehoff H, Vollertsen F (2003) Determination of the friction coefficient in deep drawing: 1st colloquium processscaling, Bremen, 28./29., pp 27–35Google Scholar
  6. 6.
    Filzek J, Ludwig M (2013) Berücksichtigung der Reibung in der FEM-Simulation. In: Tagungsband TB-036 des EFB-Kolloquiums Blechverarbeitung 2013, 16./17. April in Fellbach, pp 359–370Google Scholar
  7. 7.
    Grueebler R, Hora P (2008) Temperature and velocity dependent friction modeling for sheet metal forming processes. In: Proceedings of Numisheet 2008 - 7th international conference on numerical simulation of 3d sheet metal forming processes - Part A, InterlakenGoogle Scholar
  8. 8.
    Hol J, Wiebenga JH, Dane C, Meinders VT, van den Boogaard AH (2014) A software solution for advanced friction modeling applied to sheet metal forming. In: Proceedings of the IDDRG 2014 , ParisGoogle Scholar
  9. 9.
    Meinders VT, Hol J, van den Boogaard AH (2014) Boundary and mixed lubrication friction modeling under forming process conditions. In: Numisheet 2014, Melville, pp 912–917Google Scholar
  10. 10.
    Abaqus Documentation: 37.1.5. Frictional behaviour - Using the basic Coulomb friction model. In: Abaqus Analysis User’s Guide, Chapter 37.1.5., 2014.Google Scholar
  11. 11.
    Shi JQ, Choi T (2011) Gaussian process regression analysis for functional data. CRC Press, Boca RatonzbMATHGoogle Scholar
  12. 12.
    Sa JPM (2007) Applied statistics using SPSS, STATISTICA, MATLAB and R. Springer Science & Business MediaGoogle Scholar
  13. 13.
    Coleman TF, Li Y (1994) On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Math Program 67(1–3):189–224zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    King S, Richards T (2013) Solving contact problems with Abaqus. Abaqus contact seminar available online, DS UK Ltd, Coventry, pp 1–325
  15. 15.
    Hager G, Wellein G (2010) Introduction to high performance computing for scientists and engineers. CRC Press, Boca RatonCrossRefGoogle Scholar
  16. 16.
    Bleicher F, Lechner C, Habersohn C, Kozeschnik E, Adjassoho B, Kaminiski H (2012) Mechanism of surface modification using machine hammer peening technology In: CIRP annals - manufacturing technology, vol 61, no 1, pp 375–378Google Scholar
  17. 17.
    Klocke F, Trauth D, Schongen F, Shirobokov A (2014) Analysis of friction between stainless steel sheets and machine hammer peened structured tool surfaces. In: WGP production engineering, vol 8, no 3, pp 263–272Google Scholar
  18. 18.
    Klocke F, Trauth D, Terhorst M, Mattfeld P (2014) Wear analysis of tool surfaces structured by machine hammer peening for foil-free forming of stainless steel. In: Advanced materials research, vol 1018, pp 317–324Google Scholar
  19. 19.
    Trauth D, Klocke F, Terhorst M, Mattfeld P (2015) Physicochemical analysis of machine hammer peened surface structures for deep drawing. J Tribol 137(2):1–7Google Scholar
  20. 20.
    Klocke F (2013) Manufacturing processes 4: Forming, RWTH edition. Springer, BerlinCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • F. Klocke
    • 1
  • D. Trauth
    • 1
    Email author
  • A. Shirobokov
    • 1
  • P. Mattfeld
    • 1
  1. 1.Forming TechnologyLaboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen UniversityAachenGermany

Personalised recommendations