A Thermo-elastic Annular Plate Model for the Modeling of Brake Systems

José Luis Reyes Péres
German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Germany

Andreas Heckmann
German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Germany

Ingo Kaiser
German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Germany

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp11063295

Ingår i: Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany

Linköping Electronic Conference Proceedings 63:33, s. 295-303

Visa mer +

Publicerad: 2011-06-30

ISBN: 978-91-7393-096-3

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


The friction forces generated during braking between brake pads and discs produce high thermal gradients on the rubbing surfaces. These thermal gradients may cause braking problems such as hot spotting and the associated hot judder phenomenon in the frequency range below 100 Hz.

Some consequences of these undesirable vibrations are comfort reductions; a defective braking process; inhomogeneous wear; cutbacks of the brake performance and even damage of brake components.

The present paper proposes a modeling concept that is targeted on this field of application and introduces the new Modelica class ThermoelasticPlate; which is implemented in the DLR FlexibleBodies library.


Disc brake; Modal multifield approach; Thermoelasticity


[1] S. Panier; P. Dufrénoy; and D. Weichert. An experimental investigation of hot spots in railway disc brakes. Wear; 256:764 – 773; 2004. doi: 10.1016/S0043-1648(03)00459-9.

[2] T.K. Kao; J.W. Richmond; and A. Douarre. Thermo-mechanical instability in braking and brake disc thermal judder: an experimental and finite element study. In Proc. of 2nd International Seminar on Automotive Braking; Recent Developments and Future Trends; IMechE; pages 231–263; Leeds; UK; 1998.

[3] A. Rinsdorf. Theoretische und experimentelle Untersuchungen zur Komfortoptimierung von Scheibenbremsen. H¨oppner und G¨ottert; Siegen; 1996.

[4] T. Steffen. Untersuchung der Hotspotbildung bei Pkw-Bremsscheiben. Number 345 in VDI–Fortschrittsberichte Reihe 12. VDI-Verlag; Düsseldorf; 1998.

[5] T. Tirovic and G.A. Sarwar. Design synthesis of non-symmetrically loaded high-performance disc brakes; Part 2: finite element modelling. Proc. of the I Mech E Part F: Journal of Rail and Rapid Transit; 218:89 – 104; 2004. doi: 10.1243/0954409041319678.

[6] P. Dufrénoy. Two-/three-dimensional hybrid model of the thermomechanical behaviour of disc brakes. Proc. of the I Mech E Part F: Journal of Rail and Rapid Transit; 218:17 – 30; 2004. doi: 10.1243/095440904322804402.

[7] K. Lee and J.R. Barber. Frictionally excited thermoelastic instability in automotive disk brakes. Journal of Tribology; 115:607 – 614; 1993. doi: 10.1115/1.2921683.

[8] C. Krempaszky and H. Lippmann. Frictionally excited thermoelastic instabilities of annular plates under thermal pre-stress. Journal of Tribilogy; 127:756–765; 2005. doi: 10.1115/1.2000980.

[9] B.A. Boley and J.H. Weiner. Theory of Thermal Stresses. Dover Publications; Mineola; New York; 1997.

[10] H.J. Bathe. Finite Element Procedures. Prentice Hall; New Jersey; 1996.

[11] R.W. Lewis; K. Morgan; H.R. Thomas; and K.N. Seetharamua. The Finite Element Method in Heat Transfer Analysis. John Wiley and Sons; Chichester; UK; 1996.

[12] W. Ritz. Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. Journal f¨ur Reine und Angewandte Mathematik; 135:1–65; 1908.

[13] Carl de Boor. A practical Guide to Splines. Springer–Verlag; Berlin; 1978.

[14] A. Heckmann. The Modal Multifield Approach in Multibody Dynamics. Number 398 in Fortschritt-Berichte VDI Reihe 20. VDI-Verlag; D¨usseldorf; 2005. PhD thesis.

[15] J. Salencon. Handbook of Continuum Mechanics. Springer-Verlag; Berlin; 2001.

[16] A. Heckmann; S. Hartweg; and I. Kaiser. An Annular Plate Model in Arbitrary Lagrangian-Eulerian-Description for the DLR FlexibleBodies Library. In 8th International Modelica Conference; 2010. submitted for publication.

[17] O. Wallrapp and R. Schwertassek. Representation of geometric stiffening in multibody system simulation. International Journal for Numerical Methods in Engineering; 32:1833–1850; 1991. doi: 10.1002/nme.1620320818.

[18] F. Bloom and D. Coffin. Handbook of Thin Plate Buckling and Postbuckling. Chapman & Hall/CRC; Washington; D.C.; 2001.

[19] P.E. Nikravesh. Computer-aided Analysis of Mechanical Systems. Prentice Hall; Engelwood Cliffs; New Jersey; 1988.

Citeringar i Crossref