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.
Keywords: Disc brake; Modal multifield approach; Thermoelasticity
Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany
[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.