Instability of Thermoelastic Contact
The thermal boundary conditions in thermoelastic contact problems are typically coupled to the mechanical boundary conditions. For static thermoelastic contact, surface roughness effects causes a thermal contact resistance which is dependent on local contact pressure. The effects of this thermomechanical coupling are illustrated in a simple one-dimensional rod model, which exhibits instability if the transmitted heat flux is sufficiently large. The stability problem is analyzed using a linear perturbation method which is then extended to problems in two and three dimensions. An important application concerns the development of non-uniformities in the nominally one-dimensional solidification of a metal in contact with a plane mould.
Related instabilities are obtained when two bodies slide together causing frictional heating that is proportional to the local contact pressure. The stability of idealized geometries such as half-planes and layers can be investigated by analytical methods, but the perturbation problem must be solved numerically for practical geometries, such as those arising in brakes and transmission clutches. Results for such cases are compared with experimental observations of thermal damage under industrial test conditions.
KeywordsContact Pressure Critical Speed Heat Conduction Problem Thermal Contact Resistance Migration Speed
Unable to display preview. Download preview PDF.
- Anderson, A.E. and Knapp, R.A. (1989). Hot spotting in automotive friction systems, International Conference on Wear of Materials, Vol. 2, 673–680.Google Scholar
- Barber, J.R. (1987). Stability of thermoelastic contact, International Conference on Tribology, Institution of Mechanical Engineers, London, 981–986.Google Scholar
- Berry, G.A. (1976). The Division of Frictional Heat - A Guide to the Nature of Sliding Contact, PhD Dissertation, University of Newcastle upon Tyne.Google Scholar
- Borri-Brunetto, M., Carpinteri, A. and Chiaia, B. (1998). Contact, closure and friction behaviour of rough crack concrete surfaces, in Framcos 3, Fracture of Concrete Structures, Mikashi, H. ed., Gifu, Japan, Aedificato Publ., Freiburg.Google Scholar
- Clausing, A.M. (1963). Thermal Contact Resistance in a Vacuum Environment, Ph.D. Thesis, University of Illinois.Google Scholar
- Duvaut, G. (1979). Free boundary problem connected with thermoelasticity and unilateral contact, Free Boundary Problems, Vol 11, Pavia.Google Scholar
- Lee, K. and Dinwiddie, R.B. (1998). Conditions of frictional contact in disk brakes and their effects on brake judder. SAE 980598.Google Scholar
- Richmond, O. and Huang, N.C. (1977). Interface stability during unidirectional solidifcation of a pure metal, Proceedings of the Sixth Canadian Congress of Applied Mechanics, Vancouver, 453–454.Google Scholar
- Thorns, E. (1988). Disc brakes for heavy vehicles, Institution of Mechanical Engineers, International Conference on Disc Brakes for Commercial Vehicles, C464 /88, 133–137.Google Scholar
- Yavuz, G. (1995). Instability Problems in Unidirectional Solidification Process, Ph.D. Thesis, University of Michigan.Google Scholar
- Zagrodzki, P., Lam, K.B., Al-Bahkali, E. and Barber, J.R. (1999). Simulation of a sliding system with frictionally-excited thermoelastic instability, Thermal Stresses ‘89, Cracow, Poland.Google Scholar