A thermoelastic instability (TEI) analysis is presented for determining the threshold of instability in a friction pair consisting of a conducting surface rubbing against a rough surface with very low thermal conductivity. The theory predicts that TEI is initiated when the operating speed exceeds a limiting value of U* given by:  
U*/Us=1+Λ
where Us is identical to the critical equation developed by Burton (1980) for highly loaded surfaces in contact defined as: Us=2Ωks/fαE. The dimensionless parameters on the right-hand-side of the above equation emerge from the consideration of the surface roughness and are defined as Λ = σΩE/2χ, and ℑ′ = Ho/F′. The results indicate that the magnitude of the applied load and the surface roughness characteristics tend to play an important role in the prediction of the onset of TEI instability.
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