AIAA 2003-4198 Thermal Contact Resistance of Non- Conforming Rough Surfaces, Part 2: Thermal Model

Thermal contact resistance (TCR) of non-conforming rough surfaces is studied and a new analytical model is developed. TCR is considered as the superposition of macro and micro components accounting for the effects of surface curvature and roughness, respectively. The effects of roughness, load and radius of curvature on TCR are investigated. It is shown that there is a value of surface roughness that minimizes the TCR. Simple correlations for determining TCR, using the general pressure distribution introduced in Part 1 of this study, are derived which cover the entire range of TCR ranging from conforming rough to smooth spherical contacts. The comparison of the present model with more than 700 experimental data points shows good agreement in the entire range of TCR. Nomenclature A = area, ¡ m 2 ¢ a = radius of contact, (m) b = flux tube radius, (m) a 0 L = relative radius of macrocontact, a L /a Hz b L = specimens radius, (mm) B = relative macrocontact radius, a L /b L CS = Carbon Steel c 1 = Vickers microhardness coefficient, (GP a) c 2 = Vickers microhardness coefficient, (−) d v = Vickers indentation diagonal, (µm) dr = increment in radial direction, (m) E 0 = equivalent elastic modulus, (GP a) F = external force, (N) h = contact conductance, ¡ W/m 2 K ¢ H mic = microhardness, (GP a) H 0 = c 1 (1.62σ 0 /m) c2 , (GP a) k = thermal conductivity, (W/mK) m = mean absolute surface slope, (−) n s = number of microcontacts P = pressure, (P a) P 0 0 Greek α = non-dimensional parameter, σρ/a 2 Hz γ = general pressure distribution exponent δ = maximum surface out-of-flatness, (m) ε = flux tube relative radius, a s /b s η s = microcontacts density, ¡ m −2 ¢ κ = H B / H BGM λ = dimensonless separation, Y/ √ 2σ ξ = dimensionless radial position, r/a L ψ = spreading resistance factor ρ = radius of curvature, (m) σ = RMS surface roughness, (µm) τ = non-dimensional parameter, ρ/a Hz Ω = dimensionless parameter Subscripts 0 = value at origin 1, 2 = solid 1, 2 a = apparent B = Brinell b = bulk c = critical Hz = Hertz j = joint L = macro mac = macro mic = micro r = real s = macro, …