Thermal Contact Resistance of Nonconforming Rough Surfaces, Part 1: Contact Mechanics Model
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Bibliographic record
Abstract
A new analytical model for spherical rough contacts, in the form of a set of relationships, is developed and solved numerically. It is shown that the maximum contact pressure is the parameter that specifies the contact pressure distribution. Simple correlations for calculating the maximum contact pressure and the radius of the macrocontact area as functions of the nondimensional parameters are proposed. A relationship for pressure distributions is derived where the load is higher than the critical load. A general pressure distribution is developed that covers the entire range of spherical contacts from the smooth Hertzian to the conforming rough contact. Finally, a criterion is derived to identify flat surfaces where the surface curvature has negligible effect on the contact pressure. Nomenclature A = area, m2 a = radius of contact, m a ′ L = relative radius of macrocontact, aL/aH as = radius of microcontacts, m b = flux tube radius, m c0 = function of τ, 1.8 τ −0.028 c ′ 0 = function of τ, 0.31 τ 0.056 c1 = Vickers microhardness coefficient, GPa c2 = Vickers microhardness coefficient dr = increment in radial direction, m dv = Vickers indentation diagonal, µm E = Young’s modulus, GPa E ′ = equivalent elastic modulus, GPa F = external force, N F ∗ = relative force error fi = discrete point forces, N Hmic = microhardness, GPa m = mean absolute surface slope ns = number of microcontacts P = pressure, Pa P ′ 0 = relative maximum pressure, P0/P0,H r, z = cylindrical coordinates u = sphere profile, m u0 = maximum indentation, m Y = mean surface plane separation, m α = nondimensional parameter, σρ/a2 H β = summits radii of curvature, m γ = general pressure distribution exponent δ = max surface out-of-flatness, m ηs = microcontacts density, m−2 λ = nondimensional separation, Y / √ (2)σ ν = Poisson’s ratio
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it