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arxiv: 2604.15969 · v1 · submitted 2026-04-17 · ❄️ cond-mat.soft

Flash temperature in sliding contacts: comparing theory with experiments

B.N.J. Persson This is my paper

Pith reviewed 2026-05-10 07:59 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords flash temperaturesliding contactrough surfacesfrictionwearcontact mechanicssteel
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The pith

Analytical theory for flash temperatures in rough sliding contacts matches steel experiments within input uncertainties

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests an analytical theory that calculates the temperature spikes, called flash temperatures, at the tiny contact spots formed when two randomly rough surfaces slide past each other. The theory works for surfaces whose roughness spans many length scales and relies on correlation functions between local stress and temperature. It is compared directly to published experiments in which steel slides against steel. The predicted temperatures line up with the measured values once the main sources of experimental uncertainty are taken into account.

Core claim

The analytical theory based on stress and temperature correlation functions predicts flash temperatures that agree with experimental data for steel-on-steel sliding within the uncertainties arising mainly from the measured surface roughness power spectrum and the steel penetration hardness.

What carries the argument

An analytical theory based on stress and temperature correlation functions that is valid for randomly rough surfaces with roughness extending over arbitrarily many decades in length scale.

If this is right

  • Flash temperatures can be calculated for any sliding speed and normal load once the surface roughness power spectrum and hardness are known.
  • Temperature-dependent changes in friction and wear can be estimated directly from the roughness spectrum without solving the full temperature field numerically.
  • The same correlation-function approach extends to other material pairs provided their roughness statistics and hardness are measured.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the agreement persists for other material combinations, surface finishing processes could be optimized specifically to keep flash temperatures below critical thresholds for wear or lubricant breakdown.
  • The theory offers a route to include flash-temperature effects in large-scale simulations of brakes, gears, or rail-wheel contact without resolving every asperity.
  • Independent high-resolution profilometry of the same steel surfaces used in the original experiments would tighten the uncertainty bounds and provide a stricter test of the correlation-function method.

Load-bearing premise

The surface roughness power spectrum and the steel penetration hardness supplied to the theory are accurate representations of the actual surfaces used in the experiments.

What would settle it

New measurements of the roughness power spectrum or penetration hardness that produce predicted flash temperatures lying clearly outside the range observed in the sliding experiments would show the claimed agreement does not hold.

Figures

Figures reproduced from arXiv: 2604.15969 by B.N.J. Persson.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) A macroasperity contact area and (b) the contact [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The temperature distribution in a stationary Hertz [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The temperature distribution in a fast moving Hertz [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The hot track on the sliding steel surface from the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Spatial temperature distribution along [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Thermography of the sliding surface at the sliding [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The black line is the surface roughness power spec [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) The weighted average flash temperature [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The temperature slope-length [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The Hertz circular contact region moves with the [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
read the original abstract

The temperature increase in the contact regions between solids in sliding contact has a huge influence on friction and wear. Here we test an analytical theory for the flash temperature, valid for randomly rough surface with multiscale roughness, by comparing the theory predictions with the experimental results of Sutter et al \cite{Sutter} for steel sliding on steel. The theory, which is based on the study of stress and temperature correlation functions, is valid for randomly rough surfaces with roughness on arbitrary many decades in length scale. Within the uncertainty of the experimental data (mainly the surface roughness power spectrum and the steel penetration hardness), there is good agreements between the theory and the experimental results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The manuscript presents an analytical theory for flash temperature in sliding contacts between solids with randomly rough multiscale surfaces, derived from stress and temperature correlation functions. It tests the theory against independent experimental data from Sutter et al. on steel-on-steel sliding and reports good agreement within the dominant experimental uncertainties, which are identified as the measured surface roughness power spectrum and the steel penetration hardness.

Significance. If the reported agreement holds, the work validates a low-parameter analytical framework for predicting flash temperatures that influence friction and wear, applicable to surfaces with roughness spanning many length scales. The explicit use of independent experimental data and identification of input uncertainties constitute a strength, providing a practical alternative to numerical simulations in tribology.

major comments (1)
  1. Comparison section: The central claim of agreement 'within the uncertainty' is load-bearing, yet the manuscript does not show a quantitative propagation of the stated uncertainties (roughness power spectrum and hardness) into a predicted temperature range or confidence interval for the theory. Without this, it is difficult to verify that the observed match is not sensitive to plausible variations in the inputs.
minor comments (3)
  1. Abstract: 'good agreements' should read 'good agreement'.
  2. Theory section: Ensure all symbols appearing in the correlation-function expressions are defined on first use, including any cutoffs for the multiscale roughness.
  3. Figures: Add explicit error bands or shaded uncertainty regions to the theory curves in the comparison plots to match the experimental data presentation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading, the positive assessment of the work, and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: Comparison section: The central claim of agreement 'within the uncertainty' is load-bearing, yet the manuscript does not show a quantitative propagation of the stated uncertainties (roughness power spectrum and hardness) into a predicted temperature range or confidence interval for the theory. Without this, it is difficult to verify that the observed match is not sensitive to plausible variations in the inputs.

    Authors: We agree that an explicit quantitative propagation of the dominant input uncertainties would strengthen the comparison and make the central claim easier to verify. The manuscript identifies the measured roughness power spectrum and steel penetration hardness as the primary sources of uncertainty and states that agreement holds within these uncertainties, but it does not provide a sensitivity analysis or explicit temperature bounds. In the revised manuscript we will add a short discussion (or appendix) that estimates the range of predicted flash temperatures by varying the power-spectrum amplitude within the typical experimental scatter for such measurements (roughly a factor of two) and the hardness within the range of literature values for the steels used. This will show the predicted temperature band and confirm that the experimental data of Sutter et al. fall inside it. The addition will not change the main conclusions but will directly address the referee's concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity: theory tested against external experiments

full rationale

The paper applies an analytical theory for flash temperature (derived from stress/temperature correlation functions on multiscale random roughness) to predict outcomes and compares them directly to independent experimental measurements from Sutter et al. The central claim is qualified agreement within stated uncertainties of the experimental inputs (roughness power spectrum and steel penetration hardness). No derivation step reduces by construction to a fit, self-definition, or load-bearing self-citation chain; the experiments are external data providing a test, and the theory's assumptions are stated as holding for the domain. This is a standard non-circular comparison of first-principles model to measured data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the analytical theory derived from stress and temperature correlation functions, and the accuracy of experimental parameters such as roughness power spectrum and penetration hardness. No new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The theory is valid for randomly rough surfaces with roughness on arbitrary many decades in length scale.
    Stated in the abstract as the basis for the theory.

pith-pipeline@v0.9.0 · 5395 in / 1260 out tokens · 36591 ms · 2026-05-10T07:59:01.093833+00:00 · methodology

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Reference graph

Works this paper leans on

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