On the flash temperature in sliding contacts

Abstract

The temperature increase in the contact regions between solids in sliding contact can easily reach several hundred Kelvin and thereby dramatically affect friction and wear. The classical theories by Jaeger, Archard, and Greenwood, commonly used to estimate flash temperature, ignore the multiscale nature of real surfaces and instead approximate the frictional heat sources with circular or square shapes. Here, we present an analytical theory for the flash temperature valid for randomly rough surfaces with roughness across arbitrarily many decades in length scale. The theory extends established methods for stress correlation functions and peak stresses to temperature. Numerical results for rubber sliding on concrete, and granite on granite, are presented as illustrations. We show that classical theories for flash temperature fail severely for surfaces with multiscale roughness.

Figures (21)

• Figure 1: The temperature on the surface of a semi-infinite solid with a periodic set of heat sources, where each unit cell contains four circular heat sources of constant intensity. Different panels show the heat distribution at various sliding stages. Top row is for $vR/D=20$ and bottom row for $vR/D=0$, where $D$ is the thermal diffusivity.
• Figure 2: Temperature increase at the center point of a microasperity: absolute increase (full, red line), relative to the mean surface temperature (dashed, green line), and relative to the asperity's annulus (dash-dotted, blue line).
• Figure 3: Temperature increase at a surface point as a function of time: absolute increase (solid red line) and increase relative to a reference stripe containing the centers of two circular heat sources (dash-dotted blue line).
• Figure 4: The surface roughness power spectrum of the concrete surface used in the present study. The fitted spectrum was employed in the numerical calculations to eliminate non-monotonic artifacts in the correlation functions that would otherwise be induced by stochastic scatter in the raw data.
• Figure 5: The mean square temperature fluctuation $\langle T^2 \rangle$ as a function of the sliding speed (log-log scale). The results are for an elastic solid with Young's modulus $E=14 \ {\rm MPa}$ and Poisson ratio $\nu = 0.5$ sliding on a rigid concrete surface. The following parameters were assumed: nominal contact pressure $\sigma_0 = 0.1 \ {\rm MPa}$, friction coefficient $\mu = 1$, mass density $\rho = 1000 \ {\rm kg/m^3}$, specific heat capacity $c_{\rm p} = 1000 \ {\rm J/kgK}$, and thermal conductivity $\kappa = 0.1 \ {\rm W/Km}$.