Friction-Heating Maps and Their Applications
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friction-Heating Maps and Their Applications
Bulk Température Tb The bulk température, Tb, is the température that would appear at the surfaces if the frictional heat was injected uniformly across the nominal contact area A„; it can be thought of as the average surface température. For ail geometries, it can be written
H.S. Kong and M.F. Ashby
Introduction Friction is of ten a nuisance, but it can be useful too. Brakes, clùtches, and tires rely on it, of course, though the inévitable frictional heat remains a problem. Other applications use frictional heat: friction cutting and welding, skiing, skating, and curling. The damage to magnetic disks caused by head-disk contact and the striking of matches are also examples. This article illustrâtes a framework where the thermal aspects of friction can be analyzed in an informative way. It uses a unified approach to the calculation of flash and bulk heating,1 and a helpful diagram—the frictional température map— to display the results. The method is approximate, but the approximations hâve been carefully chosen and calibrated to give précision adéquate to most tasks, and the gain in simplicity is great. The symbols used in this article are defined in Table I.
Vu,
script 2. Solid 1 can hâve properties which differ from those of solid 2. There are two températures of interest. The first is the mean or bulk surface température Tb: it is the surface température that would be reached if the frictional heat was injected uniformly across the nominal contact area A„, and it is a good approximation to the température a few tens of microns below the actual surface. The second is the local or flash température Tf; it is higher than Tb because the heat, in reality, enters the surfaces at the small asperities where contact is actually made. The analysis, drawing on ideas and resulting from numerous previous studies,2"18
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where T0 is the température of the remote sink to which the heat flows, k\ and k2 are the thermal conductivities of the material of the two surfaces and /lb and /a, are two lengths. The complexity of the problem is contained in the lengths /«, and /a,- They measure the équivalent linear heat-diffusion distance for surfaces 1 and 2. Heat can be lost by conduction, by convection, and by radiation. In almost ail dry-sliding tests, conduction is found to dominate. But the équivalent lengths /R, and /a, still cannot simply be equated to obvious physical lengths, such as lu shown on Figure 1 (the real linear distances from heat source to heat sink). The équivalent lengths do dépend on thèse, but also on the geometry of beat f low (linear, radial, etc.), on whether
F
SINK CONTACT 1 PROPERTIES A c ,,h c ,
Equations for Surface Température When two contacting solids 1 and 2, pressed together by a normal force F, slide at a relative velocity v and with coefficient of friction fi, heat is generated at the surface where they meet. The heat generated, q, per unit of nominal contact area, A n, per second is
PIN : PROPERTIES H, ,k, .a, DISK = PROPERTIES M2 »k 2>^2
Th
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