Demystifying flash temperatures I. Analytical expressions based on a simple model

Abstract

Equations by which flash temperatures at contact spots may be calculated in a straight-forward manner are presented and partly derived for the first time. They apply to arbitrary speeds and elliptical contact spots with axes A and B = A/ e in sliding direction and at right angles thereto, for cases in which (i) heat is evolved at the mathematically flat interface, (ii) the two materials are free of surface films and (iii) the two materials have the same temperature. With the characteristic dimension r = (AB) 1 2 /2 , with q the rate of heat input per unit area of contact spot, and with λ 1 the thermal conductivity of the substrate (side 1), the average value of the temperature increase at the interface is ΔT = f( Z, S) ΔT 0 where ΔT 0 = ( π/4) qr/ λ 1 is the value of ΔT for a circular contact spot at rest when the asperity (side 2) is an insulator. f( Z, S)⩽1 expresses the reduction in flash temperature due to motion (via the velocity function Z( ν r), due to ellipticity (via the shape function S( e, ν r)) and due to the finite heat conductivity of the substrate ( via λ r = λ 2/ λ 1). The velocities are expressed in terms of the relative velocities ν r = ν/ ν 0 where ν 0 = κ i / r with κ 1 the heat diffusivity of the substrate and κ 2 the heat diffusivity of the asperity side. In general, for a contact spot moving relative to both sides, ▪ and, to within about 3%, Z(ν r <2)= 1 1+ν r /3 ▪ ΔT max, the maximum value of the flash temperature at the interface, is about one-third larger than ΔT, i.e. ΔT max = (4/ π) ΔT for ν r ≪1 and ΔT max = 1.42 ΔT at high relative speeds. In the accompanying paper, Part II, the equations are applied to friction heat at plastically deformed contact spots and numerical values are presented which permit quick estimates to be made of the flash temperature in a wide range of cases. Also a more realistic model of the contact spot is considered in Part II, and an upper limit of the flash temperature which follows therefrom.