Specific Friction Force in a Graphite Brush Contact as a Function of the Temperature in the Contact Spots

Measurements by different workers have indicated that the friction coefficient μ of a graphite brush contact decreases with rising contact temperature T. If P = mechanical load, A_b = load bearing area and F = friction force, the average pressure is p̄ = P/A_b and the specific friction force ψ = F/A_b. Hence μ = F/P = ψ/p̄. It will be shown in this paper that the measured μ(T) effect during smooth sliding is caused by the decrease of ψ with rising T. The specific friction force is a function of the character of the sliding surface alone, and μ is, in addition, a function of the actual pressure in A_b. It is shown that sliding, after a relatively short time, leads to a stage during which A_b, thus also p̄, remains practically constant for more than 10 hr. The (μ,T) test begins when such an ``initial stage,'' defined by μ=μ<sub>0</sub>, T = T<sub>0</sub> and constant contact voltage U, has been reached. It involves T increasing above T<sub>0</sub> and then decreasing to T<sub>0</sub> again, whereby the time of the test is short enough for constancy of p̄. During a perfect (μ,T) test, the forward and reversed curves agree with each other indicating that A<sub>b</sub> has remained constant. For all sliding stages with constant p̄, the relationship mentioned above can be written: μ(T) = constψ(T), which makes it possible to study ψ as a function of T by studying μ as a function of T. The decrease of ψ with rising T is explained by assuming that adherence bonds in A<sub>b</sub> are broken or loosened by T according to a probability exp(−φ/kT) = exp(−11600 φ/T) with φ in ev. The measured, strong dependence on T results from the activation energy φ=0.07 to 0.1 ev between the graphite ``platelets'' being of the order of kT. Hence it is expected that μ and ψ are inversely proportional to the probability factor. It was found that at constant A_b up to about 500°K (the upper limit measured): $$\frac{\mathrm{\psi (T)}}{{\mathrm{\psi (T}}_0)}=\frac{\mathrm{\mu (T)}}{{\mathrm{\mu (T}}_0)}=\exp \left[{11600}_{\mathrm{[open\; pi]}}\left(\frac{1}{T}-\frac{1}{T_0}\right)\right]$$ gives a very good agreement in the case of graphite members when the binding energy is assumed to be φ=0.09 ev. For these contacts, ψ decreases from 0.12 to about 0.065 ton/cm²; simultaneously μ decreases from 0.13 at 115°C to 0.07 at about 200°C. This has been found at atmospheric air pressure with dew point about 279°K and also in vacuum of 10⁻⁴ mm Hg with dew point about 75°K. With a copper and gold ring at atmospheric air pressure, the (μ,T) curves have a somewhat steeper slope and agreement with theory requires ψ=0.12 or 0.10 ev, respectively. At temperatures of about 500°K, μ and ψ decrease very slowly and may reach a lower limit at temperatures when the chemisorbed gases on the graphite platelets begin to evaporate.