Discussion: “An Application of Dimensional Analysis to Entropy-Wear Relationship,” (Amiri, M., Khonsari, M. M., Brahmeshwarkar, S., 2012, J. Tribol., 134 , P. 011604)

Abstract

The authors present an interesting thermodynamic interpretation of the Archard wear coefficient. However, their interpretation is confined to the steady state. The purpose of this discussion is, first, to extend the domain of the authors’ derivation to the entire regime of rubbing (running-in to steady state), and, second, to point out a possible thermodynamic functional interpretation of wear rate resulting from the current derivation. The starting point is to represent the hardness of the material as a linear function of the melting temperature Tm , viz: Display FormulaH(T)=Ho[Tm-TTm]=Ho[T′Tm] (1) Where T′ is the difference between the melting temperature and the temperature rise above ambient, T. Here T′ represents a degradation metric that indicates how close the material is to reach the energy barrier needed to degrade the volume active in rubbing from a solid to a liquid state. Substituting Eq. 1 in Eq. (A4) of the authors’ work, and following the authors’ method, we obtain: Display FormulaK=wo[μH(T)TSo+μ(l.N)To/T′] (2) The term To in Eq. 2 represents the time rate of change in the temperature rise above ambient. This quantity is a vanishing function in time, and at steady state, the temperature reaches a constant value that does not depend on time, i.e., To{=0 steady state< 0 running-in Equation 2 expresses a ratio between two fundamental quantities: the energy barrier to be overcome for complete degradation of the solid state of the active volume, and the net heat transferred away from that volume. The net heat transfer is the balance of the heat transfer (TSo ) and the maximum possible amount of work extracted due to the temperature difference between the various parts of the active volume (i.e., the term μlNTo/ T′). This later quantity may be considered as leakage from the heat flux transferred out of the active volume. It is of maximum value at the start of running-in and zero at steady state. At steady state, considering the contact is under constant pressure, the heat transfer will equal the enthalpy of the active volume. Thus, Display FormulaK=wo[μH(T)E] (3) K in this formulation is interpreted as the ratio of the total energy needed to degrade the wear volume to the enthalpy of the active volume. Noting that To decreases during running-in, Eq. 2 may be recast in terms of the first law, viz: Display Formulawo=K[Q-w′u]≡KΔuu (4) with u being the internal energy per unit volume.