The Fundamentals of Sliding Contact Melting and Friction

This paper focuses on the phenomenon of melting and lubrication by the sliding contact between a phase-change material and a smooth flat slider. The first part of the study considers the limit in which the melting is due primarily to "direct heating," that is, to the temperature difference between the solid slider and the melting point of the phase-change material. It is shown that in this limit the relative motion gap has a uniform thickness and that the friction factor decreases as both the normal force and the temperature difference increase. The second part considers the limit where the melting is caused mainly by the frictional heating of the liquid formed in the relative motion gap. This gap turns out to have a converging-diverging shape that varies with the parameters of the problem. As the normal force increases, a larger fraction of the melt is pushed out through the upstream opening of the relative motion gap. Means for calculating the melting speed, the friction factor, and the temperature rise along the slider surface are developed. 1 Introduction The subject of this paper is a most basic phenomenon of combined melting and lubrication that can occur at the inter­face between two solid parts, one of which is at its melting point. One way to visualize this phenomenon rapidly is to think of the kitchen experiment in which a stick of butter is rubbed against a metallic plate, or against a well-polished wooded block. These two situations are, more or less, covered by the isothermal-base and adiabatic-base models presented in sections 3 and 4, respectively. The melting and lubrication phenomenon addressed here has both classical and modern applications. The classical ap­plication is the explanation it provides for the relatively low coefficient of sliding friction on ice and snow. The original ex­planation offered for this observation is due to Osborne Reynolds (1901), who suggested that the liquid film formed between skate and ice is due to "pressure melting," that is, to the fact that the melting point of ice decreases as the pressure increases (Cravalho and Smith, 1981). Careful studies con­ducted over the past five decades have shown that the liquid film is created in fact by the viscous friction in the liquid film itself (see, for example, Bowden and Hughes, 1939; Bowden, 1953; Evans etal., 1976; Oksanen and Keinonen, 1981; Akkok et al., 1987). The theoretical work that has been done on this problem is concerned primarily with the heat transfer pro­cesses external to the relative motion gap, namely, the heat transfer into the ice and into the skate. The analytical models described in this literature are one-dimensional, in the sense that they neglect the spatial (longitudinal and sideway) varia­tions of the heat and fluid flow characteristics over the sliding-contact area. In the two problems considered in this paper, the focus is on the variation of the temperature and velocity fields over the area wetted by the melt. Among the more modern applications of the phenomenon worth noting is the coating of a metallic part with another metal whose melting point is considerably lower. The function of the latter is to melt and serve as lubricant in the manufac­turing process to which the former may be subjected. Another application is in the field of interior ballistics, where a projec­tile (e.g., brass bullet) melts superficially as it travels along the gun barrel (Aung, 1986). A third application—the one that first drew my attention to this phenomenon—is to the subject of "close-contact" melting, which now is receiving increased attention (see, for example, Moallemi and Viskanta, 1986a, 1986b; Prasad and Sengupta, 1987; Bahrami and Wang, 1987). In the close-contact melting problem the relative mo-