Thermal matching of coating-tool materials to optimize dry machining of steels is an interesting idea. Grezesik et al. find that the thermal properties of the materials involved, namely, the thermal diffusivity and the thermal conductivity, control the thermal and tribological behavior outputs of the machining process. Such a finding has been detailed in the discussor’s own work when studying dry sliding of metallic contacts 1,2, however, the physical interpretation of the contact parameter b in the manuscript is not apparent.

The parameter b is originally given by: b=KρC1/2 where K is the thermal conductivity, ρ is the mass density, and C is the specific heat. In this form, the contact coefficient b represents the interaction between the injection of frictional heat normal to the surface of contact and the thermal storage of the bulk material. Now recasting the contact coefficient to the form b=KD1/2 is perhaps more revealing of its physical significance. Note that in this form, b represents the interaction between the speed of heat injection through the surface and the speed by which the heat spreads through a given area. Now, the diffusivity will attempt to homogenize the distribution of heat throughout a given area of the material, thus attempting a uniform distribution of temperature. The conductivity, on the other hand, will attempt to inject heat normal to the contact surface. Thus, the parameter b represents a balance between heat injection and heat distribution, that is, b is a measure of heat intensity at the contact spot. Perhaps more indicative of the physical role of the parameter b is the term “coefficient of heat penetration” 3 or thermal effusivity, which indicates another physical attribute of transient thermal transport between sliding contacts. The effusivity plays a detrimental role in the evolution of heat transfer in sliding as it represents the effects of thermal inertia on a medium. In two contacting materials, the material with higher effusivity will resist the penetration of the thermal flux. Whereas the material with lower effusivity will allow deeper penetration. As such, the ratio of the effusivity of two conducting materials (such as the coating and the substrate) will influence the thickness of the thermal layer and, thereby, the dissipation of the heat flux generated in machining. Moreover, the rate of change in the effusivity will affect the rate of change in the depth of thermal penetration and, thereby, the growth of the temperature gradient. The ultimate effect will be the creation of a thermally supersaturated layer 4 that controls the quality of the machined surface and tool wear.

While the generation of heat flux in machining is not directly linked to the variation in the thermal conductivity, conduction of heat away from the surface is linked to that variation. The variation of the thermal conductivity, along with the evolution of the temperature gradient, will affect the partition of the generated heat among the tool-coating assembly, the work piece, and the chip. That is, the thermal loads on each of the previous components will follow the change in the conductivity. An increase in the conductivity will lead to a corresponding increase in the heat conducted to either the work piece or the tool. If such an increase is associated with a decrease in thermal diffusion, the intensity of heat will increase locally. This will reduce the material flow stress and, therefore, frictional stress.

The notion that the contact length can be effectively used for the control of heat flux and temperature at the interface was based on the temperature dependence of the thermal number Pec. It seems that the authors have avoided the physical interpretation of that number. Figure 5 of Grezesik’s paper shows a delay in reaching the maximum temperature at higher thermal numbers. This is due to the dominance of convection, which helps cooling the interface. Thus Fig. 5 suggests that the rate of temperature rise and not the temperature (and thereby thermal property variation) may be controlled by controlling the thermal number. However, this may prove difficult to achieve, as the thermal number is not a process parameter.

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Grigull, U., and Sandner, H., 1984, Heat Conduction, Hemisphere, New York, International Series in Heat and Mass Transfer.
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