Nonlinear thermodynamic model of boundary friction

Abstract

Abstract-Melting of an ultrathin lubricant film confined between two atomically flat surfaces is studied. An excess volume parameter is introduced, the value of which is related to the presence of defects and inhomo geneities in the lubricant. Via minimization of the free energy, the Landau-Khalatnikov kinetic equation is obtained for this parameter. The kinetic equation is also used for relaxation of elastic strains, which in its explicit form contains the relative shear velocity of the rubbing surfaces. With the numerical solution of these equations, a phase diagram with domains corresponding to the sliding and dry stationary friction regimes is built at a fixed shear velocity. A simple tribological system is used to demonstrate that in the dynamic case, three friction regimes can occur, namely, dry, stick slip, and sliding friction. It is shown that a lubricant can melt when the shear velocity exceeds a critical value and with elevation of its temperature. The dependence of the dynamic friction force on the pressure applied to the surfaces, the temperature of the lubricant, and the shear velocity is considered. It is shown that growth of pressure leads to the forced ordering and solidification of the lubricant.

Зв’язок Між Параметрами Порядку Модуляції Густини І Надлишкового Об’єму При Описі Стаціонарних Структурних Станів Межового Мастила

“…While describing the phase transition of the second order, the expansion of the free energy in a power series in the excess volume order parameter 𝑓 is based on an ideology proposed in works [26,27] and has the form 1 [17,33]…”

“…with the positive expansion constants 𝜆, 𝜇, 𝜑 * 0 , λ, μ, 𝛼 ′ , and 𝜑 1 . The first and second invariants of the strain tensor in expression (15) are given by the formulas [17,27,34] (see Appendix A)…”

“…The specific features of phase transitions of the first order were studied by us in works [23][24][25] in the framework of the ideology proposed in works [10,18,19]. In particular, we have developed an approach in which the excess volume 𝑓 arising, when the lubricant melts owing to the structure randomization of the solid body [26,27], is used as an order parameter. The advantage of this approach consists in that it explicitly involves the influence of an external load on the friction surfaces, which is introduced via normal external stresses −𝑛.…”

“…As the magnitude of 𝑛 increases, the excess volume 𝑓 decreases owing to the compression of the lubricant layer by the confining walls. Two approaches were considered: the asymmetric [27] and symmetric [26] expansions of the thermodynamic potential. The former case describes the phase transition between two non-zero values of the excess volume 𝑓 .…”

Thermodynamic Theory of Two Rough Surfaces Friction in the Boundary Lubrication Mode

“…4b shows a different behavior. Here, according to (23), at increase in velocity the total friction force at first grows due to the increase in the viscous stresses σ v , and because of the increase in the elastic component of F caused by the increase in the elastic component of strain (10). However, the shear modulus decreases with growth of velocity leading to reduction of the elastic component of force F .…”