The modern technics contains a considerable quantity of friction units. The resource of all mechanism depends on work of friction units. The resource (durability) of a product is understood as term of its service during which product characteristics do not leave admissible limits.

Theoretical basis of calculation of a wide class of units of friction is the theory of lubrication of deformable bodies

Mathematical modeling of process of lubrication of deformable bodies represents an intricate problem which consists in the joint decision of the equations of movement of a lubricant layer, the equations defining deformations of contacting bodies , and also the equations describing distribution of heat , allocated in a lubricant layer at its movement. Generally loading and speeds of movement of bodies change in due course, therefore all processes are non-stationary. Besides the equations the initial and boundary conditions should be set.

On the given site in a short kind substantive provisions of the theory of lubrication are resulted. The basic attention is given to the analysis of the simplest mathematical models of the theory of lubrication. In particular:

One of variants of process of transformation of dry contact of bodies into lubricated contact of bodies is resulted. During the initial moment of time dry contact of bodies is carried out. For definition of parameters of contact the contact problem is solved. Further cylinders under loading start to rotate and lubricant is tightened by surfaces in a gap between them and through some moment of time of surfaces appear divided by a lubricant layer. Evident representation about this process is given by dynamic graphs of a thickness of a lubricant layer and contact pressure which it is possible to look, having clicked here. The mathematical model of this process is described in the short course of the theory of lubrication resulted here.

On one example of external linear contact it is shown, what contribution to a thickness of a lubricant layer is brought by elastic deformation of bodies, and what contribution to it brings increase of viscosity of lubricant at pressure increase. It is shown that the thickness of a lubricant layer can be defined with necessary accuracy only at the account of both specified factors.

It is shown, how the thickness of a lubricant layer and pressure in a lubricant layer change at reduction of speed of rotation of cylinders to zero and the further growth of speed in an opposite direction (reverse movement). At the moment of time when speeds of bodies are equal to zero, the thickness of a lubricant layer can accept high value. Evident representation about character of changing of a thickness of a lubricant layer and pressure in it at reverse movement is given in due course by dynamic graphs which it is possible to look, having clicked here . The mathematical model of this process is described in the short course of the theory of lubrication resulted here.

Characteristic functions of a thickness of a lubricant layer and pressure in it for a case when point contact of the bodies divided by a thin layer of lubricant takes place are presented

On an example of one EHD problem at internal contact of cylindrical bodies it is shown, as the thickness of a lubricant layer and pressure in it in the sliding bearing changes at loading growth.

The example of calculation of the sliding bearing in which for calculation of deformations the spatial problem of the theory of elasticity is solved is presented. For the decision of this spatial problem the finite-element method is used. It is shown that the thickness of a lubricant layer accepts the least value in face sections of the bearing. At certain loading in these sections the contact of surfaces is possible while in the central section the thickness of a lubricant layer can accept high value.

In the resulted short course of the theory of lubrication thermal processes are not considered. It is due to that qualitatively the results does not change at their account. The quantitative values of parameters of lubricated contact change only. However at calculation of real lubricated units of a friction thermal processes are necessary for considering.

The Tribology laboratory is engaged in working out of mathematical models of process of lubrication of friction units, working out of numerical methods of solution of the received systems of the equations, calculation of characteristics of lubricated units of friction, the numerical decision of contact problems of deformable bodies, the numerical decision of contact problems taking into account wear process.