**INTRODUCTION**

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**1. The physic-mechanical phenomena in lubricated contact**

The elastohydrodynamic theory of lubrication explains the phenomena occurring in the field of contact of two elastic bodies, divided by a thin layer of a liquid and moving one concerning another. Such contact we will name EHD contact.

The EHD theory of lubrication differs from the classical hydrodynamic theory of lubrication that considers normal and tangents displacements of moving surfaces of elastic bodies of any form, the viscoelastic and thermal phenomena in a liquid and in bodies, strong dependence of viscosity of a liquid on pressure and temperature, a condition of the limited lubrication. Taking into account of these factors allows to define with reliability the basic characteristics of contact - a thickness of a lubricant film, stresses, temperature and to enter them into calculation technical EHD systems while the classical theory of lubrication gives errors on one or several orders.

On the basis of calculation recommendations for choice materials and geometry of details of mechanisms and devices, a kind and a way of lubricating, processing of surfaces, refrigerating conditions and installation, a lubricating mode can be made. Settlement formulas and algorithms of EHD theory can form a basis for machine designing of mobile connections.

As a rule, lubricated contact works in extreme conditions. Pressure reaches values, shear rate has an order, the temperature reaches and above, and the temperature gradient reaches values. Time of passage of a particle of lubricant through contact area usually is little. All it creates difficulties for construction of the theory and experiment statement. Apparently, on one experimental installation, except the installations reproducing direct working conditions of rolling-sliding contact, it is impossible to provide all characteristic values for mechanical and thermodynamic parameters of contact. Therefore mathematical modeling of EHD processes, analytical both numerical research of models and comparison of results with experiment are the most effective and fundamental approach to the decision of problems of EHD lubrication.

In EHD rolling-sliding contact lubricant moves together with surfaces of bodies and is involved in a gap between them. The big contact pressure deforms bodies and increases area of a gap and in a stationary case does its almost plane-parallel.

When lubricant pressure increases from atmospheric to maximum value the viscosity of lubricant increases many times. Near to outlet of EHD contact the backlash decreases, and lubricant encounters the big resistance to an exit from the narrow slit almost closed from different directions, except that, whence lubricant arrives. As a result in the field of contact the lubricating film of a considerable thickness is formed.

The form of gap, pressure distribution and film thickness can be defined experimentally, as a result of numerical decision of the EHD equations or the approached methods. The film thickness received by any of these ways, approximately on an order surpasses a thickness calculated under the usual hydrodynamic theory of lubricating for rigid bodies and a liquid of constant viscosity.

Sliding and considerable gradients of pressure in contact lead to the big shear rate in lubricant. The thermal emission from shift raises lubricant temperature on tens degrees and increases temperature of bodies near to contact. The field of temperatures in the field of contact can be found in result of the joint decision of the equations of movement and energy in lubricant and the heat conductivity equations in bodies.

The big shear rate, high pressures and small times of process lead to difficult behavior of lubricant, in particular to viscoelastic effects. The joint account of thermal processes and complicated rheological behavior of lubricant is necessary for estimation and at least the approached calculation of pressure and temperature in contact. The classical theory of lubrication which are not considering specified factors, and decision of HD problems for Newtonian liquids lead to tensions in lubricant, more than on an order different from the experimental.

**2. Scopes of the theory and limits of its applicability**

** **The EHD theory of lubrication can be applied at calculation and designing, and also at the analysis of damages of those mechanisms and devices in which there are mobile lubricating contacts to the big contact pressure. Practically it concerns almost all areas of technics. Materials of contacting bodies are steel and other metals, polymers. Lubricants are also various - usual technical oils on the basis of mineral and synthetic oils, water, liquid metals, glass bath etc.

The widest scope of the EHD theory of lubrication is rolling bearings and gearings. Rolling bearing calculation includes definition of its dynamics and kinematics, a thickness of a film in contacts, corners of contact, rigidity, the moment of resistance to rotation, forces of interaction of a separator with rolling bodies and of some other characteristics. It is a challenge about definition of movement of many bodies in the diphasic environment. It cannot be solved traditional methods without application of the EHD theory.

EHD calculation of gearings should give a film thickness and pressure distribution in contact of teeth, a field of temperatures in a zone of contact and to lead to an estimation of durability and well-founded criterion of jamming.

Heavy-loaded sliding bearing also is inexpedient to count on the basis of the classical theory of lubrication. The account of deformations of surfaces and dependence of viscosity of lubricant on pressure is necessary.

Applications of the EHD theory in the biomechanics (joints, movement of bodies, for example erythrocytes, in the liquid environment on elastic channels) are interesting.

Among other applications - consolidations, friction gears, persistent crests of cogwheels, mobile spline connections, guides of various types, front contacts of rollers.

From the resulted variety of scopes of EHD theory of lubrication follows that its calculations and recommendations have general technical character. Universal calculation of a film thickness concerns any mobile lubricated contact, irrespective of the mechanism and friction unit in which it is available.

As basis for calculations the uniform mathematical apparatus serves. The equations describe movement of a thin layer of a liquid, contact deformations and a field of temperatures in a contact zone.

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