Education of the republic of uzbekistan tashkent state technical university named after islam karimov

Figure-2. Physical model that demonstrates the initial angular displacement of a stationary 
wheel relative to the rail under the influence of torque 
It is known that inertia distinguishes frictional force and sliding frictional force. Quiet, 
motionless friction is usually understood as its maximum value, the excess of which causes the 
sliding of objects in contact with each other. At smaller values, we call it the non-frictional force 
of rest. At rest, the occurrence of an incorrect or complete frictional force causes the initial 
displacement of the contacting objects. When other conditions are maintained, the magnitude of 
the initial shear increases with increasing magnitude of the frictional force. 
The value of the coefficient of friction in the quiescent state increases with increasing 
exponential law according to the approximate exponential law. This is due to the fact that the 
actual contact area increases with increasing elasticity, and primarily due to plastic deformations. 
According to modern friction theory, in the sliding of an object, in other words, at their 
frictional contact, auto-vibrations of molecules occur, as a result of which the stationary state of 
the contact is continuously alternated with the excited state. In this process, existing relationships 
are constantly changing and disintegrating, and new relationships are emerging. The frictional 
force that occurs in the stationary state of the contact at rest is much greater than the frictional 
force at the moving contact. 

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Mechanical Engineering
233 
In fact, we take the sliding friction force as its average value over the period of auto-
vibrations. This means that the longer the contact is stationary, the greater the sliding friction 
force [6]. 
The following events occur when the rate of mutual displacement of objects increases: 
- the duration of the stationary contact is reduced; 
- the temperature of the contact rises and the contact surfaces come into contact, which, 
under certain conditions, can cause the actual contact surface to enlarge or shrink. 
Sliding of the wheel along the rails can be complete and inaccurate. In the case of 
improper sliding, in one part of the contact spot there may be a rolling between the wheel and the 
rails, and in another - slipping between their contact fibers. In nonlinear slip, adhesion forces 
develop similar to nonlinear (or boundary full) frictional forces in the quiescent state. Slippage in 
this case is the result of the initial displacements of the objects in contact with each other, which 
occur continuously and then disappear, held by the frictional forces at rest. 
When the wheel slides completely along the rail, this sliding process affects all the fibers 
of the contact spots. 
Especially misaligned slippage requires special study. Lorentz's theory is more in line 
with modern theories about the nature of dry friction than theories that explain the course of this 
process [6]. 
According to this theory, the length of the rolling zone is assumed to be equal to the 
width of one conditional fiber, in the flat scheme (Fig. 1) this area is represented by a single 
point. The coefficient of friction in the entire contact spot zone maintains a constant value of a. 
Its size is from 0 to

0

, the external torque, which varies up to the coefficient of friction at rest 
depending on 
к
М
.
The specific shear load on the contact spot element is equal to the product of 
q
the specific normal load and the coefficient of friction:
q




(1) 
Thus, according to this theory, the flat plot of the specific experimental load remains 
elliptical in all modes [7]. 
According to experimental data, the rate of sliding motion in the study of the dynamic 
processes of crawling and sliding from the description of the coupling 
v
and the vertical load 
falling from the wheel to the rail 
Р
the coefficient of adhesion of the wheel to the rails at smaller 
variations 

and the ratio between the slip velocity v is considered sufficient by the condition 
itself that it is determined by a single functional relationship.
The maximum value of the coupling coefficient that remains constant at small variations 
in the sliding speed is called the potential value of the coupling coefficient [8, 10], in this case 
.
.
0
уст
м ак



.
Today, it can be said that under other equal conditions, the value of ψ
0
decreases slightly 
with increasing velocity v, and this can be explained by a decrease in the duration of the 
stationary contact [10]. 

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