Scientific progress volume ǀ issue ǀ

ǀ
ISSUE 2 
ǀ
2022 
ISSN: 2181-1601
Uzbekistan
 
www.scientificprogress.uz
 
Page 687
the value of which is determined by the magnitude of the applied force, the dimensions 
of the deforming elements and the mechanical properties of the deformable surface. Let 
us calculate the deformation of the deforming element when it is compressed by two 
opposite forces. The decrease in the diameter of a cylindrical deforming element located 
between two faces compressing it, taking into account contact and general 
deformations, is determined by the formula [4]. 
√
where P-forces acting on the roller from opposite sides; 
μ
-Poisson's ratio; E-
modulus of elasticity; D
p
-diameter of the squeezed cylinder 
Rice. 1 Features of deformation of two cylindrical bodies: a) - with identical 
elastic properties of bodies, b) - with elastic-plastic deformation of a part by a solid 
deforming element 
The results of calculations using this formula are shown in the graphs (Fig. 2). The 
relative deformation of the rollers when they are loaded depends little on the diameter, 
but only on the loading force and does not exceed 3% at the maximum values assigned 
under production conditions (up to 30 kN). Consequently, the deforming element during 
SPD can be assumed to be sufficiently rigid and the change in its radius during 
deformation can be ignored. 
This makes it possible to estimate the deformation of only the roller itself. As can 
be seen from the presented results, the deformation of the roller is insignificant, 
therefore, as stated in a number of literary sources, the deforming roller in analytical 
calculations can be taken almost rigid, that is, when determining the geometric 
parameters, its deformation cannot be taken into account. 
Since all parameters of the contact zone: maximum length, width, contact area, 
volume and surface area of the contact zone are determined through the law of change 

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