Scientific progress volume ǀ issue ǀ

ǀ
ISSUE 2 
ǀ
2022 
ISSN: 2181-1601
Uzbekistan
 
www.scientificprogress.uz
 
Page 686
unity of the solution of this problem, which makes it difficult to comprehensively 
analyze the obtained dependencies. Along with this, there is the problem of finding the 
optimal shape and size of the deforming elements that provide the best processing 
conditions from the point of view of simultaneously ensuring the accepted criteria for 
productivity and quality of the surface layer. The urgency of solving this problem is 
obvious. 
Therefore, in order to analyze the influence of the geometric parameters of the 
deforming elements and technological factors of processing on the productivity and 
quality of the surface layer, it is necessary to establish a universal mathematical 
relationship between the design parameters of the deforming elements, the dimensions 
and type of the surface to be machined, the technological factors of processing, the 
geometric parameters of the contact zone and the surface quality of the part during 
processing. PPD. 
Obviously, all the parameters of the contact zone listed above are determined 
through the law of change in the half-width of the contact along its length and the law of 
change in the depth of penetration of the deforming element along the line of maximum 
load, which in turn depend on the radius of the workpiece, the shape and size of the 
deforming element, and also from the depth of its penetration into the part. When 
solving the problem, it is necessary to make some assumptions. 
Theoretical and experimental studies have shown that the deforming elements 
during SPD can be considered sufficiently rigid with an accuracy of several percent. 
This assumption simplifies the development of a mathematical model, since it does not 
require taking into account the elastic deformations of the deforming element for the 
contact geometry. We also assume that there is no seizure between the surfaces of the 
deforming element and the part, the material of the part is elastic-plastic. During 
deformation, the material of the part is continuous and has no gaps, the deforming 
element has a hardness much higher than the workpiece [3]. 
When solving the problem, it is necessary to take into account that the axes of the 
deforming rollers during processing are rotated relative to the axis of the part by the 
angle of penetration and self-tightening. The penetration angle is necessary to create a 
drop-shaped contact, and the self-tightening angle helps to reduce axial forces by 
moving the deforming element along a helical line on the surface of the part, and in 
some cases is used to ensure self-tightening of the tool. 
The difference between the static introduction of a deforming element during 
elastic deformation of bodies with the same mechanical properties and elastic-plastic 
deformation when it rolls along an elastic-plastic surface is that in the first case (Fig. 
2.1, a) the contact is a flat figure, since the bodies are deformed in the same way and 
have practically the same mechanical properties. In the second case (Fig. 1), a 
deforming element with a high hardness is introduced into the part to a certain depth, 

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SCIENTIFIC PROGRESS
VOLUME 3