# Mathematical model of force and deformation interaction of strip and rolls during rolling with intense plastic deformation

## Authors

• D. Bohdan
• V. Balakin
• M. Shtoda
• Yu. Nykolayenko

## Keywords:

severe plastic deformation, strip, rolls, mathematical model, mechanical properties, corrosion resistance

## Abstract

The operating conditions of oil and gas pipes determine strict requirements for their structure and properties, in particular, corrosion resistance. It is known that the mechanical properties and corrosion resistance of steels significantly depend on the degree of grinding of the grain and the homogeneity of the structure. One of the ways to form a fine-grained structure, increase mechanical and corrosion properties is intense plastic deformation. In order to determine the effect of intense plastic deformation on the deformation treatment of steel strips, a scheme of a simple rolling process with a blank roller was developed. The possible influence of intense plastic deformation in such a scheme on the structure of the metal required the development of a mathematical model, the purpose of which is to determine the magnitude of the true plastic deformation. Based on the results of mathematical modeling, laboratory experiment in rolling strips and determining their corrosion resistance in the proposed scheme, it is envisaged to develop an industrial installation for processing the inner surface of pipes. The mathematical model of the proposed rolling scheme with a certain value of intense plastic deformation is expected to be described in four stages. The first is to determine the force of pressing the idler roller into the material at a fixed amount of force applied to the lever of the mechanism. The second is to determine the magnitude of the pressure force of the idler roller on the rolled strip and the working roll. The third is to determine the depth of indentation of the roller in the strip at a given load in the absence of rotation of the rolls. Fourth - determining the actual and equivalent degree of deformation of the strip by a blank roller. Conclusion. Comparison of equivalent deformation roller and deformation rollers with a diameter of 180 mm with compression =0,2 мм; =1,15; =0,139 shows an order of magnitude greater deformation of the roller. The mathematical model of the offered way of rolling with intensive plastic deformation is developed, the carried-out calculations give the chance to assume considerable changes of structure of material, reduction of the sizes of grains. The latter should certainly be reflected in the change of physical and mechanical properties of the material, namely the increase of its corrosion resistance and the level of mechanical properties.

## References

Bronstein IN Handbook of mathematics for engineers and students of universities / IN Bronstein, K.A. Semendyaev. - М.: Nauka, 1986. - 544 p.

Dinnik AA Energy and kinematic parameters of the rolling process: Textbook / AA Dinnik. - Dnepropetrovsk: DMetI, 1974. - 85 p.

Thomsen E. Mechanics of plastic deformations in metalworking / E. Thomsen, C. Young, S. Kobayashi. - M.: Mashinostroenie, 1968. - 504 р.

2021-12-10

Статьи