MATHEMATICAL MODELING OF CONTINUOUS METAL BEHAVIOR WITH DEFECTS OF MACROSTRUCTURE IN THE ROLLING PROCESS The mathematical model of the process of rolling a continuous cast billet with defects of macrostructure on a smooth barrel and in calibers is presented. The boundary conditions are given by the speed of rotation of the rolls, the restriction of degrees of freedom of the workpiece and the rolls, as well as the coefficient of friction on the contact surface of the rolls-workpiece. For hot rolling, it

The mathematical model of the process of rolling a continuous cast billet with defects of macrostructure on a smooth barrel and in calibers is presented. The boundary conditions are given by the speed of rotation of the rolls, the restriction of degrees of freedom of the workpiece and the rolls, as well as the coefficient of friction on the contact surface of the rolls-workpiece. For hot rolling, it was considered permissible to consider rolling rolls as a rigid, non-deformable rigid body. For the workpiece material used an elastic-plastic model of environmental behavior. There have been two cases considered: rollerless rolling on a smooth barrel and rolling in rectangular caliber. The roll material is steel, the surface is smooth. On the example of rolling in the first pass of the crimp mill, a comparative analysis of caliber rolling and rolling in calibers was carried out. It is shown that rolling on a smooth barrel has the potential to be used in the case of rolling continuous casting with macrostructure defects. The influence of the basic rolling parameters: absolute compression and temperature on the "healing" of macrostructure defects is made.


Problem's Formulation
In conditions of constant technological innovation and globalization of markets in front of enterprises, rolled metal manufacturers the problem of increasing production efficiency and ensure competitive products in demand quality. The use of continuous cast billets (CCB) of small cross section revealed a number of problems that did not previously occur with using hot rolled. In the greatest degrees this is typical for cases of production long products from quality structural and spring-spring brands steels. Formulation of the problem. CCB defects formed during solidification and may to develop both inside the cast billet and on outer surface.

Analysis of recent research and publications
In most cases defects have a negative effect on production causing rejection or increase production costs as a result the need to bring blanks in line with the required specifications before they by rolling. Defects expending on the cause can be divided into two groups [1][2][3]: -defects specific to a particular streams (found only on one stream due to hardware problems or its settings, for example, due to mold defects, irregularities secondary cooling, improper settings pulling and ruling rolls, etc.); defects specific to a particular swimming trunks (associated with the properties of liquid steel and caused by overheating, the presence of impurities, deoxidation at the stage of out-of-furnace steel processing). In relation to production conditions metal rolling from CCB obtained in conditions: -high-speed varietal caster with small bending radius, average figures of marriage by type have the form: violations of the geometry of the CCB -36.4%; -macrostructure defects -17.2%, cracks 31.9%; -slag inclusions -4.5% [2]. On many axial porosity is observed in the templates segregation strips and cracks, developed columnar structure and asymmetry of the ingot zones. In this regard, questions related to the study the behavior of defects in the macrostructure of continuously cast billets (shrink shell, gas bubbles, axial porosity) in the process deformations are relevant following the behavior of these defects in recently widespread mathematical (computer) methods simulation using software complexes like ANSYS, DEFORM, QFORM, PLAST, etc. in which modeling carried out using the finite method elements. Moreover, the variety of processes in each case requires its own approach to modeling techniques. So in [3,5] presented the results simulation of cutting and screw rolling processes solid blanks in the software package Deform-3D. We studied the effect on the depth of the weight work piece diameter, feed angle, roll calibration crimp mill, as well as the original shape of the ends blanks. In [4], a mathematical simulation of the process of screw firmware blanks large diameter. The aim of the work was to study with using the Deform-3D software package such parameters as a stress-strain state.
In [4], mathematical modeling of the process of screw-piercing large-diameter workpieces was carried out. The aim of the work was to study using the Deform-3D software package such parameters as the stress-strain state metal, the accumulated deformation in terms of the volume of the workpiece, the nature of the development of the deformation, power parameters, firmware time, etc.
Of great interest is the work [5][6][7] in which mathematical modeling of the process of metal deformation in calibers of various shapes was carried out. During the study, the influence of the stressstrain state on the flow of the deformed metal in various zones of high-quality calibers, depending on their shape, was analyzed. For modeling, the Deform-3D software package was also used. In [6], the problems of calibration design were studied in order to reduce energy consumption and reduce the likelihood of defect formation.
Thus, the aim of the work was to develop a mathematical model and conduct research into the behavior of defects in the macrostructure of continuously cast metal during rolling.
Formulation of the purpose of the study For mathematical modeling of the behavior of macrostructure defects during rolling, a computer simulation software package using the Deform-3D finite element method was used.
The rolling process is quite complicated for modeling since it combines the rotational movement of the rolls and the translational motion of the workpiece. To obtain correct results, it is necessary to accurately position the workpiece relative to the rolling rolls and take into account the