ANNOTATION

to the report of prof., Y. Vasilev on the topic: "Model of friction stresses is the main unsolved problem in the modern theory of longitudinal rolling"

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During longitudinal rolling, all the energy for reducing the strip with the rolls is transferred by the frictional way and the theoretical determination of the process parameters depends solely on the accuracy of description, thorn stresses, i.e. on the accuracy of the friction stress model. It is shown that the friction stress models used in the modern theory of longitudinal rolling are physically unjustified, by the essence of the assumptions, and are distinguished by low accuracy and insufficient reliability, which gives grounds to qualify the published theoretical solutions as approximate.

Due to the lack of a correct model of friction stresses in the modern theory of longitudinal rolling, there are no solutions for determining the torque by friction forces, there are many controversial positions (dividing the deformation zone into three kinematic zones, the conditions for "Coefficient of plastic friction", etc.) and erroneous ideas about the process parameters ("rolling with a negative advance", "solid sticking zone", "the presence of two neutral sections in the deformation zone", "Amonton's law" in the form 𝜏 = 𝑓𝑝, “ coefficient of friction at the point "), etc. Therefore, the creation of a physically substantiated and reliable model of friction stresses during longitudinal rolling is urgent.

The proposed work is devoted to the creation of such a model in relation to the conditions of rolling thin strips. In the new model, for the first time, the influence of the features of the kinematics of the deformation zone was taken into account, which contributed to an increase in its accuracy and made it possible to predict the direction of the vector of friction stresses. The joint solution of the differential equation for the equilibrium of longitudinal forces during longitudinal thin-sheet rolling with a new model of friction stresses by the numerical method made it possible to obtain new scientific results, which constitute the basis on which a physically substantiated and reliable modern theory of longitudinal rolling can be developed, reflecting the features and regularities of the frictional interaction of rotating rolls with a strip. The results of these studies are presented in detail in the report and reflected in the conclusions of the work.

 

CONCLUSIONS

1. It has been established that the friction stress models used in the modern theory of longitudinal rolling are excessively rough, physically unjustified, essentially assumptions and are characterized by low accuracy, which gives grounds to qualify the published theoretical solutions only as approximate.

2. A new, physically substantiated mathematical model of friction stresses during rolling of thin strips has been developed, taking into account the peculiarities of the kinematics of the frictional interaction of the metal with the rolls, which contributed to an increase in its accuracy and determination of the direction of the friction stress vector.

3. The joint solution of the differential equation of equilibrium of longitudinal forces during longitudinal rolling of thin strips with a new model of friction stresses by a numerical method made it possible to obtain the following new scientific results:

- it was found that the theoretical diagrams of normal and frictional stresses during rolling practically coincide with the experimental ones;

- for the first time, quantitative data were obtained theoretically, confirming that the cross section of the maximum on the diagrams of normal stresses does not coincide with the neutral cross section;

- it is shown that the wedging out of the advance zone occurs at significantly lower values ​​of the parameter 𝛼𝛽 (1.13-1.15 versus 2.0) than it follows from the traditional theory of longitudinal rolling;

- for the first time it was theoretically established that the methods for determining the torque during longitudinal rolling by frictional forces and by rolling force are equivalent;

- a dependence is proposed for the calculated determination of the stress state coefficient during cold rolling of thin and especially thin strips, when the parameter av varies in the range from 4 to 85;

- the method for determining the coefficient of friction by experimental diagrams of contact stresses during rolling has been refined.

4. The results obtained in the course of the work represent a scientific basis on the basis of which a physically substantiated and reliable theory of longitudinal rolling can be developed, reflecting the features and regularities of the frictional interaction of rotating rolls with a strip.