Özet:

The analysis of complex stress-strain state of the metal during rolling was performed and many assumptions and contradictions that affect the accuracy of the theoretical calculations were identi­fied. Such simplifications and contradictions in the modern rolling theory make the rheological concept problems urgent. To determine the metal flow when rolling - laminar or turbulent, it is necessary to define the Reynolds and Froude numbers for identifying the heat transfer type in the deformation zone using the Peclet and Prandtl numbers. This will help to choose a model for calculating stresses and strains. The most characteristic rolling modes, which are used in both hot and cold processing were highlighted. The studies were conducted on slabbing, sheet rolling mill, cold rolling mill of the thin sheet. Draughting schedules and processing temperature were varied on this equipment. Theoretical analysis and experimental verification of the hypotheses adopted and the results obtained was used. The theoretical research was based on fundamentals of continuum mechanics, plasticity theory, methods of solving dynamic problems of elastic-plastic deformation. For determining the metal properties in the deformation zone, Reynolds, Froude, Peclet and Prandtl numbers were used. The obtained values of the Reynolds and Froude numbers confirm the process modeling theory in the fact that at large values of these numbers, inertia plays a major role in the cold rolling processes, and at small – during hot rolling – viscosity and friction. Reynolds numbers show that the metal flow in the deformation zone is laminar, rather than turbulent. Peclet numbers have indicated the possibility of molecular thermal conductivity, but convective heat transfer prevails. Prandtl numbers prove that the viscous medium model should be used in the rolling process simulation since this value is greater than one. The research results allow to more accurately determine the internal stresses of the metal and energy transfer during rolling. Studies of the deformation zone by the Froude and Reynolds numbers indicate that the metal flow in it is laminar, the values of the Reynolds and Froude numbers are the most affected by temperature and pressure through the value of viscosity or yield strength. Investigations have shown that the deformation zone should be considered as a continuous viscous medium that obeys the Newton’s laws and formulas of viscosity. The research allows to perform more accurate calculations of stresses and strains that occur in the deformation zone during rolling and heating of the metal.  Author Biographies Николай Николаевич Бережной, State institution of higher education «Kryvyi Rih National University» 11, XXII Partz’yizdu str., Kryvyi Rih, 50027, Ukraine Doctor of technical science, Associate Professor Department of Metal pressure working and materialoznavstvo

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