National University of Science and Technology “MISiS” (Moscow, Russia):

V. N. Shinkin, Dr. Phys.-Math., Prof., E-mail: shinkin-korolev@yandex.ru

The proportion of sheet products in the total volume of rolling production in Russia is more than 40%. The constant growth of the volumes of the sheet products is connected with the development of the metallurgical pipe plants, the oil and gas main pipelines, the shipbuilding, the capital construction, the automotive, aviation and electrotechnical industries. The hot-rolled sheet steel is supplied in the rolls and sheets and is divided into thick-sheet steel (sheet thickness is from 4 to 160 mm) and thin-sheet steel (sheet thickness is up to 3.9 mm inclusively). The main reason of the nonflatness of the rolled steel sheets (for example, a waviness of the edges or a camber of the center of the sheets) is the uneven compression of sheets across the rollers’ width of the rolling mills due to the uneven size of the gap between the rollers, which leads to a different size of the extension of sheet’s individual sections — the more compressed sections get a large extension on the sheet’s length than the less compressed sections. The interaction of the residual compressive stresses in the more elongated sections and the residual stretching stresses in the less elongated sections causes a loss of stability of the planar shape of the sheet. Therefore, in the metallurgical plants almost all produced sheet metal (steel sheets up to 50 mm thickness and 5000 mm width) undergoes the operation of a cold flattening in the sheet-straightening multi-roller machines, which is a more productive process compared to a transverse bending on presses and a stretch flattening. At that they achieve a higher accuracy of a flatness of sheets’ surface in the range of 1–3 mm/m. In this paper we propose the mathematical method for determining of the optimal parameters for a cold straightening of a steel sheet from a hot-rolled coil on the fi ve-roller sheet-straightening machine of the cut-to-length line by Spanish company Fagor Arrasate. The calculations allow us to determine the shape and curvature to the neutral axis of steel sheet under flattening, the residual curvature of sheet after flattening and the reactions of working rollers of the sheet-straightening machine depending on the radius of working rollers, the step between the rollers of the straightening machine, the magnitude of sheet’s compression by the upper rollers, the sheet thickness and the young’s modulus, yield stress and hardening modulus of sheet’s metal. The results of the investigation can be used in the metallurgical plants in the production of steel sheets from the hot-rolled coils.

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