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A method for calculating the modes of strips cold rolling on multiple-stand (reversing) rolling mill is considered providing minimum power consumption with maximum process stabilization at high speeds and obtaining the given quality of cold-rolled strips (minimum probability of surface defects, compliance with thickness tolerances and flatness requirements of the used standards). The problem is solved using the conditional optimization method. As an optimization criterion, it is proposed to use the total energy expenditure spent on the rolling process, as conditions – technological and structural limitations on the rolling parameters and conditions of strips stability to breaks and surface defects formation. The decision to develop this innovative method is due to the fact that a large number of existing approaches to calculation and design of rolling modes have visible advantages and disadvantages. In many cases, the researchers are trying to take into account several requirements that ensure stability of rolling process, its quality, the equipment operating conditions, reduction of energy consumption, metal, auxiliary materials and the specified (maximum) mill productivity. However, some of these requirements can be contradictory and the best one will be the mode that with a high degree of probability guarantees the fulfillment, in a certain proportion, of the entire set of requirements. Therefore, such calculation method is the presented in this article. Calculation of the cold rolling regimes was limited to selection and distribution of the crimping along the cages (passages in the reversing mill). Also, the strip strains are selected in the intercellular spaces, on the decoiler and coiler, and in setting the speed wedge in a particular system of constraints imposed on the input and output process variables as a function of the adopted optimality criterion. As it was noted earlier, the problem was solved with the help of the conditional optimization method with specification of the optimization criterion.

The second part of the paper describes the method practical use on four-stand rolling mill 1400. When rolling the chosen typical sizes, the task was to determine the specific rolling mode, which will ensure a minimum of the total specific energy consumption at the maximum rolling speed, maximum process stabilization (minimum breaks, idle times, etc.) and obtaining the specified quality of the rolled strips (no surface defects, meeting the thickness and flatness requirements). It was achieved by including the above requirements in the constraint system with respect to the determined rolling modes for the selected strip sizes. For example, ensuring a given (maximum) performance for a specific size and brand of a strip is equivalent to realizing a gi673 ven (increased) rolling speed in the absence of unscheduled downtime occurring in emergency situations (in particular, in strip breaks). The speed limit depends on the power of engines, which is included in the complex of structural and technological limitations. The obtained examples, given in the article, have shown that the use of the method leads to fulfillment of all the specified requirements, which, in turn, ensures a reduction in production cost and an increase in the mill’s productivity. The calculation of the cold rolling modes was reduced to selection and distribution of the crimping along the stands (passages – in the reversible mill) and to a choice of specific strip tension in the interstand spaces, on decoiler and coiler, and in setting the wedge of speeds in a particular system of constraints imposed on the input and output process variables as a function of the adopted optimality criterion. The task was solved using the conditional optimization method, through the specification of the optimization criterion. As such criterion, the total energy consumption of the rolling process was used, as requirements – technological and design constraints on the rolling parameters and conditions for strip stability to breaks and to formation of rolls surface defects (“brews”, “chippings”, etc.), as well as to strip breaks.

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