Lipetsk State Technical University (Lipetsk, Russia):

A. I. Bozhkov, Cand. Eng., Prof., Chair of Metall Forming, e-mail: bozhkov_51@mail.ru

The mathematical model for formation of non-flatness in the strips of electrotechnical isotropic steel during heat-treatment in a continuous annealing line is presented. The urgency of the developed model is caused not only by the toughening of the requirements of consumers to the product quality of the rolling mills, but also by the absence in the technological chain of production of dressing and straightening operations that could provide high flatness and the required product type. The mathematical model of strip non-flatness a heat treated in a continuous annealing line described in the article is constructed taking into account the laws of its formation, established in theoretical and experimental studies. The model includes three submodels with which it is possible to calculate the non-uniformity of the temperature distribution across the width of the strips as a function of their cooling rate, the internal residual stresses arising in the strip due to this unevenness, and the characteristics of the actual non-flatness of the annealed strips formed under the action of residual stresses. The paper provides description of the first submodel - the differential equation of nonstationary thermal conductivity under boundary conditions of the third kind, taking into account the heat exchange by radiation on the upper and lower surfaces of the strip. Based on the results of the study, an experimental verification of the mathematical model of the formation of non-planarity of heat-treated in the continuous annealing line was carried out, confi rming the adequacy of the model presented.

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