Numerical methods for solving mathematical models of the temperature distribution of strips and rolls during hot rolling with interval parameters

The article considers the problem of temperature distribution in the strip and working rolls during hot rolling under the conditions of uncertainty of input parameters. The zone of the deformation gap with the formation of a rolling scale strip on the surface is regarded, as a result of which a system of thermal conductivity equations with different initial and boundary conditions is solved in the area of the deformation gap being studied. Next, the zone of the interstand gap is considered, where the heat exchange of the strip with the environment occurs. In all zones, the input parameters are represented as interval numbers. The deformation gap and the interstand gap were discretized from a continuous region into a grid one, systems of linear algebraic equations with tridiagonal interval coefficient matrices were derived using finite difference approximation, and a counter-run method with interval coefficients was presented to solve the obtained systems. The article considers the calculation results for 7 stands running one after another and consisting of a deformation gap and an interstand gap for the case with real input parameters and for the case with interval input parameters, calculations were performed using the developed software for both cases.

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