Development of Algorithm for Forming Optimal Mode of Heating Billets in Through-Type Furnace

This study proposes a calculation algorithm to calculate the optimal furnace thresholds for operation with minimum fuel consumption, and to transfer this information to a furnace operator under non-stationary furnace performance conditions. The algorithm provides calculation regarding optimal thresholds per two modes. The first mode searches for the optimal fuel loads under current billet travel rate. The second provides a search for an optimal billet motion rate while maintaining current fuel thresholds. To perform the calculation under optimal parameters in the real time mode, the mathematical tool is based on the model of external heat transfer upon considering mutual influence of heating zones, and the model of internal heat transfer using a grid model of a massive body heating. The procedure for coordinating the mathematical models with each other, taking into account the movement of billets within the furnace zone, is described. Calculating optimal parameters: fuel loads and billet movement rate was performed using the Nelder-Mead simplex method. The total fuel consumption used to heat billets at the furnace outlet is taken as the target function. The coefficients of units statistical significance to be used in a search algorithm. The internal heat transfer model takes into account thermophysical characteristics dependence on a billet temperature, and is described by a one-dimensional differential heat conduction equation. The algorithm proposed will allow a furnace operator to heat a billet in the optimal mode, and to prevent possible delivery of underheated billets.