Non-linear Standard Model for Optimization of Charge Materials in Crucible and Induction Melting Furnaces

Melting furnace charge calculation is often performed based on the mass balance of alloying elements between input materials and output melt. However, real melting processes are concerned with phenomena and complexities, which are ignored in simplified mass balance calculations. That causes uncertainty in the charge calculations, which further leads to multiple melt corrections, delays in tapping, cost raises, and melt quality problems. This study aimed to develop a model that not only optimizes charge materials for a specified target melt, but also considers non-homogeneous element loss, non-metal contaminations in charges, and correction of initial melt in the furnace. This paper proposes a standard optimization approach with an iterative algorithm for non-linear mass balance in the melting problem. A test case was introduced to find charge materials for target brass alloy C47940 in a 10-ton induction furnace, with an initial 7-ton out-of-range melt. The matrix of coefficients was built according to the numerical algorithm of the model. The results of the test case showed the optimum mass fractions of charge burdens. An optimality analysis was conducted and showed that the solution has reached the minimum possible cost. The non-linear iterative algorithm revealed a convergent and fast performance which has potential for reliable optimization in melting operations with significant benefit for industrial automation.