A Reduced-Order Model for Dynamic Vacuum Arc Remelting Pool Depth Estimation and Control

Abstract

Vacuum arc remelting (VAR) is an industrial metallurgical process widely used throughout the specialty metals industry to cast large alloy ingots. A reduced-order model of the growing and solidifying ingot was developed specifically for dynamic control and estimation of the depth of molten liquid pool atop the ingot in a VAR process. This model accounts only for the thermal aspects of the system ignoring high-fidelity physics such as fluid flow and electromagnetic effects. Spectral methods were used to obtain a set of nonlinear dynamic equations which capture the transient characteristics of liquid pool shape variations around a quasi-steady operating condition. These nonlinear equations are then linearized about this operating condition and further simplified by suppressing fast modes. The resulting system can be described by only six state variables. The reduced order model compares favorably to pool depth changes predicted by an accurate finite-volume model. A first approach to use this model in the design of a dynamic VAR pool depth estimator and controller is also proposed.