Ingot solidification controller for vacuum arc remelting

摘要

A method of model-based ingot solidification control for the vacuum arc remelting process is presented. Specifically, the model predicts the pool depth as a function of radial position from ingot centerline and time, given melting current, and electrode melting efficiency. The analysis leading to the model assumes that the electrode gap is being accurately controlled during the melting process. The controller has both 2-dimensional and 3-dimensional embodiments.

主权项

1. A method to actively set the pool depth during the physical transformation from liquid to solid of an alloy ingot in vacuum arc remelting using a low-order, ingot solidification model, the method being capable of predicting the ingot's pool depth as a function of radial position from the ingot centerline and time, the method comprising the steps of:
a. manually setting a constant mean distance between an electrode tip being melted and a pool surface being formed; b. applying standard heat conduction, fluid flow, electromagnetic and a mass conservation differential equations equationH.=m.eρ⁢⁢Aiwhere {dot over (H)} is the time derivative of the ingot height, {dot over (m)}e is the electrode melt rate, ρ is the superheat density of the alloy, and Ai is the cross-sectional area of the ingot, combined with a specification of boundary conditions at the ingot's surface required to solve said equations;
c. using numerical methods selected from the group consisting of finite volume, finite difference, finite element and spectral method, to provide high order solutions to the heat conduction, fluid flow, electromagnetic and mass conservation equations; d. using an order reduction method to produce a low order set of equations; e. using solutions of the low order set of equations to predict the physical depth of the ingot pool at chosen ingot radii as a function of vacuum arc remelting process inputs; f. incorporating the low order set of equations into a control scheme to control pool depth during vacuum arc remelting, the low order set of equations comprising the form {dot over (x)}=f(x,u), where x is a state vector that adequately defines the state of transformation from liquid to solid the metal alloy ingot being formed during the vacuum arc remelting process and u is the input vector defining both the controlled and uncontrolled inputs, and the output pool depths defined in a vector y are also a function of x and u, manually setting pool depth references at pre-determined radial positions resulting in a controller that controls the ingot's pool depth at pre-determined radial positions, the radial positions comprising radii selected from the group including about 0 and mid-radius; and g. steps a-f resulting in the alloy ingot with a constant pool depth.