J. Douglas Lavers

Real-Time Measurement of Electric Arc-Furnace Disturbances and Parameter Variations

The general nature of electrical-supply network disturbances caused by arc-furnace operation is reviewed, including the guidelines adopted in several countries concerning disturbance-level estimation for single-and multifurnace installations. The meters available for the measurement of voltage flicker, including the international standard meter proposed by the International Union of Electroheat (UIE) are briefly described. The basic statistical properties of arc-furnace disturbances and parameter variations, treated as random variables, are discussed. Measured data are used to examine the probability distributions for variations in furnace voltage and current. Particular attention is given to methods of reliably measuring the disturbance and parameter-variation levels in real time on-line. Strategies are developed, and a microprocessor-based data-acquisition system, developed for this purpose, is described.

An Analysis of an Electromagnetic Mold for the Continuous Casting of Nonferrous Metals

Electromagnetic molds are presently being used in the continuous casting of aluminum billets and slabs. Various theoretical models that can be used to predict electromagnetic pressure differentials and forces for this application are examined. Dimensionless pressure and force factors are first derived using a one-dimensional field model. These factors are then refined using a two-dimensional semi-infinite model. This latter model is also used to examine the effect that coil coupling has on the field strength, pressures and forces. Finally, the coupled circuit method is used to predict pressure distributions for an actual mold geometry, including the essential effect of the field shaping short-circuited turn (screen). The effect of varying the location of the inductor and screen is examined.

An Efficient Method of Calculating Parameters for Induction and Resistance Heating Installations with Magnetic Loads

An efficient method of solving one-dimensional linear or nonlinear induction and resistance heating problems is described. Previous methods have formulated these problems in terms of matrix equations that can require a considerable amount of computer storage during solution. The method described avoids the matrix formulation. Rather, the solution proceeds in a step-by-step fashion so that when fields are calculated at a point within the conductor, the previously calculated fields at other points are all utilized. In this sense, the solution requires only a minimum of storage capacity and is particularly appropriate for small desk calculators. The linear hollow cylinder problem has been programmed for the HP-25 had calculator.

Rotary In-Mold Stirring in a Cylindrical Continuous Casting Geometry

An analysis of in-mold rotary electromagnetic stirring forces and induced power is presented for a multilayer round continuous casting geometry. The required fields, forces, and power are derived using a convenient multilayer model that neglects end effects. Stirring characteristics are presented as a function of melt resistivity, slip, frequency, and mold wall thickness. Means of scaling these results to other round geometries are described, and the application of the model to the round corner square geometry is discussed.

A Finite-Element Package for the Analysis of Electromagnetic Forces and Power in an Electric Smelting Furnace

In a conventional matte smelting or slag resistance furnace electrical conduction currents flowing in a molten slag are used to generate the required process heat. Such furnaces generally involve a 6-in line electrode geometry, with the electrodes generally being in excess of 1m diameter and the electrode currents being on the order of 100 kA. One of the principal electrical design problems is the calculation of the power and current distribution. These parameters directly influence the furnace operating practice and the design of the furnace electrical equipment and refractories. An additional design problem is that of refractory and electrode erosion due to the slag motion. The electromagnetic body forces are among the principle forces which drive the recirculatory slag flow. A finite-element numerical model, which determines the distribution of the furnace power and the electromagnetic body forces as a function of the furnace operating parameters is described. The advantages of this method over existing methods are described.

Resistance Heating of a Circular Billet - Two Simple Analytic Models

Two simple models are presented for calculating the ac-dc resistance ratio and power factor of a resistance heated magnetic biliet of circular cross section. The step-function magnetization model yields a normalized ac-dc resistance ratio graph applicable to any homogeneous magnetic billet for which the magnetization characteristic is known. The coupled-circuit model yields a set of unidirectionally coupled algebraic equations that may be solved serially. For the case of a billet of radially inhomogeneous conductivity and permeability both of which are linear, the system may be solved in one pass. When the permeability is a function of field strength an iterative solution is required.

A Mathematical Model Describing Forces and Circulation in an Electric Smelting Furnace

Conditions in the slag bath of an electric smelting furnace are examined as are several existing models for such furnaces. A digital model that provides an improved simulation of the slag bath is described. The model is used to determine the electrical resistance between electrodes and can be used to examine the nature of the electromagnetic forces that exist near the electrode tips. The mechanism by which these forces produce bath circulation is described.

Force Distributions Produced by an Electromagnetic Mold

The electromagnetic force and consequent fluid flow patterns that can occur in a conventional electromagnetic mold for continuous casting of aluminum are described. The role of system geometry, specifically the placement of the confinement coil and shield, is examined in detail. The distribution of electromagnetic pressure as well as the curl of the lorentz force are presented. The effect of frequency is also considered. The coupled circuit method is used to predict the current density distribution for a specific mold geometry. The induced currents are then used to predict the pressures and forces. Nonlinear stream function/vorticity equations are solved under the assumption of constant turbulent viscosity to obtain the flow patterns. The role of the screen in shaping the force patterns is critically examined.

One-Dimensional Model for the Single-Sided Linear Induction Pump for Molten Metal

A simple one-dimensional model of the single-sided linear induction pump is presented. The electromagnetic fields and forces (thrust and lift) are obtained by using a semi-infinite geometry that neglects pump edge and end effects. The forces are subsequently derated for edge effects by means of correction factors. The field solution is also used to determine the air gap impedance, while conventional expressions from electric machine theory are used to determine the stator impedance. The throughput produced by a given thrust is determined by assuming turbulent slug flow. Throughput versus kVA characteristics are presented for a variety of pump operating conditions.

Mathematical Modeling in the Design of Large Electric Smelting Furnaces

The problem of scaling a slag resistance electric smelting furnace from the pilot plant stage to a full size production unit is considered. Several of the existing scaling methods are discussed with a view to pointing out their limitations. It is shown that some are clearly inappropriate for the scaling process since they neglect significant factors that influence the furnace performance. Among these factors are the finite furnace geometry, the nonhomogeneous slag, and the slag/ alloy interface. Methods of including these factors in the analysis are described. In particular, a finite difference simulation has been developed for the furnace. Such a model can be used to derive design parameters for the furnace and to indicate the manner in which such parameters vary with furnace geometry.