Calculation method for operating resistance in dual-electrode dc electric-smelting furnace for magnesium

Patent metadata

Field	Value
Publication number	US-11096251-B2
Application number	US-201816093849-A
Country	US
Kind code	B2
Filing date	May 21, 2018
Priority date	Nov 8, 2017
Publication date	Aug 17, 2021
Grant date	Aug 17, 2021

Abstract

The invention provides a calculation method for operating resistance in a dual-electrode DC electric-smelting furnace for magnesium, including the following steps of: calculating a raw material resistance: simplifying a raw material model as an electrode-centered cylindrical model, determining an electric-field strength of each point in an electric field generated by a raw material layer around an electrode in the cylindrical model, calculating a raw material voltage between two electrodes according to the electric-field strength of each point in the electric field, and further obtaining the raw material resistance between the two electrodes; calculating an electric arc-resistance relation model: determining a relation between an actual electric arc length and a distance from the electrode to a surface of a smelting pool, and calculating a relation between an electric arc voltage and the actual electric arc length, namely the electric arc-resistance relation model; and calculating a smelting pool resistance, namely the sum in series of the smelting pool resistance of the two electrodes.

First claim

What is claimed is:

1. A calculation method for operating resistance in a dual-electrode DC electric-smelting furnace for magnesium, comprising the following steps of:
calculating a raw material resistance: simplifying a raw material model as an electrode-centered cylindrical model, determining an electric-field strength of each point in an electric field generated by a raw material layer around an electrode in the cylindrical model, calculating a raw material voltage between two electrodes according to the electric-field strength of each point in the electric field, and further obtaining the raw material resistance between the two electrodes;
calculating an electric arc-resistance relation model: determining a relation between an actual electric arc length and a distance from the electrode to a surface of a smelting pool, and calculating a relation between an electric arc voltage and the actual electric arc length, namely the electric arc-resistance relation model;
calculating a smelting pool resistance, namely a sum in series of the smelting pool resistance of the two electrodes; and
controlling an output power of the dual-electrode DC electric-smelting furnace for magnesium based on the raw material resistance and the smelting pool resistance,
wherein the calculating the smelting pool resistance comprises:
simplifying a smelting pool model as a semi-sphere model with a bottom center of the electrode as a center of a sphere and a distance from a bottom of the electrode to a surface of the smelting pool as a radius;
calculating an electric-field strength of a spherical surface being a distance r away from the center of the sphere in the semi-sphere model;
integrating the electric-field strength being the distance r away from the center of sphere in the semi-sphere model from the bottom of the electrode to the surface of the smelting pool so as to obtain a voltage drop from the bottom of the single electrode to the surface of the smelting pool; and
calculating the sum in series of the smelting pool resistance of the two electrodes, namely the calculated smelting pool resistance.

2. The method according to claim 1 , wherein the calculating the raw material resistance comprises:
simplifying the raw material model as the electrode-centered cylindrical model according to an inserting depth of the electrode in a raw material and a distance between center lines of the two electrodes in the dual-electrode DC electric-smelting furnace for magnesium;
determining the electric-field strength of each point in the electric field generated by the raw material layer around the electrode in the cylindrical model; and
integrating the electric-field strength being a distance x away from the center line of the electrode in the cylindrical model from a surface of the electrode to half the distance between the center lines of the two electrodes to obtain half the raw material voltage between the two electrodes, and calculating the raw material voltage between the two electrodes so as to further obtain the raw material resistance.

3. The method according to claim 1 , wherein the calculating electric-arc resistance relation model comprises:
determining the electric arc-resistance relation model;
describing the electric arc voltage according to changes of an ideal electric arc length and a current;
establishing an electric arc magnetic-field model and an electric arc deflection trajectory model by assumptions on shape and position of electric arcs during an operation of the electric-smelting furnace for magnesium;
determining a relation between the actual electric arc length and the ideal electric arc length in combination with a radius of an electric arc deflection trajectory as well as the electric arc deflection trajectory model; and
calculating a relation between the electric arc voltage and the actual electric arc length, namely the electric arc-resistance relation model.

4. The method according to claim 3 , wherein the electric arc deflection trajectory model is as follows:

L
a

=

R
a

⁢
arc
⁢

⁢

sin
⁡

(

L

R
a

)

wherein R a is an electric arc deflection trajectory radius, L a is the actual electric arc length and L is the ideal electric arc length namely the distance from the electrode to a surface of the smelting pool.

5. The method according to claim 3 , wherein the establishing the electric arc magnetic-field model and the electric arc deflection trajectory model by assumptions on the shape and position of the electric arcs during the operation of the electric-smelting furnace for magnesium comprises:
making theoretical model assumptions on actual electric arcs, and establishing the electric arc magnetic-field model, namely a sum of an electrode-generated magnetic field and an electric arc-generated magnetic field; and
determining a motion trajectory of the electric arcs in an X-Y plane, namely, the electric arc deflection trajectory following a circular path, and establishing the electric arc deflection trajectory model.

6. The method according to claim 5 , wherein the making theoretical model assumptions on the actual electric arcs comprises that:
the electric arcs are assumed to have mutual deflections only, namely a main electric arc deflection effect occurs in a plane defined by the two electrodes;
an electrode length is assumed to be infinite, wherein an ultimate effect is ignored;
the electric arcs are assumed to follow a straight line in deflection; and
an effect of a magnetic field generated by a current of the smelting pool on the electric arc is ignored.

Assignees

• Univ Northeastern

Inventors

• Zhang Yingwei
• Xue Xiaoguang
• Li Yongxu

Classifications

• H05B7/20 Primary

  Direct heating by arc discharge, i.e. where at least one end of the arc directly acts on the material to be heated, including additional resistance heating by arc current flowing through the material to be heated · CPC title

• G01R27/02

  Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant (by measuring phase angle only G01R25/00) · CPC title

• G16C20/10

  Analysis or design of chemical reactions, syntheses or processes · CPC title

• G06F17/13

  Differential equations (using digital differential analysers G06F7/64) · CPC title

• G01R27/08

  Measuring resistance by measuring both voltage and current · CPC title