Abstract
The Maxwell 3D module in Ansys Electromagnetics Suite was used to establish a mathematical and physical model for electromagnetic field in the vacuum arc remelting process of titanium alloy, and the interaction law of current, magnetic field and electromagnetic force in the melting process was analyzed. The results show that the current in the ingot is centripetal and concentrated within 350 mm of the upper part of the ingot. Tangential magnetic field is generated by smelting current and axial magnetic field is generated by stirring current, which are simply coupled. Under the action of smelting current and its self-induced magnetic field, radial and axial electromagnetic forces are generated; the electromagnetic force rotates under the action of the stirring magnetic field, generating tangential electromagnetic force. With the change of smelting current, the tangential component of magnetic field and the radial and axial resultant force of electromagnetic force change linearly. The axial component of the magnetic field and the radial component of the electromagnetic force change linearly with the stirring current.
Because titanium alloy has a series of remarkable advantages such as high specific strength, good corrosion resistance and high melting point, it has been widely used in aerospace, equipment manufacturing, medical equipment, sporting goods and other field
VAR is a metallurgical production process in which an arc is formed by low voltage and high current is used as a heat source to smelt metals and to produce ingots under vacuum condition
It is difficult to observe and to detect the physical and chemical phenomena and ingot morphology of VAR process, and the cost of production test is very high, so the numerical simulation becomes the main method. In this study, the Maxwell 3D module of Ansys Electromagnetics Suite was used to establish the mathematical and physical model for electromagnetic field in VAR process of titanium alloy, and the interaction law of current, magnetic field and electromagnetic force in the smelting process was analyzed and mastered, so as to provide a theoretical guidance for the production process of VA
In the process of VAR of titanium alloy, the induced magnetic field is mainly generated by melting current and stirring current. The induced magnetic field and melting current interact to produce electromagnetic force, that is, Lorentz force, which promotes the flow of liquid metal. The control of electromagnetic field and electromagnetic force is mainly described by Maxwell's equations.
The main equations used in the model are as follow
Gauss's law
(1) |
Ampere's law:
(2) |
Faraday's law:
(3) |
Ohm's law:
(4) |
where ; is the magnetic flux density, T; is the induced current density, A·
To simplify the model reasonably, the following assumptions are mad
1) The stirring coil is simplified as a conductive region of the same volume.
2) The surface of molten pool is assumed to be plane, and the influence of liquid metal flow on magnetic field is ignored.
3) Since the relative permeability of crucible cooling water and stainless steel protective sleeve is close to 1, they are treated as air domain in the model.
4) The crucible, ingot and electrode are regarded as isotropic materials, and their physical parameters such as bulk conductivity and relative permeability are set as constants.
5) The arc area is regarded as a conductor with a certain resistance, and its resistivity is calculated by Ohm's law.
1) The magnetic flux parallel boundary condition was applied to the external surfaces of the surrounding air zone.
2) The stirring coil was loaded with current density (j)according to the following equation:
(5) |
where is the number of coil turns; is stirring current, A; is the cross-sectional area of the coil,
3) The melting current was loaded with the top of the crucible as the positive electrode and the top of the electrode as the negative electrode.
The mathematical model of VAR electromagnetic field mainly includes crucible, stirring coil, ingot, electrode, arc and air domai

Fig.1 Schematic diagram of VAR electromagnetic field model: (a) whole model and (b) longitudinal section of the model (excluding air domain)
The Maxwell 3D module of Ansys Electromagnetics Suite was used to perform the calculations. Tetrahedral meshes were used in the computational domain, mesh adaptive techniques were used for mesh encryption, and finer meshes were used for crucible, electrode, and ingot to improve computational accuracy. Detailed parameters of the model are shown in
Parameter | Value |
---|---|
Ingot diameter/mm | 660 |
Ingot height/mm | 1000 |
Electrode diameter/mm | 570 |
Electrode height/mm | 970 |
Crucible diameter/mm | 700 |
Crucible height/mm | 2000 |
Stirring coil diameter/mm | 800 |
Arc zone height/mm | 30 |
Melting current, Im/kA | 21, 22, 23 |
Stirring current, Is/A | 8, 9, 10 |
Material | Value | |
---|---|---|
Bulk conductivity/S· | Relative permeability | |
Ingot, electrode |
1.82×1 | 1.000 18 |
Coil, crucible |
5.8×1 | 0.999 991 |
Arc zone | 656.72 | 1 |
Air domain | 0 | 1 |
In order to compare the calculation results of stirring mag-netic field with the actual measurement results, a Gauss meter was used to measure the magnetic field intensity without ingot in the crucible every 200 mm along the central axis.

Fig.2 Comparison of the calculated and measured magnetic field intensity on the central axis without ingot in the crucible

Fig.3 Comparison of magnetic field distribution in crucible with- out (a) and with (b) ingot

Fig.4 Comparison of magnetic field intensity on the central axis of crucible with and without ingot

Fig.5 Current distribution in crucible, ingot and electrode without stirring magnetic field: (a) total distribution, (b) contact area between ingot and electrode, and (c) current vector diagram on the upper surface of ingot

Fig.6 Comparison of current distribution in ingot and electrode with (a) and without (b) stirring magnetic field

Fig.7 Magnetic field distribution in ingot and electrode with (a) and without (b) stirring magnetic field

Fig.8 Comparison of magnetic field intensity in the diameter direction of ingot upper surface with and without stirring magnetic field

Fig.9 Distribution of electromagnetic force vector on the upper surface of ingot with (a) and without (b) stirring magnetic field
In order to analyze the distribution of the electromagnetic force on the upper surface of the ingot, the components of the electromagnetic force along the y-axis diameter in x, y and z directions are plotted, as shown in

Fig.10 Distribution of electromagnetic force in y-axis diameter direction on upper surface with and without stirring magnetic field

Fig.11 Variation of total electromagnetic force with ingot height
In order to compare the influence of the change of melting current on the magnetic field and electromagnetic force, the current, magnetic field and electromagnetic force distribution were calculated when the melting current was 21, 22 and 23 kA and the stirring current was constant.

Fig.12 Current distribution in ingot and electrode under different me- lting currents: (a) Im=21 kA, (b) Im=22 kA, and (c) Im=23 kA
According to the analysis in Section 3.2, the melting current only affects the tangential component of the magnetic field.

Fig.13 Distribution of tangential component of magnetic field on ingot surface along diameter
According to the analysis in Section 3.3, the melting current has an effect on the radial and axial electromagnetic forces of the ingot, so the sum of the radial and axial electromagnetic forces on the upper surface of the ingot is analyzed, as shown in

Fig.14 Variation of the sum of radial and axial electromagnetic forces on the upper surface of ingot along the diameter
In order to compare the influence of stirring current change on magnetic field and electromagnetic force, the distribution of current, magnetic field and electromagnetic force was calculated when the stirring current was 8, 9 and 10 A respectively under the condition of constant melting current.

Fig.15 Current distribution in ingot and electrode under different stirring currents
According to the analysis in Section 3.2, stirring current only affects the axial component of the magnetic field.

Fig.16 Variation of the axial component of the central magnetic field on upper surface of ingot with stirring current
According to the analysis of Section 3.3, the stirring current has an effect on the tangential electromagnetic force of the ingot. The tangential electromagnetic force on the upper surface of the ingot is analyzed, as shown in

Fig.17 Variation of tangential electromagnetic force on upper surface of ingot along diameter
1) The current distribution in the ingot and electrode is almost the same with or without stirring magnetic field, and the current distribution in the ingot is concentrated in the upper part of the ingot within 350 mm, and the current distribution in the ingot is centripetal.
2) The melting current produces tangential magnetic field, the stirring current produces axial magnetic field, and the two magnetic fields are simply coupled. The radial magnetic field is almost zero. The intensity of the tangential component of the magnetic field increases gradually with the increase in the radius, reaches the maximum value of 15.1 mT when the radius is 285 mm, and then decreases gradually.
3) Under the action of melting current and its self-induced magnetic field, radial and axial electromagnetic forces are generated. The electromagnetic force rotates under the action of stirring magnetic field, producing tangential electromag-netic force. The radial component of the electromagnetic force points to the center of the ingot and is linearly distributed, which reaches the maximum value when the radius is 270 mm, and then rapidly decreases to 0. The electromagnetic force points downward along the axial component and increases with the increase in the radius, reaching the maxi-mum value when the radius is 290 mm, and then gradually decreases. The tangential component of the electromagnetic force increases gradually with the increase in radius. The electromagnetic force is concentrated in the upper part of the ingot within 200 mm.
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