Download modelling of magnetic fields generated by cone

Journal of the University of Chemical
I. Kostov,
Technology
A. Andonov
and Metallurgy, 40, 3, 2005, 261-264
MODELLING OF MAGNETIC FIELDS GENERATED BY CONE-SHAPED COILS
FOR WELDING WITH ELECTROMAGNETIC MIXING
I. Kostov1, A. Andonov2
1
Technical University-Sofia
University of Chemical Technology and Metallurgy
8 Kl.Ohridski, 1756 Sofia, Bulgaria
E-mail: [email protected]
2
Received 14 March 2005
Accepted
20 June 2005
ABSTRACT
Modelling of magnetic fields (MF) of cone-shaped (truncated cone) is au object of interest. Models concerned with
a magnetic system including different numbers of coils and with/without a closing part of the magnetic yoke are discussed.
The results are presented graphically as maps of the magnetic field induction in both axial and radial directions.
Keywords: magnetic field, welding, electromagnetic mixing.
INTRODUCTION
Magnetic field application for magnetic levitation of molten metals is widely encountered in molding
of metals, among them titanium, molybdenum, vanadium, etc. The high temperature range of the welding
process is associated with unwanted contacts with the
metals and with the surfaces of the pots (usually carbon-made) and consequent chemical reactions. The
magnetic levitation or more precisely the magnetic mixing, has a potential to solve the problem. The eddy currents generated in the metal, in case of a vacuum or in
an atmosphere of innert gas, causes forces of repulsion
between an outside magnetic field and the molten metal,
thus avoiding contacts with the pot surface. This approach is applicable mainly in cases of inductive highfrequency welding and melting.
For instance, such a system [1] consists of an
electromagnet with an industrial frequency electric supply. If an aluminum disc is placed above its pole surface it will levitate because the eddy currents induced
in the disc generate a magnetic field that is phase-shifted
with respect to the magnetic field of the electromagnet.
So, repulsive forces are generated, that is, a magnetic
levitation of the disc above the electromagnet pole.
The same idea is attractive for creation of systems for magnetic levitation of molten metals [2]. For
example, such a system consists of co-axial single layer
coils connected in series. The coils are energized by
low-frequency current supply. Usually, a variable condenser connected in parallel to the coil is used to achieve
a resonant mode of operation. The bottom part of the
coil has a large angle of opening at the top of imaginary
cone. The other coil is used for avoiding the lateral
spreading of the molten metal. In some experiments a
sphere of a high-conductivity metal is placed between
the coils. As a result of the induced eddy currents the
metal starts to melt, but it cannot drop at the pot surface because the repulsive forces (mentioned above) create magnetic levitation conditions and the sphere is “suspended” in the inner atmosphere of the gas assisting the
process. The suspended sphere melts and the molten part
of the metal is taken away through a suitable reduction
of the current strength (intensity). Very often the sphere
rotates around its vertical, but this is usually avoided by
generation of an asymmetric external magnetic field. The
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Journal of the University of Chemical Technology and Metallurgy, 40, 3, 2005
current strengths are with in the range of 600- 800 A and
for a complete levitation of 1 kg of molten metal the
required energy is about 50 kVA .
The analysis of designs of magnetic levitation systems shows that the most suitable, and frequently used,
are the cone-shaped coils. Investigations [6, 7] provide
information that ultrasonic treatment of the molten
metal as well as other low-frequency mechanical vibrations lead to an enhancement of the structures of the
alloyed steels treated. For improving welding additional
external magnetic fields [8-14] such as running fields
generated by 3-pahse inductors are also used [3].
ties. The analysis becomes complicated since the model
consists of hydrodynamic equations with additional
terms representing the contribution of the magneto hydrodynamic interaction of the field and conducting fluidmolten metal [4]. Two versions of au welding burner
RESULTS AND DISCUSSION
equipped by magnetic systems of cone-shaped coils are
illustrated in Fig. 1.
Hereunder, the following examples are concerned
with models of one or two cone-shaped coils equipped
with/without magnetic yokes. The coils are mounted over
the welding electrode with vertically oriented axes of
symmetry. This model has been solved by FEM [5] for a
2-D field satisfying the Poison equation of the magnetic potential with Dirichlet boundary conditions at
the barrier zone around the magnetic systems. This is a
non-linear problem taking into account the of the steel
properties variations with the field intensity.
The samples tested are of non-magnetic chromenickel steel welded by the VIG method without additional welding material.
The FEM code is Quick Field, version 4.3. For
enhancement of the modelling efficiency a special code
written in Lua was created. It was employed for fasten
changing of data concerning variable geometry of the
object, material properties variations and various geometrical situations between the elements of the welding
device. Triangle elements of 1st order were used.
For defining the accuracy of the computations,
especially those of the magnetic field induction, each
sub-domain was filled with meshes with decreasing sizes
of the triangle elements when the space distribution of
the mechanical laments was changed. Over each subdomain integration is carried out in order to calculate
the force in the zone of the welding joint - the Maxwell stress tensor is used for this purposes.
The investigations with two coils were performed
with variable current intensity as with a condition ensuring that counter-phase shift of currents was satisfied. The
resultant magnetic fields for three different geometries of
the magnetic yoke are illustrated by Fig. 2 a, b, c.
Problem Formulation
The present work is concerned with modelling
of magnetic field (MF) topology in case of cone-shaped
(truncated cone) coils. The magnetic field generated is
used for magnetic levitation/mixing of a molten metal
pool of chrome-nickel steels in the case of external field
controlled welding.
The magnetic systems and the auxiliaries employed for control of the welding pool should satisfy
the following conditions:
• The gas torch is designed for a hard melting
tungsten electrode, requiring an additional element fitting it in the core of the magnetic yoke.
• The welding head consists of elements (gas supply elements, water cooling system, etc) requiring an
intensive chilling.
• Additional coils of the magnetic system should
not reduce the rate of the welding process determined
mainly by the movement of the mechanical parts of the
welding machine.
• The magnetic system used should generate fields
with inductions from 20 up to 100 mT over a gap covering a distance of 5 mm from the top of the gas burner.
Modelling with Finite Elements Method
The Finite Elements Method (FEM) allows magnetic field computations in complex geometries, mainly
2-D and 3-D anisotropic and non-linear media.
In the case discussed here, the challenging problem is the interaction between the magnetic field and
moving parts of the welding machine as well as the flows
of ionised gases and liquid media with high conductivi-
262
Fig. 1. General view of welding burners: Left - with an external
magnetic yoke, Right - without magnetic yoke.
I. Kostov, A. Andonov
The results obtained indicate that the field topology is symmetric with respect to the vertical axis.
The magnetic force alters the sign (i.e. its direction) in
the case of the two-coiled magnetic system. The force
orientation in a given zone corresponds to the current
direction in a certain coil with a definite orientation.
The curves represent the field induction distributions in both the axial and radial directions. The radial variations of the field induction in a plane parallel
to the magnet pole at a distance r is illustrated in Fig. 3.
With the increase of the distance r, i.e. the distance between the point of measurement and the welding line, the field becomes more uniform if it is generated by a single-coil magnetic system. In case of a twocoil system the effect of the iron yoke on the field distribution over the welding zone is negligible. The relative variation of the field induction along the axis of
symmetry of a cone-shaped coil is illustrated in Fig. 4.
Fig. 3. Radial distribution of the field induction in a plane parallel
to the magnet pole at a distance r.
Fig. 4. Axial distribution of the field induction at a distance
r=1mm in all the three cases mentioned above.
Fig. 2a. Magnetic Field with a single cone-shaped coil.
Fig. 2b. Magnetic field generated by two coils without a magnetic
yoke.
Fig. 2c. Magnetic field generated by 2 coils with a magnetic
yoke.
The effect of the iron yoke (single-coil magnet) on
the magnetic field induction is mainly to maintain high
values of it in the welding zone or at a desired distance
from the pole (see Fig. 5a and Fig. 5c). For instance, the
use of a cone-shaped coil with an iron yoke placed at its
symmetry axis (at L1=0, L2=7,5mm, L3=15mm ) leads to
5 times higher values of the magnetic flux density with
respect to only an air-suspended coil.
The field induction at the coil axis (2 coils) and
without an iron yoke, at the same distances (see above),
have maxima of 0,2 T, 0,014 T and 0,013 T, respectively within a radius of 4-5mm. The effect of the iron
yoke material properties on the field induction distribution over the welding pool is notimportant.
Analysis of the results
The melting of metals by electric arcs is usually
performed in small welding pools but with high current
strengths from 600 up to 800 A. The mixing of the
molten metal is usually driven by conduction. The latter implies relatively weak axial magnetic fields (generated by external magnets) provoking mixing motions of
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Journal of the University of Chemical Technology and Metallurgy, 40, 3, 2005
CONCLUSIONS
The effect of a second (additional) coil with a
current shifter in a counter phase to that in the main
coil is characterized by a significant reduction of the
lateral metal dispersion and formation of needles during welding.
Further investigations are needed on the welding
with different welding heads and cone-shaped electromagnets.
Fig. 5a. Single-coil electromagnet.
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Fig. 5b. Two-coil electromagnet without an iron yoke.
Fig. 5c. Two-coil electromagnet with an iron yoke.
the melt. The mixing enhances both the mass transfer
and distribution of species over the welding pool.
External magnetic fields, irrespectively of their relatively weaknesses, may agitate welding melts with sufficient
electric conductivities. The conditions created at such circumstances are characterized by more uniform temperature and concentration fields over a the whole volume of
the welding pool. Moreover, the processes of physical dissolution of alloying species are augmented. All these enhancements lead to better characteristics of the welded joint,
i.e. heat conductivity and mass diffusivity, determining the
metal heating and consequent metallurgical processes.
264
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