2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)
The Study and Calculation of Magnetic Field of the
DC Electromagnet with the Split Poles and Polar Tips
Tatevosyan A.A., Tatevosyan A.S., Zaharova N.N.
Omsk State Technical University
Omsk, Russia
karo1@mail.ru, ast_51@mail.ru, nvzdm@mail.ru
Abstract—Among magnetic systems of electromagnets of a
direct current with polar tips, the valve magnetic system is the
most widespread and well-studied due to its broad application in
drives of electromagnetic switching devices, devices of automatic
equipment and control. However, even at synthesis of such
magnetic system of an electromagnet, developers have a problem
of definition of a share of a magnetic flux under a polar tip
leaving in a working gap. The solution of a task becomes even
more complicated at absence of a rotary anchor in a direct
current electromagnet as the magnetic field in an inter-polar gap
is sharply non-uniform, fading in process of removal of the
studied point from the plane of poles. Such distribution of a
magnetic field takes place in special electromagnets of a direct
current - suspended separator used for extraction of
ferromagnetic objects from various bulks transported by tape
conveyors.
Keywords—electromagnet DC lipolysis the gap; pole pieces;
split poles; verification of the law of full current; the attenuation of
the magnetic field; ponderomotive force
I.
INTRODUCTION
Magnetic separation in resource-saving technologies allows
to exclude hit of steel impurity in machines and mechanisms,
their exit from a working condition and to reduce wear of the
equipment. Thanks to magnetic separation at the enterprises of
processing of vegetable raw materials the probability
emergence of explosion of air dust mix, owing to emergence of
a spark at hit of steel inclusions in the line of transportation
decreases [1].
At a preliminary design stage of separator the greatest
interest causes research of a magnetic field for points of a
vertical of the middle of an interpolar gap where it is the most
difficult to take ferromagnetic objects, owing to the maximum
thickness of the cleared layer and the minimum value of the
ponder motive force arising in a non-uniform magnetic field [2]
Fм.п. = −grad P ,
(1)
μ 0 χ0 H 2
dV – potential energy of the
2
V
magnetized particle, H – the module of intensity of a magnetic
field, V – particle volume, χ0 – magnetic susceptibility of a
particle, μ 0 – magnetic constant.
where
P=
At the small sizes of the magnetized particle in volume of
V module of intensity of a magnetic field of H it is possible to
consider identical and expression for force becomes simpler
Fм.п. = −μ0 χ0 VHgradH .
(2)
As intensity of a magnetic field with increase in distance
from a surface of magnetic system of an electromagnet
decreases (gradH < 0) , positive value of force means that
under her action ferromagnetic particles will move to poles. In
expression (2) size
Fм = HgradH ,
(3)
it is accepted to call magnetic force, it doesn't depend on a
form, the sizes and the nature of the taken body, and
characterizes only properties of a magnetic field and criterion
of quality of the developed design of an electromagnetic
separator.
II.
THE ANALYTICAL DECISION FOR CALCULATION OF
THE MAGNETIC FIELD
Calculation of a magnetic field on the middle of an
interpolar gap for a suspended electromagnetic separator at a
preliminary design stage can be reduced to analytical
calculation of a plane-parallel magnetic field of two infinite
plates L wide remote from each other at distance 2δ having a
difference of magnetic potentials U 0 (fig. 1). On an axis of
symmetry of magnetic system intensity of a magnetic field has
only a horizontal component [3], namely:
H = H x (y) =
U0
(L + δ)
,
⋅
2K(k) δ2 + y 2 ⋅ (L + δ) 2 + y 2
(4)
where y – distance down from the plane of poles to a
settlement point of A in which intensity of a magnetic field is
defined, K(k) – the full elliptic integral of the first sort with the
module k approximated by expression (to within the fourth sign
after a comma)
n 
2
1 

K(k) =  (1 − k 2 ) ⋅ a i + bi ⋅ ln

n =0
(1 − k 2 ) 
978-1-5090-1322-7/16/$31.00 ©2016 IEEE
,
(5)
2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)
where module
k=
a 0 = 1.3862944 ,
b 0 = 0.5 ,
L
L+δ ,
a 1 = 0,19723 , a 2 = 0, 0725296 ;
b1 = 0.213478 , b 2 = 0.0288729 .
a)
b)
Fig. 2. Sketch (a) and appearance (b) magnetic system DC electromagnet: 1 pole pieces; 2.3 - coil consisting of two identical coils; 4 - split poles; 5 yoke; 6 - laboratory stand; 7 - digital milliteslametr equipped with a Hall
sensor.
Fig. 1. The settlement scheme of the magnetic system.
The submitted analytical decision (3) for the module of
intensity of a magnetic field on the middle of an interpolar gap
is used at a stage of preliminary design calculations of
electromagnetic separator. At this stage calculation of
distribution of intensity of a magnetic field for all interpolar
space and under polar tips, as a rule, isn't carried out as on the
middle of an interpolar gap it is the most difficult to provide
extraction of ferromagnetic objects, owing to the maximum
thickness of a layer of the purified material
[4, 5].
The purpose of this article is the integrated approach to
research of a magnetic field of a suspended electromagnetic
separator of a direct current with the split poles and polar tips.
Approach is based on comparison of results of a pilot study of
a magnetic field and magnetic force Fм = HgradH for a
prototype of an electromagnetic separator by means of a digital
induction measurement with the sensor of the Hall [6, 7],
numerical calculation of a magnetic field (a static task) in a
complex of the ELCUT 6.0 programs (the professional version)
and analytical calculation of intensity of a magnetic field with
use of expression (3).
III.
DESCRIPTION OF THE LABORATORY STAND
The experimental part of research of a magnetic field is
executed on an electromagnet prototype. The sketch of an
electromagnet and appearance of the laboratory stand is shown
in fig. 2 (a, b). The electric circuit of the laboratory stand is
shown in fig. 3.
The prototype of an electromagnet has full number of
rounds of a winding of w = 1100. Current of a winding of I =
2,1 A. The magnetic conductor is made of sheet hot-rolled steel
of brand of Art. 20: the sizes of a yoke of the core 376 x 140 x
20 mm, six type-setting poles with sizes of 20 x 140 x 140 mm,
two polar tips with sizes of 160 x 140 x 20 mm. Thickness of
the coil is 20 mm, height of the coil is 140 mm, a gap between
type-setting poles of 20 mm, thickness of walls of a framework
of coils of 5 mm.
Fig. 3. Electrical scheme of the laboratory device: 1 - rectifier; 2 - DC
electromagnet with two pole pieces.
IV.
RESEARCH OF THE MAGNETIC FIELD WITH ELCUT 6.0
The settlement part of research of a magnetic field is
constructed by a numerical method on the solution of a
problem of linear statics in a complex of the ELCUT 6.0
programs (the professional version) [8, 9]. In a task the
magnetic field is accepted plane-parallel (vectors B and H lie
in the plane xy depend on coordinates x and y , and don't
depend on coordinate z ). The vector of density of current
J = J z has one component directed along an
axis z . In the Cartesian system of coordinates the magnetic
field of an electromagnet in piecewise homogeneous
environments is described by means of Laplace's equation Poisson of rather vector magnetic potential [10-14]
∂  1 ∂A z

∂ x  μ ′ ∂x
 ∂  1 ∂A z
+  ′
 ∂y  μ ∂y

 = −μ 0 ⋅ J z .

(6)
The area of area of modeling taking into account piecewise
homogeneous environments with various permeability (steel, a
winding with current, air) makes 500 × 300 mm 2 .
On external border of area the condition that vector
magnetic potential Az = 0 , relative magnetic permeability
became, relative magnetic permeability of air μ′ = 2000 and a
copper winding wire is accepted μ ′ = 1 . The geometry of
model of an electromagnet is set by the sizes a = 376 mm, h =
140 mm, L = 170 mm, 2 = 36 mm, b = 20 mm (fig. 2).
Check of numerical calculation of a picture of a magnetic
field of an electromagnet in an Elcut 6.0 package under the law
of a total current for any contour has shown that at the set
sampling step the error of calculation doesn't exceed one
percent [15, 16].
2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)
By the calculated picture of a magnetic field of an
electromagnet it is possible to determine change of a vector of
intensity of a magnetic field and its components in any set
direction, for example by an arrow (fig. 4). From the schedule
it is visible that intensity of a magnetic field on the middle of
an interpolar gap, that is ability to perform his work, appears
much more, than under polar tips.
For clarification of influence of this divergence on the
magnetic force of an electromagnet we approximate the curves
1 and 3 set table, a cubic spline in a MATLAB package. For a
cubic spline of functions we use procedure of calculation of
magnetic force for a formula (3). Results of calculation of
magnetic force of an electromagnet on the middle of an
interpolar gap on an axis y are shown in fig. 6.
Fig. 4. The distribution modules and components of the field vector along a
straight line: 1 – field vector intensity; 2 – vector component HY; 3 – vector
component HX.
V. RESULTS
Comparison of results of experiment and calculation of
distribution of intensity of a magnetic field on the middle of an
interpolar gap on an axis y is shown in fig. 5.
Experimental values of intensity of a magnetic field in
settlement points were determined by the values of magnetic
induction measured induction on a formula H = B / μ0 . On the
schedule (fig. 5) good rapprochement of an experimental curve
1 from the settlement curve 2 constructed with use of an
ELCUT 6.0 package, especially in the area where the magnetic
field has sharp heterogeneity is observed. The analytical
method of calculation of intensity of a magnetic field (a curve
3) in this area has a bigger divergence with experiment.
Fig. 6. The magnetic force of the electromagnet in the sharp magnetic field
inhomogeneity.
The analysis of the constructed curves in drawing shows
that in the field of sharp heterogeneity of a magnetic field the
magnetic force of an electromagnet reaches a maximum. And
experimental and settlement curves in this area significantly
differ among themselves that testifies to a possibility of use of
an analytical method at a preliminary design stage of an
electromagnet. When performing optimizing calculations of
his design it is necessary to be based on results of numerical
calculation of the magnetic field executed by means of an
ELCUT 6.0 package (the professional version) [15, 16].
Fig. 7. The attenuation of the magnetic induction with increasing distance
from the surface of the magnetic system.
Fig. 5. An integrated approach to the research of the magnetic field in the
middle of the pole gap along the axis Y.
With increase in distance from a surface of magnetic
system of an electromagnet intensity of a magnetic field (also
magnetic induction) fades after an exhibitor, however this law
in the field of sharp heterogeneity of a magnetic field on the
middle of an interpolar gap where magnetic force reaches the
2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)
maximum value, isn't carried out. An experimental curve of
magnetic induction along an axis y and the exponential trend of
function constructed in an Excel [17–20] package in this area
significantly differ (Fig. 7).
VI. CONCLUSION
1. By an experimental and settlement way on the basis of
research of a magnetic field of an electromagnet with the split
poles and polar tips it is shown that in the field of an interpolar
gap with sharp heterogeneity of a magnetic field, the maximum
of magnetic force is observed.
2. The numerical model of a magnetic field of an
electromagnet constructed in an Elcut 6.0 package most
precisely describes distribution of a magnetic field in an
interpolar gap and under polar tips. In the area attenuation of a
magnetic field happens to sharp heterogeneity not under the
exponential law.
3. The problem of optimum design of an electromagnet
with the split poles and polar tips can be solved on the basis of
numerical calculation of a magnetic field by means of an
ELCUT 6.0 package (the professional version). As criterion of
an optimality of a design of magnetic system the maximum of
magnetic force on the middle of an interpolar gap, by a
parameter k = L / δ variation can serve under other invariable
conditions, including constancy of IW of a winding.
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