Note: Descriptions are shown in the official language in which they were submitted.
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60557-3150
This invention relates to a process of optimizatlon for
iron-cored electromagnets used with biomedical stimulators of the
type used to stimulate healing of bone ~ractures.
It is known that healing of an ununited bone fracture is
sometimes stimulated by the passage of electric currents through
the reyion of the ~racture. Currents may be induced by ~he
external application of maynetic fields as described in some
detall in "DEVELOPMENT OF THE IRON-CORED ELECTROMAGNET FOR THE
TREA~MENT OF NON-UNION AN~ DELAYED UNION", E.M. Downes and J.
Watson, published in ~he Journal of Bone and Joint Suryery, 1984.
As discussed more fully therein, the magnetic fields may be
produced by a pulsing current applied to a winding on a generally
C~shaped maynetic core having spaced apart pole faces which are
disposed on opposite sides of a limb in the region of the
~racture.
Different leg and arm cast sites require different
magnet shapes, air gaps and proportions but successful clinical
tests suggest that the pulse timing and magnetic field strength
characteristics should be substantially the same for the different
magnets. Hereto$ore the design of the magne~s has been a purely
emperical proeess, which is understandable a~ most electrical
magnetic taxts discount mathematical solutions for magnetic
circuits with cores containing large air gaps.
It is also desirable to minimize the siæe, welght and
electrical power consumptlon of the electromagnet.
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Thus, an object of the inven-tion is to minimize the
size, weight and elect.:rical power consumption of an iron-cored
electromagnet for use with a biomedical stimulator while maintain-
ing simiiar magnetic field characteristics through a range of
sizes.
According to a broad aspect of the invention there is
provided a method of optimizing the structure of an electromaynet
having an iron core and an associated coil formed oE wire having a
gauge size so that when said coil is energized by electrical
pulses of predetermined dura~ion and amplitude said el ctromagnet
induces voltages of first and second predetermined magnitudes in a
standardized search coil located midway between pole faces of said
iron core at times corresponding to the beginning and end of said
pulses, said method comprising the steps of:
(a) applying said pulses to said associated coil,
(b) measuring the voltage induced in said search coil at the
beginning of said pulses and, if it is greater than said first
predetermined magnitude, increasing the number of turns of said
associated coil whereas, if it is less than said first
predetermined magnitude, decreasing the number of turns of said
associated coil,
(c) measuring the voltage induced in said search coil at the
end of said pulses and, if it is greater than said second
predetermined magnitudel reducing said gauge size of said wire
forming said associated coil whereas, if it is less than said
second predetermined magnitude, increasing said gauge size of said
wire, and
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(d) calculating the current flowing in said associated coil
occurring a-t the end of said pulses, checking where ~he point of
intersection of said current with a saturation curve of said iron
core is and, if necessary, altering the cross-sectional area of
said iron core to ensure that said point of intersection is near
the upper limit of the linear region of said saturation curve.
The invention will now be further described in conjunc-
tion with the accompanying drawings, in which:
Figures lA and lB illustrate electromagnets of a type
with which the optimization method of the invention is particu-
larly concerned,
Figure 2, parts A, B and C, are waveforms useful in
explaining the invention,
Figures 3 and 4 illustrate measurement arrangements used
in the method of this invention,
Figures 5 and 6 are sample core saturation curves such
as used in the method of this invention, and
Figure 7 is a flow chart illustrating the method
according to the invention.
The following symbols are used in the following
description:
SYMBOLS
Vl = search coil voltage at time to
V2 = search coil voltage at time tl
~s = number of turns of wire on search coil
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Nm = number of turns of wire on electromagnet coil
Nma = adjusted number of turns on electromagnet coil
E = voltage applied ~o electromagnet circuit
il = current in electromagnet coil at time tl
Rs = internal resistance of electromagnet voltage source
rn = resistance of pulse drive circuit at time t
RL = resistance of electromagnet coil (13
L = inductance of electromagnetcoil (13)
Figures lA and lB show electromagnets 10 of the type
used in biomedical stimulators~ They both comprise a generally
C-shaped iron core 12 with a single winding 13. The core has end
faces 16 and 17 with an air gap 15 between them. In use in a
stimulator, the end faces 16 and 17 are placed on opposite sides
of a fracture zone of a limb and electrical pulses are applied to
the coil 13.
One of the authors of the above-mentioned article,
Dr. Watson, produced an electromagnet similar to that shown in
Figure lB. It weighed 0.5 kg with an overall size of 204 mm x
20 80 mm and an air gap of 133 mm. Because of varying sizes of leg
and arm casts, it is desirable to provide a variety of sizes of
magnets for a biomedical stimulator. On the other hand, the
success of Dr. Watson's prototypes in clinical tests made it
preferable to retain the pulse timing and magnetic field strength
characteristics of his magnet, which are:
(a) pulse duration = 10 mS
(b) pulse repetition frequency = 10-15 pulses/sec.
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(c) 7 millivolt peaX pulse amplitude at the magnet pole face
measured with a standardized search coil (this value depends on
the particular type of search coil used).
(d) less than 2.0 milli Tesla (20 gauss) peak field inten-
sity measured centrally between the magnet polesO
Regarding (c) above, another search coil with greater
sensitivity enabled induced voltage readings to be taken at the
midpoint between the pole faces of the magnet. This resulted in a
search coil peak pulse amplitude of 100 mV dropping to 60 mV over
the 10 mS. pulse for the Watson magnet. This search coil can be
used with magnets of different sizes to ensure identical induced
voltage waveforms as the Watson magnet (or o~her reference magnet)
when the search coil is located midway between the magnet's pole
faces.
In developing suitable electromagnets, laminated cores
are constructed and insulated in the area where the electrical
windings are applied. Magnet wire is then wound directly on the
core to form the electromagnet. The wire gauge, number of turns
of wire, and the resistance of the winding are noted. The
inductance of the electromagnet is measured and recorded. The
dimensions of the core (cross-sectional area) are also do~umented.
A square cross-section is preferred to minimize the circumference
of the winding which will minimize the size, weight and electrical
resistance.
The electromagnet is then connected to a standardized
pulse drive circuit, for example one providing a 12,0 volt pulse
10 milliseconds in duration at a pulse repetition frequency of
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12.5 Hertz. Referring to Figure 3, an oscilloscope 20 is used to
measure the peak amplitudes of the pulse voltages induced in a
standardized search coil 22 placed at fixed points within the
magnetic field between the pole faces of electromagnet 10 when its
coil 13 is energized by a standardized pulse circui-t 24 which is
powered by a regulated power supply 26.
Figure 2A illustrates an example oE standard pulse
timing which can be used, i.e. 10 mS duration and 82.2 mS between
pulses.
Figure 2B is an enlarged view of a 10 mS voltage pulse
as detected by a search coil located midway between the pole faces
of magnet 10. At time to, the voltage is at a maximum, Vl, and at
time tl it is at a lesser voltage V2.
Figure 2C illustrates current through the magnet coil.
At time to the current io is 0 and it increases exponentially to
some value il, at time tl.
A Watson type magnet, as described above, was tested
using the setup shown in Figure 3. The pulse circuit provided a
13.6 volt pulse 10 mS in duration at a pulse repetition frequency
20 of 12,5 Hz. With the search coil 22 located midway between the
magnet's pole faces, the search coil induced voltages were: Vl =
100 mV, V2 = 60 mV. Identical testing was used in developing
optimized magnets according to the invention.
With Vl and V2 values for prototypes, the process-of
magnet optimization is no longer empirical because electrical
relationships can now be applied to indicate the direction and
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proportion of changes required to align them with the standard,
here assumed to be the Watson magnet,
Vl, the initial induced search coil voltage, occurs at
the beginning of the pulse, i.e. at time to = seconds. The
magnitude of Vl is only affected by one elec~rical para~eter: the
inductance (L) of the magnet. Inductance dictates the initial
rate of change of current through the magnet winding upon
application of the pulse, assuming a fixed drive voltage, E. At
time to:
di = E
dt L (1)
Vl is induced in the search coil by loosely-coupled
transformer action. The coupling factor is affected by the
geometry and dimensions of the electromagnet but is constant after
these. have been defined~
Considering the electromagnet coil of Nm turns as a
primary winding and the seach coil winding of ~s turns as a
secondary winding, the voltage across each at time to will be
proportional to the turns ratio:
~m
Vl ~ Ns
E N~ (2)
Nm ~ Vl
In a practical case the cons-tant of proportionality is
not known so if the observed value of Vl is different from the
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desired value (such as the 100 mV of the Watson electrom~gnet),
then the number of turns of wire on the electromagnet can be
adjusted proportionally:
~m = lOo
~ma Vl
where ~ma is the adjusted number of turns.
Vl
that is ~ma = Nm 1OO (3)
The second observed search coil voltage V2 occurs at the
end of the pulse at time tl as shown in Fig, 2B, where ~1 = 10 mS
in the case of the Watson magnet and V2 = 60 mV. The magnitude of
V2 is affected by the to~al resista~ce in the pulse drive circuit,
rT. This resistance can include a dynamic value dependant on
the nature of the pulse drive circuitry which is in operation at
time t. The time constant for the electromagnet, T = L/rT
affects the rate of rise of current, di/dt in the coil.
The coil current il is then given by:
rT tl
E ( 1 - e
il = rT (4)
where e is the base of the natural logarithms.
The total resistance rT is:
rT = Rs ~ rn + RL
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where Rs is the internal resistance of the source of voltage,
rn is the resistance oE the pulse drive and associated circuitry
in operation at ti~e tl, and RL is the resistance of the
e lectromagnet coil 13.
Corrections to V2 are achieved by adjusting rI, and the
simplest method of adjustment is to change the wire gauge of the
magnet coil. The resistance per length of wire changes appro~i~
mately 25% per gauge. In practice, changing wire gauge does not
change RL by 25% as the change in wire diameter from gauge to
gauge requires more or less physical length to achieve the same
number of turns of wire on the coil. This factor also affects the
design geometry of the magnet core to ensure suffîcient space to
achieve the required winding producing the required magnetic field
strength between the magnet poles. With larger magnets Rs and
rn become more significant as RL is respectively lower.
Prior to any adjustments to the magnet coil, a core
saturation curve must be plotted. Referring to Figure 4, a vari-
able direct current source 30, e.g. 0 - 25 Vdc, is connected to
the coil 13 of magnet 10 via an ammeter 32. The current through
the coil 13 is increased in increments by incrementing the voltage
of source 30. The current increments as m~asured by ammeter 32
are documented. Simultaneously, the magnet pole face flux density
(gauss) i5 measured with a gaussmeter 35 having a probe 36. The
flux density measurements (gauss) are recorded for each current
increment. The measurements of current and gauss are then used to
plot a saturation curve. The point of intersecti~n of the curve
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and the calculated peak magnet current (from equation 3) is of
particular interest. The peak current must intersect the satur-
ation curve in the linear ramp portion as any excursion into
non-linear core operation will produce noticeable non-linearities
in the induced voltage waveform of the search coil.
It should be noted that, in using Equation 4, the
maximum source voltage must be used. This is important when
sources such as a battery are used as fully charged voltage may
differ from the nominal.
The core cross-sectional area can be adjusted to ensure
that peak current occurs immediately prior to non-linear operation
of the core. The amount of adjustment can be derived graphically
from the saturation plot on a percentage basis.
Four electromagnets were designed utilizing the process
described above. Air gaps for these magnets ranged from 60 mm to
140 mm. When energized with a 13.6 Volt, 10 millisecond pulse,
a) all magnets presented search coil voltages of Vl =
100 mV, V2 = 60 mV and
b) all magnets presented a peak magne~ic field intensity
midway between the magnets poles of between 17.5 and 19 gauss.
This performance matches the Watson prototype magnet.
The beneiits of the optimization process are best
illustrated by comparison of an optimized magnet with the Watson
prototype magnet.
air gap length depth weight average current
Watson 133 mm 204 mm 80 mm S00 gm 28 mA
Optimized 139.7 mm 172 mm 90 mm 326 gm 27 mA
magnet
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The optimized electromagnet has a larger air gap yet it
is 35~ lighter than the Watson prototype and consumes slightly
less electrical energy in producing the identical magnetic field
intensity.
This optimization process produces iron-cored electro-
magnets for use with biomedical stimulators that are minimum in
size, weight and electrical power consumption while maintaining a
like magnetic output through a range of air gap sizes. This
allows connection of such magnets to a common pulse drive source
wlthout adjustments to the source relative to particular magnet
slze .
Figures 5, and 6 are saturation curves plotted during
two stages of testing of a particular size of magnet. The current
at the end o-E 10 mS (ipeak) is also shown in both cases.
Tables I and II below set forth measured and calculated data for
the stages resulting in the curves of Figures 5 and 6,
respectively,
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TABLE I
core width 9.53 mm
core thickness 6.6 mm
core area 62.9 mm2
average current (calculated) 20.8 mA
~1 106 mV
V2 62 ~V
coil turns (Nm) 1360
wire gauge ~26 A.~.G.
RL 7.85 ohms
L 317 ~1
T = L/rT 5.49 mS
il = ipeak at 10 mS 342.1 mA
It can be seen from Table I that the measured values
Vl and V2 are higher than the desired values for Vl and V2.
Vl can be altered by adjusting the number of turns of wire on the
winding in accordance with equation (3):
Vl
~ma = ~ = 1360 . 106 = 1442
That is, (1442 - 1360) = 82 more turns are needed.
Measurements are repeated after adding turns to see if
optimization has ~een achieved; if not, further adjustments are
made.
As seen in Figure 5, the core is just starting to
saturate (become non~linear~ above the 342 mA for i at 10 mS. The
aore is therefore increased by one lamination thickness.
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TABLE I I
core width 9.53 mm
core thickness 6.8 mm
core area 64.804 sq. mm
average current (calculated) 19.18 mA
Vl 101 mV
V2 62 mV
coil turns t~m) 1440
wire gauge #26 A.W.G.
RL 8.67 ohms
L 349 mH
T = L/rT 5.95 mS
il = ipeak at 10 mS 315.45 mA
As seen in Figure 6, the core in this example i5
operating at the upper part of the linear region and is
satisfactory, Vl and V2 being also satisfactory. The magnet can
be considered to be optimized.
Tables I and II also include calculated values of
average current. This is an important factor, particularly where
battery operated squipment is concerned. Th~ difference between
19.18 mA (Table II) and 20.8 mA (Table I) can translate to 2
additional hours of operation before charging is required (in
excess of 8% increase in run time).
A reasonablP approximation of average current can be
calculated from the following;
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il
average = 2 d pulse duration
puLse repetition rate
for the above example I avg ~ 315.45 . 10 = 19.18 mA.
2 82.2
Figure 7 is a flow chart of a practical implementation
of the method according to the invention. Referring to Figure 7,
the method starts at 50 and a prototype magnet is constructed,
step 51. Pulses are applied to the coil of the electromagnet,
step 52, and voltage measurements (Vl) are made at the beginning
of pulses in a standardized search coil, step 53. The measured
voltage for (Vl) is compared with a predetermined magnitude for(Vl)
at step 55 and, if it is less than the predetermined magnitude for
Vl, the number of turns in the coil is to be decreased, step 56,
whereas, if it is greater, the number of turns is to be increased,
step 57. If it is equal, no change in the number of turns of the
coil is required. The method then proceeds to step 58, a
measurement of the voltage (V2) at the end of the pulses in the
standardized search coil. In step 59, V2 is compared with the
predetermined (desired) value for V2. If it is equal, the method
proceeds to step 62. If it is less, the wire size is to be
increased (step 60) and if greater the wire size is to be reduced
20 (step 61). The method proceeds to step 62. In step 62 the
current in the coil at the end of the pulses is calculated and at
step 63 a check is made of its point of intersection with a
saturation curve of the iron core of the electromagnet. If the
point of intersection is not satisfactory, the cross-sectional
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area of the core is to be altered (by adding or subtracting
laminations, for example), step 65 and the method proceeds to step
66. If the point of intersection is satisfactory (near upper
limit of linear region of saturati.on curve) the method proceeds to
step 66. At step 66 a decision is ~ade as to whether the design
is complete, i.e. all tests have given satisfactory results. If
so, the method ends, step 67. If not, the method returns to step
51 where a new prototype magnet is made with, as indicated by the
tests, a different number of turns, a different wire size, or a
different cross-sectional are~ of iron core. Although in some
cases it would be possible to alter these on the original
prototype electromagnet, it is less practical than simply making a
new prototype.
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