CA1323907C - Optimization of iron-cored electro magnets for biomedical stimulators - Google Patents

Abstract

ABSTRACT

Disclosed is a method of optimizing the structure of an electromagnet so that when its coil is energized by electrical pulses of predetermined duration and amplitude the electromagnet induces voltages of first and second predetermined magnitudes in a standardized search coil located midway between pole faces of the iron core at times corresponding to the beginning and end of the pulses. The voltage induced in the search coil at the beginning of the pulses is measured and, if it is greater than the first predetermined magnitude, the number of turns of the coil is increased whereas, if it is less than the first predetermined magnitude, the number of turns is decreased. The voltage induced in the search coil at the end of the pulses is also measured and, if it is greater than the second predetermined magnitude, the gauge size of the wire forming the coil is reduced whereas, if it is less than the second predetermined magnitude, the gauge size is increased. Also, the coil current flowing at the end of the pulses is calculated and the point of intersection of the current with a saturation curve of the iron core is checked; if necessary, the cross-sectional area of the iron core is altered to ensure that the point of intersection is near the upper limit of the linear region of the saturation curve.

Description

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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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J~ 557-3150 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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~ 3 ~) 557-3150 (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 :, t ~
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~ ~ ~J ~ ~ 3 i 557 3150 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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~c3~ 557-3150 (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 ,', ' ~ ~ ~ ' ' , , , i . - . ..

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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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f~ ; t 557-3150 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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~ , 2 ~ f~ ;! 5S7-3150 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 ~ f~ 3 1 557~3150 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 _ 10 ---.

; ~ ' 3 1 557-31~0 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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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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:~ ?~2 .J .J' 3 l 557-3150 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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~ 2 ~.J~ 557-3150 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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Claims (6)

1. A method of optimizing the structure of an electromagnet having an iron core and an associated coil formed of wire having a gauge size so that when said coil is energized by electrical pulses of predetermined duration and amplitude said electromagnet 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 magnitude, 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 (d) calculating the current flowing in said associated coil occurring at the end of said pulses, checking where the point of intersection of said current with a saturation curve of said iron core is checked; if necessary, the cross-sectional area of the iron core is altered to ensure that the point of intersect ion is within the upper limit of the linear region of the saturation curve.

2. A method as claimed in claim 1 wherein the measurements of steps (a) and (b) and the calculation and checking of step (c) are all performed before making any changes in the number of turns of said associated coil, the gauge size of the wire or cross-sectional area of said iron core.

3. A method as claimed in claim 2 wherein said iron core has a square cross-section.

4. A method as claimed in claim 3 wherein said electrical pulses have a duration of 10 milliseconds and an amplitude of 13.6 volts.

5. A method as claimed in claim 2, 3 or 4 wherein any said changes are made by constructing a new electromagnet incorporating said changes.

6. An electromagnet constructed according to the method of claim 1, 2 or 3.