INST. r
8
j
OPT 1929
t/l, A R*4
A FURTHER INVESTIGATION OF BARKEHAUSEN EFFECT
by
ARTHUR R. ELLIOTT
and
DENNISTOUN W. VER PLANCK
Submitted in Partial Fulfillment of the Requirement
for the Degree of
MASTER OF SCIENCE
from the
Massachusetts Institute of Technology
1929
Signatures of Authors
Signature redacted
Signature redacted
*.
aa9e0 *. e@
O-b
e *00
Certification by the Department of Electrical Engineering
)
Committee on Graduate Students)
Head of Department
.
(I Signature redacted
..
0
..............................
..
*
Chairman of Departmental
,.Signature redacted
)
Professor in charge of Research
ACKNOWLEDGMENT
The authors wish to acknowledge the advice
and encouragement given them by Professor Stratton,
the supervisor of this investigation, and by Dr. Bush.
They also wish to thank Professor Lansil
for his assistance with their magnetic flux measurements,
and Mr. J. B. Russell, Jr. for his help with their
photographic problems.
TABLE OF CONTENTS
I.
II.
HISTORICAL INTRODUCTION
History
1
Plan
4
APPARATUS
General
6
Excitation System
8
Search Coil
16
Amplifier
19
Oscillograph
24
Flux Measurements
26
Operation
31
III. BARKHAUSEN EFFECT VERSUS HYSTERESIS LOOP
IV.
Solenoid Tests
34
Fahy Permeameter Tests
36
Barkhausen Effect vs.Hysteresis Loop
38
EXPERIMENTS ON COMPOSITE SPECIMENS
Purpose
46
General Method
50
Brass Gap
51
-
Air Gap Test
Extended End Test
55
Weighted End Test
58
Conclusions and a Tentative
Theoretical Explanation
62
APPENDIX A - Amplifier Transient Analysis
67
APPENDIX B - Search Coil Response Characteristic 74
APPENDIX C - Hysteresis Loop Data
I.
HISTORICAL INTRODUCTION
History
The "Barkhausen Effect" is the name given to the
fact that the process of magnetization is discontinuous.
It is so named after H. Barkhausen, who experimentally
discovered in 1919 that the process was not smooth, -that it apparently involved the magnetization of units
greater in size than molecules.
He found that the ampli-
fied voltage, induced in an exploring coil placed about an
iron wire subjected to a smoothly varying magnetizing force,
was not smooth.
On the contrary, he found it was very
irregular by listening to head phones through which the amplifier output was passed.
His work was taken up by other investigators,
mostly European.
To detect the Effect, all used the same
general method as did Barkhausen.
They differed principally
in the manner by which the amplifier output was observed.
Head phones, oscillographs, and galvanometers coupled with
rectifiers were used.
From the nature of the subject and
the characteristics of the apparatus involved in its detection, the greater part of the information gathered has been
qualitative rather than quantitative.
The observed results
have led to different opinions about the process of magnetization.
Barkhausen and Van der Pol believed that there
1.
were sudden orientations of given small masses of magnetic
material, such as crystals.
Gerlach, Lertes, and
Zschiesche believed that the effect was dependent on magnetostriction.
Tyndall found that the discontinuities did
not result from single definite sizes of particles orienting themselves, such as crystals.
Dr. Griffith found
that the discontinuities were random in size but proportional
in some manner to the length of specimen, and rate of change
of field, varying in the same direction as these factors.
From his work, he suggested a travelling mechanical wave
theory.
This wave was set up by a succession of differen-
tial magnetostrictive effects which resulted when elementary
magnetic particles suddenly oriented themselves.
This wave
would be reflected from the end of the specimen, arriving
at the portion of the specimen being investigated after a
lapse of time.
During this lapse, the changing field had
left some particles in an unstable state.
The shock of the
wave would cause the unstable particles to suddenly orient
themselves in a group.
If the field rate of change were
greater, then more particles would be rendered unstable by
the time they were jarred by the wave, resulting in larger
discontinuities.
If the specimen were longer, the time for
2.
the travelling wave to return would be greater, since the
speed is fixed by the elasticity and density of the medium.
The number of particles rendered unstable would be greater,
hence larger discontinuities.*
Later work has been done by Pfaffenberger and
Bozorth.+
The first found that "the magnitude and number
of 'effects' are dependent on the rapidity of the change of
field, but the sum of the effect amplitudes is independent
of this speed."
Bozorth came to the conclusion that, for
many different metals, there was one average size of the
groups of atoms acting as a unit.
The differencein the
For a more complete summary of the early history,
*
and for a complete account of the travelling wave theory,
the reader is referred to the thesis of Dr. B. C.
Griffith on "A Study of Barkhausen Effect," done at the
Massachusetts Institute of Technology in 1928.
+
At this time of writing, only abstracts of the
articles are available to us.
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Sec.-A
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Part-.3
p2,?78.
Bvlletin Amn.P ys- Soc.
Feb. qIq92
p15
3.
Vol.4 A/*.I
appearance of the effect was due to different rates of
decay of eddy currents in themp
He also found that the
sum of all the sudden differential flux changes as evidenced by the Barkhausen Effect account for all the change
in magnetization over the steep part of the hysteresis loop.
Plan
After viewing the history of the Barkhausen Effect, we came to the conclusion that previous investigators
had taken a rather near-sighted view of the subject.
Its
details were examined, while a general study of it was
lacking.
Many questions were in our minds.
What was its
relation to other well known magnetic phenomena?
it related to the hysteresis loop?
the Effect occur?
How was
Where on the loop did
In short, where was there a bird's eye
view of the subject?
In our small way, we planned to
supply it to the best of our ability.
In the first place, the Effect was to be -studied
in connection with the hysteresis loop.
location on the loop was to be noted.
In particular, its
Secondly, it was
planned to investigate the theory set forth by Dr. Griffith.
Some doubts had arisen as to whether or not there was a
travelling wave, and if so, it was not definitely proven
that the wave was of the nature suggested.
With these plans in mind, we commencedwork.
It soon became impressed on our minds that the Barkhausen
1 1L
Effect as evidenced by the oscillograph, was a very indirect
manifestation of the discontinuities of magnetization.
Much
apparatus was necessary in order that a view of the Effect
might be had.
This apparatus was able to influence the ob-
served result very considerably because of some inherent
characteristics.
Therefore, to interpret intelligibly the
observed results, a careful study of the apparatus characteristics was necessary.To such an extent wis this true
that the greater part of this investigation was spent
studying and altering the required apparatus.
5.
II.
APPARATUS
General
To be of value, any set of experimental data
must be accompanied by an account of the manner in which,
and the particular conditions under which, they were
taken.
This is particularly true of the records of the
Barkheusen Effect because of the very limited state of
the general knowledge of this phenomenon.
By giving a
description of our apparatus and a discussion of its
characteristics, bad as well as good, we hope to place
the reader in a position to draw his own conclusions from
our results and to value them at their true worth.
The general method by which we observed the Effect is as follows --
the iron specimen in the form of a
short straight piece of wire is placed with its axis in
the direction of a magnetic field.
A small search coil is
put around the specimen with its axis coinciding with the
axis of the specimen.
The magnetic field is then varied
smoothly and nearly linearly with time between equal positive and negative maximum values so that the specimen is
carried around a hysteresis loop.
The voltage induced
in the search coil is amplified in order that oscillograms
6.
may be taken of it.
smooth
The oscillogram does not show a
rise and fall of voltage as might be expected,
but a series of voltage kicks of varying size and varying
These kicks are the outward manifestations of
frequency.
the Barkhausen Effect.
In order that we may have a sound
basis for reasoning backward from the form of these manifestations to their cause we must closely examine the apparatus used in exciting and observing the Effect.
The apparatus consists of four principal elements
(1)
--
An Excitation System whose function is to subject
the specimen to a field varying smoothly between equal
positive. and negative values.
(2)
A Search Coil
in which the voltage impulses due
to the Effect are generated.
(3)
An Amplifier which replaces the small voltage
variations of the search coil by current variations sufficiently large to operate a recording device.
(4)
An Oscillograph which makes visible the form of
the current variations supplied by the amplifier and which
enables permanent records of them to be taken.
A number of investigators have used apparatus of
this general form, the differences being in the nature of
the four chief elements.
We began our work by building ap-
paratus as nearly like that used by Dr. Griffith as we could
from his description, using the few of his parts which we
could find.
This apparatus worked successfully, but it had
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a number of inherent disadvantages which caused us to
modify some parts of it and to scrap other parts, developing new ones to replace them.
None of our final records
were obtained with the old apparatus,
not describe it here.
therefore we shall
We shall, however, mention briefly
some of its points in connection with the discussion of
the final apparatus to which we shall now turn.
First we
take up the Excitation System.
The Excitation System
The function of the excitation system is to carry the specimen smoothly around a symmetrical hysteresis
loop.
Our excitation system consists of two main parts:
a magnetizing coil in whose field the specimen is placed,
and a motor driven potentiometer which supplies, with the
aid of a battery, the linearly varying current to the coil.
The coil is connected between the slider of the potentiometer and the neutral of the battery, as shown in the sketch
below
--
Fa-4y 11-7
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The purpose of the choke coil and condenser is to prevent any small, rapid fluctuations in the magnetizing current caused by irregularities in the potentiometer or by
induction in the battery leads which are very long.
The potentiometer is the chief feature of our
excitation system.
As will be seen belowit enabled us to
get a very smooth, nearly linear variation of current without any undue complications.
Its resistance is formed by
a very weak salt solution in a large battery jar.
The end
points are formed by two copper plates, one at each side
of the jar.
The "slider" is a sort of paddle pivoted in
such a way that its copper blade may be moved back and forth
between the end plates.
The paddle is driven by a va-
riable speed direct current motor through a pulley and belt
reduction system.
The motion is transmitted from the last
belt to the paddle by a double cross-head fastened to the
belt.
One part of the cross-head slides on the paddle, the
other part on a fixed guide parallel to the belt.
The speed
at which the paddle moves can be varied so that the traversing time is from five seconds to one minute.
The following considerations show that a nearly
linear variation of magnetizing current is possible with
our potentiometer.
With an ordinary slide-wirethe rate of
change of current with respect to slider position increases
q7.
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as the slider is moved from the center to the end of the
slide-wire.
Two factors tend to compensate for this ef-
fect in our potentiometer.
First, the paddle moves more
slowly near the ends of its stroke than near the center if
the cross-head is driven at uniform speed.
Thus the tenden-
cy is for the current to vary more uniformly when the
cross-head moves at uniform speed than if the paddle itself
moved at uniform speed.
Second, since the paddle swings
on the are of a circle, the blade moves up near the end
of the stroke out of the direct path between the end
plates, effectively limiting the rate of increase of current near the end of the stroke.
With a little juggling
of the geometrical relations of the paddle mechanism, we
were able to get a very nearly linear current-time charvery
acteristic except in the regionnear the ends of the
stroke.
The potentiometer drive must operate as smoothly
and quietly as possible.
A jerkiness o
the paddle so
small as to be invisible to the eyeand vibrations so small
as to be scarcely felt are very objectionable.
Vibration
of the drive can be detected by the appearance on the Effeet oscillograms., of a frequency,characteristic of the
drive speed.
This disturbance gets into the system both
directly through fluctuations of the magnetizing current,
10.
and indirectly by mechanical vibration of various parts
of the apparatus.
We secured almost perfect freedom from
such troubles by supporting all vibration--sensitive parts,
as well as the driving mechanism itself, on sponge rubber,
and by smoothing the action of the mechanism.
Rather than
go to the expense of using accurately machined metal parts
to secure smoothness ,we used linen belts on fibre pulleys
and a sheet copper cross-head on well greased wooden guides.
With a little care we obtained excellent results from this
arrangement.
This question of disturbances originating in the
excitation system was the chief reason for our abandonment
of Griffith's system.
His method was to apply the direct cur-
rent transient of a condenser-resistance circuit to the
magnetizing coil after a single stage of vacuum tube amplification.
By superposing this transient on a component of
current which flowed steadily all of the time,the effect
of reversing the magnetizing current was obtained.
The
range of the hysteresis cycle and its time of completion
were controlled by the value of steady current, and by the
time-constant and charging voltage of the condenser-resistance circuit.
Theoretically the scheme is beautiful but
practically it was too complicated and too inflexible of
control for our use.
But its chief fault was that the am-
plifier tubes were microphonic.
I/.
Not only were they
sensitive to vibration transmitted through their supports
but they responded to the sound waves of coughs, sneezes,
and loud conversation.
Examination of oscillograms taken
under these conditions show ripples in the magnetizing
current with correspondingly increased magnitude of Effect.
Rather than attempt to remedy these difficulties,we perfected an entirely new arrangement as we have described
above.
Not the least of the improvements was the simpli-
fication of the amount and kind of equipment involved.
item of equipment will serve to illustrate this --
One
the old
system required over four hundred volts of portable storage
batteries for its operation, the new potentiometer uses only the regular 220-volt battery of the laboratory power
system.
The current output of the potentiometer is fed
through the magnetizing coilwhich is the other chief part
of the excitation system.
The ideal magnetizing arrangement
would subject the specimen to flux conditions which are
determinable for each part of the specimen at all times of
the cycle.
The type of arrangement for approximating this
ideal of course varies with the form. of specimen which is
used.
For our specimenswhich are moderately long wires,
170 diameters in length, magnetized longitudinally, we had
two arrangements available.
One, the long solenoid, in-
herited from previous investigators, approaches the ideal
IZ.
only remotely.
The other, the magnetizing yoke of the
Fahy Simplex permeambter, adapted by ourselves, approximates
the ideal comparatively closely.
As we used sometimes the
solenoid,and sometimes the Fahy according to the nature of
the particular experiment, we sha;il discuss them both.
The long solenoid was the first arrangement that
we tried.
It has the seeming advantage that it produces a
magnetizing force which is uniform and easily evaluated.
However, complications arise as soon as the iron wire specimen is introduced on the solenoid axis.
The specimen be-
comes magnetized, and, since its ends are free, polar regions are produced.
The effect of the poles is to produce
a demagnetizing component of force which varies along the
specimen.
The problem of finding the resultant flux dis-
tribution is a very complicated one; and, as far as we could
However
determine from the literature, no one has solved it. ,*here
are several methods for getting the approximate value of
flux at the center of a cylinder which is statically magnetized.
These methods involve the use of experimentally
determined demagnetization factors, or the assumption that
the specimen is a long ellipsoid, or the assumption that
point poles exist near the ends of the piece.
Their re-
sults become better as the piece is made longer, since the
demagnetization is then not only smaller but more nearly
'3.
uniform in the central region.
For the results to be pre-
cise enough for our use, the specimen would have to be inconveniently long.
Our specimens are not nearly long enough
even though they are much longer than those used by previous investigators.
Anyway, even if very long pieces were
used, these methods would be difficult, though not impossible to apply to hysteresis loops.
After trying out
these methods and finding that they were very uncertain, we
turned to other apparatus for determining the relation between Effect and magnetic condition.
We did, however, make
measurements of relative flux distribution along the specimen in the solenoid to correlate with variation of Effect
along the length.
We used the ballistic method of flux
measurement with the Effect search coil as the measuring
coil.
This gave us relative hysteresis loops for each
eighth of the length of our specimen, to be compared with
oscillograms of Effect at the same points along the specimen.
The solenoid proves valuable in those tests whereflux conditions do not need to be known and where mechanical
freedom of the specimen is essential.
We thus used it in
tests to determine the influence of non-magnetic end extensions on Effect in the specimen.
The solenoid is 47 cm. long with a length to diameter ratio of about thirteen.
on a split brass tube.
It has a multilayer winding
The specimen is placed inside of a
/ 4A.
glass tube which is held along the solenoid axis.
The
specimen can be placed exactly in the center of the solenoid
with the aid of a graduated ram rod which just fits
of the glass tube.
the bore
The search coil is mounted on a carri-
age which slides on the outside of the glass tube.
The
search coil position can be readily determined from outside
by means of graduations on the brass rod which is used to
move its carriage.
The Fahy permeameter yoke is the other magnetizing
arrangement which we used.
It
consists of a U - shaped
laminated steel core woutd with a magnetizing coil.
It is
arranged with suitable clamps permitting a specimen to be
fastened securely across the open part of the U.
When the
coil is energized the flux is quite nearly uniform along the
length of the specimen, provided, of course, that the specimen is of uniform section and material.
We checked this
experimentally using the small measuring coil ballistic method mentioned above for the solenoid.
The cross section of
our specimen is so small in comparison to the cross section
of the yoke that the reluctance of the yoke is entirely negligible.
The result is that the magnetizing force exerted
on the specimen is not only uniform but nearly directly
proportional to the.magnetizing current.
The determination of the flux values corresponding
to points on an oscillogram is simple and direct.
After
taking an oseillogram using the Fahy as part of the excitation system, the search'coil is replaced by a measuring coil
IS.
and the Fahy is connected again in its regular permeameter circuit.
A hysteresis loop of appropriate range,
is then taken in the standard manner except that magnetizing current readings are also taken.
We thus obtain da-
ta connecting flux and magnetizing current to compare with
our oscillogram which shows the Effect as a function of
this same magnetizing current.
The Fahy thus meets the
ideal of giving uniform, determinable flux.
There are, however, two factors which may have a
disturbing influence on the Effect.
One is that the magne-
tizing force is applied between the ends rather than conThe other
is that the ends of the piece are rigidly clamped which may
cause modifications if magnetostriction plays an important
part in the mechanism of the Effect.
These points will
be discussed more at length later.
We have now covered that part of the apparatus
which excites the Effect.
Next we turn to those parts
which detect the Effect.
The Search Coil
The search coil is the pick-up device of the detecting apparatus.
It is acted upon by the Jerkily changThe voltage impulses which result
ing flux of the Effect.
are the manifestations of the Effect.
/6.
,
tinuously along the piece as with the solenoid.
It is a small, concentrated,circular coil of about
seven thousand turns of fine wire wound on a paper form.
It is placed around the specimen with its axis coinciding
with that of the specimen.
Its effective area is so large
in comparison to the cross sectional area of the specimen
that all parts of the specimen may be assumed to be on the
axis of the coil.
We inherited this coil but no accurate
winding data was included in the bequest.
However, we de-
termined the chief dimensions and effective number of turns
roughly by experiment.
From these data can be calculated
the response characteristic of the coil.
The response characteristic is based on the assumption that the Effect is produced by the change in magnetization of separate particles of the specimen.
It is a
graph of the relation between the relative number of flux
linkages with the coil,of an infinitesimal magnet whose
axis coincides with the coil axis, and the position of the
magnet on the axis.
It follows that it also gives the re-
lation between the position of the magnet on the coil axis
and the relative voltage that would be induced in the coil
if the infinitesimal magnet was changed in strength or
direction at a fixed rate.
Dr. Griffith gives the deriva-
tion of the formula in his Thesis.
Our figure 4
is a
plot of this formula.
There are three factors governing the size of
single voltage impulses induced in the coil.
17.
They are
5EARCH
COIL.
CHARACTERISTIC
RESPONS
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the size of the change of flux, the rate at which it changes,
and the distance of the center of the disturbance from the
center of the coil.
The first two are inseparably bound
up together and no conclusions as to their relative importance can be obtained by comparing the voltage impulses
alone.
The third factor is important with our coil as
indicated by the gently sloping response characteristic.
This factor can be reduced greatly in importance, at least
theoretically, by designing a coil with a more nearly reetangular response characteristic.
The design of a search coil depends on the necessary number of turns fixed as a minimum by the highest
sensitivity of amplifier which is practical and on the
smallest size of wire which can be conveniently used.
When
these two factors have been determined,the proportions of
the coil can be juggled to give the most rectangular and
narrowest characteristic possible.
Preliminary calcula-
tions in this direction indicate that our coil has not the
best form but that the best does not appear sufficiently better to justify the labor of constructing it.
curve in Fig.
4
The dotted
indicates what appears to be the best
characteristic obtainable with the given number of turns
and wire size.
The response region is narrower but the
I8.
characteristic is not enough steeper, as it drops to the
axis, to warrant its construction.
We made no attempts to better the search coil
because we are not primarily interested in the size of
single impulses.
All that is essential for our purpose
is that the response characteristic be narrow enough so
that all parts of the specimen which influence the coil
are simultaneously on the same point of the hysteresis
loop.
We accomplished this end by making the magnetic
conditions more uniform rather than by changing the seardh
coil.
The Amplifier
The function of the vacuum tube amplifier is to
replace the voltage variations of the search coil by similar current variations large enough to operate the oscillograph.
Our amplifier, which is similar to the one
used by Dr. Griffithhas four resistance-capacity coupled
stages.
Its sensitivity is such that one millivolt im-
pressed on the first stage causes a one-half centimeter
deflection of the oscillograph.
An amplifier such as ours gives two main types
of trouble.
Firstit is a very vulnerable point for
electrical and mechanical disturbances to get into the
system, and second, even under perfect conditions, it
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introduces distortion.
The first of these troubles can
be reduced to as small a degree as desired by the use of
proper shielding.
The second, is mainly an inherent
feature of the particular amplifier circuit; the only
thing that can be done about it is to determine its magnitude and then take it into account in interpreting the
oscillograms.
First we shall describe the means employed
to minimize the effect of outside disturbances.
For protection against electrostatic disturbances,each tube and each coupling circuit is enclosed in a
separate copper box.
All leads with the exception of those
going to the "A" and "B" batteries are enclosed in brass
tubes or in copper braid.
Each element of the shiblding
is insulated except for a single bond to a grounded bus.
This precludes the possibility of current circulating among
the shields.
To avoid electromagnetic pick-up and back coupling
between stages, twisted pairs are used wherever practical.
Grid and plate leads are kept well apart from each other and
they are made as short as possible.
Filter circuits in the "B" battery leads were
found to be not only unnecessary~but quite objectionable.
Their function is to prevent back coupling between stages
through the batteriesby confining the signal currents
to the shielded part of the set.
Evidently no tendency
toward such back coupling exists among the first
20.
three
stages because they operate successfully from a cbvntm-O
battery with no filters.
The last stage requires a com-
pletely separate battery because even the filters could not
stop it from feeding back into the first stages when a
common battery was used.
The objectionable feature of the
filters is that they increase the inherent distortion introduced'by the amplifier.
The above described precautions against electrical disturbances were successful insofar as they counteracted any tendency toward instability of the amplifier itself.
They gave protection against all outside distur-
bances with the exception of that originating in the
"Integraph".
This disturbance was so bad that we gave up
trying to guard against it and worked only when no integration was in progress.
The vibrations from a machine shop in the next
room and from our own motors made special precautions against
microphonic action of the tubes necessary.
We placed the
tube sockets on sponge rubber pads held in wooden clamps.
By properly adjusting the pressure on the rubberit is
possible to make the motion of the tube highly damped and
at the same time provide a soft cushion to absorb outside
vibration.
Spring sockets cannot be used because they
foster continued swinging of the tube,which causes a regular wave to appear in the amplifier output current.
2-
In
addition to the socket shock absorbers the whole amplifier
is placed on rubber sponges.
These features make the am-
plifier almost perfectly vibration-proof.
The inherent distortion of the amplifier is of
two kinds, that due to the non-linearity of the tube
characteristics and that introduced by the coupling circuits.
The first kind can be reduced by using the proper
grid bias on each tube.
In our case,it gives no bother ex-
cept with exceptionally large Barkhausen kicks which sometimes have their tops distorted by this cause.
The distortion introduced by the coupling circuits varies greatly with the type of signal.
For short
impulses such as single Barkhausen kicks,it is quite small,
while for steady voltages,it is bad.
The cause of the
distortion is the insulating device, a condenser in our
case, which for practical reasons must be used between
tubes.
The presence of the condenser makes the voltage
applied to each tube depend upon the rate of change of voltage applied to the preceding tube.
The response of the amplifier to simple voltage forms can be easily found experimentally.
It is
not very difficult to calculate the response also.
The
purpose of both the experimental and analytical determination is to provide assurance that all of the distortion is
really due to the amplifier characteristic and not to
some other trouble.
Such experimental and analytical
determinations have been made and are found to check closely.
The analyses and method of experimental check are
given in Appendix A.
Oscillograms of the response to various signals
are given in Fig.
6
The one with small time constant
is like a single Barkhausen kick.
The ones with larger
time constants might be approximated by groups of Barkhausen kicks closely superimposed.
These oscillograms
indicate the whole range of time-constants for which the
distortion is appreciable,and yet none of the negative
swings are greater than 30% of the positive peaks.
Our oscillograms of Effect often show large
swings of the amplifier line both above and below the
axis.
When swinging occurs, negative as well as positive
peaks appear.
It is believed that the Effect gives only
unidirectional peaks so it seems likely that the amplifier
may be introducing the swinging.
An explanation which
may easily account for at least some of the swinging is as
follows.
Suppose that single kicks are coming in bunches
so as to give transients like the
Fig. 6.
third
one in
Transients like these,if superposed at random will
23.
y
V
'-PZIj
29coJ'a
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9
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f\~I\JP~fJ\/AJ IT4
VIAl
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I
give negative as well as positive swings of the line and
also the appearance of negative peaks.
The sketch shows
the beginning of a negative swing
Such random superposition could probably account for negative swings as large as the positive ones because,while the
negative portion of a single transient has less amplitude,
it lasts longer than the positive portion.
Another pos-
sible explanation of the swinging is that it is the transient response of the amplifier to the average voltage induced in the search coil.
These points will be considered
more at length in the discussion of our experiments.
The Oscillograph
The function of the oscillograph is to give
visible evidence, and permanent records, of the Effect.
The oscillograph used is the General Electric Type EM
having three elements.
Since this is a standard piece of
*
2
apparatus in common use, we shall discuss only those features which required special adaptation to our needs.
The vibrators were strung by us in the standard
manner.
"High sensitivity" stringing was used on the vi-
brator showing the Effect and on the one indicating the
excitation current.
The6O-cycle timing wave vibrator is
of ordinary low sensitivity.
Damping fluid, vibratbyr-.
tension, and galvanometer field strength are all standard.
It was necessary to substitute a direct current
motor for the regular synchronous motor which drives the
shutter and mirror.
The synchronous motor had a very bad
strxty; field which acted on the search coil at a distance
of several feet.
The synchronous motor could not be driv-
en idle because the permanent magnetism in its rotating
structure produced a strayT field almost as bad as when the
motor was running under its own power.
We had to remove
the rotating magnetic structure entirely.
The oscillograph arc light is always a potential
source of trouble because the search coil is very seriously
affected by any irregularities in the are current.
We
found it necessary to operate the are from a battery to
avoid commutator singing.
A choke was connected in series
with the arc to reduce hissing and spluttering.
With these
precautionstogether with careful attention to the electrode
adjustment, we succeeded in staving off the trouble.
If
we were to begin againwe should surely use an incandescent
lamp.
Our final oscillograms show an inappreciable amount
of pick-up from the are with the exception of a few splutters which are distinguishable by the white band across the
picture and a corresponding kick in the amplifier line.
Our oscillograms are taken directly on bromide
paper.
Since the Effect cycle is quite long and because
we want oscillograms of convenient size, a very slow film
speed is necessary.
This requires an extra-reduction pul-
ley in the drive of the film drum.
The field vibrator was calibrated before and after each series of oscillograms.
It was done by observing
the change in current necessary to change the deflection
5 centimeters at the film surface.
Immediately after ex-
posing each oscillogram~a zero field line was exposed with
the light blocked off from the other vibrators.
plifier vibrator was not calibrated alome.
The am-
It was cali-
brated as a part of the amplifier by applying transients of
known form to the amplifier and taking osoillograms of the
result.
Since the oscillograms closely check calculations
based on amplifier distortion alone it seems evident that
the oscillograph follows the changes in current faithfully.
Flux Measurements
Since one of our chief purposes was to correlate
the Barkhausen Effect with the hysteresis loops of the
specimen, it was essential for us to have a simple means of
determining these loops of our iron wires.
Professor
Lansil of the Measurements Laboratory suggested the use of
the Fahy Simplex Permeameter and very kindly advised us on
how to fit it to our needs.
Later we had the happy thought
of making the permeameter an integral part of the excitation
system,thus greatly simplifying the compna -rionof hysteresis
loops with oscillograms.
V
H~~
ciIcoil
The Fahy consists of the magnetizing coil and yoke
described in connection with the excitation system, and two
measuring coils.
One, the "B" coil, is a distributed winding
covering the entire specimen bar between the clamps.
27.
The
other, the "He coil,is a distributed winding on a non-magnetic core which is parallel to the specimen between the
clamps.
When the magnetization is reversed the deflection
of a ballistic galvanometer connected to the '"H" coil is
proportional to the magneto-motive force exerted on the
When connected to the "B" coil,the reading is
specimen.
proportional to the total flux in the specimen plus the
leakage between the coil and the specimen.
The values of
B and H in the specimen corresponding to these deflections
may be easily calculated from the constants of the permeameter, the dimensions of the specimen, and the cAlibration
of the ballistic galvanometer which is obtained by the mutual inductance method.
Hysteresis loops are taken by the
usual method of partly reversing the magnetizing current.
For our small iron wires,the regular "1B" coil
had too few turns and permitted too much leakage.
We
made a special "B" coil just large enough to slip over the
specimen and with enough turns to give good galvanometer
deflections.
This coil had to be wound very carefully in
order that its constants could be accurately found from its
dimensions.
It consists of nine layers of #38 wire, 1010
turns per layer, wound on small cambric tubing known as
spaghetti.
We also had to procure special clamping blocks
to fit the small specimens.
28.
We took our hysteresis loops in the standard
manner except that we also took readings of the magnetizing
current at each point to be used in determining flux conditions on the oscillograms.
To determine the distribution of flux along a
specimen for the cases when it was not uniformwe took
hysteresis loops using the search coil instead of the "B"
coil.
This made it possible to obtain a plot of the rela-
tive value of flux against magnetizing current for a particular part of the specimen, and then to take an oscillogram
of Effect against magnetizing current for exactly the same
part.
As long as the same search coil is used for both
measurementseach element of the specimen contributes the
same proportion of the total coil voltage whether that voltage is being used to deflect the ballistic galvanometer or
the- oscillograph.
The chief difference in the two measure-
ments is that the hysteresis loop is taken point by point
while the corresponding oscillogram is taken continuously.
This type of measurement was used for air-gap specimens in
the Fally and for a continuous specimen in the solenoid.
The loops which we obtained are plots of relative search
coil readings against magnetizing current.
Since no data
on the true value of magnetizing force at each point could
be obtained easily, no correction could be made for leakage
29-.
between coil and specimen.
The relative loops are suffi-
cient for the purpose of showing that variation of Effect
along a specimen can be accounted for by variation of the
r4ysteresis loop.
30.
Operation
In making the experimental runs, we followed a
general procedure that was much the same for all tests.
In the first
place, it
would be well to state that
the amplifier and its vibrator were not calibrated during
each test.
All pictures for a given series were taken in
a short interval of time, always less than one hour.
this short interval, conditions were constant.
In
On two dif-
ferent days, conditions were often altered to suit circumstances.
The"B'and"C battery voltages on the last stage
of the amplifier were sometimes changed.
Thus it is
necessary to compare only the pictures of a given series.
Unfortunately flux measurements could not be made
simultaneously with oscillograms.
The permeameter circuit,
with its galvanometer and switching arrangement, is located
in another laboratory.
The time intervening between oscil-
lograms and corresponding flux measurements was less than
two days in all cases.
It is unlikely that this had any
ill effects for we checked hysteresis loops very closely
after a lapse of two months.
All of the final experiments were run either at
night or on holidays when disturbances of all kinds were at
a minimum.
Notwithstanding all our precautions against
31.
disturbances, the elimination of one disturbance always
uncovered a smaller one which had been hidden before.
However, in our final results, the disturbances were very
small.
To take the oscillograms, the specimen,magnetizing
coiland search coil were arranged according to the requirements of the experiment.
The oscillograph was made ready,
care being taken that the optical system was in proper condition.
It was very important that the are lens be clean,
and that all oil be wiped off the vibrator cell windows.
After calibrating the vibrator carrying the excitation current, the loaded film dxtum was put in position, and the rate
of change of field set to the desired value.
While bring-
ing the specimen around a number of hysteresis loops of
correct amplitude to establish the cyclic state, we observed
the Effect visually in the oscillograph in order to determine its duration in relation to the readings of a small,
shuntedcenter-zero galvanometer which indicated the magnetizing current.
When the range of field current had been
found, the film speed was adjusted so that the desired
range would be included on the oscillogram.
The film drJ=:
was stopped with an end of the film opposite the photographic slit.
Then, after carefully adjusting the are so as to
31.
give intense illumination without the very objectionable
hissing, the oscillogram was ready to be taken.
When the
changing field current passed a predetermined value, the
film drum was started and the shutter opened while the drum
made one complete revolution.
Lastly, the drum was exposed
for another revolution to the light of only the excitation
current vibrator while its circuit was open.
The film was developed immediately, and examined
for possible flaws, before taking the next of the oscillograms in order that the set-up might not be changed if it
were necessary to retake the film.
As a precaution, we calibrated the excitation
current vibrator frequently.
33.
III
Barkhausen Effect Versus The Hysteresis Loo
Solenoid Tests
In order that the Barkhausen Effect might be
studied in connection with the hysteresis loop, it
is
necessary to know the exact magnetic state of the specimen
under the search coil from knowledge of the value of the
excitation current.
When the solenoid was used to supply
the uniformly varying field, difficulties were encountered
because of the demagnetizing force exerted by the free
ends of the specimen.
The exact magnetic condition corres-
ponding to the excitation current could not be determined
with sufficient precision.
We first became aware of the fact that flux
conditions varied widely along the length of the specimen
when we took some oscillograms of the Effect along the
specimen's length.
number five.
The specimen used was known as specimen
It was a soft iron wire eight inches long and
0.0472 inches in diameter.
It had been heated to a
bright red heat, then cooled slowly to room temperature in
thirty minutes.
With this specimen in the center of the
solenoid, oscillograms were taken with the search coil at
center, and off center by inch steps, while the current
3 -.
in the solenoid winding was varied nearly linearly from
plus forty milliamperes to minus forty milliamperes.
This
10.8 gilberts per centimeter.
The pictures (Fig. 7
)
corresponded to a maximum air core magnetizing force of
showed a progressive variation as the search coil was displaced from center.
The Effect became smaller in magni-
tude and was longer drawn out.
We were led to investigate the flux distribution,
using the ballistic method of measuring.
was used as the flux exploring coil.
The search coil
Hysteresis loops
were taken along the specimen Et length at the same points
the oscillograms were taken.
The results were graphed
(Figure8) by simply plotting the galvanometer deflections
against the solenoid current.
A large proportion of the
galvanometer deflections was due to the magnet.zing force
about the specimen, because the ratio of the effective
area of the search coil to the area of the specimen was
great
(370 to 1).
Correction could not be made
for the magnetizing force as it was unknown (the result
of the demagnetizing Ly the specimens free ends).
Because
we only wished to know the extent of the variation of the
loops in a rough comparative way, and because correction
could only be made by the use of an extremely laborious
SFiure 7
Solenoid Te'st
Search Coila dtCenter
j Isee.
.4---
Ii
I
Search Coil- /"off
-
dii~*~M
A
~e
.k
~
-20+0-
sec.
5earch Coil-2"off
oil,
i,
~V7~f~TWWVYV'V'Y~...y
-20
LO
IJ sec
1~+ 0o--+20
I
1
9
1
5earch Coil -3" off
---
-20
A
tAL.A"##L&.'&-
&k L AiiRi
0
- 10
1 sec.
A
I+
l0m-c?)
JA~
;>j~~
RELATIVE HYSTERES15 LOOPS
qpeclmen 5 /n -Solenoid
K
/01
p
I)
bD1
4,
I
I
Ii
I
xfcItet#t0n
Curr
4t
.//e4neres
2off
5-carch
4 -
I#
Coll at
"Off
'
F1 9 ure 8
Cen-er
cef
cut and try process, the curves were not reduced to terms
of absolute flux measurement.
The resulting distortion of
the loops is very evident.
The specimen itself was magnetically homogeneous.
It follows that each portion of the specimen along its length
is on a different hysteresis loop than its neighbor.
Also, because the different magnetic states were reversed
in the same time interval, the rate of change of magnetizing force was different for each loop.
We conclude
that the solenoid is not suitable when we wish the magnetic state to be unif orm along the length of the specimen,
and would like to know just what that state is.
It is to
be noted, however, that variations of magnetic state are
small at the center of the specimen within the response region of the search coil.
Fahy Permeameter Tests
It occurred to us that the magnetizing force
could be applied by means of a yokesuch as the Fahy
Permeameterinto which the specimen might be clamped.
There being no free ends, the problem of the self-demagnetizing force would be done away with.
Moreover, because
the yoke was the permeameter in which we made our flux
measurements, it was a simple matter to determine our flux
"3'.
conditions from the excitation current readings, once
having recorded the values of magnetizing current when
making the usual flux measurements.
To test the uniformity of magnetic conditions
along the specimen,a set of oscillograms w*.s. taken similar
to thztt
taken along the same specimen in the solenoid.
The magnetizing current was varied nearly linearly from
plus eighty to minus eighty milliamperes.
The correspond-
gilberts per centimeter.
The oscillograms (Figure 9
show practically no difference.
)
ing maximum magnetizing force was eight and seven tenths
Ballistic flux measure-
ments show that there is a small difference, however.
The
flux is less at the center than at the ends because of
leakage.
This is because the area of the specimen is very
small compared to the area of the yokes.
Therefore, the
yokes are at very low flux density when the specimen is
well magnetized.
The yokes being still highly permeable,
and being geometrically located as they are, leakage is
facilitated.
It is not serious, however.
As the yokes are at low flux density, the magnetizing force is nearly directly proportional to the excitation current.
The closeness of the proportionality can
be seen from Fig. 13 , in which there is a plot of magnetizing force versus the current.
3-7.
Search Coil- Center
f
-W -.
I
i'?d
ec
Search Coil- /"off
4
.
.aT
'I...-&"
Search Caul -2" off
i- Ir7-r
I
Search Coil-3 "off
96JLA.-A J6
A Aj
We conclude that the magnetic conditions are
uniform to a satisfactory degree in the permeameter.
Therefore, the tests to locate the Effect on the hysteresis loop were made using the Fahy Permeameter.
ysteresis Lo
Barkhausen Effect Versus
Oscillograms of the Effect were taken with a
silicon-steel specimen and specimens of soft iron wire
subjected to different heat treatments.
The specimen on
which most tests were made was specimen number five.
The silicon-steel specimen was a strip of a transformer
sheet.
cent.
Its silicon content was three and one-half per
Its dimensions were 91" by .0.063 inches by 0.0172
inches.
Characteristic oscillograms of these two specimens are' attached, together with their hysteresis lobps
(FiguresiO,I
,
J,2., 13)
To facilitate comparison between
the pictures and the loops, the magnetic induction has been
plotted against excitation current.
That is, the
abscissae of the hysteresis loops are in the same units
(milliamperes) as the ordinates of the sloping excitation
line shown on the oscillogram.
However, the curve of mag-
netizing force is also plotted against the excitation current.
38.
Silicon Steel Specinen
so m.a. Loop
Search Coil-lI
off cente
Field Change-
.I
i
-20
4.,,
-/0.1
I.
!
K
1-0I1.
Figure I0
-
4.
I
-
S$!~Jmer, *q~5*
'iae. L..p
Ch Coil- if
center-
I
d Chesigeb4 u.afsec.
.1
Figure
//
111,
.
$Y5TERES1
%5illcon .Steel
LOOP
7
Spec-ime 17
10
a-Il
71
4o0
$6
70
60
SC
4-0 .0
20
)o
0 W20
30
40
3-
40 70
r Excitaion Cvrrelit
-Millamperes
4000
4
6000)
7
8000
4
EL
10000
FAlure 12
80
A study of the oscillograms in connection with
the hysteresis loops reveals the significant fact that there
is a relation between the Effect and the slope of the
Looking at Figures I I and 13, we see
hysteresis loop.
that the Effect increases as the slope increases, until the
magnetizing current has reached a value of minus six
milliamperes.
The Effect seems to have reached a maxi-
mum in that region.
Then the Effect gradually diminishes
though the slope of the loop has not reached its maximum.
The larger kicks comnence at the knee of the loop (minus
two m.a.) and are over as the slope begins to decrease
(minus eighteen m.a.).
The region embraced is that in
which the slope is greatest.
Because the rate of change of field influenced
the Effect, it was investigated to see whether it altered
in any way the position of the beginning and ending of the
worst part of the Effect.
Many tests were
made, the ratio
of the maximum to the minimum rate of change sometimes
being as great as eight to one, the greatest ratio we could
obtain witbur apparatus.
The maximum rate of change was
limited by the maximum load the amplifier would carry. The
minimum was limited by the slowness with which our excitation drive could be made to run smoothly.
mennumber five, was used.
The same speci-
It was carried around the same
sized hysteresis loop (eighty milliampere maximum) at the
different rates of change of field.
We found that the rate
did not influence the position of the Effect on the
hysteresis loop.
A characteristic set of oscillograms are shown
in Figure (14).
four to one.
The speed range was a little better than
Evidence of bad amplifier distortion can be
seen in the oscillogram taken at the fastest rate.
A relation between the slope of the loop and the
Effect can be logically deduced with little trouble.
The
amplifier, and consequently, the oscillograph vibrator,
responds to the voltage applied to the first stage.
Let
us assume that the amplifier and oscillograph are distortionless.
Then the Effect curve is a true curve of
voltage applied to grid of the first tube by the search
coils.
The voltage is induced in the coil by the changing
Effect
flux.
Hence theAcurve is a curve of
glect the portion of
d4
Let us ne-
.
due to the changinghflux.
It
would be negligible if the ratio of the area of the search
coil to the area of the specimen were small.
Then the
flux is proportional to the flux density within the specimen, and the curve is a curve of
dB
against time.
Now,
the excitation current varied linearly with respect to
time.
Therefore, the curve is one of
dB
against
1.
In other words, it should be a curve of the instantaneous
4o.
Figure 14
Rdte of Change
of Field Test
Field Chanye -/4.3 m.a/sec.
Iii k~~diiA~if
I-I-
kM
~AL.ALAA~AU1~
SL
m
,~,~!W WW~W(V~WYF~~ YYrw 4
-tl
Field Chnye
-
1.2 m.I/sec.
IMP)
I
f -e /a( Clyawe - 6.6
non~
s.e.
~ ~~~~~~~~~~~~~~~~~~"
niainnuuusiu
uuamuuinuua u
n
Tnninnm
FieM1 Chanye - J .maIsec.
~gI~
~
A.~i.
..
j
values of the slope of our hysteresis loop plotted in
Figure 13, and the area under it should be proportional
to the total change of flux.
As the magnetizing force
was nearly proportional to the excitation current, the curve
should also be very nearly a curve of
dB
against H.
Going back to our oscillogram of specimen number five and its hysteresis loop, it is very obvious that
the actual curve is not in agreement with the above statements.
We have noted that although the slope of the hy-
steresis curve is still increasing until the excitation
current has dropped to minus fourteen m.a., the Effect has
been decreasing, contrary to the theoretical considerations.
This is due to the fact that our amplifier was not a distortionless
d.c.
amplifier.
It was resistance-condenser
coupled, and therefore would not transmit steady-state
voltages, or reproduce faithfully slowly varying voltages.
So long as it handled single pulses, it served its purpose.
But because our rate of change of field was fast,
and because the response region of the search coil was
comparatively long, there was a good deal of superposition
of impulses.
The voltage impressed on the first stage
17 1.
probably had the following wave form:
Splitting the wave form into two components along the
dotted line, we have a slowly varying component and a very
irregular voltage.
The slowly varying component will
change in magnitude as the rate of change of slope of the
hysteresis curve varies.
It changes fastest at the knee
of the curve, but its rate of change is so slow that it
is either badly distorted or it does not come through
the amplifier at all.
When it comes through, it makes
itself known by causing an irregular swinging of the Effeet curve.
Figure J( .
This is shown in the top oscillogram of
The irregular voltage has little difficulty
in coming through because of the greater rapidity with which
it
varies.
We conclude that the oscillograms of the Ef-
feet give a very distorted picture of the actual changes
of magnetic state within the specimen.
Let us consider just how an oscillogram might be
obtained that faithfully indicated the changes of magnetic
conditions within the specimen.
For such a purpose, our
apparatus is far from ideal as it stands.
4-I2.
Also, a different
type of oscillogram would be needed.
It would be necessary
to increase the film speed greatly in order that the details
of the Effect might be seen.
Then it would be necessary
to decrease the rate of change of field greatly, and to
restrict the size of the portion of the specimen under
observation.
By doing this, the individual pulses would
be made apparent for inspection, and superposition of impulses would be avoided.
So far as the apparatus is concerned, the osThe excitation system would
cillograph is very suitable.
have to be such that the true magnetizing force were varied
linearly with respect to time, a not too difficult task.
It is the search coil and amplifier that offer the great
difficulties.
Considering the search coil, we have pointed
out that two identical magnetic units might undergo identical magnetic changes, yet produce different pulses
on the oscillogram if the two units were located at different positions along the axis of the search coil.
This
defect is fundamental with the type of search coil used.
If it
were possible that all
parts of the portion of the
specimen under observation were of such a size that they
all might be considered to occupy the same position relative
to the search coil, the difficulty
would be removed.
how such an arrangement might be madewe do not know.
L43.
Just
It
is just a suggestion to a possible solution.
approach it
We tried to
by wrapping the specimen quite heavily with
aluminum foil except for a small region immediately under
the search coil.
It was hoped that induced eddy currents
in the foil would greatly reduce the Effect coming from the
wrapped portions.
There was a large reduction, but not
as much as we required.
The defect can be minimized by
redesigning the search so as to give a better response
characteristic.
Then from a study of the distribution of
the magnetic -material in conjunction with the response
characteristic of the coil, a correction factor might be
compUted to be applied to the total area under the voltage
curve on the oscillogram.
The ideal amplifier would be a distortionless
direct current amplifier of great sensitivity.
But a
d. e. amplifier of great sensitivity is notoriously difficult to build and operate.
The amplifier can be ap-
proached in a fairly satisfactory manner by a resistancecondenser coupled amplifier such as.we used) if the entire
change of magnetization takes place in sudden jerks.
If
there is an initial slow yielding of the magnetic particles
before the sudden reorientation, and this yielding accounts
for a recognizable fraction of the whole process, as Ewing's
elementary theory of magnetism suggests, then only a
straight d. c. amplifier would do.
Our amplifier could be greatly improved by changing some
of its circuit constants.
A consideration of the equa-
tions derived in the Transient Analysis, Appendix A, will
indicate what changes these should be.
Its distortion of
single Barkhausen kicks would be small, and could be allowed
for from the results of a calibration test.
To increase
the sensitivity, a different tube should be used in the
last stage.
We used a
UX-250, as the last stage was
called upon to handle a large output)that resulted from
our use of rather large rates of change of field.
Be-
cause the rate of change of field was large, causing superposition of impulses, the distortion shown by our oscillograms is large.
/r
This will not both/an investigation
following along the suggested line, though.
We sincerely hope that this portion of our investigation has succeeded in fulfilling its original purpose, namely, that of giving the reader a broad view of the
subject in general.
/_5
IV.
EXPERIMENTS ON COMPOSITE SPECIMENS
Purpose
Our purpose in making these experiments on composite specimens was to obtain more knowledge of the influence of specimen length on Barkhausen Effect in long,
thin specimens.
Dr. Griffith deduced from his results that
the character of the Effect varied in a regular fashion
with the length of the specimen.
Moreover, by using a
composite specimen, consisting of a magnetic center seetion with a non-magnetic extension brazed onto each end,
he found that the Effect with the extensions on bore the
same relation to the Effect with the extensions cut off,
as that between the Effect
in long and short homogeneous
specimens.
The variation in the character of the Effect
observed by Dr. Griffith was that the number of large
pulses increased)as longer specimens were used.
The ex-
planation which he advancedas we mentioned in the introduction,is that the sudden orientation of a magnetic
particle is accompanied by a sudden magnetostrictive force
which sets up a compressional wave like a sound wave in
the material.
The wave travels along the specimen until
it strikes the end where it is reflected back.
As the wave
travels along, it encounters groups of particles which
have been rendered unstable by the changing field, and it
supplies the shock necessary to orient these groups. Thus
there are waves starting at all points, travelling down to
the ends and being reflected back.
Now the longer a spec-
imen is, the longer it will take for a particular wqve to
return to a given point.
The longer the wave takes,the
larger will have become the number of unstable particles
in a given section when the wave returns.
Thus the orient-
ing group will have a tendency to be larger and to produce
larger waves to continue the process.
An experiment with
the same length specimenbut different rates of change of
field, indicated larger pulses with hvigher rate, which is
in line with Dr. Griffith's explanation
The explanation
has many attractive points, but as its author points out,
grave mathematical difficulties hamper analytical work on
it, and besides, an examination of the method of experiment
indicates the possibility of other factors linked with
change of length having an influence on the results.
We feel considerably in doubt about the value of
Dr. Griffith's experiments on the Effect in continuous
specimens of different lengths.
This is partly because,
as Dr. Griffith himself points out, of the difficulty of
obtaining identical flux conditions in all of the specimens
J17.
by the use of demagnetization factors.
However, the chief
cause of doubt lies in the small ratio of specimen length
to search coil dimensions which he used.
Even assuming
that each of the specimens of different lengths had exactly similar flux distribution curves, the fraction of each
specimen influencing the search coil was much greater for
the short specimens than for the long.
Referring to our
search coil response characteristic in Fig. 4
,
which is
for the same coil as used by Dr. Griffith, it will be seen
that the coil responds appreciably to disturbances as far
as two centimeters from its center.
Now the shortest
specimen used in the experiments was 6 cm. long while the
longest was 18 cm., thus the ratio of "response length"
to total length varied from 0.66 to 0.22.
The significance
of this can best be appreciated by considering Fig.
7
which
shows Effect in different portions of a specimen having a
length thirteen percent greater than Dr. Griffith's longest
and a length-breadth ratio about equal to that of his
14 cm. specimen.
Now we may, reasonably assume that the
Effect varies along the axis of a single specimen in a
fashion similar to that of Fig.
of the specimen.
7
regardless of the length
Thus an oscillogram of the 6 cm. specimen
is a distorted superposition of the small amplitude Effect
'18.
near the ends on that of larger amplitude which occurs
near the center, while one of the 18 cm. specimen is a
relatively true record of the Effect in a limited portion
of the specimen.
Therefore the preponderance of small
amplitude Effect in short specimens over that in long ones
can be accounted for at least to some extent without recourse to the travelling wave theory.
Dr. Griffith seems
to have considered the above pointsbut due to an unfortunate misinterpretation of his search coil response fonmula, he appears to have underestimated their importance.
However, the travelling wave theory is still
the only explanation for the results of Dr. Griffith's
composite specimen experiment) although a skeptic might
lay the increased Effect with end extensions to the slight
ripple observable in the exbitation line.
At any rate, we
decided to try a similar experiment ourselves, and we
checked Dr. Griffith to the extent that we found that nonmagnetic extensions do influence the Effect.
We performed
three experiments, differing considerably from each other,
on the Effect in composite specimens.
Our aim was to ob-
tain really convincing evidence that the Effect in long
specimens does involve mechanical reactions, and to determine as many of the factors governing such reactions as
our limited time would allow.
14U
General Method
Our general method was to use specimens of a
nature that would permit the magnetic portion to remain
entirely unaltered during an experiment while the nonmagnetic portions were being changed.
In all cases, the
magnetic material was a piece of soft iron wite, 0.047
inch, in diameter, similar in compositionthough differing in heat treatment.,to that used in our Effect vs. flux
experiments.
The non-magnetic material which inrqediately
abutted the iron was either brass or phosphor bronze wire
of 0.050 'Adiameter.
The brass or bronze wire was brazed
onto the end of the iron-wire in a butt joint using an
ordinary gas-compressed air torch with borax for a flux.
After the brazing operation, the surplus brass was filed
away from the sides in order to make the joint a true
butt.
After all joints were made and twisted around a
little to test their strength, the iron portion was annealed to restore its uniform magnetic qualities.
The
specimens were allowed to age before use for a day in the
first experiment and several weeks in the last experiments.
During the experiments, all alterations were performed by cutting or filing the non-magnetic parts.
The
magnetic part was left entirely undisturbed during these
alterations except for a slight vibration or jarring.
The
details of the alterations will be discussed in connection
with each experiment.
50.
Oscillograms of Effect in the iron were taken before and after each alteration.
They were of the slow
speed type which we had already found useful in our Effeet vs. flux experiments.
The rough and ready method
of comparing them by general appearance was used.
While
this method lacks the scientific exactitude of methods
used by previous investigators in similar cases, it is
justified in that the differences in Effect with which we
dealt could be very readily detected by it.
That the dif-
ferences are not due to the random nature of the Effect is
evidenced by the close similarity of successive oscillograms when no alteration is made.
We shall now turn to a description of the separate experiments.
They shall be referred tofor reasons
which will become clear later as the "Brass Gap-Air Gap
Test", the "Extended End Test", and the "Weighted End Test".
The Brass Gap - Air Ga
Test
The specimen of this experiment consisted of two
iron wire portions, each about five inches long joined together by a brass segment about 0.075 inch. long.
It was
fastened securely across the yoke of the Fahy with the gap
midway between the clamps.
5/.
Oscillograms were taken with
the search coil at each of the four positions along the
specimen indicated in the following sketch
--
The magnetizing current was varied between plus
and minus 80 milliamperes.
Of course, due to leakage
caused by the presence of the gap, each portion of the
specimen was traversing a different hysteresis loop during
the current cycle, hence the character of the Effect differed considerably for each search coil position.
In the
upper part of Fig.1 5 , we have plotted the relative hysteresis loop maxima for each search coil position.
These
values were obtained with the search coil and a ballistic
galvanometer by the method mentioned in the section on Flux
Measurements.
After taking the four oscillograms, the search
coil was slid out of the way, and the brass segment
52.
-
1«
I
......
V
.. ...
xx
+- - - --- - - ---- -------- - -
----
...... .. .x....---
0 rop
-
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10
$
s1
vdt
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r4
3.04 Crop
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A.
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r
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i
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i- I
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e~i
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---
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carefully cut through.
This operation was performed with
the specimen in place and without loosening the clamps
holding the iron.
edged, fine file.
The cutting was done with a thin, sharp
A specially made wooden mitre box was
used to firmly support the specimen during the cutting.
Enough brass was left at each side of the gap to make sure
that the iron was not touched by the file.
To prevent the
free ends of the iron from getting out of alignment during
the remainder of the experiment, a small bakelite sleeve
was slipped over the gap.
Four more oscillograms were then taken with the
search coil in the same positions as for the first four.
Each of these oscillograms is paired in Fig. /6 with its
mate of the same position.
The first oscillogram for each
search coil position is the one taken before cutting; the
second, after.
Along the field zero line are marked in-
tervals of magnetizing current in 10 milliampere steps.
These are the reference marks from which comparisons are
made.
A one-second interval is marked on the timing wave
of each oscillogram for the purpose of keeping a check on
the field rate of change.
It will be noted that in all cases, the Effect
begins earlier and lasts longer with the air gap than with
the brass gap, but that the heavy swinging begins earlier
53.
.Bi-'mss coop
litt
LlI
&p
t
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rij vre F~jure
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rre
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Ir
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Air- Gap
FiR ure 16
(contin rus)
and more abruptly with the brass gap.
The differences in
the two sets of oscillograms are evident enough to require
no further comment.
However, are the differences really due to the
substitution of air for the relatively rigid brass in the
gap, or did some other factor seriously influence the reThe possibility of three such factors occurred to
sults?
ud.
First, would a very small change in the gap length,
caused during the cuttingchange flux conditions appreciably?
The plots of hysteresis loop maxima against gap
length for different search coil positions shown in Fig.15
indicate that even a considerable change in gap length
would make very little difference.
Second, variations
of the search coil position upon resetting might influence
the results.
We are sure that the search coil was relo-
cated for the second series of oscillograms to within
0.05 inch of its positions for the first series.
The up-
per plot in Fig.15 indicates that this was close enough
for the first and last positions but that an appreciable
error might be introduced for the second and third positions.
The third possibly disturbing factor is that the
field rate for each of the second series was greater than
for each of the first
series because of heating of the
potentiometer electrolyte.
These rates are indicated -on
the oscillograms, the greatest variation being 6 per cent.
Our experience has been that such variations are not
sufficient to cause the differences observed in the oscillograms.
On the Wholewe feel quite sure that our re-
sults really indicate what they purport to, namely a difou*
ference in Effect through\the length of the specimen
caused by the substitution of air for brass in the gap.
The Extended End Test
The specimen of this test was similar in form
though different in proportions to the one used by Dr.
Griffith in his composite specimen experiment.
It con-
sisted of an iron wire eight inches long with phosphor
bronze wires, thirteen inches long, butt jointed to each
end.
This specimen was centered in the long solenoid and
carried around a magnetizing cycle corresponding to 40
milliamper
magnetizing current.
Oscillograms were taken
with the search coil at the center of the iron and with it
displaced one inch from center.
After taking these oscillo-
grams, the specimen was removed from the solenoid and four
inches was clipped from each end extension with a pair of
wire cutters.
It was then replaced in the solenoid, the
magnetic cycle re-established and two more oscillograms
were taken.
This procedure was repeated twice more, so that
55-.
one inch was finally all that remained of each end
extension.
We thus obtained two sets of oscillograms showing the change of Effect with length of end extension.
These two sets both indicate the same thing.
Therefore, we
give only the one with the search coil at the center position.
taken.
Fig. 17
is this set in the order in which it was
Intervals of 10 milliampe# are indicated on the
excitation zero line.
It will be noted that as the extensions are
shortened, the heavy Effect begins earlier and with increasing abruptness although the first small kicks begin at about
the same time for the whole series.
The end of the heavy
swinging seems to occur at about minus 10 milliamperes for
all cases, while the period of finer swinging which follows
ends sooner as the extensions are shortened.
A careful com-
parison shows other features which change progressively as
F re /7
-
Extended End -7est.
at cetew-
J,0% . QI/
of iU'Oh
L~nM4of &acA ezxtepision
IM1ASs
cases.-
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n
of
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the extensions are shortened.
To assure ourselves that the alterations were
really causing the changes and not the handling to which
the specimen was subjected, we took an oscillogram under a
certain condition, removed the specimen, gave it the ordinary amount of handling without altering it, replaced it in
the solenoid and took another oscillogram.
We then re-
moved the specimen again and repeated the procedure.
three oscillograms are shown in Fig.18
.
The
The differences
between them are obviously far smaller than the differences
between the oscillograms of the test.
There is one factor which somewhat blemishes this
otherwise conclusive experiment.
This is that the excita-
tion line has a 60-cycle ripple in it of very small magnitude.
Nothing could be done about this because it was not
noticed until several days after the experiment.
We traced
its origin to the timing wave circuit but we could not determine just how the coupling was taking place.
Fortunately
the pick-up appears to be about equally bad in all of the
oscillograms.
Thus, if
it
had any influence on the Bark-
hausen Effect, that influence should have been the same for
each of the four cases.
Despite this questionable ripple in the excitation
current, we are convinced by the marked progressive change
-5-7-
%M
18
-
OscJ;/o0
w
of crn tfrcrn
Spec
,
Vig vre
Leh9h
~eq~ACo;/ oaug inmch fl-ovi Copeter
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-
of u'~i.~a /
of eictenseh
~~iA
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IIIllLll~
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,
20,i
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-the
show' vSIPiq
e~id
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o
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A1e so~e'rio~d
ft
and
of Effect with change of end extension length that the
presence of the extensions has a decided
influence on the
Effect.
The Weighted End Test
During a consideration of the results of the Extended End Test, we were confronted with the question of
whether it was really the length of the extentions that was
influencing the Effect.
Suppose that it was not a travelling
wavebut discontinuous magnetostriction of the specimen as
a whole, that was causing the mechanical reaction connected
with the Effect.
Then it would be the mass of the end ex-
tensions that would control the form of the Effect.
To investigate this,we built up a specimen
with weighted ends.
We took the specimen of the previous
experiment which still had one inch bronze extensions.
We
bent a little hook on the end of each extension, timed the
bronze, and cast a nine gram lead weight on each.
The weights
were in the form of cylinders, coaxial with the specimen,
58.
roughly a quarter of an inch thick and a half an inch in
diameter.
The specimen was supported at its eentfral region by a special carriage which also held the search coil.
To facilitate alteration of the weights, the carriage was
arranged so that it could be easily slid in and out of the
solenoid, from which the regular glass tube and search coil
carriage had been removed.
While the specimen was in the
solenoid,its heavy ends were supported by cotton to prevent excessive bending stresses which might influence the
magnetic properties of the iron.
The weights were then removed in five
oscillograms being taken after each change.
increments,
The two
weights were reduced as nearly equally as possible by
cutting off a little
at a time and weighing the chips.
After the second increment, we removed the specimen, handled
it, replaced it, and took a second oscillogram, to make
sure that the changes we were getting were really due to the
removal of weight.
The two oscillograms agreed as close-
ly as those of Fig. 18 taken under similar circumstances
in the last test.
To guard against the 60-cycle pick-up in the excitation system which appeared during the previous test
and which we were unable to eliminate, we took our Effect
oscillograms with no timing wave.
We then exposed a tim-
ing wave with the zero field line.
This was justifiable
because the film drum runs at very nearly constant speed.
This method eliminated the 60-cycle ripple from the active
excitation line)but,strange to say,it was picked up on the
zero line although the excitation circuit was then open.
However, a ripple on the zero line has no influence on the
Effect so we do not need to worry about it further.
The series of oscillograms with the corresponding
mass of each end weight are shown in Fig. 13 . Although
these oscillograms differ greatly from each other)they do
not show the orderly progression that was so evident in
the Extended End Test.
However, we doubt if any of these
oscillograms are freaks, for with one exception.,we took at
least twoand sometimes threelseparate pictures for each
60.
Fi ure 13
--
wei hI7 d
EhcA
st
oP Lead
mass
flas
.1: Lea *)I- e4ACh e.%e'75OD1
= 9.Z
9
72
3
or-er"S.
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Williffilifflill ill Will li Ill 11111 ll
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e~I~ts
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i --
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T-TTI
d'
-
"one,
- MWENR
AA.
-k-
weight increment.-
These duplicate and triplicate os-
cillograms agree closely in general character with the
ones which we show here.
The first part of the series indicates that our
weight increments were too large to give a good idea of
the manner in which the character of the Effect changes.
The last two oscillograms, on the other hand, are very
instructive when considered in conjunction with the last
two of the Extended End Test, because the changes in mass
are similar.
The progression from the first to the second
in each of these groups of two is the same; an increased
abruptness of start of the heavy
Effect, together with
a shortening and earlier ending of the final period of
fine swinging.
A close scrutiny of the four oscillo-
grams reveals the similarity much better than words can
describe it.
The similarity of the two cases becomes
significant when it is remembered that the iron part of
the specimen is identical in the two cases, that the alteration in the first case was the removal of four inches of
6/.
bronze wire weighing 1.1 grams3 and that in the second
case it was the removal of a concentrated mass of lead
weighing 1.0 gram.
From this it
appears that it
was
the change of mass of the extension and not the change
of length that caused the observed variation in the Effect.
This line of reasoning indicates that we should
find a similarity of change between the third and second
oscillograms from the end of each test, where the masses
were changed respectively from 2.3 to 1.1 and from 2;1
to 1.0.
However, we find no such similarity whatever,
and we are forced to conclude that length of the extension
as well as mass is an influential factor in some cases.
Conclusions and a Tentative Theoretical Explanation
For convenience, the results of the three experiments on composite specimens will be summarized briefly.
1.
With a bisected specimen forming part of a
magnetic circuit which was closed except for a short gap
between the halves of the specimen, the character of the
Effect was definitely influenced by the removal from the
gap of a brass segment which connected the specimen
halves together.
The change of the Effect was that it
commenced and finished its cycle less abruptly in all
parts of the specimen after the brass was cut.
2.
With an iron wire specimen magnetized by a
long solenoidthe character of the Effect was influenced
by a change in length of phosphor bronze wires brazed to
(02.
each end of the iron wire.
The Effect became increas-
ingly abrupt in its start as the bronze extensions were
shortened.
3.
The Effect in an iron wire magnetized by
a long solenoid was influenced by changes in the
masses of lead discs fastened on each end of the iron
wire.
The influence on the Effect when the last por-
tion of the lead was removed was strikingly similar to
that when the last portion of the extension was removed in
The
the previous experiment.
mass of this last portion
of lead was approximately equal to that of the last portion of the extension.
Removal of previous portions of the
lead influenced the Effect decidedly, but in an irregular
fashion which bore no further resemblance to the results
of the second experiment.
These results lead clearly to the one definite
conclusion, that there is a mechanical reaction of some
sort connected with the Effect in long, thin specimens.
As to the nature of this reaction, nothing definite can
be said about it.
The travelling wave theory is neither prcr ed nor
disproved by these experiments.
In one experiment where
we decreased the mechanical length of the specimen by
63.
cutting the brass gap,we obtained an exactly opposite
change in Effect to that when we decreased the mechanical
length by removing end extensions.
culiar, if
the wave theory holds, it
While this seems pemust be remembered
that the conditions of these two experiments were so vastly different that no comparisons between them can be
safely drawn.
The comparisons between the weight expe-
riment and the extension experiment for one case seem to
disprove the wave theory by indicating that mass and not
length is important while for other cases no such thing
is indicated.
It can be safely said that if the travelling
wave theory is correct, then the situation is vastly more
complicated than indicated by Dr. Griffith.
Although our results prove nothing more than that
a mechanical reaction is related to the Effect, they suggest that magnetostriction plays a more extensive part in
the mechanism of the Effect than is required by the traveling wave theory as set forth by Dr. Griffith.
The theory
which is suggested to us by these results is intended
not to replace the travelling wave theory, but to enlarge
it.
Magnetostriction is the phenomenon of the change
of dimensions which accompanies a change of magnetization
0 i.
in a ferromagnetic material.
For the range of magnetiza-
tion which we used, the change is an increase in length
along the axis of magnetization with increase in magnetization.
Thus as the specimen is carried from one maxi-
mum of a hysteresis loop to the other, it first shortens,
and then lengthens.
Now it is natural to conclude that
the separate Particles which are the magnetic units,change
their dimensions in a manner similar to that of the body
of which they form a part.
Since the Barkhausen Effect
indicates that separate particles magnetize discontinuously,it seems logical to believe that these particles
also "magnetostrict" discontinuously.
This discontinuous
magnetostriction of separate particles forms the basis
of the travelling wave theory.
Since the magnetostricting
particle is situated in an elastic medium, waves are
sent out from it when its dimensions are suddenly changed.
We have already discussed the influence of these waves.
Now we come to the new part of the theory which the results suggest to us.
After the particle has "magneto-
stricted" and the waves have subsided, there must be a
net displacement of all the other particles of the substance, or if the substance is constrained, a stress must
be set up between the particles.
65~
It is a well known fact
that a mechanical force acting to oppose the magnetostricti6n of a large body tends to oppose the change of
magnetization also.
Thus it seems reasonable to believe
that the stresses set up within the substance after a
single particle has "magnetostrictedt' will have an influence on the ease with which the magnetization of other
particles can be changed.
Since the Barkhausen Effect is
believed to be the manifestation of the magnetization of
separate particles, we should expect its character to be
altered by a change in the restraint with which the specimen is held, as well as by a change of the paths provided
for the waves.
indicate.
This is exactly what our results seem to
By adding masses to the speciments ends a par-
tial constraint to sudden change of the speciments dimensiont
was brought about and the character of the Effect
was influenced.
In other experiments,the constraint of
the specimen and the length of the wave paths were altered
simultaneously so there are no indications of the relative
influence of the waves and of the magnetostrictive forces.
The question of whether such a theory has any
real basis, and if so,the question of the relative importance of the factors which it involves will have to be
answered by the results of future experiments.
66.
APPENDIX
A
AMPLIFIER TRANSIENT ANALYSIS
V
represent a change in
Let di
i
etc&
p
p
dv
di=
=
p dv p
p,
+
ap
di
dv, .
-
di
p
pv
p
dv,
1+
FTp]
&a =
Gm and
p
p
tube characteristics; and
1
the slopes of the
p
= rpGm, the amplification
factor.
Gmr p
rprp
+
rp
+
dig =
>7.
a
a
V
V3
R,
TV
For each stage 9 =
1
+
1+
R2 +-C
RlR 2 Cp + R
PC(
+
2) + 1
Let
i
[1
dv2
dv
3
dv4
=
B di 2
R2
-
r
=
AB dv 2
AB dv 3
B di3
3
3
(rP + Z)
68.
=
Bd
AB dv 1
A2 B 2 dvI
A3B3 dv1
3
2
I
I
7
Substituting the value for 9 and QObining,
this reduces to --
dv
4
3
= p RlR2
_
_
_
p
pRlR + rPR +
R1 R 2
2
_
_
+ r
dv
SLrpRl+rpR 2 +RiRd
For our amplifier R. = 100,000
R2
500,000
C = 10465
r
P1
which gives
= 30
--
17.4
dv 4
= 60,000
4
x
p
p + 186
= a3
dv
1
p
3
dv1
-
p + b
dv , the voltage applied to the power tube has
the same form as the output current if the tube is linear.
3
a , the amplification of the first three stages, does not
concern us further.
We shall now give dv1 , the applied vol.
tage,two forms and derive the resulting forms of dv4
69.
Let
dv 1=
= a3 (
dv
3
i
=
= a3 E-bt [.-
a3r-bt
2b
p~~
""2
= a3 6gbt [1 - 2bt + b 2t 2
2E~ 1 1
where b = 18.6
A plot of this form is given in Fig. 20.
oscillogram which checks it is shown in Fig.
dv 4 = a3
.
=
Let dv
6.
p3
kt
a3
(p+b
)
(p+b)*
3 .-bt
p
p4
(p+k)
:1
(p-b)4
p (p-b+k)
a3 C-bt (p 3 - 3p 2b + 3pb 2 - b 3 ) 1
p + k-b)
p2
= a3 6
-bt
+ 3b 2
1-3b
I p
= a3 -bt t,
- b3
p+M
P2
- 3b
+
F'70,
3b2
me b3
V-Mt
lP
An
as-3b (-
-b 3
+
+ 1
-
j3
(M3
t
j2
-
Mt
3b2(0Ml
2 +
4b
+ t2
)
IE
-
= a3 E-bt
This form may be reduced by purely algebraic
transformations to the form --
dv4 = a3
3- 3
)k-b
4
-bt
1
3k-2b
+ a3 b 2
k - b Ik-b
2 t
-b
-bt
-kt
+ a3k3
(k-bf
A plot of this form is given for k = 100 in
Fig.
0.
An oscillogram for k = 96 in Fig. 6
checks very
closely.
For the particular case when k = b, a special
solution is necessary.
dv
dv4 = a3
= C-bt
p3 _'6bt
(p+b)1
=a
-bt (p-b) 3
P3
= a3 -bt
1 - 3b + 3b 2
r.7W
7/.
-b 3
;;s3
1
t
4
VV
I
Iv
Qj~4'
c-nds
-0
x
I
FIs Lr-r
20
Seel --)I-
=a3
-ht [1 - 3bt + 3b2t2
- b3 0
A plot of this form is given in Fig.20 , for comparison with the oscillogram for k = 19.2 shown in Fig. 6.
(For the plot k = 18.6).
The method of making the experimental check was
to use the circuit shown below --
4fC5
Amplifier
The transient has an initial value of about 4.5
millivolts as may be seen from a consideration of the above
circuit.
The oscillograms indicate that the amplifier
gives an initial deflection of roughly one-half centimeter
per millivolt applied (See Fig. 6.)
72.
The values of C in microfarads for the different transients are tabulated below:
C
Exponent Constant
Time Constant
2.0
4.8
0.208
1.0
9.6
0.104
0.5
19.2
0.052
0.1
96
0.010
0.016
Short Circuit
576
0
7.3.
0.0017
X0
APPENDIX
B
RESPONSE CHARACTERISTIC
SEARCH COIL
N
x
CL
E
Li
Li
a0.-
N
~
r~
~~1~
-0
13*
7
The voltage, E, induced in the coil by the
reversal of an elementary magnet at
x
is from a formula
derived by Dr. Griffith -E 0
x + a
R2
where 9 = tan
W
+ (x+a)
R
x-
(xa'.
i2+
=
,and
a
tan-
X-9
x+a
R, the mean radius = 1.72 + 2.84
4a, the semi-length = 1.47
7'/.
R
= 1.14 cm.
= 0.735 cm.
R = 1.14
W
01735
= 1.55
The simplest form for computation is --
cos 9
-
cos
cos tan'
1.55
-
cos tan'
x. + 1
The tabulated computations are
-..
--
cos 9 - cos
x
1.55
cos 9
1.55
cos
o
1.55
0.540
-1.55
-0.540
1.08
0.5
1.033
.695
-3.10
-
1.00
1.0
0.775
.790
-
1.5
0.620
.850
+3.10
+0.305
.545
2.0
.516
.888
1.55
.540
.348
3.0
.388
.932
0.775
.790
.122
4.0
.310
.955
.516
.888
.067
0<
1.55
.305
0
.790
The plot of the search coil characteristic is
shown in Fig.4.
The number of turns on the search coil was found
by placing the coil inside of a long solenoid of known
constants, and observing the deflection of a ballistic galvanometer connected to the coil as the solenoid current was
reversed.
757
The ballistic galvanometer was calibrated by means of a
standard mutual inductance and ammeter.
Using an effective
area calculated from its dimensions, the coil was found
to have 7000 turns
10%.
APPENDIX C
APPENDIX C
HYOTERES IS LOOP
DATA
HYSTERESIS LOOP DATA
Magnetic measurements were taken by the usual
ballistic method, using the Fahy Permeameter.
All flux
and magnetizing force observations are made with reference to one tip of the hysteresis loop.
After the obser-
vations are worked up, the results are referred to the
usual coordinate axis
by subtracting the co6rdinates of
the original reference point.
H =
B = K4D- H(A 3 -Aw)
KhDn
Aw
Kh =
M x 6Ic=
X 10 g
hAh x Dh.
M X Ic'
Where A. = effective area of B coil
Aw = area of specimen
M.
= mutual inductance of calibrating coil whose
secondary is in the galvanometer circuit
NhAh = product of effective area and turns of the
H coil
N
= turns on the B coil
Dh = galvanometer deflection when measuring magnetizing force
= galvanometer deflection when measuring fluz.
77.
o
=
galvanometer deflection when calibrating
with
H
coil in circuit
galvanometer deflection when calibrating with
B coil in circuit
=
total change of current through primary of
calibrating coil
.
Dh
78.
HYSTERESIS LOOP OF SPECIMEN FIVE
Die = 10.75
Aw = 0.01143 sq.cm.
As-Aw = 0.18 sq. cm.
Dh
= 10.95
n. 0= 0.300 amp.
M = 0.030 henries
WhAh = 30220
14 = 9090
-80.0
-61.0
-40.0
-25.0
-20*0
-17 * 0
-16.0
-15.0
-13.5
-12.0
-10.0
0.0
+10.0
+20.0
+40.0
+60.0
+80.0
Dh
DH
H -17.40 '-29,200
B
(ilb./cm.)(gausses)
-
Magnetizing
Current
(m.a.)
22.67
22.28
21.32
19.30
17.40
14.78
12.91
3*75 10.88
7.79
3.69
5.30
3.61
3.39
3.53
1*22
3 * 14
0085
2.73
2.30- 0.57
0.30
1*49
0.11
0.70
0
0
6*40
5.61
4.78
4.12
3.95
3.81
3.78
-17.40
-15.26
-13.00
-11.20
-10.74
-10.36
-10.28
-10.20
-10.03
- 9.82
-
9.60
8.54
7.43
6.25
4.05
1.90
0
-29,200
-28,700
-27,500
-25,000
-22,500
-19,000
-16,700
-14,000
-10.000
-
6,700
4,300
1,500
900
600
300
100
0
-8.70
-6.56
-4.30-2.50
-2.04
-1.66
-1*58
-1.50
-1.33
-1*12
-0.90
+0.16
+1*27
+2*45
+4.65
+6.80
+8.70
-14,600
-14,100
-12,900
-10,400
- 7,900
- 4,400
- 2,100
+
600
+ 4,600
+ 7,900
+10,300
+13,100
+13,700
+14,000
+14,300
+14,500
+14,600
HYSTERESIS LOOP OF SILICON STtEL SPECIMEN
Aw = 0.0070 sq.cm.
Doe = 10.08
A;Aw
= 0.182 sq. cm.
Dhe = 10.21
M
= 0.030 henries
NhAh
N
= 0.280 amp.
= 30,220
= 9,090
Magnetizing
Current
(m.a.)
D
H
B
H- 1 6 .3 6 B - 19,000
2
2
(gilb/cm)(gausses)
D
-80.0
6.01
14.75
-16.36
-19,000
-8.18 . -9,500
-60.0
5.29
13.91
-14.40
-17,900
-6.22
-8,400
-40.0
4.50
12.59
-12,24
-16,200
-4.06
-6,700
-30.0
4.10
11.33
-11.16
-14,600
-2.98
-5,100
-20.0
3.73
9.07
-10.15
-11,700
-1.97
-2,200
-16.0
3.57
7.35
-
9.71
- 9,400
-1.53
+
-11.0
3.36
4.92
-
-
6,200
-0.96
+3,300
2.97
2.92
-
8 Q8
-
3,600
+0.10
+5,900
+20.0
2.17
1.51
-
5.90
-
2,000
+2,28
+7,700
+40.0
1.40
0.70
-
3.81
-
800
+4.37
+8,700
+60.0
0.69
0.29
-
1.88
-
300
+6.30
+9,200
+80.0
0
0
0
+8.18
+9,500
0
80.
9.14
0
100