ASTM A 343/A 343M

JANVIER 2014

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Designation: A343/A343M − 14

Standard Test Method for

Alternating-Current Magnetic Properties of Materials at
Power Frequencies Using Wattmeter-Ammeter-Voltmeter
Method and 25-cm Epstein Test Frame1
This standard is issued under the fixed designation A343/A343M; the number immediately following the designation indicates the year
of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval.
A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.

1. Scope standard. Within this standard, SI units are shown in brackets

1.1 This test method covers tests for the magnetic properties except for the sections concerning calculations where there are
of basic flat-rolled magnetic materials at power frequencies (25 separate sections for the respective unit systems. The values
to 400 Hz) using a 25-cm Epstein test frame and the 25-cm stated in each system may not be exact equivalents; therefore,
double-lap-jointed core. It covers the determination of core each system shall be used independently of the other. Combin-
loss, rms exciting power, rms and peak exciting current, and ing values from the two systems may result in non-
several types of ac permeability and related properties of conformance with this standard.
flat-rolled magnetic materials under ac magnetization. 1.8 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
1.2 This test method shall be used in conjunction with
responsibility of the user of this standard to establish appro-
Practice A34/A34M.
priate safety and health practices and determine the applica-
1.3 This test method2 provides a test for core loss and bility of regulatory limitations prior to use.
exciting current at moderate and high magnetic flux densities
up to 15 kG [1.5 T] on nonoriented electrical steels and up to 2. Referenced Documents
18 kG [1.8 T] on grain-oriented electrical steels. 2.1 ASTM Standards:3
1.4 The frequency range of this test method is normally that A34/A34M Practice for Sampling and Procurement Testing
of the commercial power frequencies 50 to 60 Hz. With proper of Magnetic Materials
instrumentation, it is also acceptable for measurements at other A340 Terminology of Symbols and Definitions Relating to
frequencies from 25 to 400 Hz. Magnetic Testing
1.5 This test method also provides procedures for calculat- A677 Specification for Nonoriented Electrical Steel Fully
ing ac impedance permeability from measured values of rms Processed Types
exciting current and for ac peak permeability from measured A683 Specification for Nonoriented Electrical Steel, Semi-
peak values of total exciting currents at magnetic field processed Types
strengths up to about 150 Oe [12 000 A/m]. A876 Specification for Flat-Rolled, Grain-Oriented, Silicon-
Iron, Electrical Steel, Fully Processed Types
1.6 Explanation of symbols and abbreviated definitions A889/A889M Test Method for Alternating-Current Mag-
appear in the text of this test method. The official symbols and netic Properties of Materials at Low Magnetic Flux
definitions are listed in Terminology A340. Density Using the Voltmeter-Ammeter-Wattmeter-
1.7 The values and equations stated in customary (cgs-emu Varmeter Method and 25-cm Epstein Frame
and inch-pound) or SI units are to be regarded separately as E177 Practice for Use of the Terms Precision and Bias in
ASTM Test Methods
E691 Practice for Conducting an Interlaboratory Study to
1
This test method is under the jurisdiction of ASTM Committee A06 on Determine the Precision of a Test Method
Magnetic Properties and is the direct responsibility of Subcommittee A06.01 on Test
Methods.
E1338 Guide for Identification of Metals and Alloys in
Current edition approved May 1, 2014. Published May 2014. Originally
approved in 1949. Last previous edition approved in 2008 as A343/A343M-03
3
(2008). DOI: 10.1520/A0343_A0343M-14. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
2
Burgwin, S. L., “Measurement of Core Loss and A-C Permeability with the contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
25-cm Epstein Frame,” Proceedings, American Society for Testing and Materials, Standards volume information, refer to the standard’s Document Summary page on
ASTEA, Vol 41, 1941, p. 779. the ASTM website.

Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States

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A343/A343M − 14
Computerized Material Property Databases current drain in the secondary is quite small, especially when
using modern high-input impedance instrumentation, the
3. Significance and Use switches and wiring should be selected to minimize the lead
3.1 This test method is a fundamental method for evaluating resistance so that the voltage available at the terminals of the
the magnetic performance of flat-rolled magnetic materials in instruments is imperceptibly lower than the voltage at the
either as-sheared or stress-relief annealed condition. secondary terminals of the Epstein test frame.
3.2 This test method is suitable for design, specification
6. Apparatus
acceptance, service evaluation, and research and development.
6.1 The apparatus shall consist of as many of the following
4. Test Specimens component parts as are required to perform the desired
4.1 The specimens for this test shall be selected and measurement functions:
prepared for testing in accordance with provisions of Practice 6.2 Epstein Test Frame:
A34/A34M and as directed in Annex A3 of this test method. 6.2.1 The test frame shall consist of four solenoids (each
having two windings) surrounding the four sides of the square
5. Basic Circuit magnetic circuit, and a mutual inductor to compensate for air
5.1 Fig. 1 shows the essential apparatus and basic circuit flux within the solenoids. The solenoids shall be wound on
connections for this test method. Terminals 1 and 2 are nonmagnetic, nonconducting forms of rectangular cross sec-
connected to a source of adjustable ac voltage of sinusoidal tion appropriate to the specimen mass to be used. The solenoids
waveform and sufficient power rating to energize the primary shall be mounted so as to be accurately in the same horizontal
circuit without appreciable voltage drop in the source imped- plane, and with the center line of solenoids on opposite sides of
ance. All primary circuit switches and all primary wiring the square, 250 6 0.3 mm apart. The compensating mutual
should be capable of carrying much higher currents than are inductor may be located in the center of the space enclosed by
normally encountered to limit primary circuit resistance to the four solenoids if the axis of the inductor is made to be
values that will not cause appreciable distortion of the flux perpendicular to the plane of the solenoid windings.
waveform in the specimen when relatively nonsinusoidal 6.2.2 The inner or potential winding on each solenoid shall
currents are drawn. The ac source may be an electronic consist of one fourth of the total number of secondary turns
amplifier which has a sine-wave oscillator connected to its evenly wound in one layer over a winding length of 191 mm or
input and may include the necessary circuitry to maintain a longer of each solenoid. The potential windings of the four
sinusoidal flux waveform by using negative feedback of the solenoids shall be connected in series so their voltages will
induced secondary voltage. In this case, higher primary resis- add. The outer or magnetizing winding likewise shall consist of
tance can be tolerated since this system will maintain sinusoi- one fourth of the total number of primary turns evenly wound
dal flux at much higher primary resistance. Although the over the winding length of each solenoid. These individual

FIG. 1 Basic Circuit for Wattmeter-Ammeter-Voltmeter Method

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solenoid windings, too, shall be connected in series so their 6.4 RMS Voltmeter, Vrms—A true rms-indicating voltmeter
magnetic field strengths will add. The primary winding may shall be provided for evaluating the form factor of the voltage
comprise up to three layers using two or more wires in parallel. induced in the secondary winding of the test fixture and for
6.2.3 Primary and secondary turns shall be wound in the evaluating the instrument losses. The accuracy of the rms
same direction, with the starting end of each winding being at voltmeter shall be the same as that specified for the flux
the same corner junction of one of the four solenoids. This voltmeter. Either digital or analog rms voltmeters are permit-
enables the potential between adjacent primary and secondary ted. The normally high-input impedance of digital rms voltme-
turns to be a minimum throughout the length of the winding, ters is desirable to minimize loading effects and to reduce the
thereby reducing errors as a result of electrostatic phenomena. magnitude of instrument loss compensations. The input resis-
6.2.4 The solenoid windings on the test frame may be any tance of an analog rms voltmeter shall not be less than 5000
number of turns suited to the instrumentation, mass of Ω/V of full-scale indication.
specimen, and test frequency. Windings with a total of 700 6.5 Wattmeter, W—The full-scale accuracy of the wattmeter
turns are recommended for tests in the frequency range of 25 must not be poorer than 0.25 % at the frequency of test and at
through 400 Hz. unity power factor. The power factor encountered by a watt-
6.2.5 The mutual inductance of the air-flux compensating meter during a core loss test on a specimen is always less than
inductor shall be adjusted to be the same as that between the unity and, at magnetic flux densities far above the knee of the
test-frame windings to within one turn of the compensator magnetization curve, approaches zero. The wattmeter must
secondary. Its windings shall be connected in series with the maintain adequate accuracy (1.0 % of reading) even at the most
corresponding test-frame windings so that the voltage induced severe (lowest) power factor that is presented to it. Variable
in the secondary winding of the inductor by the primary current scaling devices may be used to cause the wattmeter to indicate
will completely oppose or cancel the total voltage induced in directly in units of specific core loss if the combination of basic
the secondary winding of the test frame when no sample is in instrument and scaling devices conforms to the specifications
place in the solenoids. Specifications for the approximate turns stated here.
and construction details of the compensating mutual inductor 6.5.1 Electronic Digital Wattmeter—Electronic digital watt-
for the standard test frame are given in Table A1.1 of Annex meters have been developed that have proven satisfactory for
A1. use under the provisions of this test method. Usage of a
6.3 Flux Voltmeter, Vf—A full-wave true-average, voltmeter, suitable electronic digital wattmeter is permitted as an alterna-
tive to an electrodynamometer wattmeter in this test method.
with scale reading in average volts times =2 π/4 so that its
An electronic digital wattmeter oftentimes is preferred in this
indications will be identical with those of a true rms voltmeter
test method because of its digital readout and its capability for
on a pure sinusoidal voltage, shall be provided for evaluating direct interfacing with electronic data acquisition systems.
the peak value of the test magnetic flux density. To produce the
estimated precision of test under this test method, the full-scale 6.5.1.1 The voltage input circuitry of the electronic digital
meter errors shall not exceed 0.25 % (Note 1). Meters of 0.5 % wattmeter must have an input impedance sufficiently high that
connection of the circuitry, during testing, to the secondary
of more error may be used at reduced accuracy. Either digital
winding of the test fixture does not change the terminal voltage
or analog flux voltmeters are permitted. The normally high-
of the secondary by more than 0.05 %. In addition, the voltage
input impedance of digital flux voltmeters is desirable to
input circuitry must be capable of accepting the maximum peak
minimize loading effects and to reduce the magnitude of
voltage that is induced in the secondary winding during testing.
instrument loss compensations. The input resistance of an
analog flux voltmeter shall not be less than 1000 Ω/V of 6.5.1.2 The current input circuitry of the electronic digital
full-scale indication. A resistive voltage divider, a standard- wattmeter must have an input impedance of no more than 1 Ω.
ratio transformer, or other variable scaling device may be used Preferably the input impedance should be no more than 0.1 Ω
to cause the flux voltmeter to indicate directly in units of if the flux waveform distortion otherwise tends to be excessive.
magnetic flux density if the combination of basic instrument In addition, the current input circuitry must be capable of
and scaling device conforms to the specifications stated above. accepting the maximum rms current and the maximum peak
NOTE 1—Inaccuracies in setting the test voltage produce errors approxi-
current drawn by the primary winding of the test fixture when
mately two times as large in the specific core loss. Voltage scales should core loss tests are being performed. In particular, since the
be such that the instrument is not used at less than half scale. Care should primary current will be very nonsinusoidal (peaked) if core-
also be taken to avoid errors caused by temperature and frequency effects loss tests are performed on a specimen at magnetic flux
in the instrument. densities above the knee of the magnetization curve, the crest
6.3.1 If used with a mutual inductor as a peak ammeter at factor capability of the current input circuitry should be three
magnetic flux densities well above the knee of the magnetiza- or more.
tion curve, the flux voltmeter must be capable of accurately 6.5.2 Electrodynamometer Wattmeter—A reflecting-type
measuring the extremely nonsinusoidal (peaked) voltage that is dynamometer is recommended among this class of
induced in the secondary winding of the mutual inductor. instruments, but, if the specimen mass is sufficiently large, a
Additionally, if so used, an analog flux voltmeter should have direct-indicating electrodynamometer wattmeter of the highest
a minimum input resistance of 5000 Ω/V of full-scale indica- available sensitivity and lowest power-factor capability may be
tion. used.

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6.5.2.1 The sensitivity of the electrodynamometer wattme- with a crest factor of up to 5. The standard resistor should be
ter must be such that the connection of the potential circuit of a non-inductive resistor with an accuracy rating of 0.1 % or
the wattmeter, during testing, to the secondary winding of the better. This resistor must be capable of handling the full
test fixture does not change the terminal voltage of the exciting current of the test winding at the maximum test
secondary by more than 0.05 %. Also, the resistance of the magnetic flux density without destructive heating or more than
potential circuit of the wattmeter must be sufficiently high that specified loss of accuracy due to self-heating. To avoid
the inductive reactance of the potential coil of the wattmeter in intolerable levels of distortion, the value of the resistor should
combination with the leakage reactance of the secondary be kept reasonably low. A fixed resistor between 0.1 and 1.0 Ω
circuit of the test fixture does not result in appreciable defect is usually appropriate.
angle errors in the measurements. Should the impedance of this 6.7.2 Air-Core Mutual Inductor and Flux Voltmeter—An
combined reactance at the test frequency exceed 1.0 Ω per air-core mutual inductor and a flux voltmeter may be used to
1000 Ω of resistance in the wattmeter-potential circuit, the measure the peak exciting current. Use of this apparatus is
potential circuit must be compensated for this reactance. based upon the same theoretical considerations that indicate the
6.5.2.2 The impedance of the current coil of the electrody- use of a flux voltmeter on the secondary of the test fixture to
namometer wattmeter should not exceed 1 Ω. If flux waveform measure the peak magnetic flux density; namely, that when a
distortion otherwise tends to be excessive, this impedance flux voltmeter is connected to a test coil, the flux voltmeter
should be not more than 0.1 Ω. The rated current-carrying indications are proportional to the peak value of the flux
capacity of the current coil must be compatible with the linking the coil. In the case of the air-core mutual inductor, the
maximum rms primary current to be encountered during peak value of the flux will be proportional to the peak value of
core-loss testing. Preferably the current-carrying capacity the current flowing in the primary winding. A mutual inductor
should be at least 10 rms amperes. used for this purpose must have reasonably low primary
6.6 Devices for RMS Current Measurement—A means of impedance so that its insertion will not materially affect the
measuring the rms value of the exciting current must be primary circuit conditions and have sufficiently high mutual
provided if measurements of exciting power or exciting current inductance to provide a satisfactorily high voltage to the flux
are to be made. voltmeter for primary currents corresponding to the desired
6.6.1 RMS Voltmeter and Standard Resistor—A true rms- range in peak magnetic field strength. The secondary imped-
indicating voltmeter may be used to measure the voltage drop ance of the mutual inductor must be low if any significant
across the potential terminals of a standard resistance. The current is drawn by a low-impedance flux voltmeter. The
accuracy of the rms voltmeter shall be 1.0 % of full scale or addition of the flux voltmeter should not change the mutual
less. Either digital or analog meters are permitted. A high- inductor secondary terminal voltage by more than 0.25 %. It is
input-impedance, multirange electronic digital rms voltmeter is important that the mutual inductor be located in the test
desirable for this instrument. The input resistance of an analog equipment in such a position that its windings will not be
meter shall not be less than 5000 Ω/v. The standard resistor linked by ac leakage flux from other apparatus. Care should be
should be a non-inductive resistor with an accuracy rating of taken to avoid locating it so close to any magnetic material or
0.1 % or better. This resistor must be capable of handling the any conducting material that its calibration and linearity may
full exciting current of the test winding at the maximum test be affected. Directions for construction and calibration of a
magnetic flux density without destructive heating or more than mutual inductor for peak-current measurement are given in
specified loss of accuracy as a result of self-heating. To avoid Annex A1. Even at commercial power frequencies, there can
intolerable levels of distortion, the value of the resistor should be appreciable error in the measurement of peak exciting
be kept reasonably low. A fixed resistor between 0.1 and 1.0 Ω current if winding capacitances and inductances and flux
is usually appropriate. voltmeter errors begin to become important at some of the high
6.6.2 RMS Ammeter—A true rms-indicating ammeter may harmonics frequencies present because of the extremely non-
be used to measure the exciting current. A nominal accuracy of sinusoidal character of the voltage waveform induced in the
1.0 % of full scale or better is required for this instrument. The secondary of the mutual inductor by the nonsinusoidal exciting
instrument must have low internal impedance to avoid contrib- current waveform.
uting to the distortion of the flux waveform. 6.8 Power Supply—A precisely controllable source of sinu-
6.7 Devices for Peak Current Measurement—A means of soidal test voltage of low internal impedance and excellent
measuring the peak value of the exciting current is required if voltage and frequency stability is mandatory. Voltage stability
an evaluation of peak permeability is to be made by the within 0.1 % and frequency accuracy within 0.1 % should be
peak-current method. maintained. Electronic power sources using negative feedback
6.7.1 Peak-to-Peak Voltmeter and Standard Resistor—The from the secondary winding of the test fixture to reduce flux
peak current measurement may be made with a voltmeter waveform distortion have been found to perform quite satis-
whose indications are proportional to the peak-to-peak value of factorily in this test method.
the voltage drop across the potential terminals of a standard
resistor connected in series with the primary winding of the test 7. Procedure
fixture. This peak-to-peak reading (or peak reading) voltmeter 7.1 Before testing, check the specimen strips for length to
shall have a nominal full-scale accuracy of 1.0 % or better at see that they conform to the desired length to within 61⁄32 in.
the test frequency and shall be able to accommodate voltages [0.8 mm] (Note 2). Also check the specimen to see that no

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dented, twisted, or distorted strips showing evidence of me- 7.5 Setting Magnetic Flux Density—With switches S3 and S4
chanical abuse have been included and that the strips are of closed and switches S1, S2, and S 5 open (Note 4), increase the
uniform width (Note 3). Strips having readily noticeable voltage of the power supply until the flux voltmeter indicates
shearing burrs also may be unsuitable for testing. Weigh the the value of voltage calculated to give the desired test magnetic
specimen on a scale or balance capable of determining the flux density in accordance with the equations in 8.1 or 9.1.
mass within an accuracy of 0.1 %. Record specimen weights of Because the action of the air-flux compensator causes a voltage
less than 1 kg to at least the nearest 0.5 g and within the nearest equal to that which would be induced in the secondary winding
1.0 g for specimens heavier than 1 kg. by the air flux to be subtracted from that induced by the total
flux in the secondary, the magnetic flux density calculated from
NOTE 2—Inaccuracy in shearing the length of Epstein strips is equiva-
lent to a weighing error of the same percentage. Both weight and specimen
the voltage indicated by the flux voltmeter is the intrinsic
length inaccuracies cause errors in magnetic flux density measurements, induction, Bi = (B −ΓmHp). In most cases the values of intrinsic
which result in even greater core loss errors. induction, Bi, are not sufficiently different from the correspond-
NOTE 3—The width of strips in the specimen should be checked for ing values of normal induction, B, to require that any distinc-
uniformity since nonuniform width will result in nonuniform magnetic tion be made. Where ΓmHp is not insignificant compared to Bi,
flux density in the specimen, which may have a significant but unpredict- as it is at very high magnetic flux densities, determine the value
able effect upon testing accuracy.
of B by adding to Bi either the measured value of ΓmHp or a
7.2 Divide the test specimen strips into four groups contain- nominal value known to be reasonably typical of the class of
ing equal numbers of strips, and very closely the same mass, material being tested.
for testing. Insert the strips (always a multiple of four in
number) into the test frame solenoids one at a time, starting 7.6 Core Loss—When the voltage indicated by the flux
with one strip in each of two opposite solenoids and then voltmeter has been adjusted to the desired value, read the
inserting a strip into each of the other two solenoids so that wattmeter. Some users, particularly those having wattmeters
these latter strips completely overlap the former two at the four compensated for their own losses (or burden), will desire to
corners. This completes one layer of strips constituting a open switch S4 to eliminate the flux voltmeter burden from the
complete flux path with four overlapped joints. Build up wattmeter indication (Note 4). Others will likely choose to
successive layers in this same fashion until the specimen is have S4 and S5 closed when measuring the losses, so that all
completely assembled. With specimens cut half with and half instruments may be read at the same time. In the latter case, the
cross grain, arrange all the parallel or “with-grain” strips in two combined resistance load of the flux voltmeter, rms voltmeter,
opposite solenoids and all the cross- or transverse-grain strips and potential circuit of the wattmeter will constitute the total
in the other two opposite solenoids. instrument burden on the wattmeter. Exercise care so that the
combined current drain of the instruments does not cause an
7.3 If the specimen strips are reasonably flat and have a appreciably large voltage drop in the secondary circuit resis-
reasonable area of contact at the corners, a sufficiently low tance of the test frame. In such a case, the true magnetic flux
reluctance is usually obtained without resorting to pressure on density in the specimen may be appreciably higher than is
the joints. When the joints are unavoidably poor, the use of apparent from the voltage measured at the secondary terminals
light pressure on the joints, from the use of nonmagnetic corner of the test frame. In any event, power as a result of any current
weights of about 200 g, is permissible although it may drain in the secondary circuit at the time of reading the
introduce some additional stresses in strain-sensitive materials. wattmeter must be known so it can be subtracted from the
With certain types of magnetic material, or for correct evalu- wattmeter indications to obtain the net watts caused by core
ation of properties in certain magnetic flux density ranges, it loss.
may be necessary that the specimen be given a heat treatment
to relieve stresses before testing. Follow the recommendations 7.7 Obtain the specific core loss of the specimen in watts per
of the manufacturer of the materials in performing this opera- unit mass at a specified frequency by dividing the net watts by
tion. that portion of the mass of the specimen constituting the active
magnetic flux path (which is less than the mean geometric path
7.4 Demagnetization—The specimen should be demagne- length) in the specimen. Equations and instructions for com-
tized before measurements of any magnetic property are made. puting the active mass of the specimen and the specific core
With the required apparatus connected as shown in Fig. 1 and loss are given in 8.2 and 9.2.
switches S1, S2, and S4 closed and switches S3 and S5 open
(Note 4), accomplish this demagnetization by initially applying 7.8 Measure the rms value of the secondary voltage by
a voltage from the power source to the primary circuit that is having both S4 and S5 closed (Note 4) and the voltage adjusted
sufficient to magnetize the specimen to a magnetic flux density to indicate the correct value of flux volts. On truly sinusoidal
above the knee of its magnetization curve (magnetic flux voltage, both voltmeters will indicate the same voltage show-
density may be determined from the reading of the flux ing that the form factor of the induced voltage is =2 π/ 4.
voltmeter by means of the equations in 8.1 or 9.1), and then When the voltmeters give different readings, the ratio of the
decrease the voltage slowly and smoothly (or in small steps) to rms value to that indicated by the flux voltmeter reveals the
a very low magnetic flux density. After this demagnetization, ratio by which the form factor of the induced voltage deviates
test promptly for the desired test points. When multiple test from the desired value of =2 π/4. Determining the magnetic
points are required, perform the tests in order of increasing flux density from the readings of a flux voltmeter assures that
magnetic flux density values. the correct value of peak magnetic flux density is achieved in

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the specimen, and hence that the hysteresis component of the Ef 5 =2 π B i AN2 f1028 (1)
core loss is correct even if the waveform is not strictly
sinusoidal. But the eddy-current component of the core loss, where:
being caused by current resulting from a nonsinusoidal voltage Bi = maximum intrinsic flux density, G;
induced in the cross section of the strip, will be in error A = effective cross-sectional area of the test specimen,
depending on the deviation of the induced voltage from the cm 2;
desired sinusoidal wave shape. This error in the eddy-current N2 = number of turns in secondary winding; and
component of loss can be readily corrected by calculations f = frequency, Hz.
based on the observed form factor and the approximate 8.1.1 In the case of Epstein specimens, where the total
percentage of eddy-current loss for the grade of material being number of strips is divided into four equal groups comprising
tested if the correction is reasonably small. The equations the magnetic circuit, the mass of the specimen in each of the
involved in determining this correction are given in 8.3 and
four legs of the magnetic circuit becomes m/4, and the effective
9.3.
cross section, A, in square centimeters, of each leg is:
7.9 RMS Exciting Current—Measure the rms exciting
A 5 m/4lδ (2)
current, when required, by having S1 and S4 closed; S2, S3, and
S5 open (Note 4); then with the ammeter on a suitable scale where:
range, adjust the voltage to the correct flux voltmeter indication m = total mass of specimen strips, g;
for the desired test magnetic flux density. When the setting of l = length of specimen strips, cm (usually 28 or 30.5 cm);
voltage is correct, open S4 and read the ammeter with no and
current drain in the secondary circuit. If S4 is kept closed to δ = standard assumed density of specimen material (see
monitor the magnetic flux density during the current reading, Practice A34/A34M), g/cm3.
the current drain of the flux voltmeter will be included in the
ammeter indication. If exciting current is to be reported in 8.2 Core Loss—To obtain the specific core loss of the
terms of ampere-turns per unit path length, volt-amperes per specimen in watts per unit mass, it is necessary to subtract all
unit mass, or permeability from impedance, calculate the secondary circuit power included in the wattmeter indication
values of these parameters from the equations of 8.4 and 9.4. before dividing by the active mass of the specimen, so that for
a specific magnetic flux density and frequency the specific core
7.10 Permeability—When permeability from peak exciting
current is required, determine the peak value of exciting loss in watts per pound is as follows:
current using the peak-reading voltmeter and standard resistor. P c ~ B; f ! 5 453.6 ~ P c 2 E 2 2 /R ! /m 1 (3)
Switch S1 should be closed to protect the wattmeter from the
where:
possibility of excessive current. Switches S3 and S5 should be
open to minimize secondary loading (Note 4). With switch S2 Pc = core loss indicated by the wattmeter, W;
open and S5 closed, adjust the voltage to the correct value for E2 = rms value of secondary voltage, V;
the desired magnetic flux density or the correct value of peak R = parallel resistance of wattmeter potential circuit and all
current for the desired magnetic field strength. Equations other connected secondary loads, Ω; and
m1 = active mass, g.
involved in the determination of peak magnetic field strength
using a peak-reading voltmeter are given in 8.6 and 9.6. In the 25-cm Epstein frame, it is assumed that 94 cm is the
7.11 If the mutual inductor and flux voltmeter are used to effective magnetic path with specimen strips 28 cm or longer.
determine peak current rather than the standard resistor and For the purpose of computing core loss, the active mass of the
peak-reading voltmeter, follow the same procedure as in 7.10. specimen (less than the total mass) is assumed to be as follows:
The flux voltmeter used for this purpose must meet the m 1 5 l 1 m/ ~ 4l ! 5 94m/4l 5 23.5m/l (4)
restrictions of 6.7.2. Equations involved in the determination of
peak magnetic field strength using a mutual inductor and flux where:
voltmeter are given in 8.6 and 9.6. m = total specimen mass in pounds;
l1 = effective magnetic path length, cm; and
NOTE 4—Due to the high input impedance of modern digital instru-
ments it may not be necessary to switch instruments out of the secondary
l = actual strip length, cm.
circuit when they are not utilized in a particular test. When left in the 8.3 Form Factor Correction—The percent error in form
circuit, the combined current drain of the instrumentation must not cause
an appreciable drop (>0.05 %) in the secondary voltage. Use caution not factor is given by the following equation:
to exceed the instrument’s maximum peak input range as this may damage F 5 100~ E 2 2 E f ! /E f (5)
the instrument.
assuming (Note 5) that:
8. Calculation (Customary Units)
observed P c ~ B; f ! 5 @ ~ corrected P c ~ B; f ! ! /100# h
8.1 Calculate the value of the flux voltage Ef at the desired
test magnetic flux density in the specimen (when corrected for 1 ~ corrected P c ~ B; f ! ! Ke/100,
flux due to H in the material and in the air space encircled by then, the corrected core loss, which shall be computed when
the test winding through the use of the required air-flux
F is greater (Note 6) than 61 %, is:
compensator) in accordance with the following basic equation
discussed in X1.2 of this test method: Corrected P c ~ B; f ! 5 ~ observed P c ~ B; f ! ! 100/ ~ h1Ke ! (6)

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where: where:
observed Pc(B; f) = specific core loss calculated by the equa- N1 = number of turns in primary winding;
tions in 8.2, I = rms value of exciting current, A; and
h = percentage hysteresis loss at magnetic Hz = ac magnetic field strength, Oe.
flux density B, NOTE 7—In previous issues of Test Method A343, the path length for
e = percentage eddy-current loss at magnetic permeability and exciting current has been taken as 88 cm. In the 1960 and
subsequent revisions, the path length has been 94 cm to be consistent with
flux density B, and core-loss determination.
K = (E2/Ef) 2.
The specific exciting power in rms volt-amperes per pound
Obviously, h = 100 − e if residual losses are considered is:
negligible. The values of h and e in the above equation are not
P z ~ B; f ! 5 453.6 E 2 I/m 1 (7)
critical when waveform distortion is low. Typical values at 50
or 60 Hz for the common classes of materials, strip thicknesses, where:
and specimen form are shown in Table 1. Values for materials E2 = rms value of secondary voltage, V;
other than those shown may be obtained using core loss I = rms value of exciting current, A; and
separation methods and are a matter of agreement between the m 1 = active mass, g.
producer and the user.
8.5 Permeability:
NOTE 5—In determining the form factor error, it is assumed that the 8.5.1 For various types of applications, certain types of ac
hysteresis component of core loss will be independent of the form factor permeability data are more useful than others.
if the maximum value of magnetic flux density is at the correct value (as
it will be if a flux voltmeter is used to establish the value of the magnetic
8.5.2 One type of ac permeability directly related to the rms
flux density) but that the eddy-current component of core loss, being a exciting current (or rms excitation) or ac impedance is char-
function of the rms value of the voltage, will be in error for nonsinusoidal acterized by the symbol µz and is computed as follows (Note
voltages. While it is strictly true that frequency or form factor separations 8):
do not yield true values for the hysteresis and eddy-current components,
yet they do separate the core loss into two components, one which is µ z 5 B i /H z (8)
assumed to vary as the second power of the form factor and the other
which is assumed to be unaffected by form factor variations. Regardless of where:
the academic difficulties associated with characterizing these components Bi = maximum intrinsic flux density, G, and
as hysteresis and eddy-current loss, it is observed that the equation for Hz = ac magnetic field strength, Oe (Note 8).
correcting core loss for waveform distortion of voltage based on the NOTE 8—For simplification and convenience in the calculation of ac
percentages of first-power and second-power of frequency components of permeabilities the value of Bi is used to replace Bm in the permeability
core loss does accomplish the desired correction under all practical equation. This entails no loss of accuracy until the magnetic field
conditions if the form factor is accurately determined and the distortion strength Hp becomes appreciable in magnitude when compared to the
not excessive. value of Bi. If greater accuracy is essential Bm or (Bi + Hp) should be used
NOTE 6—It is recommended that tests made under conditions where the to replace the Bi in these equations.
percent error in form factor, F, is greater than 10 % be considered as likely NOTE 9—Hz is computed from the rms value of the complex exciting
to be in error by an excessive amount, and that such conditions be avoided.
current by assuming a crest factor of =2 . Thus it is based on a sinusoidal
8.4 Exciting Current—The rms exciting current is often current having a rms value equal to the rms value of the complex current.
normalized for circuit parameters by converting to the follow- 8.5.3 For control work in the production of magnetic
ing forms: materials, it is often desirable to determine an ac permeability
rms exciting force, N 1 I/l 1 5 N 1 I/94 A/cm ~ Note 7 ! value that is more directly comparable to the dc permeability
value for the specimen. This is accomplished by evaluating Hp
or ac magnetic field strength, H z 5 0.4π =2N 1 I/l 1 Oe from the measured peak value of the exciting current at some
value of H p sufficiently above the knee of the magnetization
curve that the magnetizing component of the exciting current is
appreciably greater than the core loss component. Such a test
TABLE 1 Eddy-Current Loss (Typical) point for many commercial materials is an Hp value of 10 Oe
Assumed Eddy-Current Loss, (796 A/m). Permeability determined in this way is character-
percent (at 50 or 60 Hz), for Strip Thicknesses, ized by the symbol µp, and is computed as follows (Note 8):
Material Specimen in. [mm]
0.007 0.009 0.011 0.012 0.014 0.019 0.025 µ p 5 B i /H p (9)
[0.18] [0.23] [0.27] [0.30] [0.35] [0.47] [0.64]
where Hp is the peak exciting magnetic field strength
Nonoriented half and ... ... ... ... 20 30 40
materialsA half evaluated from measurements of peak current made either with
Nonoriented parallel ... ... ... ... 25 35 45 the permeability-inductor or peak-reading-voltmeter methods
materialsA
Oriented parallel 35 45 50 50 55 ... ...
(see 6.7.1 and 6.7.2) and in accordance with the equations in
materialsB 8.6.
A
These eddy-current percentages were developed for and are appropriate for use 8.6 Hp from Peak Exciting Current—The peak exciting
with nonoriented silicon steels as described in Specifications A677 and A683
where (%Si + 1.7 × %AI) is in the range 1.40 to 3.70.
current, Ip in amperes, may be measured using the air-core
B
These eddy-current percentages were developed for and are appropriate for use mutual inductor and flux voltmeter as follows:
with oriented silicon steels as described in Specification A876.
I p 5 E fm/ =2πfL m (10)

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where: where:
Efm = flux voltage induced in secondary winding of mutual P c = core loss indicated by the wattmeter, W;
inductor, V; E2 = rms value of secondary voltage, V;
f = frequency, Hz; and R = parallel resistance of wattmeter potential circuit and
Lm = mutual inductance, H. all other connected secondary loads, Ω; and
m1 = active mass, kg.
The peak exciting current, Ip in amperes, may be computed
from measurements using a standard resistor and a peak- In the 25-cm Epstein frame it is assumed that 0.94 m is the
reading voltmeter as follows: effective magnetic path with specimen strips 0.28 m or longer.
For the purpose of computing core loss the active mass of the
I p 5 E p2p /2R 1 (11)
specimen (less than the total mass) is assumed to be as follows:
where: m 1 5 l 1 m/4l
Ep-p = peak-to-peak voltage indicated by peak-reading 5 0.94m/4l
voltmeter, V, and
5 0.235m/l (16)
R1 = resistance of standard resistor, Ω.
The peak magnetic field strength, Hp in oersteds, may be where:
calculated as follows: m = the total specimen mass, kg;
l = the actual strip length, m; and
H p 5 0.4πN 1 I p /l 1 (12) l1 = effective magnetic path length, m.
where: 9.3 Form Factor Correction—See 8.3.
N1 = number of turns in primary winding;
9.4 Exciting Current—The rms exciting current is often
Ip = peak exciting current, A; and
l1 = effective magnetic path length, cm. normalized for circuit parameters by converting to the follow-
ing forms:
9. Calculations (SI Units) rms exciting force, N 1 I/l 1 5 N 1 I/0.94 A/m ~ Note 9 !

9.1 Calculate the value of the flux voltage Ef at the desired or

test magnetic flux density in the specimen (when corrected for
rms ac magnetic field strength, H z 5 =2N 1 I/l 1 A/m
flux as a result of H in the material and in the air space
encircled by the test winding through the use of the required where:
air-flux compensator) in accordance with the following basic N1 = number of turns in primary winding;
equation discussed in 1.3 of this test method. I = rms value of exciting current, A; and
Hz = apparent ac magnetic field strength, A/m.
E f 5 =2π B i AN2 f (13) NOTE 10—In previous issues of Test Method A343, the path length for
permeability and exciting current has been taken as 0.88 m. In the 1960
Bi = maximum intrinsic flux density, T; and subsequent revisions, the path length has been 0.94 m to be consistent
A = effective cross-sectional area of the test specimen, m2; with core-loss determination.
N2 = number of turns in secondary winding; and The specific exciting power in rms volt-amperes per kilogram is:
f = frequency, Hz.
P z ~ B;f ! 5 E 2 I/m 1 (17)
9.1.1 In the case of Epstein specimens, where the total
where:
number of strips is divided into four equal groups comprising
E2 = rms value of secondary voltage, V;
the magnetic circuit, the mass of the specimen in each of the I = rms value of exciting current, A; and
four legs of the magnetic circuit becomes m/4, and the effective m1 = active mass, kg.
cross section, A, in square metres, of each leg is:
9.5 Permeability:
A 5 m/4lδ (14) 9.5.1 For various types of applications, certain types of ac
where: permeability data (in H/m) are more useful than others.
m = total mass of specimen strips, kg; 9.5.2 One type of ac permeability directly related to the rms
l = length of specimen strips, m (usually 0.28 or 0.305 m); exciting current (or rms excitation) or ac impedance is char-
and acterized by the symbol µz and is computed as follows (Note
δ = standard assumed density of specimen material (see 11):
Practice A34/A34M), kg/m3. µ z 5 B i /H z (18)
9.2 Core Loss—To obtain the specific core loss of the where:
specimen in watts per unit mass, it is necessary to subtract all Bi = maximum intrinsic flux density, T, and
secondary circuit power included in the wattmeter indication Hz = ac magnetic field strength, A/m (Note 12).
before dividing by the active mass of the specimen, so that for NOTE 11—For simplification and convenience in the calculation of ac
a specific magnetic flux density and frequency the specific core permeabilities the value of Bi is used to replace Bm in the permeability
loss in watts per kilogram is as follows: equation. This entails no loss of accuracy until ΓmHp becomes appreciable
in magnitude when compared to the value of Bi. If greater accuracy is
P c ~ B; f ! 5 ~ P c 2 E 2 2 /R ! /m 1 (15) essential, Bm or (Bi + ΓmHp) should be used to replace Bi in these

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equations. The magnetic constant Γm is equal to 4π × 10 −7 H/m. participating laboratories. Practice E691 was followed for the
NOTE 12—Hz is computed from the rms value of the complex exciting design of the experiment and the analysis of the data for both
current by assuming a crest factor of =2. Thus it is based on a sinusoidal studies. The details of the studies are given in ASTM Research
current having a rms value equal to the rms value of the complex current. Reports A06-1000 and A06-1002.4
9.5.3 For control work in the production of magnetic 10.2 Test Result—The precision information given below
materials, it is often desirable to determine an ac permeability
for core loss or permeability as a percentage of the measured
value that is more directly comparable to the dc permeability of
value is for the comparison of two test results, each of which
the specimen. This is accomplished by evaluating Hp from the is a single measurement.
measured peak value of the exciting current at some value of
Hp sufficiently above the knee of the magnetization curve that 10.3 Precision—See Table 2.
the magnetizing component of the exciting current is apprecia- 10.4 Bias—Since there is no accepted reference material,
bly greater than the core-loss component. Such a test point for method, or laboratory suitable for measuring the magnetic
many commercial materials is an Hp value of 796 A/m. properties determined using this test method, no statement of
Permeability determined in this way is characterized by the bias is being made.
symbol µp and is computed as follows (Note 11):
µ p 5 B i /H p (19)
4
where: Supporting data have been filed at ASTM International Headquarters and may
be obtained by requesting Research Reports RR:A06-1000 and RR:A06-1002.
H p = peak exciting magnetic field strength evaluated from
measurements of peak current made either with the
TABLE 2 Repeatability and Reproducibility Limits for Specific
permeability inductor or peak-reading-voltmeter Core Loss and Peak Permeability Measurements
methods (see 6.7.1 and 6.7.2) and in accordance with
the equations in 9.6. NOTE 1—The terms repeatability and reproducibility are used as
specified in Practice E177. The respective standard deviations among test
9.6 Hp from Peak Exciting Current—The peak exciting results may be obtained by dividing the above limit values by 2.8.
current, Ip in amperes, may be measured using the air-core ASTM Type 27G051 Material
mutual inductor and flux voltmeter as follows: Specific Core Loss at 60 Hz
Relative Peak
Permeability at
and at Maximum
I p 5 E fm/ =2πfLm (20) Instrinsic Flux Density,
Peak Magnetic
Field Strength,
Bi, =
where: Hp, =
15 kG [1.5 17 kG [1.7
Efm = flux voltage induced in secondary winding of mutual T] T]
10 Oe [796 A/m]
inductor, V; Average Test Value 0.481 W/lb 0.699 W/lb 1840
f = frequency, Hz; and [1.06 W/kg] [1.54 W/kg]
Lm = mutual inductance, H. 95 % repeatability 0.6 % 0.7 % 0.12 %
limitsA
The peak exciting current, Ip in amperes, may be computed 95 % reproducibility 3.4 % 3.1 % 0.62 %
from measurements using a standard resistor and a peak- limitsB
ASTM Type 47S188 Material
reading voltmeter as follows: Specific Core Loss at 60 Hz Relative Peak
I p 5 E p2p /2R 1 (21) and at Maximum Permeability at
Instrinsic Flux Density, Peak Maximum
where: Bi, = Intrinsic Flux
Density, Bi, =
Ep-p = peak-to-peak voltage indicated by peak-reading 10 kG [1.0 15 kG [1.5 15 kG [1.5 T]
voltmeter, V, and T] T]
Average Test Value 0.698 W/lb 1.67 W/lb 1909
R1 = resistance of standard resistor, Ω. [1.54 W/kg] [3.68 W/kg]
The peak magnetic field strength, Hp in amperes per meter, 95 % repeatability 0.3 % 0.6 % 1.6 %
limitsA
may be calculated as follows: 95 % reproducibility 3.8 % 3.5 % 8.2 %
limitsB
H p 5 N 1 I p /l 1 (22)
ASTM Type 64D430 Material
Specific Core Loss at 60 Hz Relative Peak
where: and at Maximum Permeability at
N1 = number of turns in primary winding; Instrinsic Flux Density, Peak Maximum
Ip = peak exciting current, A; and Bi, = Intrinsic Flux
Density, Bi, =
l1 = effective magnetic path length, m. 10 kG [1.0 15 kG [1.5 15 kG [1.5 T]
T] T]
10. Precision and Bias Average Test Value 1.57 W/lb 3.83 W/lb 2291
[3.46 W/kg] [8.44 W/kg]
10.1 Interlaboratory Test Programs—Two interlaboratory 95 % repeatability 0.2 % 0.3 % 1.1 %
studies have been conducted. In the first study, three blended limitsA
95 % reproducibility 3.5 % 2.0 % 6.2 %
Epstein specimens each of ASTM Type 27G051 and ASTM limitsB
Type 47S188 materials were circulated to 14 participating A
95 % repeatability limits (within laboratory).
laboratories. in the second study, three blended Epstein speci- B
95 % reproducibility limits (between laboratories).
mens of ASTM Type 64D430 material were circulated to 23

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11. Keywords
11.1 alternating-current; ammeter; core loss; customary
units; Epstein; exciting power; magnetic; magnetic flux den-
sity; magnetic material; magnetic test; permeability; power
frequency; voltmeter; wattmeter

ANNEXES

(Mandatory Information)

A1. DETAILS OF CONSTRUCTION FOR EPSTEIN TEST FRAMES AND OTHER COMPONENTS

A1.1 Epstein Test Frame the order of 1 or 2 mV or less, the air-flux compensator may be
assumed to be adequately compensated.
A1.1.1 General principles involved in the construction of
standard 25-cm Epstein test frames are given in 6.2 of this test A1.2 Crest Ammeter Mutual Inductor
method. Specific details of wire sizes, turns and dimensional
A1.2.1 The permeability mutual inductors, when con-
data are given in Table A1.1 of this annex along with the
structed in accordance with Table A1.2 of this annex use
approximate electrical characteristics to be expected.
tubular winding forms and end disks made from
A1.1.2 The standard air-flux compensator, described in a nonconducting, nonmagnetic material and layer wound pri-
general way in 6.2.5, uses a tubular (or solid) winding form 2 mary and secondary windings. In this inductor the primary is
in. [50.8 mm] in diameter by 1 in. [25.4 mm] in length and two split, with one half being wound directly on the winding form,
end pieces (either square or round) about 4 to 41⁄2 in. [102 to followed by the full secondary winding, and finishing with the
114 mm] across and 1⁄4 to 1⁄2 in. [6.4 to 12.7 mm] thick. The remaining half of the primary winding. A single thickness of
winding form and end pieces may be of any nonconducting, fiber insulating material should be used between each layer of
nonmagnetic material. Screws or bolts used for assembly shall the secondary winding to facilitate winding and improve the
be nonmagnetic. The secondary winding is layer wound over frequency characteristics. The two halves of the primary shall
the primary and initially should be comprised of at least 10 % be connected in series. The mutual inductance may be mea-
greater number of turns than indicated in Table A1.1 of this sured on a suitable bridge, or the calibration may be made to
annex to provide for removal of turns to adjust the secondary acceptable accuracy by passing sinusoidal currents at 60 Hz
to the exact number of turns that will completely cancel the through the primary winding and reading the secondary voltage
mutual inductance of the solenoid windings. A layer of using the flux voltmeter which is to be calibrated to read Efm in
insulating material a few thousandths of an inch (0.001 terms of crest amperes of exciting current. The mutual inductor
in. = 0.0254 mm) thick shall be used between primary and must be so located that no appreciable externally produced
secondary windings. The adjustment of the mutual inductor leakage flux links the secondary winding in the absence of any
may be checked by passing an ac current of 2 to 5 A through primary current. If the secondary current is negligible at the
the primary winding of the test frame with no specimen in the time of measurement the voltmeter will indicate approximately
solenoids, but with the air-flux compensator connected in 0.12 π flux V/mH of mutual inductance/rms A sinusoidal
proper polarity, and observing the open-circuit ac voltage at the primary current (or 0.06 = 2 π flux V/peak A of sinusoidal
secondary terminals with a voltmeter. When this voltage is of primary current/mH).

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TABLE A1.1 Specifications for Standard Epstein Frames Having Replaceable Tube Liners
NOTE 1—All conductors are enameled copper wire and all turns are close-wound, except that the turns of single layer or incomplete layers shall be
uniformly distributed.
NominalA specimen weight, kg 2 1 0.5
Total turns 700 700 700
Approximate secondary voltage at 60 Hz and 15 kG (1.5T) 65 32.5 16.3
Dimension of forms:
Inner form (liner)
inside dimensions, in. 0.750 × 1.25 0.375 × 1.25 0.250 × 1.25
outside dimensions, in. 0.875 × 1.375 0.500 × 1.375 0.375 × 1.375
Winding form
inside dimensions, in. 0.906 × 1.406 0.563 × 1.406 0.438 × 1.406
outside dimensions, in. 1.031 × 1.531 0.688 × 1.531 0.563 × 1.531
Solenoid windings:
Primary (top) winding
layers 3 3 3
AWG wire size 2 No. 15 (0.057 18 in.) 2 No. 15 (0.057 18 in.) 2 No. 15 (0.057 18 in.)
resistance, Ω 0.57 0.50 0.48
self inductance, mH 1.26 0.99 0.91
Secondary (bottom) winding
layers 1 1 1
AWG wire size No. 19 (0.0359 in.) No. 19 (0.0359 in.) No. 19 (0.0359 in.)
resistance, Ω 2.13 1.85 1.75
self inductance, mH 0.85 0.65 0.58
Air flux compensator:
Dimension of winding form
diameter, in. 2.0 2.0 2.0
length, in. 1.0 1.0 1.0
Primary (inner) winding
layers 4 4 4
turns 44 44 44
AWG wire size No. 13 (0.072 in.) No. 13 (0.072 in.) No. 13 (0.072 in.)
resistance, Ω 0.06 0.06 0.06
self inductance, mH 0.12 0.12 0.12
Secondary (outer) winding
approximate turns 425 315 270
AWG wire size No. 19 (0.0359 in.) No. 19 (0.0359 in.) No. 19 (0.0359 in.)
resistance, Ω 3.5 2.5 2.1
self inductance, mH 15.9 8.6 6.2
Approximate mutual inductance, mH 0.83 0.64 0.57
Solenoids and Compensator:
Total resistance at primary terminals, Ω 0.63 0.56 0.54
Total inductance at primary terminals, mH 1.38 1.11 1.03
Total resistance at secondary terminals, Ω 5.63 4.30 3.82
Total inductance at secondary terminals, mH 16.8 9.3 6.8
A
Based on 28-cm-long Epstein strips.
25.4 mm = 1 in.

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TABLE A1.2 Examples of Standard Crest Ammeter Mutual Inductors For Typical Crest Ammeter UseA
B
Inductor 1 2 3 4
Winding form: C
Outside diameter, in. [mm] 4 [102] 4 [102] 4 [102] 3 [76]
Length, in. [mm] 45⁄8 [117] 15⁄8 [41] 2 [51] 2 [51]
End disk diameter, in. [mm] 81⁄4 [210] 71⁄2 [191] 9 [229] 9 [229]
Primary windings: D
AWG wire size E No. 8 sq No. 6 sq No. 9 No. 8
Layers 8 4 6 12
Turns F 240 32 96 156
Secondary Windings: B
AWG wire size E No. 28 No. 28 No. 22 No. 16
Layers 32 32 41 17
Turns 8640 3200 1540 546
Electrical characteristics:
Primary self inductance, mH 5.01 0.14 1.7 2.35
Primary resistance, Ω 0.25 0.023 0.14 0.10
Secondary self inductance, mH 7350 1650 800 50.98
Secondary resistance, Ω 860 296 65 3.65
Mutual inductance, F mH 181.2 12.9 35.1 7.066
A
To maintain accuracy, the flux voltmeter should not draw any appreciable current that can change the mutual inductor secondary“ Terminal” voltage (see 6.7.1).
B
In Inductors 1, 2, and 3, generally the primaries are divided into two sections by the secondary, that is, one-half the primary turns are placed on the form first; the complete
secondary winding second, and the remaining one-half of the primary turns placed on top of the secondary. The top and bottom primary windings shall be connected in
series.
C
The tubular winding form and the end disks shall be made of nonmagnetic, nonconducting material. Other parts of the winding form shall be nonmagnetic.
D
An insulating layer of paper should be placed between windings.
E
All conductors are at least enamel insulated.
F
It may be desirable to make the crest ammeter direct reading in peak oersteds or peak A/m. This inductor may be tapped for this purpose if desired.

A2. RECOMMENDED STANDARD TEST VALUES

A2.1 Standard Test Values A2.1.1.2 Tests for ac permeability from peak exciting cur-
A2.1.1 For tests at 50 or 60 Hz on flat-rolled materials in rent (if required) at a magnetic flux density of 15 kG [1.5 T] or
standard thicknesses, the following test points are recom- at a magnetic field strength of 10 Oe [796 A/m].
mended:
A2.1.1.1 Test for core loss (and rms exciting current if
required) at magnetic flux densities of 10, 15, or 17 kG [1.0,
1.5, or 1.7 T], and

A3. PREPARATION OF EPSTEIN TEST SPECIMENS

A3.1 Test Specimens not less than 28.0 cm [11.02 in. or 280 mm] in length. If, for
ease of assembly and disassembly of the specimen in the test
A3.1.1 When magnetic properties of the basic magnetic
material are desired (with effects of specimen shape, joints in frame, it is desired to use strips slightly longer than 28.0 cm
the magnetic circuit, and characteristics of the test windings [280 mm], a length of 30.5 cm [12.01 in. or 305 mm] is
reduced to negligible proportions), the test specimen shall, recommended.
whenever possible, consist of strips (commonly called Epstein A3.1.3 The nominal mass of an Epstein test specimen shall
strips) arranged in an Epstein frame so as to constitute a square be approximately 71.5, 36, or 18 g/cm [7.15, 3.6, 1.8 g/mm] of
magnetic circuit with the strips completely overlapped (double strip length (2-, 1-, or 0.5-kg total mass in 28-cm [280-mm]
lapped) at the corners. Flat-rolled magnetic materials supplied strip length) as determined by the instrumentation and test
as sheets or coils preferably shall be tested in this specimen frame dimensions (Note A3.1). In no case shall the specimen
form whenever dimensions permit. consist of less than 12 strips. Specimens weighing less than 15
A3.1.2 The Epstein test specimens shall consist of strips cut g/cm [1.5 g/mm] of strip length shall consist of at least 20
from sheets or coils in accordance with Practice A34/A34M. strips. In all cases, the specimen is subject to the requirement
The strips shall be 3.00 cm [1.181 in. or 30 mm] in width and that the strips be taken so as to adequately represent the areas

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FIG. A3.1 Suggested Distribution of Strips to Be Cut from Sheets for Magnetic Tests

being sampled, and that the total number of test strips be a weights of 2, 1, or 0.5 kg. Increased sensitivity of instruments will be
multiple of four. Table A3.1 gives the number of strips necessary for adequate performance on specimens of smaller than nominal
weight. Specimens weighing less than about one half the nominal mass for
frequently used to meet this requirement for various strip the test frame dimensions should not be used unless the instrumentation of
thicknesses. the test equipment has been specifically designed for operation under such
conditions.
NOTE A3.1—The dimensions of the winding form of the test frame
should be suitable for accommodating the desired specimen mass without A3.1.4 If the specimen is to comprise strips with half the
excessive unfilled space within the test windings. Standard test frames total number cut parallel or with the direction in which the
(see 6.2) are designed with dimensions accommodating nominal specimen material has been rolled and half transverse or across the
direction of rolling, it is recommended that sufficient strips be
TABLE A3.1 Suggested Number of Test Strips cut in accordance with the arrangement indicated in Fig. A3.1
Strip Thickness,
Number of 280-mm Long Strips for Test Specimens of (a) or (b). Where the material has been produced as continuous
Nominal Mass
in. [mm] cold-reduced coils, sufficient length should be discarded from
500 g 1000 g 2000 g
the end of the coil to insure uniform properties in the test strips.
0.0310 [0.79] 12 20 40
0.0280 [0.71] 12 24 44 A3.1.5 If the test specimen comprises only parallel or
0.0250 [0.64] 12 24 48 “with-grain” strips, it is recommended that sufficient strips be
0.0220 [0.56] 16 28 56
0.0185 [0.47] 16 32 64 cut in accordance with Fig. A3.1 (c).
0.0170 [0.43] 20 36 72 A3.1.6 When less than the total number of strips obtained
0.0155 [0.39] 20 40 80
0.0140 [0.36] 24 44 88 from the sampled area are needed for the test specimen, the
0.0125 [0.32] 24 48 96 excess strips should be discarded equally from all locations in
0.0110 [0.28] 28 56 112 the sampled areas. For instance, if approximately one fourth of
0.0090 [0.23] 36 68 136
0.0070 [0.18] 44 88 176 the total strips obtained is excess, every fourth strip should be
discarded.

APPENDIXES

(Nonmandatory Information)

X1. BASIC PRINCIPLES AND DEVELOPMENT OF EPSTEIN TEST EQUATIONS

X1.1 Basic Principles shall be sinusoidal within limits described in the individual test
X1.1.1 The basic features involved in these alternating- methods. To accomplish this, the power source must generate
current methods, which should be strictly adhered to by the a closely sinusoidal waveform, and the primary circuit imped-
user unless otherwise stated in the individual test methods, are ance (including the power source) shall be kept as low as
as follows: possible.
X1.1.2 The test specimen shall be of uniform cross section X1.1.4 Voltage and frequency shall be very closely con-
perpendicular to the direction of the flux path and should have trolled within limits given in the individual test methods.
uniform properties in any given direction. X1.1.5 Alternating-current normal induction, B, shall be
X1.1.3 The flux waveform, as judged by the form factor of determined (in accordance with X1.2 or X1.3) from measure-
the voltage wave induced in an unloaded secondary winding, ments made with a voltmeter responsive to the full-wave

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average value of the voltage (rectifying-type voltmeter), com- X1.1.11.2 Impedance Permeability, µz—A type of ac perme-
monly called a flux voltmeter,5 connected to an essentially ability calculated from the rms value of the exciting current.
unloaded secondary winding enclosing the specimen. The flux This requires the exciting-current harmonics to be treated as
voltmeter shall conform to the specifications given in the part of a sinusoidal current of fundamental frequency.
individual test methods. X1.1.11.3 Peak Permeability, µp—A type of ac permeability
X1.1.6 The value of the effective test specimen cross- which is calculated from the measured peak value of the total
sectional area shall be determined from mass, length, and exciting current. The effects of phase relationships and core
density of the test specimen wherever feasible (Practice A34/ loss components are ignored.
A34M). Equations for calculating this area are given in the
individual test methods. X1.2 Basic Equation for Flux Density (Customary Units)
X1.1.7 Core-loss measurements shall be made by using X1.2.1 Where a magnetic circuit of uniform cross-sectional
circuitry, given in the individual test methods, which avoids the area, as in these methods, is subjected to symmetrical ac
inclusion of the I2R (conductor resistance loss) of the primary magnetization of uniform lengthwise distribution, and the cross
test winding. In the wattmeter method, this involves the use of section of that magnetic circuit is encircled by a conductor not
a wattmeter connected so that the total exciting current of the carrying the exciting current, it can be shown that the measured
specimen flows through the current coils of the instrument, and average value of the full-wave rectified voltage induced in the
so that the induced voltage in the secondary winding of the test winding is related to the maximum value of the flux density in
frame is applied to the potential coil circuit of the instrument. the magnetic material by the equation:
In the bridge method, it involves evaluation of the component E avg 5 4 ~ B i A 1 H p A w ! N 2 f1028 (X1.1)
of the exciting current which is in phase with the induced
voltage (or the resistive component of that portion of the where:
specimen’s complex impedance that can be attributed to the E avg = average value of the fully rectified symmetrical
core material). The core loss is the product of the “in-phase” voltage, V;
current component and the induced voltage. Bi = peak value of the intrinsic flux density (B − Hp), G;
A = solid cross section of the specimen, cm2;
X1.1.8 Exciting-current measurements shall be made with Hp = peak value of the magnetic field strength, Oe;
an ammeter whose indications are proportional to the rms value Aw = area enclosed by the secondary winding, cm2;
of the current regardless of its waveform. The impedance of the N2 = number of turns in winding; and
ammeter must be low enough to avoid appreciable distorting f = frequency, Hz.
effect on the flux waveform.
Since the indications of the flux voltmeter are related to
X1.1.9 Secondary-circuit power drain must be negligible, or average volts by the equation:
its effects on the measured properties must be evaluated and
corrected by calculation. E f 5 =2π/4E avg (X1.2)
X1.1.10 Whenever tests are made under conditions in which where the factor =2 π/4 is the accepted value of the form
the effects of accidental polarization of the specimen by factor of a sine wave, and since the air flux (HpAw) is kept
handling in the earth’s magnetic field, or previous magnetic negligibly small or by the use of an air flux compensating
history, may have a significant effect on the measured mutual inductor (see 6.2.5) the induced voltage after air flux
properties, demagnetization of the test specimen shall be used, correction as indicated on the flux voltmeter is:
as dictated by the individual test methods.
E f 5 =2π B i AN2 f1028 (X1.3)
X1.1.11 Various types of ac permeability may be deter-
mined from measurements described in these methods. It This equation shall be used for relating the indications of the
should be understood that these ac permeabilities are in reality flux voltmeter, sometimes called flux volts, to the test magnetic
mathematical definitions each based on different specified flux density in these test methods. When the magnetic flux
assumptions. Therefore, their individual values may differ density is needed in terms of the normal induction B, or
considerably from each other and from the normal dc perme- Bi + Hp, the value of Hp must be added when it is of significant
ability. See also Terminology A340 for definitions. magnitude. In a properly constructed Epstein frame the coef-
X1.1.11.1 Inductance Permeability, µL—A type of ac per- ficient of coupling between its superimposed windings is so
meability related to parallel inductance is calculated from the close to unity that each winding may be considered to have the
value of the reactive of the exciting current (or the reactive same number of induced volts per turn.
component of that portion of the specimen’s complex imped-
ance attributed to the core material) as measured in the X1.3 Basic Equation for Flux Density (SI Units)
varmeter method (see Test Method A889/A889M).
X1.3.1 Where a magnetic circuit of uniform cross-sectional
area, as in these methods, is subjected to symmetrical ac
5
magnetization of uniform lengthwise distribution, and the cross
Camilli, G., “A Flux Voltmeter for Magnetic Tests,” JAIEE (Journal American
section of that magnetic circuit is encircled by a conductor not
Institute of Electrical Engineers, Vol 45 , October 1926, p. 721. See also Smith, B.
M., and Concordia, C., “Measuring Core Loss at High Densities,” Electrical carrying the exciting current, it can be shown that the measured
Engineering, ELENA, Vol 51, No. 1, January 1932. average value of the full-wave rectified voltage induced in the

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winding is related to the maximum value of the flux density in where the factor =2 π/4 is the accepted value of the form
the magnetic material by the equation: factor of a sine wave, and since the air flux (ΓmHpAw) is kept
E avg 5 4 ~ B i A1Γ m H p A w ! N 2 f (X1.4) negligibly small or by the use of an air flux compensating
mutual inductor (see 6.2.5), the induced voltage alter air flux
where:
correction as indicated on the flux voltmeter is:
Eavg = average value of the fully rectified symmetrical
voltage, V; E f 5 =2π B i AN2 f (X1.6)
Bi = peak value of the intrinsic flux density (B − ΓmHp),
T; This equation shall be used for relating the indications of the
A = solid cross section of the specimen, m 2; flux voltmeter, sometimes called flux volts, to the test magnetic
Hp = peak value of the magnetic field strength, A/m; flux density in these test methods. When the magnetic flux
Aw = area enclosed by the secondary winding, m 2; density is needed in terms of the normal induction B, or
N2 = number of turns in winding; and Bi + ΓmHp, the value of ΓmHp must be added when it is of
f = frequency, Hz, and
significant magnitude. In a properly constructed Epstein frame,
Γm = 4π × 10-7 H/m.
the coefficient of coupling between its superimposed windings
Since the indications of the flux voltmeter are related to is so close to unity that each winding may be considered to
average volts by the equation: have the same number of induced volts per turn.
E f 5 =2π/4E avg (X1.5)

X2. RECOMMENDED STANDARD DATA FORMAT FOR COMPUTERIZATION OF MAGNETIC TEST DATA BASED ON
TEST METHOD A343

X2.1 Because of the intense activity in building computer- information that users may be confident of their ability to
ized materials databases and the desire to encourage their compare sets of data from individual databases and to make the
uniformity and therefore the ease of data comparison and data database useful to a relatively broad range of users.
interchange, it is appropriate to provide recommended standard
formats for the inclusion of specific types of test data in such X2.4 It is recognized that many databases are prepared for
databases. This also has the important effect of encouraging the very specific applications, and individual database builders
builders of databases to include sufficiently complete informa- may elect to omit certain pieces of information considered to
tion that comparisons among individual sources may be made be of no value for that specific application. However, there are
with assurance that the similarities and/or differences in the test a certain minimum number of fields considered essential to any
procedures and conditions are covered therein. database, without which the user will not have sufficient
information to reasonably interpret the data. In the recom-
X2.2 Table X2.1 is a recommended standard format for the mended standard format, these fields are marked with asterisks.
computerization of power frequency (25–400 Hz) magnetic
test data as generated using the 25-cm Epstein test frame by X2.5 The presentation of this format does not represent a
Test Method A343. Also see Table X2.2, Table X2.3, and Table requirement that all of the elements of information included in
X2.4 for additional information. There are three columns of the recommendation must be included in every database.
information: Rather it is a guide as to those elements that are likely to be
X2.2.1 Field Number—a reference number for ease of useful to at least some users of most databases. It is understood
dealing with the individual fields within this format guideline. that not all of the elements of information recommended for
It has no permanent value and does not become part of the inclusion will be available for all databases; that fact should not
database itself. discourage database builders and users from proceeding so
long as the minimum basic information is included (the items
X2.2.2 Field Name and Description—the complete name of noted by the asterisks).
the field, descriptive of the element of information that would
be included in this field of the database. X2.6 This document has no implication on data required for
X2.2.3 Category Sets, Values, or Units—a listing of the materials production or purchase. Reporting of actual test
types of information that would be included in the field or in results shall be as described in the actual material specification
the case of properties or other numeric fields, the units in which or as agreed to by the purchaser and manufacturer as shown on
the numbers are expressed. Category sets are closed (that is, the purchase order and acknowledgment.
complete) sets containing all possible (or acceptable) inputs to
the field. Values are representative sets, listing sample (but not X2.7 Also, it is recognized that in some individual cases,
necessarily all acceptable) inputs to the field. additional elements of information of value to users of a
database may be available. In those cases, databases builders
X2.3 The fields or elements of information included in this are encouraged to include them as well as the elements in the
format are those recommended to provide sufficiently complete recommended format.

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TABLE X2.1 Recommended Standard Data Format for
Computerization of Magnetic Test Data per Test Method A343
(Epstein Test Method)
Field Field Category Sets,
No. A Name and Description Values, or Units
Test and Materials Identification
1.* Material identification (This information will be
supplemented
2.* Lot identification by material descriptions
3.* Data source identification based on Guide E1338.)
4.* Type of test Epstein test
5.* ASTM, ISO, or other applicable A343
standard method number
6. Date of applicable standard year (for example 1986)
Specimen Information
7. Specimen identification alphanumeric string
8. Specimen number alphanumeric string
9. Specimen type Epstein strips
10.* Specimen thickness in. (mm)
11.* Specimen condition see Table X2.2
12.* Specimen orientation see Table X2.3
13.* Specimen mass g (kg)
14.* Specimen length cm (m)
15.* Assumed density g/cm 3 (kg ⁄ m 3)
16. Assumed % eddy current loss percentage
17. Assumed % eddy current loss percentage
Test Results
18. Core loss W/lb (W/kg)
19. RMS exciting current A
20. Peak exciting current A
21. Specific exciting power VA/lb (VA/kg)
22. Impedance permeability dimensionless
23. Relative peak permeability dimensionless
24. Form factor dimensionless
B
Test Parameters
25.* Test temperature °C
26.* Test frequency Hertz
27.* Test magnetic flux density Gauss (T)
28.* Test magnetic field strength Oe (A/m)
29.* Form factor correction used yes or no
30.* Peak current measurement device see Table X2.4
31.* Primary turns dimensionless
32.* Comments
A
* Denotes essential information for computerization of test results.
Field numbers are for reference only. They do not imply a necessity to include
all these fields in any specific database nor imply a requirement that fields used be
in this particular order.
B
It is customary to determine core loss at specified test magnetic flux density and
to determine permeability at specified magnetic field strength.

TABLE X2.2 Category Set for Specimen Condition

As sheared
Annealed after shearing

TABLE X2.3 Category Set for Specimen Orientation

Parallel to rolling direction
Transverse to rolling direction
Half parallel-half transverse
Other

TABLE X2.4 Category Set for Peak Current Measurement Device

Mutual inductor method
Peak reading ammeter

X2.8 This format is only for magnetic test data generated by of magnetic test data. These items are covered by separate
Test Method A343. It does not include the recommended formats to be referenced in material specifications or other test
material description or the presentation of other specific types standards.

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