ASTM A343/A343M-14(2019)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: A343/A343M − 14 (Reapproved 2019)
Standard Test Method for
Alternating-Current Magnetic Properties of Materials at
Power Frequencies Using Wattmeter-Ammeter-Voltmeter
Method and 25-cm Epstein Test Frame
This standard is issued under the fixed designationA343/A343M; the number immediately following the designation indicates the year
of original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.
A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope separate sections for the respective unit systems. The values
stated in each system may not be exact equivalents; therefore,
1.1 Thistestmethodcoverstestsforthemagneticproperties
each system shall be used independently of the other. Combin-
ofbasicflat-rolledmagneticmaterialsatpowerfrequencies(25
ing values from the two systems may result in non-
to 400 Hz) using a 25-cm Epstein test frame and the 25-cm
conformance with this standard.
double-lap-jointed core. It covers the determination of core
1.8 This standard does not purport to address all of the
loss, rms exciting power, rms and peak exciting current, and
safety concerns, if any, associated with its use. It is the
several types of ac permeability and related properties of
responsibility of the user of this standard to establish appro-
flat-rolled magnetic materials under ac magnetization.
priate safety, health, and environmental practices and deter-
1.2 This test method shall be used in conjunction with
mine the applicability of regulatory limitations prior to use.
Practice A34/A34M.
1.9 This international standard was developed in accor-
1.3 This test method provides a test for core loss and
dance with internationally recognized principles on standard-
exciting current at moderate and high magnetic flux densities
ization established in the Decision on Principles for the
up to 15 kG [1.5T] on nonoriented electrical steels and up to
Development of International Standards, Guides and Recom-
18 kG [1.8T] on grain-oriented electrical steels.
mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.4 Thefrequencyrangeofthistestmethodisnormallythat
ofthecommercialpowerfrequencies50to60Hz.Withproper
2. Referenced Documents
instrumentation,itisalsoacceptableformeasurementsatother
frequencies from 25 to 400 Hz.
2.1 ASTM Standards:
A34/A34MPractice for Sampling and Procurement Testing
1.5 This test method also provides procedures for calculat-
of Magnetic Materials
ing ac impedance permeability from measured values of rms
A340Terminology of Symbols and Definitions Relating to
exciting current and for ac peak permeability from measured
Magnetic Testing
peak values of total exciting currents at magnetic field
A677Specification for Nonoriented Electrical Steel Fully
strengths up to about 150 Oe [12 000 A/m].
Processed Types
1.6 Explanation of symbols and abbreviated definitions
A683Specification for Nonoriented Electrical Steel, Semi-
appear in the text of this test method. The official symbols and
processed Types
definitions are listed in Terminology A340.
A876Specification for Flat-Rolled, Grain-Oriented, Silicon-
1.7 The values and equations stated in customary (cgs-emu Iron, Electrical Steel, Fully Processed Types
and inch-pound) or SI units are to be regarded separately as A889/A889MTest Method for Alternating-Current Mag-
standard. Within this standard, SI units are shown in brackets netic Properties of Materials at Low Magnetic Flux
except for the sections concerning calculations where there are Density Using the Voltmeter-Ammeter-Wattmeter-
Varmeter Method and 25-cm Epstein Frame
E177Practice for Use of the Terms Precision and Bias in
This test method is under the jurisdiction of ASTM Committee A06 on
ASTM Test Methods
MagneticPropertiesandisthedirectresponsibilityofSubcommitteeA06.01onTest
E691Practice for Conducting an Interlaboratory Study to
Methods.
Current edition approved April 1, 2019. Published April 2019. Originally
approved in 1949. Last previous edition approved in 2014 as A343/A343M–14.
DOI: 10.1520/A0343_A0343M-14R19. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
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
A343/A343M − 14 (2019)
Determine the Precision of a Test Method tance can be tolerated since this system will maintain sinusoi-
E1338Guide for Identification of Metals and Alloys in dal flux at much higher primary resistance. Although the
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
resistance so that the voltage available at the terminals of the
3.1 Thistestmethodisafundamentalmethodforevaluating
instruments is imperceptibly lower than the voltage at the
the magnetic performance of flat-rolled magnetic materials in
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
measurement functions:
4.1 The specimens for this test shall be selected and
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 tionappropriatetothespecimenmasstobeused.Thesolenoids
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,andwiththecenterlineofsolenoidsonoppositesidesof
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 evenlywoundinonelayeroverawindinglengthof191mmor
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.Theouterormagnetizingwindinglikewiseshallconsistof
FIG. 1 Basic Circuit for Wattmeter-Ammeter-Voltmeter Method
A343/A343M − 14 (2019)
one fourth of the total number of primary turns evenly wound 6.4 RMS Voltmeter, V —A true rms-indicating voltmeter
rms
over the winding length of each solenoid. These individual shall be provided for evaluating the form factor of the voltage
solenoid windings, too, shall be connected in series so their
induced in the secondary winding of the test fixture and for
magnetic field strengths will add. The primary winding may evaluating the instrument losses. The accuracy of the rms
compriseuptothreelayersusingtwoormorewiresinparallel.
voltmeter shall be the same as that specified for the flux
6.2.3 Primary and secondary turns shall be wound in the
voltmeter. Either digital or analog rms voltmeters are permit-
same direction, with the starting end of each winding being at
ted.The normally high-input impedance of digital rms voltme-
the same corner junction of one of the four solenoids. This
ters is desirable to minimize loading effects and to reduce the
enables the potential between adjacent primary and secondary
magnitude of instrument loss compensations. The input resis-
turns to be a minimum throughout the length of the winding,
tance of an analog rms voltmeter shall not be less than 5000
thereby reducing errors as a result of electrostatic phenomena.
Ω/V of full-scale indication.
6.2.4 The solenoid windings on the test frame may be any
6.5 Wattmeter, W—The full-scale accuracy of the wattmeter
number of turns suited to the instrumentation, mass of
must not be poorer than 0.25% at the frequency of test and at
specimen, and test frequency. Windings with a total of 700
unity power factor. The power factor encountered by a watt-
turns are recommended for tests in the frequency range of 25
meter during a core loss test on a specimen is always less than
through 400 Hz.
unity and, at magnetic flux densities far above the knee of the
6.2.5 The mutual inductance of the air-flux compensating
magnetization curve, approaches zero. The wattmeter must
inductor shall be adjusted to be the same as that between the
maintainadequateaccuracy(1.0%ofreading)evenatthemost
test-frame windings to within one turn of the compensator
severe (lowest) power factor that is presented to it. Variable
secondary. Its windings shall be connected in series with the
scaling devices may be used to cause the wattmeter to indicate
corresponding test-frame windings so that the voltage induced
directlyinunitsofspecificcorelossifthecombinationofbasic
inthesecondarywindingoftheinductorbytheprimarycurrent
instrument and scaling devices conforms to the specifications
will completely oppose or cancel the total voltage induced in
stated here.
the secondary winding of the test frame when no sample is in
place in the solenoids. Specifications for the approximate turns 6.5.1 Electronic Digital Wattmeter—Electronic digital watt-
and construction details of the compensating mutual inductor
meters have been developed that have proven satisfactory for
for the standard test frame are given in Table A1.1 of Annex use under the provisions of this test method. Usage of a
A1.
suitable electronic digital wattmeter is permitted as an alterna-
tive to an electrodynamometer wattmeter in this test method.
6.3 Flux Voltmeter, V —Afull-wavetrue-average,voltmeter,
f
An electronic digital wattmeter oftentimes is preferred in this
with scale reading in average volts times =2 π/4 so that its
test method because of its digital readout and its capability for
indications will be identical with those of a true rms voltmeter
direct interfacing with electronic data acquisition systems.
on a pure sinusoidal voltage, shall be provided for evaluating
6.5.1.1 The voltage input circuitry of the electronic digital
thepeakvalueofthetestmagneticfluxdensity.Toproducethe
wattmeter must have an input impedance sufficiently high that
estimatedprecisionoftestunderthistestmethod,thefull-scale
connection of the circuitry, during testing, to the secondary
metererrorsshallnotexceed0.25%(Note1).Metersof0.5%
windingofthetestfixturedoesnotchangetheterminalvoltage
of more error may be used at reduced accuracy. Either digital
of the secondary by more than 0.05%. In addition, the voltage
or analog flux voltmeters are permitted. The normally high-
inputcircuitrymustbecapableofacceptingthemaximumpeak
input impedance of digital flux voltmeters is desirable to
voltagethatisinducedinthesecondarywindingduringtesting.
minimize loading effects and to reduce the magnitude of
instrument loss compensations. The input resistance of an
6.5.1.2 The current input circuitry of the electronic digital
analog flux voltmeter shall not be less than 1000 Ω/V of
wattmeter must have an input impedance of no more than 1Ω.
full-scale indication. A resistive voltage divider, a standard-
Preferably the input impedance should be no more than 0.1 Ω
ratio transformer, or other variable scaling device may be used
ifthefluxwaveformdistortionotherwisetendstobeexcessive.
to cause the flux voltmeter to indicate directly in units of
In addition, the current input circuitry must be capable of
magnetic flux density if the combination of basic instrument
accepting the maximum rms current and the maximum peak
and scaling device conforms to the specifications stated above.
current drawn by the primary winding of the test fixture when
NOTE1—Inaccuraciesinsettingthetestvoltageproduceerrorsapproxi-
core loss tests are being performed. In particular, since the
mately two times as large in the specific core loss. Voltage scales should
primary current will be very nonsinusoidal (peaked) if core-
be such that the instrument is not used at less than half scale. Care should
loss tests are performed on a specimen at magnetic flux
also be taken to avoid errors caused by temperature and frequency effects
densities above the knee of the magnetization curve, the crest
in the instrument.
factor capability of the current input circuitry should be three
6.3.1 If used with a mutual inductor as a peak ammeter at
or more.
magnetic flux densities well above the knee of the magnetiza-
6.5.2 Electrodynamometer Wattmeter—A reflecting-type
tion curve, the flux voltmeter must be capable of accurately
measuringtheextremelynonsinusoidal(peaked)voltagethatis dynamometer is recommended among this class of
instruments, but, if the specimen mass is sufficiently large, a
induced in the secondary winding of the mutual inductor.
Additionally, if so used, an analog flux voltmeter should have direct-indicating electrodynamometer wattmeter of the highest
availablesensitivityandlowestpower-factorcapabilitymaybe
a minimum input resistance of 5000 Ω/V of full-scale indica-
tion. used.
A343/A343M − 14 (2019)
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.Afixed resistor between 0.1 and 1.0Ω
circuit of the test fixture does not result in appreciable defect is usually appropriate.
angleerrorsinthemeasurements.Shouldtheimpedanceofthis 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. baseduponthesametheoreticalconsiderationsthatindicatethe
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
namometerwattmetershouldnotexceed1Ω.Iffluxwaveform 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.Amutual inductor
should be at least 10 rms amperes. used for this purpose must have reasonably low primary
impedance so that its insertion will not materially affect the
6.6 Devices for RMS Current Measurement—A means of
primary circuit conditions and have sufficiently high mutual
measuring the rms value of the exciting current must be
inductance to provide a satisfactorily high voltage to the flux
providedifmeasurementsofexcitingpowerorexcitingcurrent
voltmeter for primary currents corresponding to the desired
are to be made.
range in peak magnetic field strength. The secondary imped-
6.6.1 RMS Voltmeter and Standard Resistor—A true rms-
ance of the mutual inductor must be low if any significant
indicating voltmeter may be used to measure the voltage drop
current is drawn by a low-impedance flux voltmeter. The
across the potential terminals of a standard resistance. The
addition of the flux voltmeter should not change the mutual
accuracy of the rms voltmeter shall be 1.0% of full scale or
inductor secondary terminal voltage by more than 0.25%. It is
less. Either digital or analog meters are permitted. A high-
important that the mutual inductor be located in the test
input-impedance,multirangeelectronicdigitalrmsvoltmeteris
equipment in such a position that its windings will not be
desirable for this instrument.The input resistance of an analog
linked by ac leakage flux from other apparatus. Care should be
meter shall not be less than 5000 Ω/v. The standard resistor
taken to avoid locating it so close to any magnetic material or
should be a non-inductive resistor with an accuracy rating of
any conducting material that its calibration and linearity may
0.1% or better. This resistor must be capable of handling the
be affected. Directions for construction and calibration of a
full exciting current of the test winding at the maximum test
mutual inductor for peak-current measurement are given in
magnetic flux density without destructive heating or more than
Annex A1. Even at commercial power frequencies, there can
specified loss of accuracy as a result of self-heating. To avoid
be appreciable error in the measurement of peak exciting
intolerable levels of distortion, the value of the resistor should
current if winding capacitances and inductances and flux
be kept reasonably low.Afixed resistor between 0.1 and 1.0Ω
voltmetererrorsbegintobecomeimportantatsomeofthehigh
is usually appropriate.
harmonics frequencies present because of the extremely non-
6.6.2 RMS Ammeter—A true rms-indicating ammeter may
sinusoidal character of the voltage waveform induced in the
beusedtomeasuretheexcitingcurrent.Anominalaccuracyof
secondaryofthemutualinductorbythenonsinusoidalexciting
1.0% of full scale or better is required for this instrument.The
current waveform.
instrumentmusthavelowinternalimpedancetoavoidcontrib-
6.8 Power Supply—Aprecisely controllable source of sinu-
uting to the distortion of the flux waveform.
soidal test voltage of low internal impedance and excellent
6.7 Devices for Peak Current Measurement—A means of
voltage and frequency stability is mandatory. Voltage stability
measuring the peak value of the exciting current is required if
within 0.1% and frequency accuracy within 0.1% should be
an evaluation of peak permeability is to be made by the
maintained. Electronic power sources using negative feedback
peak-current method.
from the secondary winding of the test fixture to reduce flux
6.7.1 Peak-to-Peak Voltmeter and Standard Resistor—The
waveform distortion have been found to perform quite satis-
peak current measurement may be made with a voltmeter
factorily in this test method.
whoseindicationsareproportionaltothepeak-to-peakvalueof
the voltage drop across the potential terminals of a standard
7. Procedure
resistorconnectedinserieswiththeprimarywindingofthetest
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 6 ⁄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
A343/A343M − 14 (2019)
dented, twisted, or distorted strips showing evidence of me- 7.5 Setting Magnetic Flux Density—Withswitches S and S
3 4
chanical abuse have been included and that the strips are of closed and switches S , S , and S open (Note 4), increase the
1 2 5
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 thevalueofvoltagecalculatedtogivethedesiredtestmagnetic
specimen on a scale or balance capable of determining the flux density in accordance with the equations in 8.1 or 9.1.
masswithinanaccuracyof0.1%.Recordspecimenweightsof Becausetheactionoftheair-fluxcompensatorcausesavoltage
lessthan1kgtoatleastthenearest0.5gandwithinthenearest equaltothatwhichwouldbeinducedinthesecondarywinding
1.0 g for specimens heavier than 1 kg. by the air flux to be subtracted from that induced by the total
fluxinthesecondary,themagneticfluxdensitycalculatedfrom
NOTE 2—Inaccuracy in shearing the length of Epstein strips is equiva-
the voltage indicated by the flux voltmeter is the intrinsic
lenttoaweighingerrorofthesamepercentage.Bothweightandspecimen
induction, B =(B−Γ H ).Inmostcasesthevaluesofintrinsic
length inaccuracies cause errors in magnetic flux density measurements, i m p
which result in even greater core loss errors. induction, B,arenotsufficientlydifferentfromthecorrespond-
i
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.WhereΓ H is not insignificant compared to B,
m p i
flux density in the specimen, which may have a significant but unpredict-
asitisatveryhighmagneticfluxdensities,determinethevalue
able effect upon testing accuracy.
of B by adding to B either the measured value of Γ H or a
i m p
7.2 Dividethetestspecimenstripsintofourgroupscontain-
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
7.6 Core Loss—When the voltage indicated by the flux
number) into the test frame solenoids one at a time, starting
voltmeter has been adjusted to the desired value, read the
with one strip in each of two opposite solenoids and then
wattmeter. Some users, particularly those having wattmeters
inserting a strip into each of the other two solenoids so that
compensated for their own losses (or burden), will desire to
theselatterstripscompletelyoverlaptheformertwoatthefour
open switch S to eliminate the flux voltmeter burden from the
corners. This completes one layer of strips constituting a
wattmeter indication (Note 4). Others will likely choose to
complete flux path with four overlapped joints. Build up
have S and S closed when measuring the losses, so that all
4 5
successive layers in this same fashion until the specimen is
instrumentsmaybereadatthesametime.Inthelattercase,the
completely assembled. With specimens cut half with and half
combined resistance load of the flux voltmeter, rms voltmeter,
crossgrain,arrangealltheparallelor“with-grain”stripsintwo
and potential circuit of the wattmeter will constitute the total
opposite solenoids and all the cross- or transverse-grain strips
instrument burden on the wattmeter. Exercise care so that the
in the other two opposite solenoids.
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
lightpressureonthejoints,fromtheuseofnonmagneticcorner
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
introducesomeadditionalstressesinstrain-sensitivematerials.
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
7.7 Obtainthespecificcorelossofthespecimeninwattsper
to relieve stresses before testing. Follow the recommendations
unit mass at a specified frequency by dividing the net watts by
of the manufacturer of the materials in performing this opera-
that portion of the mass of the specimen constituting the active
tion.
magneticfluxpath(whichislessthanthemeangeometricpath
7.4 Demagnetization—The specimen should be demagne-
length) in the specimen. Equations and instructions for com-
tizedbeforemeasurementsofanymagneticpropertyaremade.
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 S , S , and S closed and switches S and S open
1 2 4 3 5
7.8 Measure the rms value of the secondary voltage by
(Note4),accomplishthisdemagnetizationbyinitiallyapplying
having both S and S closed (Note 4) and the voltage adjusted
4 5
a voltage from the power source to the primary circuit that is
to indicate the correct value of flux volts. On truly sinusoidal
sufficient to magnetize the specimen to a magnetic flux density
voltage, both voltmeters will indicate the same voltage show-
above the knee of its magnetization curve (magnetic flux
ingthattheformfactoroftheinducedvoltageis =2 π/4.When
density may be determined from the reading of the flux
thevoltmetersgivedifferentreadings,theratioofthermsvalue
voltmeter by means of the equations in 8.1 or 9.1), and then
to that indicated by the flux voltmeter reveals the ratio by
decreasethevoltageslowlyandsmoothly(orinsmallsteps)to
which the form factor of the induced voltage deviates from the
a very low magnetic flux density. After this demagnetization,
test promptly for the desired test points. When multiple test desired value of =2 π/4. Determining the magnetic flux
points are required, perform the tests in order of increasing density from the readings of a flux voltmeter assures that the
magnetic flux density values. correct value of peak magnetic flux density is achieved in the
A343/A343M − 14 (2019)
specimen, and hence that the hysteresis component of the core 28
E 5 =2 π B AN f10 (1)
f i 2
loss is correct even if the waveform is not strictly sinusoidal.
where:
But the eddy-current component of the core loss, being caused
B = maximum intrinsic flux density, G;
by current resulting from a nonsinusoidal voltage induced in
i
A = effectivecross-sectionalareaofthetestspecimen,cm ;
the cross section of the strip, will be in error depending on the
deviation of the induced voltage from the desired sinusoidal
N = number of turns in secondary winding; and
wave shape. This error in the eddy-current component of loss 2
f = frequency, Hz.
can be readily corrected by calculations based on the observed
form factor and the approximate percentage of eddy-current
8.1.1 In the case of Epstein specimens, where the total
loss for the grade of material being tested if the correction is
number of strips is divided into four equal groups comprising
reasonably small. The equations involved in determining this
the magnetic circuit, the mass of the specimen in each of the
correction are given in 8.3 and 9.3.
fourlegsofthemagneticcircuitbecomes m/4,andtheeffective
7.9 RMS Exciting Current—Measure the rms exciting
cross section, A, in square centimeters, of each leg is:
current, when required, by having S and S closed; S , S , and
1 4 2 3
A 5 m/4lδ (2)
S open (Note 4); then with the ammeter on a suitable scale
range,adjustthevoltagetothecorrectfluxvoltmeterindication where:
for the desired test magnetic flux density. When the setting of
m = total mass of specimen strips, g;
voltage is correct, open S and read the ammeter with no
l = length of specimen strips, cm (usually 28 or 30.5 cm);
current drain in the secondary circuit. If S is kept closed to
and
monitor the magnetic flux density during the current reading, δ = standard assumed density of specimen material (see
the current drain of the flux voltmeter will be included in the Practice A34/A34M), g/cm .
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
7.10 Permeability—When permeability from peak exciting
aspecificmagneticfluxdensityandfrequencythespecificcore
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 5 453.6 P 2 E /R /m (3)
~ !
Switch S should be closed to protect the wattmeter from the c~B; f! c 2 1
possibility of excessive current. Switches S and S should be
3 5
where:
open to minimize secondary loading (Note 4). With switch S
P = core loss indicated by the wattmeter, W;
c
open and S closed, adjust the voltage to the correct value for
E = rms value of secondary voltage, V;
the desired magnetic flux density or the correct value of peak
R = parallelresistanceofwattmeterpotentialcircuitandall
current for the desired magnetic field strength. Equations
other connected secondary loads, Ω; and
involved in the determination of peak magnetic field strength
m = active mass, g.
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(lessthanthetotalmass)isassumedtobeasfollows:
The flux voltmeter used for this purpose must meet the
m 5 l m/ 4l 5 94m/4l 5 23.5m/l (4)
restrictionsof6.7.2.Equationsinvolvedinthedeterminationof ~ !
1 1
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;
NOTE 4—Due to the high input impedance of modern digital instru-
l = effective magnetic path length, cm; and
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
circuit, the combined current drain of the instrumentation must not cause
8.3 Form Factor Correction—The percent error in form
an appreciable drop (>0.05%) in the secondary voltage. Use caution not
factor is given by the following equation:
toexceedtheinstrument’smaximumpeakinputrangeasthismaydamage
the instrument.
F 5 100 E 2 E /E (5)
~ !
2 f f
assuming (Note 5) that:
8. Calculation (Customary Units)
observed P 5 corrected P /100 h
@ #
c B; f ~ c B; f !
~ ! ~ !
8.1 Calculate the value of the flux voltage E at the desired
f
1 corrected P Ke/100,
~ c B; f !
~ !
test magnetic flux density in the specimen (when corrected for
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
Corrected P 5 observed P 100/~h1Ke! (6)
~ !
discussed in X1.2 of this test method: c B; f c B; f
~ ! ~ !
A343/A343M − 14 (2019)
where: where:
observed P = specificcorelosscalculatedbytheequa- N = number of turns in primary winding;
c(B; f) 1
tions in 8.2, I = rms value of exciting current, A; and
H = ac magnetic field strength, Oe.
h = percentage hysteresis loss at magnetic
z
NOTE 7—In previous issues of Test Method A343, the path length for
flux density B,
permeabilityandexcitingcurrenthasbeentakenas88cm.Inthe1960and
e = percentageeddy-currentlossatmagnetic
subsequentrevisions,thepathlengthhasbeen94cmtobeconsistentwith
flux density B, and
core-loss determination.
K = (E /E ) .
2 f
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 5 453.6 E I/m (7)
z B; f 2 1
~ !
critical when waveform distortion is low. Typical values at 50
or60Hzforthecommonclassesofmaterials,stripthicknesses,
where:
and specimen form are shown in Table 1. Values for materials
E = 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 = 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
8.5.2 Onetypeofacpermeabilitydirectlyrelatedtotherms
it will be if a flux voltmeter is used to establish the value of the magnetic
exciting current (or rms excitation) or ac impedance is char-
flux density) but that the eddy-current component of core loss, being a
function of the rms value of the voltage, will be in error for nonsinusoidal acterized by the symbol µ and is computed as follows (Note
z
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,
µ 5 B /H (8)
yet they do separate the core loss into two components, one which is z i z
assumed to vary as the second power of the form factor and the other
where:
whichisassumedtobeunaffectedbyformfactorvariations.Regardlessof
the academic difficulties associated with characterizing these components B = maximum intrinsic flux density, G, and
i
as hysteresis and eddy-current loss, it is observed that the equation for
H = ac magnetic field strength, Oe (Note 8).
z
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 B is used to replace B in the permeability
i m
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 H becomes appreciable in magnitude when compared to the
p
not excessive.
value of B. If greater accuracy is essential B or (B + H ) should be used
i m i p
NOTE6—Itisrecommendedthattestsmadeunderconditionswherethe
to replace the B in these equations.
i
percenterrorinformfactor, F,isgreaterthan10%beconsideredaslikely
NOTE 9—H is computed from the rms value of the complex exciting
z
tobeinerrorbyanexcessiveamount,andthatsuchconditionsbeavoided.
currentbyassumingacrestfactorof =2 .Thusitisbasedonasinusoidal
current having a rms value equal to the rms value of the complex current.
8.4 Exciting Current—The rms exciting current is often
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
value that is more directly comparable to the dc permeability
rmsexcitingforce, N I/l 5 N I/94A/cm ~Note7!
1 1 1
value for the specimen.This is accomplished by evaluating H
p
oracmagneticfieldstrength, H 5 0.4π =2N I/l Oe
z 1 1 from the measured peak value of the exciting current at some
value of H sufficiently above the knee of the magnetization
p
curvethatthemagnetizingcomponentoftheexcitingcurrentis
appreciably greater than the core loss component. Such a test
TABLE 1 Eddy-Current Loss (Typical)
point for many commercial materials is an H value of 10 Oe
p
(796 A/m). Permeability determined in this way is character-
Assumed Eddy-Current Loss,
percent (at 50 or 60 Hz), for Strip Thicknesses,
ized by the symbol µ , and is computed as follows (Note 8):
p
in. [mm]
Material Specimen
µ 5 B /H (9)
0.007 0.009 0.011 0.012 0.014 0.019 0.025 p i p
[0.18] [0.23] [0.27] [0.30] [0.35] [0.47] [0.64]
where H is the peak exciting magnetic field strength
p
Nonoriented half and . . . . 20 30 40
A
evaluatedfrommeasurementsofpeakcurrentmadeeitherwith
materials half
Nonoriented parallel . . . . 25 35 45
the permeability-inductor or peak-reading-voltmeter methods
A
materials
(see 6.7.1 and 6.7.2) and in accordance with the equations in
Oriented parallel 35 45 50 50 55 . .
B
8.6.
materials
A
Theseeddy-currentpercentagesweredevelopedforandareappropriateforuse
8.6 H from Peak Exciting Current—The peak exciting
p
with nonoriented silicon steels as described in Specifications A677 and A683
current, I in amperes, may be measured using the air-core
p
where (%Si + 1.7 × %AI) is in the range 1.40 to 3.70.
B
mutual inductor and flux voltmeter as follows:
Theseeddy-currentpercentagesweredevelopedforandareappropriateforuse
with oriented silicon steels as described in Specification A876.
I 5 E /=2πfL (10)
p fm m
A343/A343M − 14 (2019)
where: where:
E = flux voltage induced in secondary winding of mutual P = core loss indicated by the wattmeter, W;
fm c
inductor, V; E = rms value of secondary voltage, V;
R = parallel resistance of wattmeter potential circuit and
f = frequency, Hz; and
L = mutual inductance, H. all other connected secondary loads, Ω; and
m
m = active mass, kg.
The peak exciting current, I in amperes, may be computed
p
In the 25-cm Epstein frame it is assumed that 0.94 m is the
from measurements using a standard resistor and a peak-
effective magnetic path with specimen strips 0.28 m or longer.
reading voltmeter as follows:
For the purpose of computing core loss the active mass of the
I 5 E /2R (11)
p p2p 1
specimen(lessthanthetotalmass)isassumedtobeasfollows:
where:
m 5 l m/4l
1 1
E = peak-to-peak voltage indicated by peak-reading
p-p
5 0.94m/4l
voltmeter, V, and
5 0.235m/l (16)
R = resistance of standard resistor, Ω.
where:
The peak magnetic field strength, H in oersteds, may be
p
m = the total specimen mass, kg;
calculated as follows:
l = the actual strip length, m; and
H 5 0.4πN I /l (12)
p 1 p 1
l = effective magnetic path length, m.
where:
9.3 Form Factor Correction—See 8.3.
N = number of turns in primary winding;
9.4 Exciting Current—The rms exciting current is often
I = peak exciting current, A; and
p
normalized for circuit parameters by converting to the follow-
l = effective magnetic path length, cm.
ing forms:
rmsexcitingforce, N I/l 5 N I/0.94A/m ~Note9!
9. Calculations (SI Units)
1 1 1
or
9.1 Calculate the value of the flux voltage E at the desired
f
test magnetic flux density in the specimen (when corrected for
=
rmsacmagneticfieldstrength, H 5 2N I/l A/m
z 1 1
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
N = number of turns in primary winding;
equation discussed in 1.3 of this test method.
I = rms value of exciting current, A; and
H = apparent ac magnetic field strength, A/m.
z
E 5 =2π B AN f (13)
f i 2
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
B = maximum intrinsic flux density, T;
i
andsubsequentrevisions,thepathlengthhasbeen0.94mtobeconsistent
A = effective cross-sectional area of the test specimen, m ;
with core-loss determination.
N = number of turns in secondary winding; and
2 The specific exciting power in rms volt-amperes per kilogram is:
f = frequency, Hz.
P 5 E I/m (17)
z~B;f! 2 1
9.1.1 In the case of Epstein specimens, where the total
where:
number of strips is divided into four equal groups comprising
E = 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
fourlegsofthemagneticcircuitbecomes m/4,andtheeffective
m = 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
permeability data (in H/m) are more useful than others.
where:
9.5.2 Onetypeofacpermeabilitydirectlyrelatedtotherms
m = total mass of specimen strips, kg;
exciting current (or rms excitation) or ac impedance is char-
l = length of specimen strips, m (usually 0.28 or 0.305 m);
acterized by the symbol µ and is computed as follows (Note
and z
11):
δ = standard assumed density of specimen material (see
Practice A34/A34M), kg/m .
µ 5 B /H (18)
z i z
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
B = maximum intrinsic flux density, T, and
i
secondary circuit power included in the wattmeter indication
H = ac magnetic field strength, A/m (Note 12).
z
before dividing by the active mass of the specimen, so that for
NOTE 11—For simplification and convenience in the calculation of ac
aspecificmagneticfluxdensityandfrequencythespecificcore
permeabilities the value of B is used to replace B in the permeability
i m
equation.ThisentailsnolossofaccuracyuntilΓ H becomesappreciable
loss in watts per kilogram is as follows: m p
in magnitude when compared to the value of B. If greater accuracy is
i
P 5 ~P 2 E /R!/m (15)
c B; f c 2 1 essential, B or (B +Γ H ) should be used to replace B in these
~ !
m i m p i
A343/A343M − 14 (2019)
−7
equations. The magnetic constant Γ is equal to 4π×10 H/m.
participating laboratories. Practice E691 was followed for the
m
NOTE 12—H is computed from the rms value of the complex exciting
z
design of the experiment and the analysis of the data for both
currentbyassumingacrestfactorof =2.Thusitisbasedonasinusoidal
studies.The details of the studies are given inASTM Research
current having a rms value equal to the rms value of the complex current. 4
Reports A06-1000 and A06-1002.
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 permeabil
...