ASTM E2428-22

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:E2428 −22
Standard Practice for
Calibration and Verification of Elastic Torque Measurement
Standards
This standard is issued under the fixed designation E2428; 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* 2.2 ASME Standard:
B46.1Surface Texture (Surface Roughness, Waviness, and
1.1 The purpose of this practice is to specify the procedure
Lay)
for the calibration and verification of elastic torque measure-
2.3 BIPM Standard:
ment standards.
JCGM200Internationalvocabularyofmetrology–Basicand
1.2 Units—The values stated in SI units are to be regarded
general concepts and associated terms (VIM)
as standard. The values given in parentheses after SI units are
providedforinformationonlyandarenotconsideredstandard.
3. Terminology
1.3 This practice is intended for the calibration of static
3.1 Definitions:
elastic torque measurement standards. The practice is not
3.1.1 Refer to Terminology E6 for the definitions of
applicable for dynamic or high-speed torque calibrations or
calibration, metrological traceability, resolution, and verifica-
measurements, nor can the results of calibrations performed in
tion.
accordance with this practice be assumed valid for dynamic or
3.1.2 primary torque measurement standard, n—A dead-
high-speed torque measurements.
weight force applied through a moment arm, all with metro-
1.4 This standard does not purport to address all of the logical traceability to the International System of Units (SI).
safety concerns, if any, associated with its use. It is the
3.1.3 secondary torque measurement standard, n—An in-
responsibility of the user of this standard to establish appro-
strument or mechanism, the calibration of which has been
priate safety, health, and environmental practices and deter-
establishedbyacomparisonwithprimarytorquemeasurement
mine the applicability of regulatory limitations prior to use.
standard(s).
1.5 This international standard was developed in accor-
3.2 Definitions of Terms Specific to This Standard:
dance with internationally recognized principles on standard-
3.2.1 calibration equation, n—A mathematical relationship
ization established in the Decision on Principles for the
between deflection and torque established from the calibration
Development of International Standards, Guides and Recom-
data for use with the elastic torque measurement standard in
mendations issued by the World Trade Organization Technical
service.
Barriers to Trade (TBT) Committee.
3.2.2 creep, n—The change in indication of the elastic
torque measurement standard under constant applied torque.
2. Referenced Documents
3.2.2.1 Discussion—Creep is expressed as a percentage of
2.1 ASTM Standards:
theindicatedchangeataconstantappliedtorquefromaninitial
E6Terminology Relating to Methods of MechanicalTesting
time following the achievement of mechanical and electrical
E29Practice for Using Significant Digits in Test Data to
stability and the time at which the test is concluded. The
Determine Conformance with Specifications
stabilities of secondary torque measurement standards and
E2624Practice for Torque Calibration of Testing Machines
primary torque measurement standards are usually adequate to
measure creep during the test time interval. Creep results from
a time-dependent, elastic deformation of the elastic member of
ThispracticeisunderthejurisdictionofASTMCommitteeE28onMechanical
the elastic torque measurement standard. In the case of elastic
Testing and is the direct responsibility of Subcommittee E28.01 on Calibration of
torque measurement standards, creep is minimized by strain
Mechanical Testing Machines and Apparatus.
Current edition approved Nov. 1, 2022. Published January 2023. Originally
approved in 2008. Last previous edition approved in 2015 as E2428–15a. DOI:
10.1520/E2428-22. Available from American Society of Mechanical Engineers (ASME), ASME
For referenced ASTM standards, visit the ASTM website, www.astm.org, or International Headquarters, Two Park Ave., New York, NY 10016-5990, http://
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM www.asme.org.
Standards volume information, refer to the standard’s Document Summary page on Available from BIPM, Pavillon de Breteuil, F-92312 Sèvres Cedex. http://
the ASTM website. www.bipm.org
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2428−22
gagedesignandprocessmodificationstoreducethestraingage 3.2.8.1 Discussion—The center of moments may be the
response to the inherent time-dependent elastic deformation. actual point about which the force causes rotation. It may also
be a reference point or axis about which the force may be
3.2.3 creep recovery, n—The change of indicated from the
considered as causing rotation.
elastic torque measurement standard at zero torque after the
3.2.8.2 Discussion—Moment arm is synonymous with cali-
removal of the maximum applied calibration torque and initial
bration beam (radius, single- or double-ended), torque arm,
zero-torque indication.
wheel, or lever unless specifically referenced otherwise.
3.2.3.1 Discussion—Thezero-torqueindicationistakenata
time following the achievement of mechanical and electrical 3.2.9 verified range of torques, n—The range of indicated
torqueforwhichtheelastictorquemeasurementstandardgives
stability and a time equal to the time at the calibration torque.
For many elastic torque measurement standards, the creep results within permissible variations specified.
characteristicandthecreeprecoverycharacteristicareapproxi-
3.3 Refer to JCGM 200 International vocabulary of
mate mirror images.
metrology- Basic and general concepts and associated terms
3.2.4 deflection, n—The difference between the indication (VIM) for definitions of the terms coverage factor, expanded
measurement uncertainty, indication, maximum permissible
of the elastic torque measurement standard under applied
torque and the indication with zero applied torque. measurement error, measurement error, measurement
uncertainty, measurement repeatability, measurement
3.2.5 elastic torque measurement standard, n—A system
reproducibility, reference measurement standard, and sensitiv-
consisting of an elastic member combined with an electronic-
ity.
indicating measurement instrument for measuring the strain of
the elastic member under an applied torque.
4. Significance and Use
3.2.5.1 Discussion—An elastic torque measurement stan-
4.1 Testing machines that apply and indicate torque are in
dard is a specific “measurement standard” as defined in JCGM
general use in many industries. Practice E2624 has been
200.
written to provide a practice for the torque calibration and
3.2.5.2 Discussion—An elastic torque measurement stan-
verification of these testing machines. A necessary element in
dard is commonly referred to as a torque transducer, torque-
Practice E2624 is the use of elastic torque measurement
measuring transducer, or torque cell.
standards whose torque characteristics are known to be metro-
3.2.6 lower limit factor, LLF, n—Astatisticalestimateofthe
logically traceable to the International System of Units (SI).
measurement error in torque computed from the calibration
Practice E2428 describes how these elastic torque measure-
equation of the elastic torque measurement standard when the
ment standards are to be calibrated. The procedures are useful
elastic torque measurement standard is calibrated in accor-
to users of testing machines, manufacturers and providers of
dance with this practice.
elastic torque measurement standards, calibration laboratories
3.2.6.1 Discussion—The lower limit factor is used to calcu-
that provide calibration services and documents of metrologi-
late the lower torque limit of the verified range of torques.
cal traceability, service organizations using elastic torque
Otherfactorsevaluatedinestablishingthelowertorquelimitof
measurement standards to calibrate and verify testing
the verified range of torques are the resolution of the elastic
machines, and testing laboratories performing general struc-
torque measurement standard and the lowest non-zero torque
tural test measurements.
applied in the calibration torque sequence. The lower limit
5. Reference Measurement Standards
factor is one component of the measurement uncertainty.As a
component of measurement uncertainty, the lower limit factor 5.1 Elastic torque measurement standards used for the
is often described as the relative reproducibility error with calibrationandverificationofthetorque-measuringsystemsof
rotation. Other measurement uncertainty components should testing machines may be calibrated by either primary or
be included in a comprehensive measurement uncertainty
secondary torque measurement standards.
analysis.
5.2 Elastictorquemeasurementstandardsusedassecondary
3.2.6.2 Discussion—The lower limit factor was termed un-
torque measurement standards for the calibration of other
certainty in revisions prior to E2428-15a.
elastic torque measurement standards shall be calibrated by
3.2.7 mode, n—The direction of torque, either clockwise or primary torque measurement standards.
counter-clockwise.
5.3 Primary Torque Measurement Standard—Weights used
3.2.8 moment arm, n—The component that couples the as primary force measurement standards shall be made of
perpendicular line of action of the force and the center of rolled, forged, or cast metal. Adjustment cavities shall be
moments to create a torque and whose length or radius length closed by threaded plugs or suitable seals. External surfaces of
displays metrological traceability to the International System weights shall have a surface roughness average of 3.2µm or
of Units (SI) less as specified in ASME B46.1.
E2428−22
5.3.1 Calculatetheforceexertedbyaweightinairusingthe 5.3.4 The moment arm shall be calibrated to determine the
following equation: length or radius length with a known measurement uncertainty
that is metrologically traceable to the International System of
d
F 5 M 3 g 1 2 (1)
Units (SI) for length.
S D
D
5.3.5 The expanded measurement uncertainty for the pri-
where:
marytorquemeasurementstandardshallnotexceed0.012%of
F = force, N
applied torque, with an approximate coverage factor of 95 %
M = true mass of the weight, kg,
(k=2).
g = local acceleration due to gravity, m/s ,
5.4 Secondary Torque Measurement Standards—A second-
d = air density (approximately 1.2 kg/m ), and
ary torque measurement standard is typically an elastic torque
D = density of the weight in the same units as d.
measurement standard used with a machine for applying
5.3.2 For the purposes of this practice, g can be calculated
torque.An alternative is a force-multiplying system that uses a
with sufficient uncertainty using the following formula:
mechanical or hydraulic mechanism to apply or multiply a
force to a moment arm.
g 59.7803@1 1 0.0053 ~sin [! # 20.000001967h (2)
5.4.1 Elastic torque measurement standards used as second-
where:
ary torque measurement standards shall be calibrated by
g = local acceleration due to gravity, m/s ,
primary torque measurement standards and used only over the
Ø = latitude,
ClassAAverifiedrangeoftorquesinthispractice(see7.4.1.2).
h = elevation above sea level in meters.
5.4.2 Other types of torque measurement standards may be
NOTE 1—Eq 2 corrects for the shape of the earth and the elevation
used and shall be calibrated. The expanded measurement
above sea level. The first term, which corrects for the shape of the earth,
uncertaintyshallnotexceed0.06%oftheappliedtorque,with
is a simplification of the World Geodetic System 84 Ellipsoidal Gravity
an approximate coverage factor of 95 % (k=2).
Formula. The results obtained with the simplified formula differ from
thoseinthefullversionbylessthan0.0005%.Thesecondtermcombines
a correction for altitude, the increased distance from the center of the
6. Calibration
earth, and a correction for the counteracting Bouguer effect of localized
increased mass of the earth. The second term assumes a rock density of 6.1 Basic Principles—The relationship between the applied
3 3
2.67 g/cm . If the rock density changed by 0.5 g/cm , an error of 0.003 %
calibration torque and the deflection of an elastic torque
would result.
measurement standard is, in general, not linear.As the calibra-
tiontorqueisapplied,theshapeoftheelasticmemberchanges,
5.3.3 In some cases, a mass might not be designated in
progressively altering its resistance to deformation. The result
kilograms, for instance it might be denoted in pounds, and it
is that the slope of the torque-deflection curve changes gradu-
might be desired to know the force exerted in pound-force
allyandcontinuouslyovertheentirerangeoftheelastictorque
units. In other cases, it might be desired to know the force
measurement standard. This characteristic curve is a stable
exertedinkilogram-forceunitswherethemassisdesignatedin
property of the elastic torque measurement standard that is
kilograms. In these cases, the force in non-SI units exerted by
changed only by a severe overload or other similar cause.
a weight in air is calculated as follows:
6.1.1 Superposed on this curve are local variations intro-
M 3 g d
duced by imperfections in the elastic torque measurement
F 5 1 2 (3)
S D
C
9.80665 D
standard. Examples of imperfections include instabilities in
where: excitation voltage, voltage measurement, or ratio-metric volt-
age measurement in an elastic torque measurement standard.
F = force expressed in customary units, such as,
C
Some of these imperfections are less stable than the character-
pound-force or kilogram-force,
isticcurveandcanchangesignificantlyfromonecalibrationto
M = true mass of the weight, in the corresponding
another.
mass units of the force, F is being expressed,
C
such as, pound or kilogram, 6.1.2 Curve Fitting—To determine the torque-deflection
g = local acceleration due to gravity, m/s ,
curve of the elastic torque measurement standard, known
9.80665 = thefactorconvertingSIunitsofforceintonon-SI
calibration torque values are applied and the resulting deflec-
units of force; this factor is equal to the value for
tions are measured throughout the verified range of torques of
standard gravity, 9.80665 m/s ,
the elastic torque measurement standard. A polynomial equa-
d = air density (approximately 1.2 kg/m ), and
tion is fitted to the calibration data by the least squares method
D = density of the weight in the same units as d.
to predict deflection throughout the verified range of torques.
Such an equation compensates effectively for the nonlinearity
5.3.3.1 If M, the mass of the weight is in pounds, the force
of the calibration results. The standard deviation determined
will be in pound-force units (lbf). If M is in kilograms, the
fromthedifferenceofeachmeasureddeflectionfromthevalue
force will be in kilogram-force units (kgf). These non-SI force
derived from the polynomial curve at that calibration torque
units are related to the newton (N), the SI unit of force, by the
provides a measure of the error of the measurement data to the
following relationships:
calibration equation. A statistical estimate, called the lower
1 lbf 54.448222 N (4)
limit factor, LLF, is derived from the calculated standard
1 kgf 59.80665 N exact (5) deviation and represents the width of the band of these
~ !
E2428−22
deviations about the basic curve with a probability of approxi- applied at or below this lower torque limit. The smallest
mately 95 %. The LLF is, therefore, an estimate of one source calibration torque value applied shall be less than or equal to
of measurement uncertainty contributed by the elastic torque thetheoreticallowertorquelimitoftheelastictorquemeasure-
measurement standard when calibration torque values mea- ment standard.The smallest calibration torque value applied is
sured in service are calculated by means of the calibration defined by the values: 400 × resolution for Class A verified
equation.Actual measurement errors in service are likely to be range of torques and 1667 × resolution for Class AA verified
different if calibration torque values are applied under me- range of torques. In elastic torque measurement standard
chanical and environmental conditions differing from those of calibration with an electronic-indicating measurement instru-
calibration. Other sources of measurement errors could in- ment capable of linearizing the indicated signal, whenever
crease the measurement uncertainty of the elastic torque possible, select calibration torque values other than those at
measurement standard in service. The calibration laboratory which the linearity corrections were made.
shall calibrate the elastic torque measurement standard in
6.2.2 Resolution Determination—The resolution of an
accordance with the requirements of this practice, and the user
electronic-indicating measurement shall be one increment of
shall determine the measurement uncertainty of the elastic
the last active number on the electronic-indicating measure-
torque measurement standard in service.
ment instrument of the elastic torque measurement standard. If
6.1.3 Curve Fitting Using Polynomials of Greater Than 2nd
the indication fluctuates by more than plus or minus one
Degree—Calibration equations of the 3rd, 4th, or 5th degree
increment, the resolution shall be equal to half the range of
shall only be used with elastic torque measurement standards
fluctuation when zero-torque is applied to the elastic torque
having a resolution of 1 increment of count per 50000 or
measurement standard.
greater active counts at the maximum calibration torque value.
6.2.3 Number of Calibration Torque Values:
Annex A1 specifies the procedure for obtaining the degree of
6.2.3.1 Atotal of at least 30 calibration torque applications
the best-fit calibration equation. Equations of greater than 5th
per mode, clockwise or counterclockwise.
degree shall not be used.
6.2.3.2 At least 10 calibration torque values shall be at
NOTE 2—For some elastic torque measurement standards, use of a
different calibration torque values.
polynomial fit higher than the second degree can result in a lower LLF
5 6.2.3.3 Apply each calibration torque value at least twice
than that derived from the second-degree fit (ASTM RR:E28-1009) .
during the calibration in both the clockwise and counterclock-
Equations of greater than 5th degree cannot be justified due to the limited
number of increments in the calibration protocol. Errors caused by
wise direction, as applies.
round-offcanoccurifcalculationsareperformedwithinsufficientdigitsof
6.3 Temperature Considerations:
resolution.Anelastictorquemeasurementstandardnotsubjectedtorepair,
overloading, modifications, or other significant influence factors that alter
6.3.1 Allow the elastic torque measurement standard
its elastic properties or its sensing characteristics will likely exhibit the
enough time to adjust to the ambient temperature in the
same degree of best fit on each succeeding calibration as was determined
calibration machine prior to calibration to ensure stable re-
during its initial calibration using this procedure. An elastic torque
sponse.
measurement standard not subjected to the influence factors outlined
above that exhibits continued change of degree of best fit with several
6.3.2 The ambient temperature during calibration should be
successive calibrations could have insufficient performance stability to
23°C, although other temperatures may be used.
allow application of the curve-fitting procedure of Annex A1.
6.3.3 During the calibration, monitor and record the tem-
6.2 Selection of Calibration Torque Values—A careful se-
perature as close to the elastic torque measurement standard as
lection of the different calibration torque values to be applied
possible.The temperature should not change more than 61°C
inacalibrationisessentialtoprovideanadequateandunbiased
during calibration.
sample of the full range of the deviations discussed in 6.1 and
6.1.1.Forthisreason,thecalibrationlaboratoryshallselectthe
6.4 Procedural Order in Calibration:
calibration torque values.
6.4.1 Immediately before starting the calibration, slowly
6.2.1 Distribution of Calibration Torque Values—Distribute
and smoothly apply the maximum calibration torque value in
the calibration torque values over the full range of the elastic
the calibration sequence to the elastic torque measurement
torque measurement standard. If possible, at least one calibra-
standard. The maximum calibration torque value may be
tion torque value should be applied for every 10 % interval
applied multiple times to help achieve stability in zero-torque
throughout the range. It is not necessary, however, that these
indication.
calibration torques be equally spaced. Calibration torque val-
NOTE 3—Exercising to the maximum calibration torque reestablishes a
ueslessthanonetenthofcapacitymaybeusedandtendtogive
stable minimum calibration torque indication and conditions the elastic
added assurance to the fitting of the calibration equation. If the
torque measurement standard for stable performance. Exercising is
lowertorquelimitoftheverifiedrangeoftorquesoftheelastic
particularly important following a change in the mode, as from clockwise
torque measurement standard (see 7.4.1) is anticipated to be
to counterclockwise. Some elastic torque measurement standards achieve
less than one tenth of the maximum calibration torque applied stability in zero-torque indication only after two exercise cycles.
during calibration, then calibration torque values should be NOTE 4—Overload or proof load tests are not required by this practice.
6.4.2 After the exercise cycles, apply the calibration torque
values.
Supporting data have been filed at the ASTM International Headquarters and
6.4.3 For ascending calibration torque, approach each cali-
may be obtained by requesting Research Report RR:E28-1009. Contact ASTM
Customer Service at service@ASTM.org. bration torque value from a lesser magnitude of torque.
E2428−22
6.4.3.1 Calibration torque values shall be applied and re- measurement standard to each position resulting in four cali-
moved slowly and smoothly, without inducing shock or vibra- bration runs per mode.
tion to the elastic torque measurement standard.
6.6 Deflection Calculation—The method selected for treat-
6.4.3.2 Thetimeintervalbetweensuccessiveapplicationsor
ment of zero should reflect anticipated usage of the elastic
removals of calibration torque values, and in obtaining indica-
torque measurement standard.The calculation shall (a) use the
tionsfromtheelastictorquemeasurementstandard,shallbeas
initial zero value only or (b) a value derived from indications
uniform as possible.
takenbeforeandaftertheapplicationofacalibrationtorqueor
6.4.3.3 If a calibration torque value is to be followed by
series of calibration torque values.
another calibration torque value of lesser magnitude, reduce
6.6.1 Method (a):
the applied calibration torque on the elastic torque measure-
6.6.1.1 Calculate the deflection as the difference between
ment standard to zero torque before applying the subsequent
the indication at the applied calibration torque and the indica-
calibration torque value.
tion at initial zero torque.
6.4.4 Ifanelastictorquemeasurementstandardistobeused
6.6.1.2 Perform a creep recovery test per the criteria of 6.7
underdecreasingcalibrationtorque,itshallbecalibratedunder
toensurethatthezero-returncharacteristicoftheelastictorque
decreasing torque with decreasing calibration torque values.
measurement standard does not result in excessive measure-
Usetheproceduresforcalibrationandanalysisofdatagivenin
ment error.
Sections 6 and 7. When an elastic torque measurement stan-
6.6.2 Method (b):
dard is calibrated with both increasing and decreasing calibra-
6.6.2.1 Whenitiselectedtoreturntozeroaftereachapplied
tion torque, the same calibration torque increments shall be
calibration torque, the average of the two zero values shall be
applied, and separate calibration equations shall be developed.
used to determine the deflection.
6.6.2.2 When a series of applied calibration torque values
NOTE 5—For any elastic torque measurement standard, the measure-
menterrorsobservedatcorrespondingcalibrationtorquevaluestakenfirst are applied before return to zero calibration torque, a series of
by increasing the torque to any given calibration torque value and then by
interpolated zero torque indications may be used for the
decreasing the calibration torque value to that calibration torque value do
calculations.Incalculatingtheaveragezerotorqueindications,
not always agree. Elastic torque measurement standards are usually used
express the values to the nearest unit in the same number of
under increasing torque.
places as estimated in the indication of the electronic-
6.5 Randomization of Calibration Torque Application Con-
indicating measurement instrument scale. Follow the instruc-
dition:
tions for the rounding method given in Practices E29.
6.5.1 During the calibration, maintain the torque measure-
6.7 Determination of Creep Recovery—Perform a creep
ment axis of the elastic torque measurement standard coinci-
recovery test to ensure that the creep characteristic of the
dent with the torque axis of the calibration machine.
elastictorquemeasurementstandarddoesnothaveasignificant
6.5.2 Rotate the position of the elastic torque measurement
effect on calculated deflections when method (a) is used to
standard in the calibration machine by amounts such as one
determine deflections.
third, one quarter, or one half turn and realign any keyed
connectors before repeating any series of calibration torque
NOTE 7—Creep affects the calculation of deflection.Alarge non-return
to zero following calibration torque application during calibration is a
applications.
demonstration of excessive creep.
6.5.3 Introduce variations in any other factors that normally
NOTE8—Creepandcreeprecoveryaregenerallystablepropertiesofan
are encountered in service, as for example, disconnecting and
elastic torque measurement standard unless the elastic torque measure-
reconnecting electrical cables.
ment standard is overloaded, has experienced moisture or other contami-
6.5.4 Allow sufficient time for the elastic torque measure- nant incursion, or is experiencing fatigue failure.
ment standard to reach temperature stability if power is
6.7.1 Method (a)—Perform the creep recovery test for
removed or cabling is removed and then reconnected.
elastic torque measurement standards that are new, that have
6.5.5 In a two-mode calibration (clockwise and counter-
neverhadacreeprecoverytestperformed,thathavehadmajor
clockwise) perform a part of the calibration in one mode.
repairs, that are suspected of having been overloaded, or that
6.5.5.1 Switch modes and continue the calibration.
show excessive non-return to zero following calibration.
6.5.5.2 Finish the calibration in the initial mode.
6.7.2 Method (b)—The creep recovery test is not required
6.5.5.3 Modes may be changed at each rotational position.
since method (b) is used to determine deflections on an elastic
torque measurement standard both during calibration and
NOTE 6—Depending on their design, elastic torque measurement
subsequent use.
standards vary in sensitivity to mounting conditions, parasitic forces, or
moments due to misalignment.Ameasure of this sensitivity can be made 6.7.3 Perform the creep recovery test as follows:
byimposingconditionstosimulatethesefactorssuchas (a)usingfixtures
6.7.3.1 Exercisetheelastictorquemeasurementstandardto
of varying stiffness or hardness, (b) applying the appropriate torque for
the maximum calibration torque value at least two times.
bolting fixtures with different torque ratings, or (c) mounting in various
6.7.3.2 Allow the zero-return indication to stabilize and
orientations with angular or eccentric misalignment, and so forth. Such
record the value of the initial zero-return indication T .
factors can sometimes be significant contributors to measurement uncer-
izr
tainty and should be reflected in comprehensive measurement uncertainty
6.7.3.3 Apply the maximum applied calibration torque used
analyses.
in calibration of the elastic torque measurement standard and
6.5.6 During the calibration of elastic torque measurement hold as constant as possible for 300 s, and then record the
standards that use a square drive, rotate the elastic torque indication of the elastic torque measurement standard, T .
c
E2428−22
6.7.3.4 Remove the applied calibration torque as smoothly best-fitpolynomialequation,fitthepolynomialequationofthat
but as quickly as possible, and record the indication at 30 s, degree,oralowerdegree,totheentirecalibrationdataset(not
T , and at 300 s, T . the average data set) in accordance with 7.3, and proceed to
30 300
6.7.4 Calculate the creep recovery error, E , as follows: analyze the data in accordance with 7.4.
cr
100 3 ~T 2 T !
7.2 Standard Deviation—Calculate a standard deviation
30 izr
E 5 (6)
cr
T
c from the differences between the individual values observed in
the calibration and the corresponding values taken from the
where:
calibration equation. Calculate the standard deviation as fol-
E = creep recovery error
cr
lows:
T = indication 30 s after zero torque is achieved
2 2 2
T = initial zero-return indication
izr d 1d .1d
1 2 n
s 5 (9)
Œ
T = indication at maximum calibration torque applied m
c
n 2 m 21
6.7.5 A zero-return error shall be calculated as follows:
where:
T 2 T
300 izr s = standard deviation
m
E 5 (7)
zr
T
d ,d , etc. = differences between the fitted curve and the n
c
1 2
observed values from the calibration data,
where:
n = number of deflections, and
E = zero-return error
zr
m = the degree of polynomial fit
T = final zero-return indication 300 s after the applied
NOTE 10—The departures of the observed deflections from the calibra-
calibration torque is removed
tion equation values are not purely random but arise partly from the
T = iinitial zero-return indication
izr localized variation and elastic torque measurement standard resolution,
T = indication at maximum calibration torque applied
discussed in 6.1.1. Consequently, the distributions of the residuals from
c
the least squares fit might not follow the normal curve of error, and the
6.7.6 Creep Recovery Maximum Permissible Measurement
customary estimates based on the statistics of random variables might not
Error—Forelastictorquemeasurementstandardscalibratedfor
be strictly applicable.
use over the following verified ranges of torques, the creep
7.3 Determination of Lower Limit Factor, LLF—Calculate
recovery maximum permissible measurement error of the
the LLF as 2.0 times the standard deviation. If the calculated
indication at the applied calibration torque value are
LLF is less than the elastic torque measurement standard
Class AA: 60.02 %
resolution, define the LLF as that value equal to the resolution.
Class A: 60.05 %.
Express the LLF in torque units, using the average ratio of
6.7.7 The creep recovery test should be repeated if the
torque to deflection from the calibration data.
zero-returnerrorexceeds50%ofthecreeprecoverymaximum
permissible measurement error limits. If the zero-return mea-
7.4 Verified Range of Torques—Calculate the verified range
surement error in the second creep-recovery test exceeds 50 % of torques of the elastic torque measurement standard as
ofthecreeprecoverymaximumpermissiblemeasurementerror
follows.
limits, either repair, replace, or use Method (b) as defined in
7.4.1 Lower Torque Limit of the Verified Range of Torques—
6.6.2.
Calculate the lower torque limit, T , of the verified range of
ll
torques as a percent of indication, P, and class of the verified
7. Calculation and Analysis of Data
range of torques as:
7.1 Calibration Equation—Fit a polynomial equation of the
100 3LLF
T 5 (10)
following form to the calibration torque and deflection ob-
P
tained in the calibration using the method of least squares:
where:
2 2
D 5 A 1A 1A τ 1.A τ (8)
0 1 2 5
T = lower torque limit
ll
LLF = lower limit factor
where:
P = percent of indication
D = Deflection ,
τ = calibration torque, and
7.4.1.1 For Class A verified range of torques P=0.25 %.
A through A = coefficients
0 5
7.4.1.2 For Class AA verified range of torques P=0.06 %.
A 2nd degree equation should be used with coefficients A ,
7.4.1.3 The lower torque limit should be 2 % (1/50) or
A ,and A ,equaltozero.Otherdegreeequationsmaybeused.
4 5
greater of capacity of the elastic torque measurement standard.
NOTE 9—For example, the coefficients A through A would be set 7.4.1.4 When a verified range of torques other than the two
2 5
equal to zero for a linearized elastic torque measurement standard.
standard ranges given in 7.4.1.1 and 7.4.1.2 is desirable, the
appropriate lower torque limit error should be specified in the
7.1.1 TheprocedureofAnnexA1shallbeusedtoobtainthe
applicable method of test.
maximum degree of the best-fit polynomial equation statisti-
cally supported by the calibration data set. Perform the 7.4.2 The verified range of torques shall not include
calculation with a polynomial equation fitted to the average calibrationtorquevaluesoutsidetherangeofcalibrationtorque
data at each applied calibration torque value following the values applied during calibration. If the lower torque limit is
method of AnnexA1.After determination of the degree of the less than the lowest non-zero calibration torque value applied,
E2428−22
the lower torque limit of the verified range of torques is equal for those elastic torque measurement standards used over the
to the lowest calibration torque value applied. Class A verified range of torques.
9.2.2 Elastic torque measurement standards not meeting the
NOTE 11—For example, an elastic torque measurement standard cali-
stability criteria of 9.2.1 shall be calibrated at intervals that
brated using primary torque measurement standards applied on a moment
shall ensure the stability criteria are not exceeded during the
arm at a known distance had a calculated LLF of 0.338 N-m. The lower
torque limit for the Class AA verified range of torques is therefore T
calibration interval.
ll
=100×LLF/0.06=563 N-m. The LLF will be less than the lower torque
NOTE 15—The above stability criteria provide minimum requirements
limit error of 60.06 % of torque for calibration torques greater than this
for establishing calibration intervals for elastic torque measurement
lower torque limit to the maximum calibration torque value of the elastic
standards.
torque measurement standard.
9.2.3 Users specifying verified range of torques other than
7.4.3 For elastic torque measurement standards used to
ClassAAor ClassAshould determine stability criteria appro-
verifytestingmachinesinaccordancewithPracticesE2624,or
priate to the instruments employed.
similar applications, the lower limit factor of the elastic torque
9.2.4 Secondary torque measurement standards should be
measurement standard shall not exceed 0.25 % of torque.
cross-checked at periodic intervals using other standards to
NOTE 12—The term “verified range of torques” used in these practices
help ensure that secondary torque measurement standards are
is parallel in meaning to the same term in Practices E2624. It is the range
performing as expected.
of calibration torque values over which it is permissible to use the elastic
torque measurement standard in a calibrating a testing machine or other
9.3 Calibration Following Repairs or Overloads—An elas-
similar device
tic torque measurement standard shall be calibrated whenever
the calibration of the elastic torque measurement standards
8. Temperature Requirement for Elastic Torque
might be suspect. Any elastic torque measurement standard
Measurement Standard During Use
sustaining an overload that produces a permanent shift in the
8.1 Temperature of Calibration—theelastictorquemeasure-
zero-torque indication amounting to 1 % or more of the
ment standard should be calibrated at 23 °C, although other
capacity of the elastic torque measurement standards shall be
temperatures may be used (see 6.3).
calibrated before further use.
8.2 Maximum permissible measurement error due to tem- 9.3.1 A means of establishing a true zero reference should
be developed to ensure that the zero-torque indication during
perature effect—If an elastic torque measurement standard is
used at a temperature other than the temperature at which it calibration has not been shifted by an amount greater than 1 %
of the elastic torque measurement standard capacity.
wascalibrated,theusershallensurethatthemeasurementerror
duetotemperature,asapercentofindication,doesnotexceed:
10. Substitution of Electronic Indicating Instruments
Class AA 6 0.01 %
Used for Elastic Torque Measurement Standards
Class A 6 0.06 %.
NOTE 13—When the LLF for either ClassAAor ClassAverified range
10.1 The elastic member and the electronic-indicating mea-
of torques is added as root-sum-squares with values for maximum
surement instrument may be calibrated separately. This allows
permissible measurement error due to temperature given in 8.2, the effect
for the substitution or repair of the electronic-indicating
on the maximum permissible measurement error due to temperature is
measurementinstrumentwithoutthenecessityforrepeatingan
negligible. Such a combination of measurement error sources is valid in
the case of independent measurement error sources.
end-to-end elastic torque measurement standard calibration.
NOTE 14—Temperature effects can cause significant measurement
When such substitution or repair is made, the user shall ensure
errorsinbothtemperature-compensatedanduncompensatedelastictorque
that the measurement performance of the elastic torque mea-
measurement standards.
surementstandardismaintained.Substitutionoftheelectronic-
indicating measurement instrument shall not extend the elastic
9. Time Interval Between Calibration and Stability
torque measurement standard calibration date. The following
Criteria
conditionsshallbesatisfiedwhensubstitutingametrologically
9.1 Theelastictorquemeasurementstandardsshallmeetthe
significant element of the electronic-indicating measurement
range, maximum permissible measurement errors, resolution,
instrument.
andstabilityrequirementsofthisstandard,andshallbesuitable
10.1.1 The electronic-indicating measurement instrument
for the intended use.
used in the initial calibration and the electronic-indicating
9.2 Elastic torque measurement standards used as second- measurementinstrumenttobesubstitutedshalleachhavebeen
arytorquemeasurementstandardsfortheverificationoftorque calibrated and their measurement uncertainties determined.
indication of testing machines shall be calibrated at intervals The electronic-indicating measurement instrument to be sub-
not exceeding two years after demonstration of stability stituted shall be calibrated with metrological traceability to the
supporting the adopted calibration interval. New elastic torque SIoverthefullrangeofitsintendeduseincludingbothpositive
measurement standards shall be calibrated at an interval not and negative values if the system is used in clockwise and
exceeding 1 year to determine stability per 9.2.1. counterclockwise modes. The calibrated range shall include a
9.2.1 During recalibration, the elastic torque measurement point less than or equal to the indication of the elastic torque
standards shall, over the range of use, only demonstrate measurement standard at the lower torque limit and a point
changesincalibrationvaluesoflessthan0.032%ofindication equal to or greater than the indication of the elastic torque
for elastic torque measurement standards used over the Class measurement standard at the maximum applied calibration
AAverifiedrangeoftorquesandlessthan0.16%ofindication torque. A minimum of five points shall be taken within this
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range. The measurement uncertainty of each electronic- error-free and contain no alteration of dates, data, etc. The
indicating measurement instrument shall be less than or equal report shall contain the following information:
to one third of the measurement uncertainty for the elastic 11.1.1 A statement that the calibration has been performed
torque measurement standard over the range from the lower in accordance with Practices E2428. The calibration should be
torque limit to the maximum calibration torque value. performed in accordance with the latest published version of
10.1.2 The measurement uncertainty of the electronic- Practices E2428;
indicating measurement instrument may be determined by one 11.1.2 Manufacturer and identifying serial number of the
of the methods outlined in Appendix X2. An elastic torque elastic torque measurement standard calibrated;
measurement standard simulator should be employed as a 11.1.3 Name of the laboratory performing the calibration;
check standard to verify and maintain calibration of the 11.1.4 Date of the calibration;
electronic-indicatingmeasurementinstrumentandinestablish- 11.1.5 Type of reference measurement standard(s) used in
ing the measurement uncertainty. An elastic torque measure- the calibration;
ment standard simulator should be capable of providing a 11.1.6 Temperatureatwhichthecalibrationwasreferenced;
series of input mV/Vsteps over the range of measurement and 11.1.7 Listing of the calibration torque values applied and
with impedance characteristics like that of the elastic member. the corresponding indications at each rotational position, in-
The measurement uncertainty of the elastic torque measure- cluding the initial and return-to-zero torque indications;
mentstandardsimulatorshallbelessthanorequaltoonetenth 11.1.8 Treatmentofzeroindeterminingindications(method
of the measurement uncertainty for the electronic-indicating (a) or (b) as described in 6.6. If method (b) is elected, also
measurement instrument. specify whether zero was determined by the average or
10.1.3 Excitation voltage amplitude, frequency, and wave- interpolated method;
form shall be maintained in the substitution within limits to 11.1.9 List of coefficients for any fitted calibration equation
ensure that the effect on the calibration is negligible. The user and the deviations of the experimental data from the fitted
shall determine limits on these parameters through measure- curve;
ment uncertainty analysis and appropriate tests to ensure that 11.1.10 Elastic torque measurement standard resolution, the
this requirement is met. Substitution of an interconnect cable measurement uncertainty associated with the calibration
can have a significant effect on calibration. If an interconnect results, and the verified range of torques;
cable is to be substituted, see 10.1.4. 11.1.11 The result of the creep recovery test, when per-
10.1.4 Ifaninterconnectcableissubstituted,careshouldbe formed;
taken to ensure that the new cable matches the original in all 11.1.12 The excitation voltage and wave form used for
aspects significant to the measurement. The electronic- calibration when known;
indicating measurement instrument/cable performance should 11.1.13 Statement that the lower torque limit of the verified
be verified using an elastic torque measurement standard range of torques expressed in this report applies only when the
simulator or other appropriate laboratory instruments. calibration equation is used to determine the calibration torque
value;
NOTE 16—The point of excitation voltage sensing, the impedance
between the point of excitation voltage sensing and the elastic torque
NOTE 17—For elastic torque measurement standards in which indica-
measurement standard, and similar factors can affect the sensitivity of the
tions are displayed in engineering units (that is, N-m) users are cautioned
device to changes in the applied calibration torque value.
that the lower torque limit expressed in the calibration report applies only
when the calibration equation is used to determine the calibration torque
10.2 A report of calibration for the original and substitute
value, that is, the direct indication
...