Metallic material - Calibration of force-proving instruments used for the verification of uniaxial testing machines (ISO 376:2011)

This European Standard covers the calibration of force-proving instruments used for the static verification of uniaxial testing machines (e.g. tension/compression testing machines) and describes a procedure for classifying these instruments. This International Standard generally applies to force-proving instruments in which the force is determined by measuring the elastic deformation of a loaded member or a quantity which is proportional to it.

Metallische Werkstoffe - Kalibrierung der Kraftmessgeräte für die Prüfung von Prüfmaschinen mit einachsiger Beanspruchung (ISO 376:2011)

In dieser Internationalen Norm ist die Kalibrierung von Kraftmessgeräten für die statische Prüfung einachsiger Prüfmaschinen (z. B. Zug-Druckprüfmaschinen) festgelegt, und es wird ein Verfahren für die Klassifizierung dieser Geräte beschrieben.
Diese Internationale Norm gilt allgemein für Kraftmessgeräte, bei denen die Kraft durch Messung der elasti-schen Formveränderung eines Verformungskörpers oder einer ihr proportionalen Messgröße bestimmt wird.

Matériaux métalliques - Étalonnage des instruments de mesure de force utilisés pour la vérification des machines d'essais uniaxiaux (ISO: 376:2011)

L'ISO 376:2011 spécifie une méthode d'étalonnage des instruments de mesure de force utilisés pour la vérification statique des machines d'essais uniaxiaux (par exemple machines d'essai de traction/compression) et décrit une procédure de classification de ces instruments.
Elle s'applique aux instruments de mesure de force dans lesquels la force est déterminée par la mesure de la déformation élastique d'un élément chargé ou d'une grandeur proportionnelle à celle-ci.

Kovinski materiali - Umerjanje merilnikov sile, ki se uporabljajo za preverjanje preskusnih strojev z enoosno obremenitvijo (ISO 376:2011)

Ta evropski standard zajema umerjanje merilnikov sile, ki se uporabljajo za statično preverjanje preskusnih strojev z enoosno obremenitvijo (npr. natezni/tlačni preskusni stroji), in opisuje postopek za razvrščanje teh strojev. Ta mednarodni standard na splošno velja za merilnike sile, pri katerih je sila določena z izmero elastične deformacije obteženega elementa ali količine, ki je sorazmerna z njo.

General Information

Status
Published
Public Enquiry End Date
24-Jul-2009
Publication Date
18-Dec-2011
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
05-Oct-2011
Due Date
10-Dec-2011
Completion Date
19-Dec-2011

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SLOVENSKI STANDARD
SIST EN ISO 376:2012
01-februar-2012
1DGRPHãþD
SIST EN ISO 376:2005
Kovinski materiali - Umerjanje merilnikov sile, ki se uporabljajo za preverjanje
preskusnih strojev z enoosno obremenitvijo (ISO 376:2011)
Metallic material - Calibration of force-proving instruments used for the verification of
uniaxial testing machines (ISO 376:2011)
Metallische Werkstoffe - Kalibrierung der Kraftmessgeräte für die Prüfung von
Prüfmaschinen mit einachsiger Beanspruchung (ISO 376:2011)
Matériaux métalliques - Étalonnage des instruments de mesure de force utilisés pour la
vérification des machines d'essais uniaxiaux (ISO: 376:2011)
Ta slovenski standard je istoveten z: EN ISO 376:2011
ICS:
77.040.10 Mehansko preskušanje kovin Mechanical testing of metals
SIST EN ISO 376:2012 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 376:2012

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SIST EN ISO 376:2012


EUROPEAN STANDARD
EN ISO 376

NORME EUROPÉENNE

EUROPÄISCHE NORM
June 2011
ICS 77.040.10 Supersedes EN ISO 376:2004
English Version
Metallic materials - Calibration of force-proving instruments used
for the verification of uniaxial testing machines (ISO 376:2011)
Matériaux métalliques - Étalonnage des instruments de Metallische Werkstoffe - Kalibrierung der Kraftmessgeräte
mesure de force utilisés pour la vérification des machines für die Prüfung von Prüfmaschinen mit einachsiger
d'essais uniaxiaux (ISO 376:2011) Beanspruchung (ISO 376:2011)
This European Standard was approved by CEN on 4 June 2011.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same
status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.





EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2011 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 376:2011: E
worldwide for CEN national Members.

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SIST EN ISO 376:2012
EN ISO 376:2011 (E)
Contents Page
Foreword .3

2

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SIST EN ISO 376:2012
EN ISO 376:2011 (E)
Foreword
This document (EN ISO 376:2011) has been prepared by Technical Committee ISO/TC 164 "Mechanical
testing of metals" in collaboration with Technical Committee ECISS/TC 101 “Test methods for steel (other
than chemical analysis)” the secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by December 2011, and conflicting national standards shall be withdrawn
at the latest by December 2011.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 376:2004.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 376:2011 has been approved by CEN as a EN ISO 376:2011 without any modification.

3

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SIST EN ISO 376:2012

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SIST EN ISO 376:2012

INTERNATIONAL ISO
STANDARD 376
Fourth edition
2011-06-15


Metallic materials — Calibration of force-
proving instruments used for the
verification of uniaxial testing machines
Matériaux métalliques — Étalonnage des instruments de mesure de
force utilisés pour la vérification des machines d'essais uniaxiaux





Reference number
ISO 376:2011(E)
©
ISO 2011

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SIST EN ISO 376:2012
ISO 376:2011(E)

COPYRIGHT PROTECTED DOCUMENT


©  ISO 2011
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland

ii © ISO 2011 – All rights reserved

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SIST EN ISO 376:2012
ISO 376:2011(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Symbols and their designations .1
5 Principle.2
6 Characteristics of force-proving instruments .3
7 Calibration of the force-proving instrument.3
8 Classification of the force-proving instrument .8
9 Use of calibrated force-proving instruments.10
Annex A (informative) Example of dimensions of force transducers and corresponding loading
fittings.11
Annex B (informative) Additional information .18
Annex C (informative) Measurement uncertainty of the calibration and subsequent use of the
force-proving instrument.21
Bibliography.30

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SIST EN ISO 376:2012
ISO 376:2011(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 376 was prepared by Technical Committee ISO/TC 164, Mechanical testing of metals, Subcommittee
SC 1, Uniaxial testing.
This fourth edition cancels and replaces the third edition (ISO 376:2004), which has been technically revised
(for details, see the introduction).
iv © ISO 2011 – All rights reserved

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SIST EN ISO 376:2012
ISO 376:2011(E)
Introduction
An ISO/TC 164/SC 1 working group has developed procedures for determining the measurement uncertainty
of force-proving instruments, and these procedures have been added to this fourth edition as a new annex
(Annex C).
In addition, this fourth edition allows the calibration to be performed in two ways:
⎯ with reversible measurement for force-proving instruments which are going to be used with increasing
and decreasing forces;
⎯ without reversible measurement for force-proving instruments which are going to be used only with
increasing forces.
In the first case, i.e. when the force-proving instrument is going to be used for reversible measurements, the
calibration has to be performed with increasing and decreasing forces to determine the hysteresis of the force-
proving instrument. In this case, there is no need to perform a creep test.
In the second case, i.e. when the force-proving instrument is not going to be used for reversible
measurements, the calibration is performed with increasing forces only but, in addition, a creep test has to be
performed. In this case, there is no need to determine the hysteresis.

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SIST EN ISO 376:2012

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SIST EN ISO 376:2012
INTERNATIONAL STANDARD ISO 376:2011(E)

Metallic materials — Calibration of force-proving instruments
used for the verification of uniaxial testing machines
1 Scope
This International Standard specifies a method for the calibration of force-proving instruments used for the
static verification of uniaxial testing machines (e.g. tension/compression testing machines) and describes a
procedure for the classification of these instruments.
This International Standard is applicable to force-proving instruments in which the force is determined by
measuring the elastic deformation of a loaded member or a quantity which is proportional to it.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
force-proving instrument
whole assembly from the force transducer through to, and including, the indicator
4 Symbols and their designations
Symbols and their designations are given in Table 1.
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SIST EN ISO 376:2012
ISO 376:2011(E)
Table 1 — Symbols and their designations
Symbol Unit Designation
b % Relative reproducibility error with rotation
b′ % Relative repeatability error without rotation
c % Relative creep error
F N Maximum capacity of the transducer
f
F N Maximum calibration force
N
f % Relative interpolation error
c
f % Relative zero error
0
a
i — Reading on the indicator after removal of force
f
a
i — Reading on the indicator before application of force
o
a
i — Reading on the indicator 30 s after application or removal of the maximum calibration force
30
a
i — Reading on the indicator 300 s after application or removal of the maximum calibration force
300
r N Resolution of the indicator
v % Relative reversibility error of the force-proving instrument
X — Deflection with increasing test force
X — Computed value of deflection
a
X ′ — Deflection with decreasing test force
X — Maximum deflection from runs 1, 3 and 5
max
X — Minimum deflection from runs 1, 3 and 5
min
X — Deflection corresponding to the maximum calibration force
N
X — Average value of the deflections with rotation
r
X — Average value of the deflections without rotation
wr
a
Reading value corresponding to the deflection.
5 Principle
Calibration consists of applying precisely known forces to the force transducer and recording the data from the
indicator, which is considered an integral part of the force-proving instrument.
When an electrical measurement is made, the indicator may be replaced by another indicator and the force-
proving instrument need not be recalibrated provided the following conditions are fulfilled.
a) The original and replacement indicators have calibration certificates, traceable to national standards,
which give the results of calibration in terms of electrical base units (volt, ampere). The replacement
indicator shall be calibrated over a range equal to or greater than the range for which it is used with the
force-proving instrument, and the resolution of the replacement indicator shall be at least equal to the
resolution of the original indicator when it is used with the force-proving instrument.
b) The units and excitation source of the replacement indicator should be respectively of the same quantity
(e.g. 5 V, 10 V) and type (e.g. AC or DC carrier frequency).
c) The uncertainty of each indicator (both the original and the replacement indicators) shall not significantly
influence the uncertainty of the whole force-proving instrument assembly. It is recommended that the
uncertainty of the replacement indicator be no greater than 1/3 of the uncertainty of the entire system
(see C.2.11).
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SIST EN ISO 376:2012
ISO 376:2011(E)
6 Characteristics of force-proving instruments
6.1 Identification of the force-proving instrument
All the elements of the force-proving instrument (including the cables for electrical connection) shall be
individually and uniquely identified, e.g. by the name of the manufacturer, the model and the serial number.
For the force transducer, the maximum working force shall be indicated.
6.2 Application of force
The force transducer and its loading fittings shall be designed so as to ensure axial application of force,
whether in tension or compression.
Examples of loading fittings are given in Annex A.
6.3 Measurement of deflection
Measurement of the deflection of the loaded member of the force transducer may be carried out by
mechanical, electrical, optical or other means with adequate accuracy and stability.
The type and the quality of the deflection measuring system determine whether the force-proving instrument is
classified only for specific calibration forces or for interpolation (see Clause 7).
Generally, the use of force-proving instruments with dial gauges as a means of measuring the deflection is
limited to the forces for which the instruments have been calibrated. The dial gauge, if used over a long travel,
may contain large localized periodic errors which produce an uncertainty too great to permit interpolation
between calibration forces. The dial gauge may be used for interpolation if its periodic error has a negligible
influence on the interpolation error of the force-proving instrument.
7 Calibration of the force-proving instrument
7.1 General
7.1.1 Preliminary measures
Before undertaking the calibration of the force-proving instrument, ensure that this instrument is able to be
calibrated. This can be done by means of preliminary tests such as those defined below and given as
examples.
7.1.2 Overloading test
This optional test is described in Clause B.1.
7.1.3 Verification relating to application of forces
Ensure
⎯ that the attachment system of the force-proving instrument allows axial application of the force when the
instrument is used for tensile testing;
⎯ that there is no interaction between the force transducer and its support on the calibration machine when
the instrument is used for compression testing.
Clause B.2 gives an example of a method that can be used.
NOTE Other tests can be used, e.g. a test using a flat-based transducer with a spherical button or upper bearing
surface.
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SIST EN ISO 376:2012
ISO 376:2011(E)
7.1.4 Variable voltage test
This test is left to the discretion of the calibration service. For force-proving instruments requiring an electrical
supply, verify that a variation of ±10 % of the line voltage has no significant effect. This verification can be
carried out by means of a force transducer simulator or by another appropriate method.
7.2 Resolution of the indicator
7.2.1 Analogue scale
The thickness of the graduation marks on the scale shall be uniform and the width of the pointer shall be
approximately equal to the width of a graduation mark.
The resolution, r, of the indicator shall be obtained from the ratio between the width of the pointer and the
centre-to-centre distance between two adjacent scale graduation marks (scale interval), the recommended
ratios being 1:2, 1:5 or 1:10, a spacing of 1,25 mm or greater being required for the estimation of a tenth of the
division on the scale.
A vernier scale of dimensions appropriate to the analogue scale may be used to allow direct fractional reading
of the instrument scale division.
7.2.2 Digital scale
The resolution is considered to be one increment of the last active number on the numerical indicator.
7.2.3 Variation of readings
If the readings fluctuate by more than the value previously calculated for the resolution (with no force applied
to the instrument), the resolution shall be deemed to be equal to half the range of fluctuation.
7.2.4 Units
The resolution, r, shall be converted to units of force.
7.3 Minimum force
Taking into consideration the accuracy with which the deflection of the instrument can be read during
calibration or during its subsequent use for verifying machines, the minimum force applied to a force-proving
instrument shall comply with the two following conditions:
a) the minimum force shall be greater than or equal to:
⎯ 4 000 × r for class 00;
⎯ 2 000 × r for class 0,5;
⎯ 1 000 × r for class 1;
⎯ 500 × r for class 2.
b) the minimum force shall be greater than or equal to 0,02 F .
f
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SIST EN ISO 376:2012
ISO 376:2011(E)
7.4 Calibration procedure
7.4.1 Preloading
Before the calibration forces are applied, in a given mode (tension or compression), the maximum force shall
be applied to the instrument three times. The duration of the application of each preload shall be between 60 s
and 90 s.
7.4.2 Procedure
Carry out the calibration by applying two series of calibration forces to the force-proving instrument with
increasing values only, without disturbing the device.
Then apply at least two further series of increasing and, if the force-proving instrument is to be calibrated in an
incremental/decremental loading direction, decreasing values. Between each of the further series of forces,
rotate the force-proving instrument symmetrically on its axis to positions uniformly distributed over 360° (i.e. 0°,
120°, 240°). If this is not possible, it is permissible to adopt the following positions: 0°, 180° and 360° (see
Figure 1).

Figure 1 — Positions of the force-proving instrument
For the determination of the interpolation curve, the number of forces shall be not less than eight, and these
forces shall be distributed as uniformly as possible over the calibration range. The interpolation curve shall be
determined from the average values of the deflections with rotation, X , as defined in 7.5.1.
r
If a periodic error is suspected, it is recommended that intervals between the forces which correspond to the
periodicity of this error be avoided.
This procedure determines only a combined value of hysteresis of the device and of the calibration machine.
Accurate determination of the hysteresis of the device may be performed on dead-weight machines. For other
types of calibration machine, their hysteresis should be considered.
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SIST EN ISO 376:2012
ISO 376:2011(E)
The force-proving instrument shall be preloaded three times to the maximum force in the direction in which the
subsequent forces are to be applied. When the direction of loading is changed, the maximum force shall be
applied three times in the new direction.
The readings corresponding to no force shall be noted after waiting at least 30 s after the force has been
totally removed.
There should be a wait of at least 3 min between subsequent measurement series.
Instruments with detachable parts shall be dismantled, as for packaging and transport, at least once during
calibration. In general, this dismantling shall be carried out between the second and third series of calibration
forces. The maximum force shall be applied to the force-proving instrument at least three times before the
next series of forces is applied.
Before starting the calibration of an electrical force-proving instrument, the zero signal may be noted (see
Clause B.3).
7.4.3 Loading conditions
The time interval between two successive loadings shall be as uniform as possible, and no reading shall be
taken within 30 s of the start of the force change. The calibration shall be performed at a temperature stable to
within ±1 °C. This temperature shall be within the range 18 °C to 28 °C and shall be recorded. Sufficient time
shall be allowed for the force-proving instrument to attain a stable temperature.
When it is known that the force-proving instrument is not temperature-compensated, care should be taken to
ensure that temperature variations do not affect the calibration.
Strain gauge transducers shall be energized for at least 30 min before calibration.
7.4.4 Creep test
If the force-proving instrument is to be calibrated in an incremental-only loading direction, record its output at
30 s and 300 s after application or removal of the maximum calibration force, in each mode of force
application, to enable its creep characteristics to be determined. If creep is measured at zero force, the
maximum calibration force shall be maintained for at least 60 s prior to its removal. The creep test may be
performed at any time after preloading during the calibration procedure.
The calibration certificate shall include the following information:
⎯ the method of creep measurement (creep at maximum force or after force removal);
⎯ when the creep measurement was performed (after preloading, after the last measurement series, etc.);
⎯ the length of time for which the force was applied prior to removal (for creep determined at zero force).
7.4.5 Determination of deflection
A deflection is defined as the difference between a reading under force and a reading without force. This
definition of deflection applies to output readings in electrical units as well as to output readings in length units.
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SIST EN ISO 376:2012
ISO 376:2011(E)
7.5 Assessment of the force-proving instrument
7.5.1 Relative reproducibility and repeatability errors, b and b′
These errors are calculated for each calibration force and in both cases, i.e. with rotation of the force-proving
instrument (b) and without rotation (b′), using the following equations:
XX−
max min
b=×100 (1)
X
r
XX++X
13 5
where X = (2)
r
3
and
XX−
21

b=×100 (3)
X
wr
XX+
12
where X = (4)
wr
2
7.5.2 Relative interpolation error, f
c
This error is determined using a first-, second- or third-degree equation giving the deflection X as a function
r
of the calibration force.
The equation used shall be indicated in the calibration report. The relative interpolation error shall be
calculated from the equation:
XX−
r
a
f=×100 (5)
c
X
a
7.5.3 Relative zero error, f
0
The zero reading shall be recorded before and after each series of tests. The zero reading shall be taken
approximately 30 s after the force has been completely removed.
The relative zero error is calculated from the equation:
ii−
fo
f=×100 (6)
0
X
N
The maximum relative zero error evaluated should be considered.
7.5.4 Relative reversibility error, v
The relative reversibility error is determined at each calibration, by carrying out a verification with increasing
forces and then with decreasing forces.
The difference between the values obtained for both series with increasing forces and with decreasing forces
enables the relative reversibility error to be calculated using the following equations:
XX′ −
43
v=×100 (7)
1
X
3
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SIST EN ISO 376:2012
ISO 376:2011(E)

XX−
65
v=×100 (8)
2
X
5
v is calculated as the mean value of v and v :
1 2
vv+
12
v = (9)
2
7.5.5 Relative creep error, c
Calculate the difference in outputs i obtained at 30 s and i obtained 300 s after the application or removal
30 300
of the maximum calibration force and express this difference as a percentage of maximum deflection:
ii−
300 30
c=×100 (10)
X
N
8 Classification of the force-proving instrument
8.1 Principle of classification
The range for which the force-proving instrument is classified is determined by considering each calibration
force, one after the other, starting with the maximum force and decreasing to the lowest calibration force. The
classification range ceases at the last force for which the classification requirements are satisfied.
The force-proving instrument can be classified either for specific forces or for interpolation, and for either
incremental-only or incremental/decremental loading directions.
8.2 Classification criteria
8.2.1 The range of classification of a force-proving instrument shall at least cover the range 50 % to 100 %
of F .
N
8.2.2 Case A: For instruments classified only for specific forces and incremental-only loading, the criteria
which shall be considered are:
⎯ the relative reproducibility, repeatability and zero errors;
⎯ the relative creep error.
8.2.3 Case B: For instruments classified only for specific forces and incremental/decremental loading, the
criteria which shall be considered are:
⎯ the relative reproducibility, repeatability and zero errors;
⎯ the relative reversibility error.
8.2.4 Case C: For instruments classified for interpolation and incremental-only loading, the criteria which
shall be considered are:
⎯ the relative reproducibility, repeatability and zero errors;
⎯ the relative interpolation error;
⎯ the relative creep error.
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SIST EN ISO 376:2012
ISO 376:2011(E)
8.2.5 Case D: For instruments classified for interpolation and incremental/decremental loading, the criteria
which shall be considered are:
⎯ the relative reproducibility, repeatability and zero errors;
⎯ the relative interpolation error;
⎯ the relative reversibility error.
Table 2 gives the maximum allowable values of these parameters for each class of force-proving instrument
and the uncertainty of the calibration forces.
Table 2 — Characteristics of force-proving instruments
Expanded
uncertainty of
Relative error of the force-proving instrument applied
calibration force

Class (95 % level of
% confidence)
of reproducibility of repeatability of interpolation of zero of reversibility of c
...

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