ISO 16063-21:2003

Methods for the calibration of vibration and shock transducers - Part 21: Vibration calibration by comparison to a reference transducer

ISO 16063-21:2003 describes the calibration of rectilinear vibration transducers by comparison. Although it mainly describes calibration using direct comparison to a standard calibrated by primary methods, the methods described can be applied between other levels in the calibration hierarchy. ISO 16063-21:2003 specifies procedures for performing calibrations of rectilinear vibration transducers by comparison in the frequency range from 0,4 Hz to 10 kHz. It is primarily intended for those who are required to meet ISO standardized methods for the measurement of vibration under laboratory conditions, where the uncertainty of measurement is relatively small. It can also be used under field conditions, where the uncertainty of measurement may be relatively large. From knowledge of all significant sources of uncertainty affecting the calibration, the expanded uncertainty can be evaluated using the methods given in ISO 16063-21. It also covers the assessment of uncertainties for calibrations performed using a check standard. This document is applicable to calibrations outside the frequency range from 0,4 Hz to 10 kHz, considering the additional facts described in 4.3. Systems have been demonstrated to cover the range from 0,01 Hz to 30 kHz.

Méthodes pour l'étalonnage des transducteurs de vibrations et de chocs — Partie 21: Étalonnage de vibrations par comparaison à un transducteur de référence

General Information

• Status: Published
• Publication Date: 18-Aug-2003
• ICS: 17.160 - Vibrations, shock and vibration measurements
• Technical Committee: ISO/TC 108 - Mechanical vibration, shock and condition monitoring
• Drafting Committee: ISO/TC 108/WG 34 - Calibration of vibration and shock transducers
• Current Stage: 9093 - International Standard confirmed
• Start Date: 23-Jan-2025
• Completion Date: 13-Dec-2025

Relations

• Consolidated By: ISO 7376:2009 - Anaesthetic and respiratory equipment - Laryngoscopes for tracheal intubation
• Effective Date: 06-Jun-2022
• Amended By: ISO 16063-21:2003/Amd 2:2024 - Methods for the calibration of vibration and shock transducers - Part 21: Vibration calibration by comparison to a reference transducer - Amendment 2
• Effective Date: 17-Sep-2022
• Amended By: ISO 16063-21:2003/Amd 1:2016 - Methods for the calibration of vibration and shock transducers - Part 21: Vibration calibration by comparison to a reference transducer - Amendment 1
• Effective Date: 21-Aug-2021
• Revises: ISO 5347-3:1993 - Methods for the calibration of vibration and shock pick-ups - Part 3: Secondary vibration calibration
• Effective Date: 15-Apr-2008

Overview - ISO 16063-21:2003 (Vibration calibration by comparison to a reference transducer)

ISO 16063-21:2003 specifies methods for the calibration of rectilinear vibration transducers by comparison to a reference (secondary) transducer. The standard is intended mainly for laboratory calibrations but is also applicable in the field. It covers procedures to determine the magnitude and, optionally, the phase shift of the complex sensitivity of vibration transducers in the nominal frequency range 0.4 Hz to 10 kHz (systems have been demonstrated from 0.01 Hz to 30 kHz). The document emphasizes traceability, documented measurement uncertainty, and practical calibration arrangements (back-to-back or in-line mounting).

Key topics and technical requirements

• Scope and transducer type: Applies to rectilinear vibration transducers (with or without signal conditioning).
• Calibration method: Direct comparison to a reference transducer; methods may be applied between other levels in the calibration hierarchy (primary → reference → working/check standards).
• Frequency & dynamic ranges: Nominal 0.4 Hz–10 kHz (with notes on optional ranges and single-point calibrations); frequency-dependent dynamic ranges and practical limits (noise floor, exciter distortion).
• Uncertainty of measurement: Mandatory uncertainty budgets per Annex A; examples provided for two system classes (Example 1 - well-controlled lab; Example 2 - less stringent conditions). Representative expanded uncertainties (coverage factor k=2) from the standard:
  • Accelerometers 0.4 Hz–1 kHz: Example 1: 1%, Example 2: 3% (magnitude)
  • Accelerometers 1 kHz–2 kHz: 2% / 5%
  • Accelerometers 2 kHz–10 kHz: 3% / 10%
  • Displacement/velocity transducers 20 Hz–1 kHz: 4% / 6%
  • Phase shift at reference conditions: 1° / 3° (Example 1 / 2)
• Apparatus & environment: Reference transducer preferably calibrated with amplifier; recommended room temperature and humidity tolerances (Example 1: 23 ±5 °C, humidity ≤75%; Example 2: 23 ±10 °C, humidity ≤90%).
• Documentation and reporting: Procedures for measurement, expression of results, and reporting are specified; Annexes provide uncertainty calculation examples, definitions of amplitude/phase sign, and nomograms.

Applications and practical value

• Provides a standardized, traceable method for accelerometer calibration, vibration sensor verification, and transfer of calibration between standards.
• Used by metrology laboratories, calibration service providers, R&D test labs, and maintenance/quality engineers who require documented measurement traceability and uncertainty evaluation.
• Applicable for laboratory-grade calibrations where low uncertainty is required and for field calibrations using portable check standards (with expected larger uncertainties).

Related standards

• ISO 16063 series (relevant parts): Part 1 (Basic concepts), Part 11 (Primary calibration by laser interferometry), Part 12 (Reciprocity), Part 13 (Primary shock calibration), Part 22 (Shock calibration by comparison).
• Guide to the expression of uncertainty in measurement (GUM) - referenced for uncertainty methods.

Keywords: ISO 16063-21:2003, vibration calibration, reference transducer, calibration by comparison, accelerometer calibration, measurement uncertainty, vibration transducers, rectilinear vibration.

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 16063-21
First edition
2003-08-15
Methods for the calibration of vibration
and shock transducers —
Part 21:
Vibration calibration by comparison to a
reference transducer
Méthodes pour l'étalonnage des transducteurs de vibrations et de
chocs —
Partie 21: Étalonnage de vibrations par comparaison à un transducteur
de référence
Reference number
©
ISO 2003
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©  ISO 2003
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ii © ISO 2003 — All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Uncertainty of measurement. 2
4 Requirements for apparatus and environmental conditions. 3
4.1 General. 3
4.2 Environmental conditions. 3
4.3 Reference transducer . 3
4.4 Vibration generation equipment. 4
4.5 Voltage measuring instrumentation. 6
4.6 Distortion measuring instrumentation. 6
4.7 Oscilloscope. 7
4.8 Phase shift measuring instrumentation . 7
5 Calibration. 7
5.1 Preferred amplitudes and frequencies . 7
5.2 Measurement requirements . 7
5.3 Calibration procedure. 8
6 Expression of results. 8
7 Reporting the calibration results. 9
Annex A (normative) Expression of uncertainty of measurement in calibration . 11
Annex B (normative) Definitions of amplitude sign and phase shift between mechanical motion
and vibration transducer electrical output. 20
Annex C (informative) Nomogram for conversion between acceleration, velocity and
displacement . 22
Annex D (informative) Example of uncertainty calculation. 24
Bibliography . 29

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 16063-21 was prepared by Technical Committee ISO/TC 108, Mechanical vibration and shock,
Subcommittee SC 3, Use and calibration of vibration and shock measuring instruments.
This first edition of ISO 16063-21 cancels and replaces ISO 5347-3:1993, which has been technically revised.
ISO 16063 consists of the following parts, under the general title Methods for the calibration of vibration and
shock transducers:
— Part 1: Basic concepts
— Part 11: Primary vibration calibration by laser interferometry
— Part 12: Primary vibration calibration by the reciprocity method
— Part 13: Primary shock calibration using laser interferometry
— Part 21: Vibration calibration by comparison to a reference transducer
— Part 22: Shock calibration by comparison to an accelerometer, velocity or force transducer
iv © ISO 2003 — All rights reserved

Introduction
The ISO 16063 series of standards is concerned with methods for the calibration of vibration and shock
transducers under both standard laboratory conditions and in the field.
As such, the intended user group of this part of ISO 16063 is wide, ranging from metrologists in mechanical
vibration to technicians evaluating the vibration characteristics of a machine or structure, or human exposure
to vibration. The key to the application of this part of ISO 16063 is in the careful detailed specification and
evaluation of measurement uncertainty, i.e. the error budget and computation of expanded uncertainty
associated with the measurement of vibration.
This part of ISO 16063 is particularly intended for those engaged in vibration measurements requiring
traceability to primary national or international standards through a secondary, reference, working or check
standard (portable calibrator intended for field use) as defined in the International vocabulary of basic and
general terms in metrology (VIM). The specifications for the instrumentation and the procedures given are
intended to be used for calibration of rectilinear vibration transducers (with or without signal conditioning) to
obtain the magnitude and (optionally) phase shift of the complex sensitivity at frequencies in the range of
0,4 Hz to 10 kHz.
INTERNATIONAL STANDARD ISO 16063-21:2003(E)

Methods for the calibration of vibration and shock
transducers —
Part 21:
Vibration calibration by comparison to a reference transducer
1 Scope
This part of ISO 16063 describes the calibration of rectilinear vibration transducers by comparison. Although it
mainly describes calibration using direct comparison to a standard calibrated by primary methods, the
methods described can be applied between other levels in the calibration hierarchy.
This part of ISO 16063 specifies procedures for performing calibrations of rectilinear vibration transducers by
comparison in the frequency range from 0,4 Hz to 10 kHz. It is primarily intended for those who are required to
meet ISO standardized methods for the measurement of vibration under laboratory conditions, where the
uncertainty of measurement is relatively small. It can also be used under field conditions, where the
uncertainty of measurement may be relatively large.
From knowledge of all significant sources of uncertainty affecting the calibration, the expanded uncertainty
can be evaluated using the methods given in this part of ISO 16063. It also covers the assessment of
uncertainties for calibrations performed using a check standard.
Comparison calibrations made in accordance with this part of ISO 16063 need to allow for the environmental
conditions of the reference transducer calibration.
NOTE Transducer calibrations made under extreme environmental conditions are covered by other International
Standards.
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 266, Acoustics — Preferred frequencies
ISO 2041:1990, Vibration and shock — Vocabulary
ISO 16063-1:1998, Methods for the calibration of vibration and shock transducers — Part 1: Basic concepts
ISO 16063-11:1999, Methods for the calibration of vibration and shock transducers — Part 11: Primary
vibration calibration by laser interferometry
Guide to the expression of uncertainty in measurement (GUM). BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML,
1)
1) Corrected and reprinted in 1995.
3 Uncertainty of measurement
3.1 All users of this part of ISO 16063 are expected to make uncertainty budgets according to Annex A to
document their level of uncertainty (see example in Annex D).
To help set up systems fulfilling different requirements two examples are given. System requirements for each
are set up and the attainable uncertainty is given. Example 1 is typical for calibrations under well-controlled
laboratory conditions with the requirement to obtain a high accuracy. Example 2 is typical for calibrations
where less than the highest accuracy can be accepted or where calibration conditions are such that only less
narrow tolerances can be maintained. These two examples will be used throughout this part of ISO 16063.
a) Example 1
The reference transducer is calibrated by primary means and documented uncertainty. The calibration
may be transferred to a working standard for practical reasons. The temperature and other conditions are
kept within narrow limits during the comparison calibration as indicated in the appropriate clauses.
b) Example 2
The reference transducer is not calibrated by primary means, but has a traceable calibration, as defined
in VIM (see [2]), with the corresponding uncertainty documented. The calibration may be transferred to a
working standard for practical reasons. The requirements on other parameters and instruments are
indicated in the appropriate clauses.
3.2 For both examples, the minimum calibration requirement for the reference transducer is calibration
under suitable reference conditions (i.e. frequency, amplitude and temperature). Normally the conditions will
be chosen as indicated in ISO 16063-11.
It is applicable for the following parameters:
Frequency range: 20 Hz to 5 000 Hz, optionally 0,4 Hz to 10 000 Hz (see Note 1)
2 2 2 2
Dynamic range: 10 m/s to 1 000 m/s r.m.s., optionally 0,1 m/s to 1 000 m/s
(frequency dependent)
NOTE The indicated frequency ranges are not mandatory and single-point calibrations are also acceptable.
At any given frequency and amplitude of acceleration, velocity or displacement, the dynamic range will be
limited by the noise floor and the amount of distortion produced by the excitation apparatus (if no filtering is
used) or its maximum power. (Techniques are also used to counteract the inherent distortion at large
displacements for spring-controlled exciters by changing the waveform of the input voltage.) Typical maximum
values for electrodynamic vibration exciters designed for the frequency range from 10 Hz to 10 kHz are
2 2
200 m/s to 1000 m/s r.m.s. acceleration, 0,5 m/s to 1 m/s r.m.s. velocity and 5 mm peak displacement. The
lower limits will be set by the noise in the two measurement channels, and by the bandwidth used. Typical
2 2
values used for measurement are 50 m/s to 100 m/s r.m.s. acceleration or 0,1 m/s r.m.s. velocity. For
2 2
calibrators, values between 1 m/s and 10 m/s r.m.s. are normally used. A graph similar to the one shown in
Annex C is useful when considering the ranges covered.
When measurements are performed at the lowest frequencies, the limiting factor is normally displacement. At
2 2
1 Hz, typical values for long-stroke vibrators are 1 m/s to 2 m/s r.m.s. acceleration or 0,1 m/s to 0,3 m/s
r.m.s. velocity.
3.3 The attainable uncertainties (expanded uncertainties calculated using a coverage factor of 2 in
accordance with ISO 16063-1) for the two examples are given in Table 1. In practice, these limits may be
exceeded depending on the uncertainty with which the reference transducer has been calibrated, the
response characteristics of the reference transducer and the transducer to be calibrated, the vibratory
characteristics of the exciter and the instrumentation used in the measurement apparatus. It is the
responsibility of the laboratory or end user to make sure that the reported values of expanded uncertainty are
credible.
2 © ISO 2003 — All rights reserved

Table 1 — Attainable uncertainties of magnitude and phase shift of the complex sensitivity
Parameter Example 1 Example 2
Magnitude
For accelerometers (0,4 Hz to 1 000 Hz) 1 % 3 %
For accelerometers (1 000 Hz to 2 000 Hz) 2 % 5 %
For accelerometers (2 kHz to 10 kHz) 3 % 10 %
For displacement and velocity transducers (20 Hz to 1 000 Hz) 4 % 6 %
a
Phase shift
b
At reference conditions (i.e. the level and frequency at which the 1° 3°
reference transducer was calibrated)
Outside reference conditions 2,5° 5°
a
Phase shift measurement is not mandatory.
b
Recommended reference conditions are as follows (from ISO 16063-11:1999, Clause 2):
 frequency in hertz: 160, 80, 40, 16 or 8 (or angular frequency ω in radians per second: 1000, 500, 250, 100 or 50),
 acceleration in metres per second squared (acceleration amplitude or r.m.s. value): 100, 50, 20, 10, 5, 2 or 1.
NOTE The expanded uncertainties given as examples (e.g. 1 %) are based on concrete uncertainty budgets such
as given in Annex D as an example (resulting expanded uncertainty 0,84 %).

4 Requirements for apparatus and environmental conditions
4.1 General
The examples referred to in this clause are those described in Clause 3.
If the recommended specifications listed below are met for each item, the uncertainties given in Clause 3
should be obtainable over the applicable frequency range depending on the uncertainty with which the
reference transducer has been calibrated, and the response characteristics of the reference transducer and
transducer to be calibrated. Other combinations of requirements can, however, lead to the same uncertainty.
Special instrumentation may be required in order to meet the expanded uncertainties given in Clause 3 at
frequencies less than 1 Hz. It is mandatory to document the expanded uncertainty using the methods of
Annex A.
4.2 Environmental conditions
These shall be the following.
Example 1 Example 2
Room temperature (23 ± 5) °C (23 ± 10) °C
Relative humidity 75 % max. 90 % max.

4.3 Reference transducer
This should preferably be calibrated together with the amplifier.
a) Example 1
The transducer shall be calibrated in accordance with suitable primary methods or by comparison against
a transducer calibrated in accordance with suitable primary methods (see ISO 16063-11 or other parts)
with an expanded uncertainty of 0,5 % (magnitude) and 0,5° (phase shift) at selected reference frequency
and acceleration (the uncertainties are those obtained when calculating expanded uncertainties using a
coverage factor of 2). Higher uncertainty values are accepted at high and low frequencies.
b) Example 2
The transducer shall be calibrated by suitable and known methods with traceability to a primary reference
transducer and an uncertainty of less than 2 % (magnitude) and 2° (phase shift) at selected reference
frequency and acceleration (the uncertainties are those obtained when calculating expanded
uncertainties using a coverage factor of 2). Higher uncertainty values are accepted at high and low
frequencies.
The reference transducer may be of the so-called back-to-back type meant for direct mounting of the
transducer to be calibrated on top of it in a so-called back-to-back configuration (see Figure 1). It may also be
a transducer with normal mounting provisions used underneath a fixture in line with the transducer to be
calibrated. It is not recommended to mount the two transducers side by side as rocking motions will often be
present, causing large errors in many circumstances. For calibrators, the reference transducer may be an
integral part of a moving element.
Subclauses 4.4 to 4.8 specify characteristics of apparatus that contribute to the uncertainty of measurement.
4.4 Vibration generation equipment
This shall fulfil the requirements given in Table 2.
Table 2 — Vibration generation equipment
Parameter Unit Example 1 Example 2
Frequency uncertainty % u 0,1 u 0,2
% of reading over the
Frequency stability 0,1 0,2
measurement period
% of reading over the
Acceleration amplitude stability 0,1 0,3
measurement period
Total harmonic distortion at
% u 5 u 10
frequencies > 20 Hz
Total harmonic distortion over the
% u 10 u 20
whole frequency range
u 10 at f u 1 kHz
Transverse, bending and rocking
%
acceleration
u 30 at f > 1 kHz
Hum and noise ( f W 10 Hz) dB below full output W 50 W 40
Hum and noise ( f < 10 Hz) dB below full output W 20 W 10

The hum and noise will only be important when inside the measurement bandwidth used. For every
combination of frequency, acceleration and load that is used during calibration, the magnitude of the
transverse, bending and rocking accelerations, hum and noise shall be consistent with the uncertainties given
in Clause 3.
Static or dynamic base strain introduced to the transducer from the attachment surfaces shall not unduly
influence the calibration result.
All mounting surfaces between any two transducers compared shall have flatness and roughness
specifications suitable for the purpose. If the highest frequency range is used, strict tolerances are necessary.
The surface on which the transducer is to be mounted shall have a roughness value, expressed as the
arithmetical mean deviation Ra of < 1 µm. The flatness shall be such that the surface is contained between
two parallel planes 5 µm apart, over the area corresponding to the maximum mounting surface of any
4 © ISO 2003 — All rights reserved

transducer to be calibrated. The drilled and tapped hole for connecting the transducer shall have a
perpendicularly tolerance to the surface of < 10 µm, i.e. the centreline of the hole shall be contained in a
cylindrical zone with 10 µm diameter and a height equal to the hole depth.
The mounting surface of the vibration exciter should be perpendicular to the direction of motion. Any deviation
from perpendicularity should be taken into account in the uncertainty budget, see Annex A.

Key
1 exciter 5 reference transducer 8 distortion meter for occasional checks
2 amplifiers 6 transducer to be calibrated 9 oscilloscope for visual inspection (optional)
3 power amplifier 7 voltmeter 10 phase meter (optional)
4 frequency generator and indicator
Figure 1 — Example of a measuring system for vibration calibration by comparison to a
reference transducer
NOTE 1 Multisine, sine or random generators can be used in conjunction with frequency analysers. Typically Fast
Fourier Transform (FFT) analysers are used for random and multisine signals and Single-Sine Correlation or Frequency
Response Analysers (FRA) are used for single-sine signals. The distortion is then normally of no importance. Therefore
analysers are normally preferred instead of broadband r.m.s. voltmeters which, although fundamentally more accurate, are
sensitive to distortion and other signals at frequencies differing from the measurement frequency. Measurement of
coherence can be used to estimate whether or not the signal-to-noise ratio and the linearity of the transducers are within
well-defined limits when spectral averaging is used. With random excitation and 64 averages a minimum coherence limit
of 0,98 will ensure that the errors due to signal-to-noise ratio and linearity are less than 0,9 % for a dual channel
measurement. In rare cases, broadband excitation can, however, create unwanted (transverse) vibration or output signals
at a measuring frequency due to non-linear behaviour of shaker or transducer at other frequencies.
NOTE 2 The items in 4.3 and 4.4 may be integrated into a calibrator.
4.5 Voltage measuring instrumentation
Two alternative set-ups are considered.
a) A single voltmeter measuring true r.m.s. at transducer amplifier output is used. The outputs from the
reference transducer and the transducer to be calibrated are measured consecutively and the reference
transducer output at least twice. This equipment shall fulfil the requirements given in Table 3.
Table 3 — Voltage measuring instrumentation — Single voltmeter
Parameter Unit Example 1 Example 2
Frequency range Hz 1 to 10 000 1 to 10 000
% of reading for max.
Maximum deviation from linearity 0,1 0,3
difference in signal levels
Maximum deviation between two
consecutive reference transducer % 0,1 0,3
measurements
NOTE The last row describes the repeatability of the measurement. This includes more than the voltmeter repeatability but is
treated here as a general requirement.

b) An instrument measuring voltage ratio between transducer amplifier outputs is used. This equipment shall
have the characteristics specified in Table 4.
Table 4 — Voltage measuring instrumentations
Parameter Unit Example 1 Example 2
Frequency range Hz 1 to 10 000 1 to 10 000
Maximum uncertainty % 0,2 0,5
4.6 Distortion measuring instrumentation
Distortion measuring instrumentation (limited use, see Note) capable of measuring total harmonic distortion of
1 % to 10 % shall have the characteristics specified in Table 5.
Table 5 — Distortion measuring instrumentation
Parameter Unit Example 1 Example 2
Frequency range Hz 1 to 50 000 1 to 50 000
Maximum uncertainty % of reading 10 10
NOTE Distortion measurement is only needed for sine calibration and is not included in the standard procedure. It is used to
check the performance of the vibration generating equipment initially and then only with suitable intervals or in case of doubt.
6 © ISO 2003 — All rights reserved

4.7 Oscilloscope
An oscilloscope or similar display may be used for examining the waveforms of the transducer signals.
Its use is strongly recommended but not mandatory.
4.8 Phase shift measuring instrumentation
This equipment shall have the characteristics specified in Table 6.
Table 6 — Phase shift measuring
Parameter Unit Example 1 Example 2
Frequency range Hz 1 to 10 000 1 to 10 000
Maximum uncertainty ° (degree) 0,2 0,5
5 Calibration
5.1 Preferred amplitudes and frequencies
Six frequencies, each with associated acceleration (amplitude or r.m.s. value) and equally covering the
transducer range, should preferably be chosen from the following series.
a) Acceleration (m/s ):
 1, 2, 5, 10 or their multiples of ten.
If broadband signals are used, these values are the total r.m.s. values.
b) Frequency:
 selected from standardized one-third-octave frequency series (see ISO 266).
If broadband signals are used, the desired range should be covered in one or more calibrations.
Values chosen should preferably be the same as those used in the reference transducer calibration. If the
transducer is to be calibrated at frequencies and accelerations other than those at which the reference has
been calibrated, the characteristics of the reference transducer should be assessed at those frequencies and
accelerations. The resulting uncertainty component shall be taken into account in the uncertainty budget (see
Annex A).
5.2 Measurement requirements
When a calibration is to be performed using a new set-up or a new transducer, it is good practice to carry out
the calibration more than once to ensure sufficient repeatability.
It is important to ensure that cable motion and base strain do not appreciably affect the measurement results,
particularly at low frequencies. Altering the attachment of the cable, the mounting of the transducer, or both,
and noting changes in the measurement results or harmonic distortion may be used to evaluate effects due to
these causes. If the measured sensitivity or distortion does not change significantly when compared to the
uncertainty in the calibration, then these influences may be neglected. The mounting conditions of the
transducer should also be repeatable. This can be verified by remounting the transducer several times and
measuring the sensitivity after each successive attachment of the transducer.
If the transducer under test is not being calibrated in combination with an associated signal conditioner or
amplifier, then the gain and frequency response (i.e. magnitude and, if needed, phase shift) of the complex
sensitivity of the signal conditioner or amplifier used with the transducer under test should be determined in a
traceable fashion at all measurement frequencies. The sensitivity and frequency response of the reference
(transducer plus amplifier) shall also be determined in a traceable fashion at all measurement frequencies.
If any variations, significant compared to the desired uncertainty, are found in the above tests, these should be
quantified by making a sufficiently large number of repeated measurements to get a good estimate of the
variance. This shall then be included in the final uncertainty statement. This is especially important if the
measurement is not made at the frequencies and amplitudes at which the reference transducer was calibrated.
5.3 Calibration procedure
The surfaces of the reference transducer (or fixture) and the transducer to be calibrated shall be examined to
verify that they are free from burrs, etc. and that they comply with the manufacturer’s flatness specifications
and the specifications of Clause 4.
Mount the reference transducer (see 4.4) and the transducer to be calibrated back-to-back or in-line on a
fixture on the exciter or on the exciter with integral working reference transducer using the recommended
torque. Below approximately 5 kHz, good fixtures with known characteristics may be used between the
transducers. At higher frequencies, the direct back-to-back configuration or integral working reference
transducer shall be used. An example of a block diagram of a typical laboratory calibration apparatus is shown
in Figure 1. The voltmeter, selector, generator and phase meter are often substituted by a two-channel
instrumentation (e.g. dual-channel analyser with internal generator or voltage ratio meter) with sufficient
accuracy.
Measure the ratio of the two outputs and the relative phase shift, if needed.
Determine the sensitivity at the reference frequency, for accelerometers preferably at 160 Hz (second choice:
2 2
80 Hz), and at the reference acceleration, for accelerometers preferably at 100 m/s (other choices: 10 m/s ,
2 2
20 m/s or 50 m/s ), then determine the sensitivity at other calibration frequencies and accelerations. The
results shall be given in absolute terms and/or as a relative deviation (percentage or decibels) and degrees
deviation from the sensitivity at the reference point.
In the case of stud-mounted transducers, a thin film of light oil, wax or grease should be used between the
mounting surfaces of the transducer(s) and exciter, particularly in the case of calibrations performed at high
frequencies (see ISO 5348 for details).
6 Expression of results
If the reference transducer and the transducer under test respond to the same vibration quantity, calculate the
magnitude S and the phase shift ϕ of the complex sensitivity of the transducer to be calibrated using the
2 2
following formulae:
Magnitude: Phase shift:
X
SS= ϕ=+ϕϕ
21 22,1 1
X
where
S , ϕ are the magnitude and phase shift of the complex sensitivity of the reference transducer;
1 1
X is the output from the reference transducer;
X is the output from the transducer to be calibrated;
ϕ is the phase shift between the outputs from the transducer to be calibrated and the reference
2,1
transducer.
8 © ISO 2003 — All rights reserved

If the two transducers measure different vibration quantities, calculate the sensitivity of the transducer to be
calibrated, using the following formulae.
a) If the magnitude and phase shift of the complex acceleration sensitivity S , ϕ were measured:
a a
Magnitude: Phase:
Sf=π2S 90ϕϕ=− °
va va
Sf=π4 S 180ϕϕ=−°
s a sa
b) If the magnitude and phase shift of the complex velocity sensitivity S , ϕ were measured:
v v
Magnitude: Phase:
Sf=π2S ϕϕ=− 90°
s v sv
where
S , ϕ are the magnitude and phase shift of the complex acceleration sensitivity;
a a
S , ϕ are the magnitude and phase shift of the complex velocity sensitivity;
v v
S , ϕ are the magnitude and phase shift of the complex displacement sensitivity;
s s
f is the frequency of the vibration, in hertz.
The phase shift is undetermined within modulus 180° until definitions of directions for the transducers, motions
and electrical signals are specified (see ISO 16063-1:1998, 3.3, and Annex B for guidance).
For calibrators designed to provide one or more fixed amplitude(s) at one or more frequencies, the sensitivity
of the transducer to be calibrated is obtained by using the specified amplitude A and the measured output X in
the formula
X
S =
A
where A and S must refer to the same vibration quantity.
7 Reporting the calibration results
In addition to the calibration method and instrumentation with calibration due dates, at least the following
conditions and characteristics shall be stated when the calibration results are reported.
a) Ambient conditions, Example 1:
 temperature of the transducer if measured, or
 ambient air temperature and estimated difference from transducer temperature if this is not
measured.
b) Ambient conditions, Example 2:
 estimated transducer temperature.
c) Mounting technique:
 material of mounting surface,
 mounting torque (if stud mounted and optional for Example 2) or adhesive used,
 characteristics of mounting components or adapters (if used),
 oil or grease or wax (if used),
 cable fixing,
 orientation (vertical or horizontal).
d) All amplifier settings (if adjustable) when the transducer is calibrated in combination with a signal
conditioner or amplifier:
 gain,
 cut-off frequencies and slope of filters.
e) Calibration results:
 values of calibration frequencies and vibration amplitudes,
 values of sensitivity (magnitude and phase shift, if measured),
 coherence of the measurement if measured,
 expanded uncertainty of the calibration (calculated in accordance with Annex A).
f) Coverage factor, if different from k = 2 (corresponding to a confidence level of 95 % for a normal
distribution).
10 © ISO 2003 — All rights reserved

Annex A
(normative)
Expression of uncertainty of measurement in calibration
A.1 Calculation of expanded uncertainty of measurement, U
A.1.1 Purpose of U
The uncertainty of measurement in calibration shall be expressed by the "expanded uncertainty" U in
accordance with GUM, based on the approach recommended by the International Committee for Weights and
Measures (CIPM). The purpose of U is to provide an interval y − U to y + U within which the value of Y, the
specific quantity subject to calibration and estimated by y, can be expected to lie with high probability. To
confidently assert that y − U u Y u y + U, the expanded uncertainty U shall be determined as follows.
A.1.2 Corrections
Every effort has to be made to identify each effect that significantly influences the measurement result and to
compensate for such effects by applying the estimated corrections or correction factors.
If an effect influencing the measurement result is appropriately described by a probability distribution
(preferably probability density, see A.1.3) having a significant expected value (in particular for an asymmetrical
distribution), the latter shall be treated as systematic error and compensated by correction.
A.1.3 Standard uncertainty estimation
Each component of uncertainty that contributes to the uncertainty of the measurement shall be represented by
a standard deviation u , termed "standard uncertainty", equal to the positive square root of the variance u .
i i
Some standard uncertainties can be obtained as statistically estimated standard deviations by the statistical
analysis of series of observations (type A evaluation of standard uncertainty). Other standard uncertainties
shall be evaluated as the standard deviation of a probability distribution describing the scientific judgement of
all possible values of the respective quantity (type B evaluation of standard uncertainty). The judgement is
based on all information available about the quantity. In particular, if there is no specific information about the
possible values of a quantity responsible for systematic effects except that these values are within the bounds
b and b , a uniform distribution over the interval [;bb] may be used to represent this information. It has a
− + − +
standard uncertainty b 3 where bb=−b 2 . The expected value is bb+ 2 to be used for
( ) ( )
+− +−
correction in this case.
If an influence quantity can be considered uniformly distributed (rectangular probability density) but is known to
be transformed into the measurement result with a specific non-linear function (e.g. sinusoidal; polynomial of
second or third order), this information shall be taken into account by choosing the associated distribution model.
EXAMPLE The sensitivity S of an accelerometer to sinusoidal accelerations in the nominal measurement direction is
calculated from the output, voltage or charge amplitude xˆ, stimulated by a vibration, acceleration amplitude aˆ, using the
formula Sx=ˆˆ/.a Among the various disturbing effects influencing the measurement result in calibration, there may be a
significant transverse motion component from the vibration exciter, acceleration amplitude aˆ , transformed into an error
T
component e in the output, in conjunction with the accelerometer's transverse sensitivity, S . It is assumed for this
xˆT
T
example that the acceleration to be measured and the transverse acceleration have the same frequency and that there is
no phase angle difference. As the transverse sensitivity is usually sinusoidally dependent on the angle β between the
direction of maximum transverse sensitivity S and the direction of a transverse excitation, the error component can
()
T,max
be expressed by
eS==aˆˆS a cos β
xˆTTTT,maxT,max
If the values of the maximum transverse sensitivity S and the maximum transverse acceleration aˆ are
()T,max ()T,max
known while the angle β is not, it is reasonable to assume a rectangular distribution of β within the interval −π;.π Thus,

the influence quantity, i.e. transverse acceleration, with rectangularly distributed angle β leads to a measurement error
component e whose probability density is described by
xˆT
we =
()
xˆT
e
xˆT
bπ−1

b

− xˆT
bS= aˆ
T,max T,max
(often referred to as arcsin distribution). The associated standard uncertainty is
ue =b 2
( )
ˆ
xT
The expected value Ee is zero in this case. This is the best estimate of the error e .
{ }
ˆ ˆ
xT xT
A.1.4 Combined standard uncertainty
The "combined standard uncertainty" u , as the standard uncertainty of the measurement of Y, shall be
c
determined by combination of the individual standard uncertainties (and covariances as appropriate) using the
law of propagation of uncertainty. Accordingly, the combined standard uncertainty is obtained from
N = 1
NN

∂∂ff∂f
uy=+u x2,uxx (A.1)
() ()
 ()
c∑∑ii∑ j
∂∂xx∂x
iij
ii==11j=i+1
This equation is based on a first-order Taylor series approximation of
Y = f (X , X ,.,X ) (A.2)
1 2 N
where Y is the measurand determined from N input quantities X , X , ., X through a functional relationship f.
1 2 N
An estimate of the measurand Y, denoted by y, is obtained from Equation (A.1) using input estimates x , x , .,
1 2
x for the values of the input quantities. Thus the output estimate, which is the result of measurement, is given
N
by
y = f (x , x ,.,x ) (A.3)
1 2 N
In Equation (A.1), the symbols ∂ f / ∂ x are often referred to as sensitivity coefficients c . They are equal to the
i i
partial derivatives ∂ f / ∂ X evaluated at X = x. The symbol u(x ,x) designates the estimated covariance
i i i i j
associated with x and x .
i j
For the case where no significant correlations are present, Equation (A.1) is reduced to
N

∂ f
uy = u x (A.4)
() ()

c ∑ i
∂ x
i
i = 1
NOTE The first-order Taylor series approximation of Equation (A.2) resulting in Equation (A.1) is only applicable if the
model function f is sufficiently linear with respect to the variation of the input estimates x within the ranges characterized
i
by the uncertainties u(x ). This is not the case in the example given in A.1.3 if the angle β is considered to be an input
i
quantity X . To overcome this obstacle, which similarly exists with other influence quantities acting in measurements within
i
calibrations of vibration and shock transducers, an adequate model has been introduced (see reference [4]). To briefly
12 © ISO 2003 — All rights reserved

specify this model for the example above, a factor (1 −ex/ ˆ) with ex/ ˆ << 1 is introduced, as an input quantity X , into
ˆ ˆ
xT xT i
the functional relationship used for calculating the measurand. Equation (A.2), specially tailored to the example, is reduced
to three input quantities
Y = f (X , X , X )
1 2 3
where
Y is the measurand (sensitivity S);
X is the accelerometer output (voltage or charge amplitude xˆ);
X is the acceleration amplitude;
ˆ
X =−1 ex .
( )
3Txˆ
Thus, the relationship
X
YX=
X
can be established. The first Taylor series approximation can be used now, leading to the relative combined standard
uncertainty
22 2
   
u(y) ux( ) u()x ux()
c1 2 3
=+ +
   

yx x x
12 3
   
if there are no significant correlations.
Using the symbols introduced in the Example, the latter relationship can be written as follows:
22 2
uS() u(xˆˆ) u(a) u(e /xˆ)
    
ˆ
cTx
=+ +
    
Sxˆˆa 1
    
where
ˆˆ
ux()/x is the relative standard uncertainty of the output voltage amplitude measurement;
ˆˆ
ua() a the relative standard uncertainty in acceleration amplitude measurement;
ˆˆ
ue( x) =u (e ) x , with ue( ) =b 2 as explained in the Example.
xxˆˆTT xˆT
Accordingly, further factors whose deviations from the value 1 are similarly expressed by the relative error component of
the respective quantity (e.g. voltage, acceleration or the sensitivity as a whole) might be introduced as input quantities
(X , X , .), allowing the variety of uncertainty sources to be taken into account separately.
4 5
A.1.5 Expanded uncertainty
The "expanded uncertainty" U shall be determined by multiplying u by a coverage factor k:
c
U = ku
c
where a value of k = 2 should preferably be used. If it can be assumed that the possible values of the
calibration result are approximately normally distributed with approximate standard deviation u , the unknown
c
value can be asserted to lie in the interval defined by U with a level of confidence, or probability, of
approximately 95 %.
A.1.6 Reporting the result
When reporting the result of the measurement y, the expanded uncertainty and the value of the coverage
factor k used, if different from k = 2, shall be stated. In addition, the approximate coverage probability or level
of confidence of the interval may be stated.
A.2 Calculation of expanded uncertainties at reference conditions
A.2.1 Calculation of the relative expanded uncertainty U (S) for the sensitivity magnitude
rel
The relative expanded uncertainty of measurement of the magnitude of the complex sensitivity, U (S), for
rel
each of the applied frequencies, accelerations and amplifier gain settings (if an amplifier is part of the
calibrated transducer) is calculated from the following formulae:
US() =ku ()S
rel c,rel
with the coverage factor k = 2 (see A.1.5);
N − 1 N
uS() 1 ∂∂ff∂f
c
uS()== u (S)+2 u(x,x)
c,rel iij
∑∑∑
SS∂∂x x∂x
iij

ii==11ji+
N − 1
N

∂∂ff∂f
=+uS() 2 u (
...