ISO 16063-12:2002

Methods for the calibration of vibration and shock transducers — Part 12: Primary vibration calibration by the reciprocity method

This part of ISO 16063 specifies the instrumentation and procedures to be used for primary calibration of accelerometers using the reciprocity method and the SI system of units. It is applicable to the calibration of rectilinear accelerometers over a frequency range of 40 Hz to 5 kHz and a frequency-dependent amplitude range of 10 m/s2 to 100 m/s 2 and is based on the use of the coil of an electrodynamic vibrator as the reciprocal transducer. Calibration of the sensitivity of a transducer can be obtained using this part of ISO 16063 provided that the signal conditioner or amplifier used with the transducer during calibration has been adequately characterized. In order to achieve these measurement uncertainties, it has been assumed that the transducer has been calibrated in combination with its signal conditioner or amplifier (the combination of which in this part of ISO 16063 is referred to as the accelerometer).

Méthodes pour l'étalonnage des transducteurs de vibrations et de chocs — Partie 12: Étalonnage primaire de vibrations par méthode réciproque

General Information

• Status: Published
• Publication Date: 24-Apr-2002
• 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
• Completion Date: 07-Mar-2023

Relations

• Revises: ISO 5347-20:1997 - Methods for the calibration of vibration and shock pick-ups — Part 20: Primary vibration calibration by the reciprocity method
• Effective Date: 15-Apr-2008

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 16063-12
First edition
2002-04-01


Methods for the calibration of vibration and
shock transducers —
Part 12:
Primary vibration calibration by the
reciprocity method
Méthodes pour l'étalonnage des transducteurs de vibrations et de chocs —
Partie 12: Étalonnage primaire de vibrations par méthode réciproque




Reference number
ISO 16063-12:2002(E)
©
 ISO 2002

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ISO 16063-12:2002(E)
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ISO 16063-12:2002(E)
Contents Page
Foreword.iv
1 Scope .1
2 Normative references.1
3 Uncertainty of measurement .1
4 Symbols.1
5 Requirements for apparatus.2
6 Ambient conditions .4
7 Preferred amplitudes and frequencies.4
8 Procedure .4
9 Computation of sensitivity.6
Annex A (normative) Calculation of uncertainty.10
Annex B (informative) Application of the theory of reciprocity to the calibration of electromechanical
transducers .14
Bibliography.20

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ISO 16063-12:2002(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 3.
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 part of ISO 16063 may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 16063-12 was prepared by Technical Committee ISO/TC 108, Mechanical vibration and shock, Subcommittee
SC 3, Use and calibration of vibration and shock measuring instruments.
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: Secondary shock calibration
Annex A forms a normative part of this part of ISO 16063. Annex B is for information only.
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INTERNATIONAL STANDARD ISO 16063-12:2002(E)

Methods for the calibration of vibration and shock transducers —
Part 12:
Primary vibration calibration by the reciprocity method
1 Scope
This part of ISO 16063 specifies the instrumentation and procedures to be used for primary calibration of
accelerometers using the reciprocity method and the SI system of units.
It is applicable to the calibration of rectilinear accelerometers over a frequency range of 40 Hz to 5 kHz and a
2 2
frequency-dependent amplitude range of 10 m/s to 100 m/s and is based on the use of the coil of an
electrodynamic vibrator as the reciprocal transducer.
Calibration of the sensitivity of a transducer can be obtained using this part of ISO 16063 provided that the signal
conditioner or amplifier used with the transducer during calibration has been adequately characterized. In order to
achieve the uncertainties of measurement given in clause 3, it has been assumed that the transducer has been
calibrated in combination with its signal conditioner or amplifier (the combination of which in this part of ISO 16063
is referred to as the “accelerometer”).
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO 16063. For dated references, subsequent amendments to, or revisions of, any of these publications
do not apply. However, parties to agreements based on this part of ISO 16063 are encouraged to investigate the
possibility of applying the most recent editions of the normative documents indicated below. For undated
references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain
registers of currently valid International Standards.
ISO 266, Acoustics — Preferred frequencies
ISO 16063-1:1998, Methods for the calibration of vibration and shock transducers — Part 1: Basic concepts
3 Uncertainty of measurement

2 2 2 2
At a reference frequency of 160 Hz and a reference amplitude of 100 m/s , 50 m/s , 20 m/s or 10 m/s , the
applicable limits of uncertainty are 0,5 % of the modulus (magnitude) of complex sensitivity and 1° of the argument
(phase shift) of complex sensitivity. Over the full range of amplitudes and frequencies, the limits of uncertainty in
the measured magnitude and phase shift of sensitivity are 1 % and 2°, respectively.
All users of this part of ISO 16063 are expected to make uncertainty budgets according to annex A to document the
uncertainty of measurement.
The uncertainty of measurement is expressed as the expanded measurement uncertainty in accordance with
ISO 16063-1 (referred to here as “uncertainty”).
4 Symbols
A general list of symbols used in this part of ISO 16063 is contained in Table 1. Specific symbols used in formulae
are defined following the formulae in which they appear.
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ISO 16063-12:2002(E)
Table 1 — General symbols
Symbol Definition Unit
f
frequency of vibration Hz
n indices of test masses (n = 0 indicates no test mass)

m mass of the test mass number n kg
n
u
complex voltage V
U complex voltage ratio
Y complex electrical admittance S
R electrical resistance
Ω
complex intercept of least-squares fit
α kg⋅Ω
β complex slope of least-squares fit Ω
–2
S
complex sensitivity of the calibrated accelerometer V/(ms )
a
–2
|S | modulus (magnitude) of S
V/(ms )
a a
ϕ argument (phase shift) of S
degree
a a
Re real part of a complex quantity
Im
imaginary part of a complex quantity
| | modulus or absolute value of a complex quantity
arg argument of a complex quantity
5 Requirements for apparatus
5.1 General
The case of the transducer shall be structurally rigid over the frequency range of interest. The sensitivity to base
strain and transverse motion and the stability of the accelerometer (transducer in combination with the signal
conditioner or amplifier) shall be included in the calculation of the expanded uncertainties in determining the
modulus and argument of complex sensitivity (see annex A).
5.2 Frequency generator and indicator or counter
Use equipment having the following characteristics:
a) maximum uncertainty in frequency: 0,01 %;
b) change in frequency: less than 0,01 % over each measurement period;
c) change in amplitude: less than 0,01 % over each measurement period.
5.3 Power amplifier/vibrator combination
Use equipment having the following characteristics for all measurement conditions:
a) maximum total harmonic distortion: 2 %;
b) transverse, bending and rocking acceleration: commensurate with the uncertainty of the measured sensitivity
(typically <10 % of the acceleration in the intended direction over the frequency range of interest);
c) minimum ratio of signal to noise at the output of the accelerometer: 30 dB;
d) change in acceleration amplitude: less than 0,05 % over each measurement period.
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ISO 16063-12:2002(E)
5.4 Seismic block for vibrator
The vibrator shall be mounted on a massive rigid seismic block so as to minimize the reaction of the vibrator
support structure to the motion of the vibrator from significantly affecting the uncertainty in the calibration results.
The mass of the seismic block should be at least 2 000 times that of the moving element of the vibrator. Examples
of seismic blocks suitable for this use include granite blocks or steel honeycomb optical tables. The seismic block
should be vibration isolated with vertical and horizontal suspension resonances of less than 2 Hz if significant
seismic vibration exists in the calibration environment.
5.5 Instrumentation for complex voltage ratio measurements
Use equipment having the following characteristics:
a) frequency range: 40 Hz to 5 kHz;
b) maximum uncertainty in the modulus (magnitude) of complex voltage ratio: 0,1 %;
c) maximum uncertainty in the argument of complex voltage ratio:  0,1°.
5.6 Resistor
The resistor shall have a maximum uncertainty in the determination of its resistance of 0,05 % over the calibration
frequency range and the range of power dissipated.
Ensure that the value of the impedance of the standard resistor used to determine current does not vary
appreciably due to inductive and thermal effects.
5.7 Set of test masses
The test masses shall
a) cover a range of at least five approximately equal intervals, with the largest test mass between approximately
0,5 to 1 times the mass of the moving element of the vibrator, and
b) have a maximum uncertainty in the determination of mass of 0,05 %.
It is recommended that the shape of the test masses be similar to that of a cube or cylinder with a length-to-width
ratio of approximately one. The maximum frequency at which the test mass behaves as a rigid body can then be
estimated by use of the formula: c/(2L) where c is the speed of sound in the material of the test mass and L is its
length. The surface finish specifications and the machining tolerances of the mounting hardware of the test masses
should meet or exceed the requirements specified for mounting the transducer being calibrated. This is particularly
critical if calibrations are performed at high frequencies. The test masses should be machined from a relatively stiff
material such as tungsten carbide to maximize the frequencies of the natural resonances occurring in them.
In practice, the number and size of the test masses selected will be a compromise between reducing the statistical
uncertainty versus increasing the measurement uncertainty due to thermal effects occurring in the drive coil as a
result of making a relatively large number of measurements with large differences in measured electrical
admittance.
5.8 Distortion-measuring instrumentation
Use equipment capable of measuring a total harmonic distortion of 0,01 % to 5 % and having the following
characteristics:
a) frequency range: 40 Hz to 5 kHz;
b) maximum uncertainty: 10 % of the measured value of distortion.
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ISO 16063-12:2002(E)
5.9 Oscilloscope
While an oscilloscope is useful for examining the waveforms of the accelerometer and electrodynamic moving coil,
its use is not mandatory.
5.10 Air-handling equipment
This shall be capable of maintaining the ambient conditions within the requirements specified in clause 6.
6 Ambient conditions
Calibrations shall be carried out under the following ambient conditions:
a) room temperature: (23 ± 3) °C;
b) maximum relative humidity: 75 %.
7 Preferred amplitudes and frequencies
The amplitudes and frequencies of acceleration used during calibration should be chosen from the following series:
2 2 2 2
a) acceleration: 10 m/s , 20 m/s , 50 m/s , 100 m/s ;
2 2 2 2
b) reference acceleration: 100 m/s , 50 m/s , 20 m/s or 10 m/s ;
c) frequency: selected from the standardized one-third-octave frequencies given in ISO 266 from
40 Hz to 5 kHz;
d) reference frequency: 160 Hz.
Calibrations performed at large acceleration amplitudes could have relatively large uncertainties due to thermal
effects occurring in the drive coil.
8 Procedure
8.1 General
Calibration of electromechanical transducers by reciprocity utilizes the linear bilateral relationship between the
electrical and mechanical terminals of the transducers being calibrated. Three transducers are required in order to
perform an absolute calibration of two of the transducers. One transducer is used only as a vibration sensor, one is
used only as a vibration source, and one is used reciprocally as both a vibration sensor and a vibration source
(generator). In principle, the electromechanical coupling of the reciprocal transducer can be either electrodynamic
or piezoelectric. However, in practice, electrodynamic transducers are much more widely used as the reciprocal
transducer in vibration calibrations by reciprocity. Therefore, the methods described in this part of ISO 16063 are
based on the use of the coil of an electrodynamic vibrator as the reciprocal transducer with the coil located in close
proximity to the transducer being calibrated.
The transducer that is used only as a vibration source may be either a second vibrator mechanically coupled to the
moving element containing the reciprocal transducer and the transducer of the accelerometer, or a second coil
attached to the same moving element. (See the bibliography for references to practical realizations of systems
utilizing either a second vibrator or a second coil.) If a second vibrator is used, it may be relatively rigidly coupled to
the moving element via a short threaded stud provided that the reciprocal transducer is otherwise adequately
isolated from the second vibrator and that the rectilinear motion of the moving element has not been affected by the
presence of the secondary vibration source. Caution should be exercised if the secondary vibration source is
electrodynamic so as to prevent mutual coupling between the two electrodynamic elements from unduly affecting
the uncertainty in the calibration results. Figures 1 and 2 contain block diagrams of one possible realization of a
calibration system based on reciprocity, with the transducer of the accelerometer shown mounted inside the
vibrator with the reciprocal transducer and with the second vibration source shown as a second vibrator.
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ISO 16063-12:2002(E)
The calibration shall be performed at frequencies well below the resonance frequencies inherent in the moving
element containing the reciprocal transducer and supporting the transducer being calibrated. Transverse and axial
resonances may be determined using a triaxial accelerometer with sufficiently high resonance frequencies.
Departures from rigid-body motion by the moving element may be determined from relative measurements made on
the top (mounting) surface of the moving element. Ideally, the transverse and axial resonances should be determined
with the triaxial accelerometer mounted on a test fixture with the sum of the masses of the accelerometer and the test
fixture equal to that of the largest test mass used to determine Y – Y . A typical upper frequency limit of calibration
n 0
would be 0,25 times the resonance frequency of the moving element when loaded with the transducer under test and
the largest test mass used to determine Y – Y . Attempts to perform calibrations at frequencies where minor
n 0
resonances occur should be avoided. These minor resonances, which include suspension and structural resonances,
are not considered part of the natural resonance(s) inherent in the moving element.
Obtain measurement results with the reciprocal transducer used as a vibration source (driver) and as a vibration
sensor (velocity coil) (see 8.2.1 and 8.2.2, respectively). The first case requires that measurements be performed
with and without a test mass attached to the moving element. It is important that these measurements be
performed under uniform thermal conditions with the coil of the reciprocal transducer in the same static position in
the magnetic gap. A typical upper limit in variability in thermal conditions would be between 1 ºC and 2 ºC. An
offset in the static position of the reciprocal transducer may be corrected by applying a d.c. bias voltage across the
reciprocal coil. Ideally, the instrumentation should be grounded at one point only to avoid ground loops. All voltages
measured across the reciprocal coil and standard resistor should be measured as close to the voltage source as
possible to minimize induced noise. The standard resistor may either be removed or shorted during the voltage
ratio measurements of U (see 8.2.2). However, if the standard resistor is shorted, it should be verified that the
v
uncertainty is not degraded at high frequencies due to inductive effects.
After establishing the instrumentation settings, perform a calibration at 160 Hz and the reference amplitude, and then
perform calibrations at the other selected frequencies and acceleration amplitudes. The measurement results can then
be expressed as the modulus (magnitude) of complex sensitivity, the argument (phase shift) of complex sensitivity, or
both. For every combination of frequency and acceleration, the distortion, transverse motion (bending and rocking
acceleration), hum and noise shall be appropriate to the uncertainties given in clause 3. During the calibration itself, all
instruments not necessary for the calibration shall be disconnected from the measurement apparatus.
8.2 Experimental
8.2.1 Experiment 1: Measurement of the complex electrical admittance Y (complex ratio of driving coil current
to accelerometer open-circuit output voltage)
With the reciprocal electrodynamic moving coil operating as a driving coil (vibration source), measure the complex
electrical admittance by dividing the complex voltage ratio (U ) by the standard resistance (R) where U is the
d d
voltage drop (u) across the standard resistance divided by the open-circuit voltage at the output of the
r
accelerometer (u ), i.e. (see Figure 1):
a1
YU==R u u 1R
( )( )
dra1
Perform a series of these measurements with and without test masses added to the moving element. In the
equations that follow, the complex electrical admittance without any mass added to the moving element and the

complex electrical admittance with test mass m added to the moving element have been denoted Y and Y ,
n 0 n
respectively.
When measuring U , it is critical to have the accelerometer and the standard resistor at the same ground potential.
d
Experiment 1 shall be performed at all the acceleration amplitudes used during calibration.
8.2.2 Experiment 2: Measurement of the complex open-circuit voltage ratio U (complex open-circuit voltage
v
ratio of the output of the accelerometer to the output of the velocity coil)
With the reciprocal electrodynamic moving coil operating as a velocity coil (vibration sensor), measure the complex
open-circuit voltage ratio of the output of the accelerometer (u ) to the output of the moving coil (u ) using an
a2 c
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ISO 16063-12:2002(E)
external vibration source or a secondary driving coil on the moving element to drive the moving element (see
Figure 2). This ratio (U = u /u ) is determined without any mass added to the moving element.
v a2 c
When measuring U , it is critical to have the accelerometer and the reciprocal coil at the same ground potential.
v
9 Computation of sensitivity
See equations (1) to (10) and annex B.
By means of a least-squares fit of the function
m
n
Fm(,Y,Y) = (1)
nn 0
YY−
n 0
obtain the complex intercept and slope of F(m ,Y ,Y ) at each calibration frequency and amplitude using the
n n 0
measured values obtained for m , Y and Y . This fit may be obtained using either uniform (w = 1) or non-uniform
n n 0 n
statistical weighting from the following formulae:
222
 
wm wm
22 2
nn n n
∑∑wm Re –∑wm ∑Re
()nn nn
 
YY––YY
nn00
 
Re α = (2)
2
222 2

∑∑w w m – ∑w m
() ( )
nnn nn


222
 
wm w m
22 2
nn nn
∑∑wm wmIIm–∑ ∑m
()nn nn
 
YY––YY
nn00
 
Imα = (3)
2
222 2

∑∑wwm –∑wm
() ( )
nnn nn


22 2
 
wm wm
22
nn nn
∑∑w wRe –∑m ∑Re
nnn
 
YY––YY
nn00
 
Re β = (4)
2
2222
∑∑wwm –∑wm
() ( )
nnn nn


22 2
 
wm wm
2
2 nn nn
∑∑IIm– ∑wm ∑m
w
nnn
 
––
YY YY
nn00
 
Im β = (5)
2
2222
∑∑wwm – w∑ m
() ( )
nnn nn


where
α is the complex intercept, in kilogram ohms, of the function F(m ,Y ,Y );
n n 0
β is the complex slope, in ohms, of the function F(m ,Y ,Y );
n n 0
n is the index corresponding to the test mass m ;
n
w is the statistical weighting factor applied to the measurement using the test mass m ;
n n
m is the test mass, in kilograms, added;
n
Y is the electrical admittance, in siemens, measured with test mass m added to the moving element;
n n
Y is the electrical admittance, in siemens, measured without a test mass attached to the moving element.
0
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ISO 16063-12:2002(E)
NOTE Depending upon how the accelerometer is being calibrated, it may not be necessary to compute the slope, and it
may not be necessary to compute the real and the imaginary parts of the intercept but rather only the magnitude; see equations
(8) to (10) [1].
The modulus and argument of the complex sensitivity of the accelerometer can then be obtained as a function of
frequency from the following formulations.
In the case of an accelerometer that has a standard reference transducer permanently mounted on the moving
element of the vibrator for the purpose of calibrating other transducers by comparison, the sensitivity varies with the
mechanical impedance loading the moving element and is determined from the following equations:

α
1V
U
v
=   (6)
S 
a
2
j2 πfY1– β –Y
()
t0 m/s


α
1
U
v
ϕ = arg  deg (7)

a
j2πfY1– β –Y
()
t0

where
|S | is the modulus (magnitude) of the complex sensitivity, in volts per metre per second squared, of the
a
accelerometer at frequency f ;
ϕ is the argument (phase shift) of the complex sensitivity of the accelerometer, in degrees, at frequency f ;
a
2
j is the imaginary unit, j = –1;
f is the frequency, in hertz;
U is the complex open-circuit voltage ratio measured at frequency f with the reciprocal transducer operating
v
as a velocity coil;
α is the complex intercept, in kilogram ohms, of the function F(m ,Y ,Y ) at frequency f ;
n n 0
β is the complex slope, in ohms, of the function F(m ,Y ,Y ) at frequency f ;
n n 0
Y is the electrical admittance, in siemens, at frequency f with a particular transducer added to the moving

t
element of the vibrator;
Y is the electrical admittance, in siemens, at frequency f without any added mass attached to the moving
0
element of the vibrator.
In the case of an accelerometer which has a standard transducer that is removed from the moving element, the
sensitivity is determined from the following equations:
α V
U
v
=  (8)
S
a
2
j2π f
m/s
α
U
v
ϕ = arg deg (9)
a
j2π f
where the symbols are as defined for equations (6) and (7).
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ISO 16063-12:2002(E)
At sufficiently low frequencies (typically for frequencies less than 1 kHz), β is approximately 0 Ω, arg (U ) is
v
approximately 90°, and arg (U ) is approximately 0°. When these conditions are satisfied, the modulus of complex
d
sensitivity of the accelerometer reduces to:
α
U V
v
=  (10)
S
a
2
2π f
m/s
where
|U | is the modulus (magnitude) of the complex open-circuit voltage ratio measured at frequency f with the
v
reciprocal transducer operating as a velocity coil;
|α| is the modulus (magnitude) of the complex intercept, in kilogram ohms, of the function F(m ,Y ,Y ) at
n n 0
frequency f ;
and the other symbols are as defined for equations (6) and (7).
In cases for which equation (10) is applicable, only the modulus (magnitude) of the complex voltage ratios needs to
be determined and the modulus of a can be determined from a least-squares fit of F(m ,Y ,Y ) using the moduli of
n n 0
differences in complex admittance.
When the calibration results are reported, the total calibration uncertainty and the corresponding coverage factor
shall be calculated according to annex A using a coverage factor k = 2.

Key
1 Frequency generator 7 Distortion analyser
2 Power amplifier 8 Vibrator with reciprocal transducer
3 Frequency counter 9 Transducer
4 Voltage ratio instrumentation 10 Standard resistor
5 Oscilloscope (optional) 11 Test mass
6 Signal conditioner or charge amplifier
Figure 1 — Block diagram of the measuring system for experiment 1 with the reciprocal transducer used as
a vibration source
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ISO 16063-12:2002(E)

Key
1 Frequency generator
2 Power amplifier
3 Frequency counter
4 Voltage ratio instrumentation
5 Oscilloscope (optional)
6 Signal conditioner or charge amplifier
7 Distortion analyser
8 Vibrator with reciprocal transducer
9 Transducer
10 Secondary vibration source
Figure 2 — Block diagram of the measuring system for experiment 2 with the reciprocal transducer used as
a vibration sensor
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ISO 16063-12:2002(E)
Annex A
(normative)

Calculation of uncertainty
A.1 Calculation of the expanded uncertainty in the measurement of the modulus
(magnitude) of complex sensitivity, and of the expanded uncertainty in the measurement
of the argument (phase shift) of complex sensitivity for the frequencies, amplitudes and
amplifier settings used at the time of calibration
A.1.1 Calculation of U(|S|)
The expanded uncertainty, U(|S|), in the measurement of the modulus (magnitude) of the complex sensitivity for the
frequencies, amplitudes and amplifier settings used at the time of calibration is calculated in accordance with
annex A of ISO 16063-1:1998 from the f
...