ISO 7626-1:2011

INTERNATIONAL ISO
STANDARD 7626-1
Second edition
2011-07-15
Mechanical vibration and shock —
Experimental determination of
mechanical mobility —
Part 1:
Basic terms and definitions, and
transducer specifications
Vibrations et chocs mécaniques — Détermination expérimentale de la
mobilité mécanique —
Partie 1: Termes et définitions fondamentaux et spécification des
transducteurs
Reference number
©
ISO 2011
©  ISO 2011
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Published in Switzerland
ii © ISO 2011 – All rights reserved

Contents Page
Foreword . iv
1  Scope . 1
2  Normative references . 1
3  Terms, definitions, and symbols . 2
3.1  Terms and definitions . 2
3.2  Symbols . 8
4  Fundamentals and general relationships . 8
5  Basic requirements for force and motion measurement transducers . 9
5.1  General . 9
5.2  Requirements for motion measurement transducers . 9
5.3  Requirements for force measurement transducers . 10
5.4  Requirements for impedance heads and attachments to the structure under test . 10
6  Calibration . 11
6.1  General . 11
6.2  Operational calibrations . 11
6.3  Basic and supplementary transducer calibrations . 11
7  Basic piezoelectric transducer calibrations . 12
7.1  General . 12
7.2  Sensitivity . 12
7.3  Frequency response . 14
7.4  Accelerometer transverse sensitivity . 15
7.5  Mass . 15
7.6  Dimensions . 15
7.7  Electrical impedance . 15
7.8  Polarity. 16
8  Supplementary calibrations . 16
8.1  General . 16
8.2  Linearity . 16
8.3  Effective end mass of force transducers and impedance heads . 17
8.4  Compliance of impedance heads . 17
8.5  Supplementary calibrations necessitated by environmental and secondary effects . 17
9  Presentation of data . 19
9.1  General . 19
9.2  Logarithmic plotting . 19
9.3  Alternative plotting methods . 19
Annex A (informative) Relationship between mechanical impedance, mobility and modal analysis . 23
Annex B (informative) Mobility as a frequency-response function . 26
Annex C (informative) Determination of impedance head attachment compliance and damping . 28
Bibliography . 30

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 7626-1 was prepared by Technical Committee ISO/TC 108, Mechanical vibration, shock and condition
monitoring.
This second edition cancels and replaces the first edition (ISO 7626-1:1986), which has been technically
revised.
ISO 7626 consists of the following parts, under the general title Mechanical vibration and shock —
Experimental determination of mechanical mobility:
 Part 1: Basic terms and definitions, and transducer specifications
 Part 2: Measurements using single-point translation excitation with an attached vibration exciter
 Part 5: Measurements using impact excitation with an exciter which is not attached to the structure

iv © ISO 2011 – All rights reserved

INTERNATIONAL STANDARD ISO 7626-1:2011(E)

Mechanical vibration and shock — Experimental determination
of mechanical mobility —
Part 1:
Basic terms and definitions, and transducer specifications
1 Scope
This part of ISO 7626 defines basic terms and specifies the calibration tests, environmental tests and physical
measurements necessary to determine the suitability of impedance heads, force transducers and motion
response transducers for use in measuring mechanical mobility. Primarily, it provides guidelines for the
selection, calibration and evaluation of the transducers and instruments for their suitability in making mobility
measurements. Procedures for carrying out mobility measurements in various circumstances are dealt with in
subsequent parts of this International Standard.
This part of ISO 7626 is limited to information which is basic to various types of driving-point and transfer
mobility, accelerance and dynamic compliance measurements. Measurements of the blocked impedance are
not dealt with.
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 2041:2009, Mechanical vibration,shock and condition monitoring — Vocabulary
ISO 5347 (all parts), Methods for the calibration of vibration and shock pick-ups
ISO 16063 (all parts), Methods for the calibration of vibration and shock transducers
IEC 60263, Scales and sizes for plotting frequency characteristics and polar diagrams
3 Terms, definitions, and symbols
3.1 Terms and definitions
For the purpose of this document, the terms and definitions given in ISO 2041 and the following apply.
NOTE As this part of ISO 7626 deals with mechanical mobility, the notes to the definitions below provide more detail
than is given in ISO 2041.
3.1.1
frequency-response function
frequency-dependent ratio of the motion-response Fourier transform to the Fourier transform of the excitation
force of a linear system
NOTE 1 Excitation can be harmonic, random or transient functions of time. The frequency-response function does not
depend on the type of excitation function if the tested structure can be considered as a linear system in a certain range of
the excitation or response. In such a case, the test results obtained with one type of excitation can be used for estimating
the response of the system to any other type of excitation. Phasors and their equivalents for random and transient
excitation are discussed in Annex B.
NOTE 2 Linearity of the system is a condition which, in practice, is met only approximately, depending on the type of
system and on the magnitude of the input. Care has to be taken to avoid non-linear effects, particularly when applying
impulse excitation. Structures which are known to be non-linear (e.g. certain riveted structures) should not be tested with
impulse excitation and great care is required when using random excitation for testing such structures.
NOTE 3 Motion may be expressed in terms of velocity, acceleration or displacement; the corresponding frequency-
response function designations are mobility (sometimes called mechanical admittance), accelerance (sometimes
unfortunately called inertance; this term should be avoided because it is in conflict with the common definition of acoustic
inertance and also contrary to the implication carried by the term inertance) and dynamic compliance (sometimes called
receptance), respectively. These are summarized in Table 1. Each of these frequency-response functions is the phasor of
the motion response at a point on a structure due to a unit force (or moment) excitation. The magnitude and the phase of
these functions are frequency dependent. Typical magnitude graphs for accelerance and for dynamic compliance,
corresponding to the mobility graph shown in Figure 1, are shown in Figures 2 and 3, respectively.
NOTE 4 Frequency response functions can be further differentiated as
a) driving point response function, where the excitation and response are measured at the same location for the
evaluation of the frequency-response function, e.g. the use of an impedance head for the measurements (i  j in the
formulae in Table 1);
b) transfer response function, where the excitation and response are not measured at the same location for the
evaluation of the frequency-response function (i  j in the formulae in Table 1).
NOTE 5 Adapted from ISO 2041:2009, 1.53.
3.1.2
mobility
mechanical mobility
Y
ij
complex ratio of the velocity, taken at point i in the mechanical system, to the excitation force, taken at the
same or another point in the system
NOTE 1 Mobility is the ratio of the complex velocity-response at point i to the complex excitation force at point j with all
other measurement points on the structure allowed to respond freely without any constraints other than those constraints
which represent the normal support of the structure in its intended application.
NOTE 2 The term “point” designates both a location and a direction.
NOTE 3 The velocity response can be either translational or rotational, and the excitation force can be either a
rectilinear force or a moment.
2 © ISO 2011 – All rights reserved

NOTE 4 If the velocity response measured is a translational one and if the excitation force applied is a rectilinear one,
the units of the mobility term are m/(Ns) in the SI system. A typical graph is shown in Figure 1.
NOTE 5 Mechanical mobility is the matrix inverse of mechanical impedance.
NOTE 6 Adapted from ISO 2041:2009, 1.54.
3.1.3
blocked impedance
Z
ij
impedance at the input when all output degrees of freedom are connected to a load of infinite mechanical
impedance
NOTE 1 Blocked impedance is the frequency-response function formed by the complex ratio of the blocking or driving-
point force response at point i to the applied excitation velocity at point j, with all other measurement points on the
structure blocked, i.e. constrained to have zero velocity.
NOTE 2 All forces and moments necessary to constrain fully all points of interest on the structure need to be measured
in order to obtain a valid blocked impedance matrix. Blocked impedance measurements (see Reference [16]) are,
therefore, seldom made and are not dealt with in the various parts of this International Standard.
NOTE 3 Any change in the number of measurement points or their location changes the blocked impedances at all
measurement points.
NOTE 4 The primary usefulness of blocked impedance is in the mathematical modelling of a structure using lumped
mass, stiffness and damping elements or finite element techniques. When combining or comparing such mathematical
models with experimental mobility data, it is necessary to convert the analytical blocked impedance matrix into a mobility
matrix, or vice versa, as discussed in Annex A.
NOTE 5 Adapted from ISO 2041:2009, 1.52.
3.1.4
free impedance
Z
ratio of the applied excitation complex force to the resulting complex velocity with all other connection points of
the system free, i.e. having zero restraining forces
NOTE 1 Historically, often no distinction has been made between blocked impedance and free impedance. Caution
should, therefore, be exercised in interpreting published data.
NOTE 2 Free impedance is the arithmetic reciprocal of a single element of the mobility matrix. While experimentally
determined free impedances could be assembled into a matrix, this matrix would be quite different from the blocked
impedance matrix resulting from mathematical modelling of the structure and, therefore, would not conform to the
requirements for using mechanical impedance in an overall theoretical analysis of the system.
NOTE 3 Adapted from ISO 2041:2009, 1.51.
3.1.5
frequency range of interest
span between the lowest frequency to the highest frequency at which mobility data are to be obtained in a
given test series
Table 1 — Equivalent definitions to be used for various kinds of frequency-response functions related
to mechanical mobility
Motion expressed as Motion expressed as Motion expressed as

velocity acceleration displacement
a b c
Term Mobility Accelerance Dynamic compliance
Symbol Y  v /F a /F x /F
ij i j i j i j
2 –1
Unit m/(Ns) m/(Ns )  kg m/N
Boundary conditions F  0; k  j F  0; k  j F  0; k  j
k k k
See Figure 1 Figure 2 Figure 3
Comment Boundary conditions are easy to achieve experimentally.
Term Blocked impedance Blocked effective mass Dynamic stiffness
Symbol Z  F /v F /a F /x
ij i j i j i j
Unit Ns/m Ns /m  kg N/m
Boundary conditions v  0; k  j a  0; k  j x  0; k  j
k k k
Comment Boundary conditions are very difficult or impossible to achieve experimentally (see also A.2).
Effective mass
Term Free impedance Free dynamic stiffness
(free effective mass)
Symbol F /v  1/Y F /a F /x
j i ij j i j i
Unit Ns/m Ns /m  kg N/m
Boundary conditions F  0; k  j F  0; k  j F  0; k  j
k k k
Boundary conditions are easy to achieve, but results shall be used with great caution
Comment
in system modelling.
a
Mobility is sometimes called mechanical admittance.
b
Accelerance is unfortunately sometimes called inertance. Inertance is not acceptable because it is in conflict with the common
definition of acoustic inertance and also contrary to the implication carried by the word inertance.
c
Dynamic compliance is also called receptance.

4 © ISO 2011 – All rights reserved

Figure 1 — Typical graph of plotted mobility test results
Figure 2 — Accelerance graph corresponding to the mobility graph plotted in Figure 1
6 © ISO 2011 – All rights reserved

Figure 3 — Dynamic compliance graph corresponding to the mobility graph plotted in Figure 1
3.2 Symbols
Symbol Quantity Sl unit
a acceleration m/s
a /F accelerance m/(Ns )
i j
U transducer output V
f frequency Hz
F force N
k stiffness N/m
m mass kg
S sensitivity V/(unit of input variable)
v velocity m/s
x displacement m
x /F dynamic compliance m/N
i j
Y mobility m/(Ns)
ij
Z free impedance Ns/m
Z blocked impedance Ns/m
ij
4 Fundamentals and general relationships
Dynamic characteristics of structures can be determined as a function of frequency from mobility
measurements or measurements of related frequency-response functions like accelerance and dynamic
compliance (see Table 1). Accelerance and dynamic compliance differ from mobility (see 3.1.2) only in that
the motion response is expressed in terms of acceleration or displacement, respectively, instead of in terms of
velocity. In order to simplify the various parts of this International Standard, mostly only the term mobility is
used. All test procedures and requirements specified in this International Standard are also applicable to the
determination of accelerance and dynamic compliance.
Typical applications for mobility measurements are for:
a) predicting the dynamic response of structures to known or assumed input excitation;
b) determining the modal properties of a structure (natural frequencies, mode shapes and damping ratios);
c) predicting the dynamic interaction of interconnected structures;
d) checking the validity and improving the accuracy of mathematical models and structures;
e) determining dynamic properties (i.e. the complex modulus of elasticity) of materials in pure or composite
forms.
For some applications, a complete description of the dynamic characteristics may be required using
measurements of translational forces and motions along three mutually perpendicular axes as well as
measurements of moments and rotational motions about these three axes. This set of measurements results
in a 6  6 mobility matrix for each location of interest. For N locations on a structure, the system thus has an
overall mobility matrix of size 6N  6N.
8 © ISO 2011 – All rights reserved

For most practical applications, it is not necessary to know the entire 6N  6N matrix. Often, it is sufficient to
measure the driving-point mobility and a few transfer mobilities by exciting with a force at a single point in a
single direction and measuring the translational response motions at key points on the structure. In other
applications, only rotational mobilities may be of interest.
Since mechanical mobility is defined as the frequency-response function formed by the ratio of the phasor of
the translational or rotational response velocity to the phasor of the applied force or moment excitation, when
measuring with an accelerometer, conversion to velocity is required to obtain the mobility. Alternatively,
accelerance, the ratio of acceleration to force, may be used to characterize a structure. In other cases,
dynamic compliance, the ratio of displacement to force, may be used.
NOTE Historically, frequency-response functions of structures have often been expressed in terms of the reciprocal
of one of the above-named dynamic characteristics. The arithmetic reciprocal of mechanical mobility has often been called
mechanical impedance. This is misleading because the arithmetic reciprocal of mobility does not, in general, represent
any of the elements of the impedance matrix of a structure. This point is elaborated upon in Annex A.
Mobility test data cannot be used directly as part of an impedance model of the structure. In order to achieve
compatibility of the data and the model, the impedance matrix of the model shall be converted to mobility or
vice versa (see A.3 for limitations).
Before carrying out mobility measurements, it is necessary to evaluate the characteristics of the force and
motion response transducers to be used in order to ensure that accurate amplitude and phase information can
be obtained over the entire frequency range of interest.
5 Basic requirements for force and motion measurement transducers
5.1 General
The basic characteristics of all measurement transducers which are important in acquiring adequate mobility
data are as follows.
a) Transducers shall have sufficient sensitivity and low noise in order to obtain a signal-to-noise ratio of the
measurement chain which is adequate to cover the dynamic range of the mobility of the structure. Since
lightly damped structures require a larger dynamic range than structures with considerable damping,
transducer noise is of particular concern when testing lightly damped structures.
b) If the frequency-response function of the measurement transducer is not compensated by suitable signal
processing, the natural frequency of the transducer shall be far enough below or above the frequency
range of interest that no unacceptable phase shift occurs.
c) Transducer sensitivity shall be stable with time and have negligible direct current drift.
d) Transducers shall be insensitive to extraneous environmental effects, such as temperature, humidity,
magnetic fields, electrical fields, acoustical fields, strain and cross-axis inputs.
e) Transducer mass and rotational inertia shall be small so as to avoid dynamic loading of the structure
under test, or at least small enough so that a correction can be made for the loading.
Low susceptibility of the measurement system to the effects of electrical ground loops and other extraneous
signals is also important.
5.2 Requirements for motion measurement transducers
5.2.1 Although motion measurement transducers require the characteristics outlined in 5.1, certain of these
characteristics are more important than others. Motion transducers used in mechanical mobility
measurements are most commonly accelerometers; however, displacement or velocity transducers are
sometimes used. The major characteristics to be considered in transducer selection are outlined in 5.2.2 to
5.2.5.
5.2.2 The motion transducer should be of low mass (or non-contacting) design so as to minimize structural
loading of the structure under test.
5.2.3 The attachment of the transducer to the structure under test should be stiff in the direction of the
[2]
primary measurement axis of the transducer (see ISO 5348 ).
5.2.4 The attachment should have a sufficiently small contact area to prevent stiffening or damping of the
structure by the transducer or its mounting fixture.
5.2.5 When applying impulse excitation, zero drift of piezoelectric accelerometers due to the pyro-electric
effect is likely to occur and this limits the accuracy of the measurement at low frequencies. Other types of
motion transducers (e.g. piezoresistive, electrodynamic or some shear-type piezo-electronic accelerometers)
can provide the solution to this problem.
5.3 Requirements for force measurement transducers
5.3.1 Some of the characteristics outlined in 5.1 are more important than others in the selection of a force
measurement transducer to be used for mechanical mobility measurements. Since compromises in design
have to be made, the items outlined in 5.3.2 to 5.3.4 shall be considered as being of prime importance.
5.3.2 The effective end mass (mass between the force-sensing element of the transducer and the structure)
should be small enough to minimize extraneous inertial signals related to such mass (see 8.4 for further
details).
5.3.3 The stiffness of the force transducer and its components should be selected so that no resonances
involving this stiffness occur within the frequency range of interest. As a compromise, the effect of such
resonances on the signal from the force-sensing element should be compensated for by suitable signal
processing.
5.3.4 The static preload shall be adequate for the range of excitation forces required by the test application.
Transducers with built-in preload are available to minimize this problem.
5.4 Requirements for impedance heads and attachments to the structure under test
5.4.1 A device which combines an accelerometer and a force transducer in one assembly for the purpose of
mobility measurement is called impedance head. The design is a compromise based on the characteristics
outlined in 5.2 and 5.3. However, certain characteristics of prime importance, given in 5.4.2 to 5.4.5, should be
borne in mind.
5.4.2 The total compliance between the structure and the internal accelerometer should be small, because
a large compliance causes errors in acceleration measurements.
NOTE The total compliance is the sum of the attachment compliance and the internal compliance of the impedance
head. The attachment compliance includes the localized die effect compliance of the structure under test. The total
compliance can be measured as described in Annex C.
5.4.3 The effective end mass (mass between the force-sensing element of the transducer and the structure)
should be small in relation to the free effective mass of the structure under test.
5.4.4 The moment of inertia of the impedance head, relative to an axis in the plane of attachment, should
be small enough to minimize structural loading due to rotational motion about that axis.
NOTE Further guidelines for avoiding loading of the structure under test by the attachment of impedance heads are
given in ISO 7626-2.
5.4.5 In the design of an impedance head, care is required to avoid cross-sensitivity of the acceleration
transducer to the applied force.
10 © ISO 2011 – All rights reserved

6 Calibration
6.1 General
Calibrations fall into three categories:
a) operational calibration of the combined measurement and analysis system;
b) basic transducer calibrations;
c) supplementary transducer calibrations.
6.2 Operational calibrations
Operational calibrations of the combined measurement and analysis system shall be carried out at the
beginning and end of each measurement series (and at intermediate times, as required). Detailed procedures
are covered in the relevant parts of this International Standard pertaining to the various types of mobility
measurements.
Combined system calibrations are easier to perform, more accurate and in wider use than the basic
calibrations discussed in Clause 7. These system calibrations are achieved by driving, in free space, a known
free mass while the acceleration and force channel gains are set at the values that are used in later
measurements. The ratio output shall follow the appropriate mass line on the resulting mobility graph. If any
difficulties are experienced in combined system calibrations, basic calibrations should be carried out.
The accuracy of the frequency scale of the response graph or other data output should always be checked
during the operational calibration.
NOTE 1 An example of the resulting mobility graph, showing the effect of the impedance head attachment compliance,
is shown in Annex C.
NOTE 2 It is usually unnecessary to perform a phase shift calibration provided that the accelerometers, force
transducers and amplifiers are selected to have nearly flat response throughout the frequency range used for mobility
measurements, and the accelerometer is of a low-damping design. However, it is good practice to display the phase angle
between the force transducer and accelerometer outputs on a phase meter and record any deviations from the proper
phase angle between the force transducer and accelerometer outputs while carrying out the operational calibration.
6.3 Basic and supplementary transducer calibrations
The basic and supplementary calibrations (see Table 2) are intended for determining the suitability of the
transducers for mobility measurements. Piezoelectric transducers are very frequently used. If other types of
transducers are used, the procedures may have to be modified to determine the suitability of such transducers.
Transducers exhibiting changes in basic or supplementary calibrations should not be used if the changes are
unacceptable, as indicated in the appropriate clauses in this part of ISO 7626.
Transducers for use with specific amplifiers or signal conditioners should have the calibration performed under
the conditions of intended use. For example, piezoelectric force transducers, impedance heads and
accelerometers are intended for use with charge amplifiers or IEPE (integrated electronic piezoelectrics
means a built-in charge amplifier) transducers with amplifiers with constant-current line drive capability and
can be calibrated together or separately. The use of high-impedance amplifiers with piezoelectric sensors is
no longer recommended. All transducers should be calibrated with their intended signal conditioning device in
accordance with the manufacturer's specifications for electrical excitation, special terminating impedance, etc.
When calibrating accelerometers, force transducers and impedance heads, special care should be taken to
use mounting conditions similar to those specified by the manufacturer. Flatness of the mounting plate and
proper torquing of the attaching screws is important. A thin film of oil, grease or wax between the transducer
and the mounting surface may increase transducer coupling and rigidity for use at high frequencies. If special
fixtures are used, every effort should be made to carry out force transducer calibrations using a mechanical
arrangement closely resembling that to be used during the mobility measurement.
Table 2 — Summary of transducer calibrations and tests
Accelerometer Force transducer
Calibration or test
Basic Supplementary Basic Supplementary
Sensitivity 7.2.1 — 7.2.2 —
Frequency response 7.3.1 — 7.3.2 —
Transverse sensitivity 7.4 — — —
Mass 7.5 — 7.5 —
Dimensions 7.6 — 7.6 —
Electrical impedance 7.7 — 7.7 —
Polarity 7.8 — 7.8 —
Linearity — 8.2.2 — 8.2.3
Effective end mass — — — 8.3
Transducer compliance — — — 8.4
Threshold in reference to the bandwidth of the transducer — 8.5.2 — 8.5.2
Thermal sensitivity shift — 8.5.3 — 8.5.3
Transient temperature sensitivity — 8.5.4 — 8.5.4
Preload effects — — — 8.5.5
Base strain sensitivity — 8.5.6 — —
7 Basic piezoelectric transducer calibrations
7.1 General
All basic calibrations and tests listed in Table 2 shall be carried out by the manufacturer on each transducer
and the results shall be recorded in the documentation supplied with the transducer. All basic calibrations
should be repeated periodically by the user or by a commercial calibration laboratory, if the user does not
have adequate calibration facilities.
The recommended time interval for repeating basic calibrations and tests is 2 years. In addition, calibrations
such as sensitivity should be repeated more frequently, particularly if the transducer is subjected to conditions
which may change its sensitivity.
Specific tests can be performed to check transducer malfunctions before and during any test in the meantime
between the calibrations, e.g. bias voltage for IEPE (built-in charge amplifier) transducers.
7.2 Sensitivity
7.2.1 Accelerometer sensitivity
Sensitivity of accelerometers and the accelerometer portion of impedance heads shall be determined by using
the comparison method in accordance with the relevant part of ISO 5347 or ISO 16063. Calibration shall be
carried out by mounting the accelerometer on a suitable vibration exciter equipped with a reference
accelerometer previously calibrated by or referenced to an absolute calibration. The calibration amplitude
should be within the range encountered in actual mobility measurements, generally between 1 m/s and
100 m/s .
The sensitivity calibration should be carried out at least at a single frequency, generally 80 Hz. A different
frequency may be used, if 80 Hz is outside the operating frequency range of the transducer or if another
frequency is more suitable for the particular transducer design or experimental application of the transducer.
12 © ISO 2011 – All rights reserved

Frequency-response calibration is recommended to ensure the right properties of the device under test.
NOTE Certain failures in an accelerometer can be detected by frequency-response measurement, e.g. broken or lost
pre-tension of the piezoelectric element.
For accelerometers designed to be used with a charge amplifier, accelerometer sensitivity shall be expressed
in pC/(m/s ). For accelerometers designed to be used with a voltage amplifier and for accelerometers with a
built-in charge amplifier or impedance transformer, accelerometer sensitivity shall be expressed in V/(m/s ).
Since the output signal of the charge or voltage amplifier associated with the accelerometer is always a
voltage, the resultant acceleration channel sensitivity should always be expressed in V/(m/s ). In general, the
acceleration channel sensitivity is determined from the knowledge of the separate sensitivities of the
accelerometer and the amplifier; in cases where precise mobility measurements are required, the
accelerometer and the amplifier to be used with the accelerometer should be calibrated together in order to
obtain the acceleration channel sensitivity directly.
7.2.2 Force transducer sensitivity
Force transducers and the force section of impedance heads shall be calibrated using a mass-loading
technique. Measurement technologies are described in the literature, e.g. in Reference [17].
The sensitivity calibration shall be carried out by mounting the force transducer on a suitable vibration exciter
using the rated preloading torque recommended by the manufacturer. The force transducer shall be vibrated
at a controlled acceleration amplitude in one axis only, a , with only a reference accelerometer attached to its
opposite face. The force transducer amplifier voltage output, U , and the applied acceleration, a , shall be
0 0
measured. A loading mass, m, shall then be attached to the opposite face of the force transducer without
changing the amplifier gain settings. The voltage output, U , shall be measured with the vibration exciter input
m
adjusted so that the applied acceleration, a, has exactly the same amplitude as before (i.e. a  a ). The
sensitivity of the force channel, S , is then given by Equation (1):
F
UU
m 0
S  (1)
F
()mmmm a(mmm)a
12 3 1 2 3 0
where
m is the loading mass;
m is the mass of the reference accelerometer;
m is the effective mass of the bolt;
m is the effective end mass of the force transducer.
All the masses are expressed in kilograms and the acceleration shall be expressed in metres per second
squared. As (m  m  m ) a  (m  m  m ) a, because a  a, Equation (1) becomes
1 2 3 0 1 2 3 0
UU
m 0
S  (2)
F
ma
CAUTION — For force transducers which have not been pre-assembled, extreme care should be taken
to ensure that the mounted preload does not change from application to application, since sensitivity
and calibration depend on transducer preload.
NOTE Using Equations (1) and (2) in a complex form also permits the phase response of the force transducer to deviate.
Equation (2) gives the sensitivity of the force channel (i.e. the transducer and amplifier combination) in volts
per newton. The sensitivity of the force transducer alone can be deduced from Equation (2) and the sensitivity
of the amplifier used.
For force transducers designed to be used with a charge amplifier, force transducer sensitivity shall be
expressed in pC/N. For force transducers designed to be used with a voltage amplifier, force transducer
sensitivity shall be expressed in V/N.
In cases where precise mobility measurements are required, the force transducer and the amplifier to be used
with the force transducer should be calibrated together in order to obtain the total force channel sensitivity
directly.
The method described is adequate only at frequencies below approximately one-fifth of the resonance
frequency due to the effective mass of the system and the stiffness, k, of the force transducer. This resonance
frequency of the mass-loaded transducer, ƒ , can be estimated by means of Equation (3):
m
1 k
f  (3)
m
2mmmm
12 3
7.2.3 Impedance head sensitivity
The sensitivity of an impedance head can be obtained from the individual calibrations of the accelerometer
and the force transducer performed using the methods given in 7.2.1 and 7.2.2, respectively. Field calibration
of an impedance head usually consists of driving two or three differently sized free masses. This ensures that
the impedance head can measure known mobilities over a wide range.
7.3 Frequency response
7.3.1 Accelerometer frequency response
The frequency response calibration shall be performed by the comparison method in accordance with the
relevant part of ISO 5347 or ISO 16063 at an acceleration amplitude chosen to provide a signal-to-noise ratio
exceeding 10 (i.e. 20 dB) and over the frequency range corresponding to the range of use of the
accelerometer. Harmonic or wide-band excitation, applied with a suitable vibration exciter, may be used to
measure the frequency responses. Wide-band excitation may be random or transient.
Harmonic excitation may be applied at discrete frequencies or by a continuous sweep. In the first case, there
shall be enough discrete frequencies, for instance 10 frequencies per decade, to ensure that the transducer is
free from local or internal resonances within the frequency range of interest. If the calibration is carried out at a
limited number of discrete frequencies, addition of a frequency sweep is useful to ensure the same objective.
When a continuous sweep is used, the frequency should be swept slowly, while the amplitude of the excitation
acceleration is maintained constant over the full frequency range by means of a feedback control system
using a reference accelerometer.
The frequency response shall be flat within 5 % in the frequency range of interest. Care shall be taken so
that transverse motion of the vibration exciter, combined with the cross-axis sensitivity of the transducer, does
not cause measurement errors of the order of the specified 5 %.
7.3.2 Force transducer frequency response
Frequency response calibration shall be performed under the same conditions described for the
accelerometer frequency response. However, the force transducer shall be mass loaded and vibrated at a
constant amplitude of acceleration at each specified frequency. The voltage output of the force transducer
amplifier, U , shall be measured at each of the frequencies, f. The frequency response deviations, expressed
f
as a percentage, shall be determined from Formula (4):
U
f
1100% (4)


U
ref

14 © ISO 2011 – All rights reserved

where the reference voltage, U , is the output of the transducer amplifier obtained at the reference frequency,
ref
generally 80 Hz.
It is important that the mass load on the force transducer does not cause a resonance involving the loading
mass and the transducer compliance. This can be checked using Equation (3). The frequency response
deviation shall be less than 5 % of the response at the reference frequency over the frequency range of
interest.
NOTE As in the sensitivity calibration of the force transducer, better accuracy is obtained by not adjusting the torque
of the force transducer mounting bolt at any time during the frequency response calibration, if force transducers without
built-in preload are used.
7.4 Accelerometer transverse sensitivity
Transverse-sensitivity calibrations shall be performed at a single frequency below 500 Hz in accordance with
the relevant part of ISO 5347 or ISO 16063. The transducer shall be mounted on a vibration exciter
perpendicular to the transducer sensing axis. Harmonic excitation shall be applied at a frequency where it is
known that the vibration exciter motion in a plane perpendicular to the sensing axis is at least 100 times the
motion in the direction of the sensing axis. For measurement of transverse-sensitivity ratios of much less than
1 %, the excitation requirements are more strict. Extreme care and skill are required to obtain valid values for
such transverse sensitivities.
The transducer shall be mounted and rotated about its sensing axis through 360°, in increments of 45° or less,
to determine the maximum transverse response. If the transverse-sensitivity ratio exceeds 5 % of the axial
sensitivity or changes significantly from an earlier calibration, the transducer should be further evaluated by
performing supplementary calibrations or it should be repaired, as required.
7.5 Mass
The mass specified is the total mass of the
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