ISO 21955:2021

INTERNATIONAL ISO
STANDARD 21955
First edition
2021-08
Acoustics — Experimental method
for transposition of dynamic forces
generated by an active component
from a test bench to a receiving
structure
Acoustique — Méthode expérimentale de transposition des forces
dynamiques générées par un composant actif d’un banc d’essai vers
une structure réceptrice
Reference number
ISO 21955:2021(E)
©
ISO 2021

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ISO 21955:2021(E)

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© ISO 2021
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ISO 21955:2021(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Principle of the method of transposition of the dynamic force . 5
4.1 General matters . 5
4.2 General formulae . 6
4.3 Geometrical considerations . 6
5 Operating mode . 7
5.1 General . 7
5.2 Synopsis of procedure . 7
5.3 Tasks and preliminary operations . 7
5.4 Transfer matrices determination . 9
5.4.1 General. 9
5.4.2 Final receiving structure transfer matrix determination Y . 9
RS
5.4.3 Test bench transfer matrix determination, Y . 9
TB
5.4.4 Connecting device spring-like matrix properties determination, S . 9
I
5.4.5 Active Component transfer matrix determination, Y . 9
AC
5.5 Measured dynamic forces transmitted to the test bench .10
5.6 Predicted dynamic forces transmitted to the final structure .10
5.6.1 General.10
5.6.2 Strong decoupling .10
5.6.3 Very similar bench and receiving structure .11
5.6.4 Case of a rigid receiving structure .11
5.6.5 Case of a non-rigid receiving structure .12
6 Requirements for data in test report .14
6.1 Specification of the integrator to the supplier .14
6.2 Data sent by the supplier to the integrator .14
Annex A (informative) Theoretical developments .16
Annex B (informative) Frequency response functions measurement .19
Annex C (informative) Dynamic forces measurement .22
Annex D (informative) Data processing .28
Annex E (informative) Study of a wiper system.31
Annex F (informative) Equivalent force torsor and block-sensor method .47
Bibliography .58
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ISO 21955:2021(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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
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expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
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ISO 21955:2021(E)

Introduction
The vibroacoustic behaviour of products has become a major challenge not only in terms of user health
protection through regulations, but also in terms of sound quality for safety, quality perception, and
attractiveness.
At the same time, requirements on products development cycles are more and more stringent, reaching
the point where component suppliers and integrators should work independently, without physical
prototypes.
To master the transmission of dynamic forces (also called structure-borne noise), one needs to adapt
the components to the receiving structure, and hence exchange information prior to manufacturing
prototypes. This information will only be valuable for the integrator if it is clearly defined and intrinsic
to the component.
This document, issued from a French experimental standard, addresses this issue. It is a user guidance
to characterize an active source on a test bench and predict the effects of its integration on a passive
structure. The component is characterized on its own, which makes the document complementary to
the ISO 20270 that describes the measurement of “in-situ” characteristics (blocked forces), where the
component is connected to its receiving structure.
The intrinsic characterization of an active source requires measuring two quantities (expressed as
a function of the frequency): the first one characterizing the dynamic aspect, blocked forces, and the
second one describing “static” behaviour, such as the impedance or the mobility.
The objective of this document is to help the user predict the component behaviour in a particular
assembly. The theoretical background is laid in Annex A. The user is then guided (see 5.2) all along the
experimental procedure enabling to reach this objective:
— Static characterization of the component, the test bench and the receiving structure.
— Force measurement: the standard proposes here direct and indirect methods. Indirect methods are
generally easier to implement, but they need a particular focus on the measurement quality and
matrix inversion.
— Interface integration (connecting device).
— Prediction of the behaviour of the component/receiving structure assembly.
This whole procedure is based on a general formula expressing the dynamic forces in the assembly
as a function of blocked forces and static characteristics. Depending on these static characteristics,
simplifications are proposed (see 5.6).
Annex B and C guide the user to measure both transfer functions and dynamic forces. It should be noted
that, in general, these quantities are expressed in the 3 directions and 3 rotations, but the procedure
can be applied on a number of degrees of freedom chosen by the user.
The Annex D informs about data processing. The Annex E contains a test example and the Annex F
describes the method using a particular test bench (block sensor).
The data obtained and assessed in this document can be used:
— as part of a specification between suppliers and integrators;
— as input data of numerical vibroacoustic simulation models;
— to drive the modification of the physical structure or the interface in order to improve the
vibroacoustic behaviour.
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INTERNATIONAL STANDARD ISO 21955:2021(E)
Acoustics — Experimental method for transposition of
dynamic forces generated by an active component from a
test bench to a receiving structure
1 Scope
This document specifies a method to predict the dynamic forces generated by an active component on a
receiving structure from measurement on a test bench.
It sets out the requirements applicable to test benches and setup measurement conditions of dynamic
forces: a criterion of validity of transfer functions measurements can be established for example.
The objective is to evaluate noise and vibrations generated by active components mounted on receiving
structures, including the possibility to optimise vibration isolators.
It can be applied to different systems connected to a building, such as a compressor or a power
generator, or to systems connected to a vehicle body, such as an engine powertrain or an electrical
actuator, for example.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
active component
active substructure which generates dynamic forces
Note 1 to entry: See Figure 1.
3.2
connecting device
mechanical interface with a specific “spring like” matrix structure which allows connecting the active
component (3.1) to the receiving structure
Note 1 to entry: See Figure 1, Key 2.
Note 2 to entry: Insulators at fixation points are typical “spring like” connecting devices.
Note 3 to entry: A “spring like” connecting device is a structure with no internal degrees of freedom and internal
mass, see 3.10.
Note 4 to entry: In the case of a connecting point, active component and receiving structure share the same
location.
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ISO 21955:2021(E)

Note 5 to entry: In the case of seals at contact surfaces, direct connections or any other connection type, the
connecting device item 2 cannot be used, and a block diagram with items 1 and 3 and 4 shall be used (see
Figure 1).
Note 6 to entry: In case of direct connection, the hypothetical surface between the active component and
receiving structure is called interface.
3.3
receiving structure
passive substructure to which the dynamic forces are transmitted
Note 1 to entry: See Figure 1, Key 3 and 4.
Note 2 to entry: The receiving structure can be a test bench or the structure for which the dynamic forces will be
predicted.
Note 3 to entry: The “test bench” can be a specific structure designed to test the active component (3.1), or any
other receiving structure.
Note 4 to entry: active device, connecting device and receiving structures are deformable structures.
Key
1 active component
2 connecting device
3 receiving structure
4 test bench
NOTE An active component (left) connected via a connecting device (centre) transmits dynamic forces to a
receiving structure (right) which may vibrate and radiate sound.
Figure 1 — Schematic of the structure assembly
3.4
degree of freedom
n degrees of freedom through which structure-borne sound or vibration is transmitted from the active
component (3.1) to the receiving structure (3.3)
EXAMPLE A connection point can have up to 6 degrees of freedom (dof).
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ISO 21955:2021(E)

3.5
dynamic force
f
d
complex force associated to a structure or an interface with n degrees of freedom, arranged into a n × 1
vector at each frequency, according to
 f ()f 
d,1
 
f f
()
 d,2 
 

 
f ()f =
d
 

 
 
f f
()
d,n
 
 
 
th
where f ()f is the complex Fourier transform of the i component of dynamic force at frequency f
d,i
Note 1 to entry: Forces f can be considered as generalised forces, that is, including moments.
d
Note 2 to entry: Generalised forces units are Newtons for dynamic forces and N·m for dynamic moments
Note 3 to entry: In case pseudo-random signals, statistical tools can help into describing the dynamic forces into
set of amplitude and phase force vectors.
Note 4 to entry: In Table 1, the specific dynamic forces f applied at particular points used in this document are
d
defined.
Table 1 — Dynamic forces symbols
Symbols and abbrevia-
Definition
tions
Force generated by the active component at the interface of the connecting device
f
AC
in operational conditions.
Forces transmitted to the receiving structure: final receiving structure (RS) or
test bench (TB) in operational conditions. An additional “pred” or “meas” give
indication about how the force is obtained (predicted from formulae, or directly
measured):
f and f
RS TB
f and f .
RS_pred TB_meas
In the case of no presence of a connecting device, ff= .
AC RS
3.6
blocked force
dynamic force (3.5) applied by an active component (3.1) transmitted to a rigid receiving structure (3.3)
Note 1 to entry: Blocked forces indirect measurement methods are detailed in Annex F and ISO 20270.
3.7
velocity
v
d
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ISO 21955:2021(E)

complex vibration velocity associated to a structure or an interface with n degrees of freedom, arranged
into a n × 1 vector at each frequency, according to
v f
()
 
d,1
 
v ()f
d,2
 
 

 
v ()f =
d
 

 
 
v ()f
d,n
 
 
 
th
where v ()f is the complex Fourier transform of the i velocity component at frequency f
d,i
Note 1 to entry: Velocity units are meters per second (m/s).
Note 2 to entry: Associated complex acceleration a ()f can be defined via derivation of the velocity.
d
Note 3 to entry: Associated complex displacement x ()f can be defined via integration of the velocity.
d
Note 4 to entry: In Table 2, the displacement, velocity and acceleration xa,,v generated at particular points
dd d
used in this standard are defined.
Table 2 — Velocity, displacement and acceleration definitions
Symbols and abbreviations Definition
xa,v and dynamic displacement, velocity and acceleration generated by the active component.
AC AC AC
xa,v and dynamic displacement, velocity and acceleration on the receiving structure.
RS RS RS
3.8
frequency response function
FRF
frequency dependent ratio of the Fourier transform of the response to the Fourier transform of the
excitation of a linear system
Note 1 to entry: See ISO 2041.
Note 2 to entry: The FRF denomination and associated unit depends on the two vibration quantities of the ratio
(See Table 3).
Note 3 to entry: In this document, any reference to mobility Y or impedance Z is related to:
— the free mobility, Y , which is defined as a ratio of a dynamic velocity response in degree of freedom i to
free ij
an excitation force in degree of freedom j, with all degrees of freedom free, except the one of the excitation
forces; or
— the blocked impedance Z , which is defined as a ratio of the response force in degree of freedom j to
blocked ij
the dynamic velocity in degree of freedom i, with all degrees of freedom blocked, except the one of the
excitation velocity v
d, j
Table 3 — Denomination of frequency response functions FRF for various vibration quantities
(displacement, x, velocity, v and acceleration, a)
Dynamic Free Mobility Accelerance Dynamic Blocked imped- Effective
Compliance stiffness ance Mass
x v a
f f f
i i i
J J J
Y =
Denomination
freeij Z =
blocked ij
f f f
J J J x v a
i i i
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ISO 21955:2021(E)

Table 3 (continued)
Dynamic Free Mobility Accelerance Dynamic Blocked imped- Effective
Compliance stiffness ance Mass
2
m m m N Ns⋅
Ns⋅
Unit
2
N Ns⋅ m m
Ns⋅
m
Note 4 to entry: Thus, in terms of matrix writing, corresponding Y and Z matrices are related:
−1
ZY=
blockedfree
3.9
transfer matrix
set of FRF between multiple degrees of freedom systems
Note 1 to entry: In this document, the terms Y , Y and Y (see Table 4) can be related to free mobility,
AC RS TB
dynamic compliance or accelerances, depending of the quantities that are commonly used by the reader, with the
same boundary conditions as the free mobility.
Table 4 — Main transfer matrices used in the document
Symbols and abbreviations Definition
Y transfer matrix of the active component
AC
Y and Y transfer matrix of the receiving structure or the test bench
RS TB
3.10
connecting device transfer matrix
connecting device (case of insulators at fixation points) transfer matrix (3.9) (see Table 5) can be
obtained via different methods
Note 1 to entry: Such methods are described in ISO 10846.
Table 5 — Different expressions of connecting device transfer matrix versus dynamic stiffness
matrix
Formula Unit Homogeneous to
21*− −−12
accelerance
SK=ω mN⋅ s
II
*−1 −−11
mobility
SK= jω mN⋅ s
II
*−1 −1
compliance (or receptance)
SK= mN⋅
II
*
with K homogeneous to a dynamic stiffness complex matrix of the connecting device.
I
3.11
operational conditions
set of conditions under which the source operates for the operational test, including speed, load and any
other settings or conditions particular to the source which might affect source operation
4 Principle of the method of transposition of the dynamic force
4.1 General matters
This subclause explains how to predict the forces generated by an active component (which comes with
its own sources) on a receiving structure from a series of measurements on a test bench and on specific
data about the receiving structure.
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ISO 21955:2021(E)

Predicted or measured dynamic forces are required when
— there is no opportunity to measure directly any dynamic force of any sort (e.g. heavy and high cost
electrical machine to be duplicated in a new place),
— there is only the possibility to work on a test bench, because the final receiving structure is still not
available,
— the active source is provided by a component supplier to an integrator, and the integrator defines a
specification on a bench, with a target to comply, and
— internal forces matrix of a specific product is needed for noise comfort prediction, or for durability
purpose.
4.2 General formulae
The first Formula (1) which detail is given in Annex A can be written as follows:
−1
fY=+YS+ ⋅⋅YY++Sf (1)
[] []
RS RS AC ITBACI TB
where
is the transmitted force vector to the receiving structure;
f
RS
Y
is the transfer matrix of the receiving structure;
RS
Y
is the transfer matrix of the active component;
AC
Y
is the transfer matrix of the test bench;
TB
S
is the spring-like matrix representation of the connecting device;
I
is the transmitted force vector to the test bench.
f
TB
The purpose of Formula (2) is to enable the prediction of a force transmitted to a receiving structure
from the measurement or the estimation of 4 different FRFs matrices:
−1
fY=+[]YS+ ⋅⋅[]YY++Sf (2)
RS__predictRSACI TB AC ITBmeas
To build this formula, there are intermediate steps that are detailed in Annex A.
Instead of a link from bench to receiving structure, in certain cases, the need is to go from receiving
structure to bench; Formula (2) is then given as Formula (3):
−1
fY=+YS+ ⋅⋅YY++Sf (3)
[] []
TB__predictTBACI RS AC IRSmeas
4.3 Geometrical considerations
Sizes and quantities handled in this document are defined in a specific coordinate system, usually the
geometric coordinate system related to the receiving structure.
During FRF functions measurements (see Annex B), it can be more practical to use a local coordinate
system for certain attachment points. In this case, it will be necessary to re-project in a global reference
system.
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ISO 21955:2021(E)

5 Operating mode
5.1 General
In this subclause, an operating mode to apply this document is proposed, as an example.
This procedure is based on the general Formula (2) allowing to transpose the dynamic forces generated
by an active component from a test bench to a receiving structure. Depending on the assumptions on the
different transfer functions, this operating mode allows the use of simplified versions of Formula (2).
The frequency range(s) for which the formulated hypotheses and steps presented below are considered
as valid or invalid shall be mentioned.
5.2 Synopsis of procedure
The various special cases discussed below can be summarized in the form of a general diagram of the
procedure (see Figure 2).
5.3 Tasks and preliminary operations
A number of tasks and processes shall be performed previous to the application of this procedure:
a) During the development of the product, the component will determine the active component
transfer matrix at the connecting points. There are many cases for which the active component is
not only connected to its fixation points, but interacts with its environment through cables, rotation
axes, hoses, pipes, friction, which do not allow to measure the transfer matrix in free conditions for
all degrees of freedom. In this case, different alternatives are proposed in the document.
b) During the development of the product, the component chooses the properties of the connecting
device between the component and the receiving structure. It is remarked that this connecting
device matrix properties are of first order influence on the final transmitted forces: the product
shall ensure a perfect decoupling in order to minimize the vibration coupling between the
component and the receiving structure. Some advices are given hereunder in this operating mode.
c) To apply the methodology to predict the forces transmitted to the receiving structure in order to
check compliance with the specifications, a test bench is generally developed, transmitted forces to
the bench are measured. Usually, in the field of noise and vibration, an infinitely rigid bench, such
as a marble, is used, but this methodology is not mandatory. Therefore, the procedure covers the
case of a not infinitely rigid test bench.
The operating mode starts with the analysis of the general equation [Formula (2)] and attempts to
cover the different real cases that may be encountered in practice in the fields covered by the document.
The choices in the flow chart not only depend on the possibilities offered by the product, but also on
the relative order of scales of different transfer matrices in Formula (2). Three different examples are
described in Annexes E and F, to scan a wide range of applications.
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ISO 21955:2021(E)

Figure 2 — Synoptic of the steps to determine predicted force
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ISO 21955:2021(E)

5.4 Transfer matrices determination
5.4.1 General
Annex B is dedicated to frequency transfer functions measurement. These measurements are generally
performed with accelerometers and force sensors, leading to accelerance measurements.
5.4.2 Final receiving structure transfer matrix determination Y
RS
In Formula (2), the transfer matrix at the connecting points is required to predict the forces on the final
structure; whenever there is a component integrator specification about the predicted forces, which
means that the component integrator shall provide to the component supplier the transfer matrix values
at the connecting points. These values are generally available at early stages of a project development
via simulation tools.
In many cases, it is impossible to decouple the active component from the receiving structure to perform
a measurement. ISO 20270 can be applied, with an indirect measurement of blocked forces.
5.4.3 Test bench transfer matrix determination, Y
TB
At design stage for the test bench, it shall be considered to let some space to position the sensors for the
matrix determination.
5.4.4 Connecting device spring-like matrix properties determination, S
I
The connecting device matrix is generally determined on its own on a specific bench. In this case only
diagonal terms of the matrix are measured; ISO 10846 can be used.
Taking into account a connecting device is not adapted when:
— the active component is rigidly coupled to the receiving structure or test bench;
— the connecting devi
...