Acoustics -- Experimental method for transposition of dynamic forces generated by an active component from a test bench to a receiving structure

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.

Acoustique -- Méthode expérimentale de transposition des forces dynamiques générées par un composant actif d’un banc d’essai vers une structure réceptrice

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Status
Published
Publication Date
16-Aug-2021
Current Stage
5060 - Close of voting Proof returned by Secretariat
Start Date
15-Jul-2021
Completion Date
14-Jul-2021
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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
---------------------- Page: 1 ----------------------
ISO 21955:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
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

5.4.3 Test bench transfer matrix determination, Y ................................................................................... 9

5.4.4 Connecting device spring-like matrix properties determination, S ................................ 9

5.4.5 Active Component transfer matrix determination, Y ................................................................ 9

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

© ISO 2021 – All rights reserved iii
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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

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

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.
iv © ISO 2021 – All rights reserved
---------------------- Page: 4 ----------------------
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.
© ISO 2021 – All rights reserved v
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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.
© ISO 2021 – All rights reserved 1
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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).
2 © ISO 2021 – All rights reserved
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ISO 21955:2021(E)
3.5
dynamic force

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 =
 
 
 
f f
d,n
 
 
 

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.

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

defined.
Table 1 — Dynamic forces symbols
Symbols and abbrevia-
Definition
tions

Force generated by the active component at the interface of the connecting device

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
© ISO 2021 – All rights reserved 3
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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 =
 
 
 
v ()f
d,n
 
 
 

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.

Note 3 to entry: Associated complex displacement x ()f can be defined via integration of the velocity.

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
4 © ISO 2021 – All rights reserved
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ISO 21955:2021(E)
Table 3 (continued)
Dynamic Free Mobility Accelerance Dynamic Blocked imped- Effective
Compliance stiffness ance Mass
m m m N Ns⋅
Ns⋅
Unit
N Ns⋅ m m
Ns⋅

Note 4 to entry: Thus, in terms of matrix writing, corresponding Y and Z matrices are related:

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
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
*−1 −−11
mobility
SK= jω mN⋅ s
*−1 −1
compliance (or receptance)
SK= mN⋅

with K homogeneous to a dynamic stiffness complex matrix of the connecting device.

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.
© ISO 2021 – All rights reserved 5
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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:

fY=+YS+ ⋅⋅YY++Sf (1)
[] []
RS RS AC ITBACI TB
where
is the transmitted force vector to the receiving structure;
is the transfer matrix of the receiving structure;
is the transfer matrix of the active component;
is the transfer matrix of the test bench;
is the spring-like matrix representation of the connecting device;
is the transmitted force vector to the test bench.

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:
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):
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.
6 © ISO 2021 – All rights reserved
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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.
© ISO 2021 – All rights reserved 7
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ISO 21955:2021(E)
Figure 2 — Synoptic of the steps to determine predicted force
8 © ISO 2021 – All rights reserved
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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

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

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

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
...

FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 21955
ISO/TC 43/SC 1
Acoustics — Experimental method
Secretariat: DIN
for transposition of dynamic forces
Voting begins on:
2021­05­19 generated by an active component
from a test bench to a receiving
Voting terminates on:
2021­07­14
structure
Acoustique — Méthode expérimentale de transposition des forces
dynamiques générées par un composant actif d’un banc d’essai vers
une structure réceptrice
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO­
ISO/FDIS 21955:2021(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN­
DARDS TO WHICH REFERENCE MAY BE MADE IN
NATIONAL REGULATIONS. ISO 2021
---------------------- Page: 1 ----------------------
ISO/FDIS 21955:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH­1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/FDIS 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

5.4.3 Test bench transfer matrix determination, Y ................................................................................... 9

5.4.4 Connecting device spring-like matrix properties determination, S ................................ 9

5.4.5 Active Component transfer matrix determination, Y ................................................................ 9

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 non­rigid 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

© ISO 2021 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO/FDIS 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

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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

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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

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ISO/FDIS 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 “in­situ” 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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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 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/FDIS 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 test bench or receiving structure
4 test bench or receiving structure

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 structure­borne 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/FDIS 21955:2021(E)
3.5
dynamic force

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 =
 
 
 
f f
d,n
 
 
 

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.

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

defined.
Table 1 — Dynamic forces symbols
Symbols and abbrevia-
Definition
tions

Force generated by the active component at the interface of the connecting device

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
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ISO/FDIS 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 =
 
 
 
v ()f
d,n
 
 
 

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.

Note 3 to entry: Associated complex displacement x ()f can be defined via integration of the velocity.

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/FDIS 21955:2021(E)
Table 3 (continued)
Dynamic Free Mobility Accelerance Dynamic Blocked imped- Effective
Compliance stiffness ance Mass
m m m N Ns⋅
Ns⋅
Unit
N Ns⋅ m m
Ns⋅

Note 4 to entry: Thus, in terms of matrix writing, corresponding Y and Z matrices are related:

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
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
*−1 −−11
mobility
SK= jω mN⋅ s
*−1 −1
compliance (or receptance)
SK= mN⋅

with K homogeneous to a dynamic stiffness complex matrix of the connecting device.

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/FDIS 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:

fY=+YS+ ⋅⋅YY++Sf (1)
[] []
RS RS AC ITBACI TB
where
is the transmitted force vector to the receiving structure;
is the transfer matrix of the receiving structure;
is the transfer matrix of the active component;
is the transfer matrix of the test bench;
is the spring-like matrix representation of the connecting device;
is the transmitted force vector to the test bench.

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

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 pe

...

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