EN ISO 10846-1:2008

SLOVENSKI STANDARD
01-november-2008
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SIST EN ISO 10846-1:1999
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Acoustics and vibration - Laboratory measurement of vibro-acoustic transfer properties of
resilient elements - Part 1: Principles and guidelines (ISO 10846-1:2008)
Akustik und Schwingungstechnik - Laborverfahren zur Messung der vibro-akustischen
Transfereigenschaften elastischer Elemente - Teil 1: Grundlagen und Übersicht (ISO
10846-1:2008)
Acoustique et vibrations - Mesurage en laboratoire des propriétés de transfert vibro-
acoustique des éléments élastiques - Partie 1: Principes et lignes directrices (ISO 10846-
1:2008)
Ta slovenski standard je istoveten z: EN ISO 10846-1:2008
ICS:
17.140.01 $NXVWLþQDPHUMHQMDLQ Acoustic measurements and
EODåHQMHKUXSDQDVSORãQR noise abatement in general
17.160 Vibracije, meritve udarcev in Vibrations, shock and
vibracij vibration measurements
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 10846-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2008
ICS 17.140.01 Supersedes EN ISO 10846-1:1998
English Version
Acoustics and vibration - Laboratory measurement of vibro-
acoustic transfer properties of resilient elements - Part 1:
Principles and guidelines (ISO 10846-1:2008)
Acoustique et vibrations - Mesurage en laboratoire des Akustik und Schwingungstechnik - Laborverfahren zur
propriétés de transfert vibro-acoustique des éléments Messung der vibro-akustischen Transfereigenschaften
élastiques - Partie 1: Principes et lignes directrices (ISO elastischer Elemente - Teil 1: Grundlagen und Übersicht
10846-1:2008) (ISO 10846-1:2008)
This European Standard was approved by CEN on 12 April 2008.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
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EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2008 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 10846-1:2008: E
worldwide for CEN national Members.

Contents Page
Foreword.3

Foreword
This document (EN ISO 10846-1:2008) has been prepared by Technical Committee ISO/TC 43 "Acoustics" in
collaboration with Technical Committee CEN/TC 211 “Acoustics” the secretariat of which is held by DS.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by February 2009, and conflicting national standards shall be withdrawn
at the latest by February 2009.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 10846-1:1998.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 10846-1:2008 has been approved by CEN as a EN ISO 10846-1:2008 without any
modification.
INTERNATIONAL ISO
STANDARD 10846-1
Second edition
2008-08-15
Acoustics and vibration — Laboratory
measurement of vibro-acoustic transfer
properties of resilient elements —
Part 1:
Principles and guidelines
Acoustique et vibrations — Mesurage en laboratoire des propriétés de
transfert vibro-acoustique des éléments élastiques —
Partie 1: Principes et lignes directrices

Reference number
ISO 10846-1:2008(E)
©
ISO 2008
ISO 10846-1:2008(E)
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ii © ISO 2008 – All rights reserved

ISO 10846-1:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Selection of appropriate International Standard . 4
5 Theoretical background . 4
5.1 Dynamic transfer stiffness. 4
5.2 Dynamic stiffness matrix of resilient elements . 5
5.3 Number of relevant blocked transfer stiffnesses . 7
5.4 Flanking transmission. 8
5.5 Loss factor. 8
6 Measurement principles. 9
6.1 Dynamic transfer stiffness. 9
6.2 Direct method. 9
6.3 Indirect method. 11
6.4 Driving point method. 14
Annex A (informative) Functions related to dynamic stiffness . 16
Annex B (informative) Effect of symmetry on the transfer stiffness matrix. 17
Annex C (informative) Simplified transfer stiffness matrices. 20
Annex D (informative) Linearity of resilient elements . 22
Bibliography . 23

ISO 10846-1:2008(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 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 10846-1 was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise, and
ISO/TC 108, Mechanical vibration, shock and condition monitoring.
This second edition cancels and replaces the first edition (ISO 10846-1:1997), which has been technically
revised.
ISO 10846 consists of the following parts, under the general title Acoustics and vibration — Laboratory
measurement of vibro-acoustic transfer properties of resilient elements:
⎯ Part 1: Principles and guidelines
⎯ Part 2: Direct method for determination of the dynamic stiffness of resilient supports for translatory motion
⎯ Part 3: Indirect method for determination of the dynamic stiffness of resilient supports for translatory
motion
⎯ Part 4: Dynamic stiffness of elements other than resilient supports for translatory motion
⎯ Part 5: Driving point method for determination of the low-frequency transfer stiffness of resilient supports
for translatory motion
iv © ISO 2008 – All rights reserved

ISO 10846-1:2008(E)
Introduction
Passive vibration isolators of various kinds are used to reduce the transmission of vibrations. Examples
include automobile engine mounts, resilient supports for buildings, resilient mounts and flexible shaft
couplings for shipboard machinery and small isolators in household appliances.
This part of ISO 10846 serves as an introduction and a guide to ISO 10846-2, ISO 10846-3, ISO 10846-4 and
ISO 10846-5, which describe laboratory measurement methods for the determination of the most important
quantities which govern the transmission of vibrations through linear resilient elements, i.e.
frequency-dependent dynamic transfer stiffnesses. This part of ISO 10846 provides the theoretical background,
the principles of the methods, the limitations of the methods, and guidance for the selection of the most
appropriate standard of the series.
The laboratory conditions described in all parts of ISO 10846 include the application of static preload, where
appropriate.
The results of the methods are useful for resilient elements, which are used to prevent low-frequency vibration
problems and to attenuate structure-borne sound. However, for complete characterization of resilient elements
that are used to attenuate low-frequency vibration or shock excursions, additional information is needed,
which is not provided by these methods.

INTERNATIONAL STANDARD ISO 10846-1:2008(E)

Acoustics and vibration — Laboratory measurement of vibro-
acoustic transfer properties of resilient elements —
Part 1:
Principles and guidelines
1 Scope
This part of ISO 10846 explains the principles underlying ISO 10846-2, ISO 10846-3, ISO 10846-4 and
ISO 10846-5 for determining the transfer properties of resilient elements from laboratory measurements, and
provides assistance in the selection of the appropriate part of this series. It is applicable to resilient elements
that are used to reduce
a) the transmission of audio frequency vibrations (structure-borne sound, 20 Hz to 20 kHz) to a structure
which may, for example, radiate fluid-borne sound (airborne, waterborne, or other), and
b) the transmission of low-frequency vibrations (typically 1 Hz to 80 Hz), which may, for example, act upon
human subjects or cause damage to structures of any size when the vibration is too severe.
The data obtained with the measurement methods, which are outlined in this part of ISO 10846 and further
detailed in ISO 10846-2, ISO 10846-3, ISO 10846-4 and ISO 10846-5, can be used for
⎯ product information provided by manufacturers and suppliers,
⎯ information during product development,
⎯ quality control, and
⎯ calculation of the transfer of vibrations through resilient elements.
The conditions for the validity of the measurement methods are
a) linearity of the vibrational behaviour of the resilient elements (this includes elastic elements with
non-linear static load-deflection characteristics, as long as the elements show approximate linearity for
vibrational behaviour for a given static preload), and
b) the contact interfaces of the vibration isolator with the adjacent source and receiver structures can be
considered as point contacts.
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.
1)
ISO 2041:— , Mechanical vibration, shock and condition monitoring — Vocabulary

1) To be published. (Revision of ISO 2041:1990)
ISO 10846-1:2008(E)
2)
ISO/IEC Guide 98-3 , Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM 1995)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 2041 and the following apply.
3.1
vibration isolator
resilient element
isolator designed to attenuate the transmission of the vibration in a certain frequency range
1)
NOTE Adapted from ISO 2041:— , definition 2.120.
3.2
resilient support
vibration isolator(s) suitable for supporting a machine, a building or another type of structure
3.3
test element
resilient element undergoing testing, including flanges and auxiliary fixtures, if any
3.4
blocking force
F
b
dynamic force on the output side of a vibration isolator which results in a zero displacement output
3.5
dynamic driving point stiffness
k
1,1
frequency-dependent ratio of the force phasor F on the input side of a vibration isolator with the output side
blocked to the displacement phasor u on the input side
=/F u
k
1,1
NOTE 1 The subscripts “1” denote that the force and displacement are measured on the input side.
NOTE 2 The value of k can be dependent on the static preload, temperature, relative humidity and other conditions.
1,1
NOTE 3 At low frequencies, elastic and dissipative forces solely determine k . At higher frequencies, inertial forces
1,1
play a role as well.
3.6
dynamic driving point stiffness of inverted vibration isolator
k
2,2
dynamic driving point stiffness, with the physical input and output sides of the vibration isolator interchanged
NOTE At low frequencies, where elastic and dissipative forces solely determine the driving point stiffness, k = k .
1,1 2,2
At higher frequencies inertial forces play a role as well and k and k will be different in case of asymmetry.
1,1 2,2
2) ISO/IEC Guide 98-3 will be published as a re-issue of the Guide to the expression of uncertainty in measurement
(GUM), 1995.
2 © ISO 2008 – All rights reserved

ISO 10846-1:2008(E)
3.7
dynamic transfer stiffness
k
2,1
frequency-dependent ratio of the blocking force phasor F on the output side of a resilient element to the
2,b
displacement phasor u on the input side
=/F u
k
2,1
2,b
NOTE 1 The subscripts “1”and “2” denote the input and output sides, respectively.
NOTE 2 The value of k can be dependent on the static preload, temperature and other conditions.
2,1
NOTE 3 At low frequencies, k is mainly determined by elastic and dissipative forces and kk≈ . At higher
1,1 2,1
2,1
frequencies, inertial forces in the resilient element play a role as well and kk≠ .
1,1 2,1
3.8
loss factor of resilient element
h
ratio of the imaginary part of k to the real part of k , i.e. tangent of the phase angle of k , in the low-
2,1 2,1 2,1
frequency range where inertial forces in the element are negligible
3.9
point contact
contact area which vibrates as the surface of a rigid body
3.10
linearity
property of the dynamic behaviour of a resilient element, if it satisfies the principle of superposition
NOTE 1 The principle of superposition can be stated as follows: if an input x (t) produces an output y (t) and in a
1 1
separate test an input x (t) produces an output y (t), superposition holds if the input a x (t) + b x (t) produces the output
2 2 1 2
ay (t) + b y (t). This must hold for all values of a, b and x (t), x (t); a and b are arbitrary constants.
1 2 1 2
NOTE 2 In practice, the above test for linearity is impractical and a limited check of linearity is performed by measuring
the dynamic transfer stiffness for a range of input levels. For a specific preload, if the dynamic transfer stiffness is
nominally invariant, the system can be considered linear. In effect, this procedure checks for a proportional relationship
between the response and the excitation.
3.11
direct method
method in which either the input displacement, velocity or acceleration and the blocking output force are
measured
3.12
indirect method
method in which the vibration transmissibility (for displacement, velocity or acceleration) of a resilient element
is measured, with the output loaded by a compact body of known mass
NOTE The term “indirect method” can be permitted to include loads of any known impedance other than a mass-like
impedance. However, the ISO 10846 series does not cover such methods.
3.13
driving point method
method in which either the input displacement, velocity or acceleration and the input force are measured, with
the output side of the resilient element blocked
3.14
flanking transmission
forces and accelerations at the output side caused by the vibration exciter on the input side but via
transmission paths other than through the resilient element under test
ISO 10846-1:2008(E)
3.15
upper limiting frequency
f
UL
frequency up to which results for k are valid, according to the criteria given in various parts of ISO 10846
1,2
4 Selection of appropriate International Standard
Table 1 provides guidance for the selection of the appropriate part of ISO 10846.
Table 1 — Guidance for selection
International Standard and method type
ISO 10846-4 ISO 10846-5
ISO 10846-2 ISO 10846-3
Direct or indirect Driving point
Direct method Indirect method
method method
Type of resilient support support other than support support
element
Examples resilient mountings for instruments, equipment, bellows, hoses, see under ISO 10846-2
machinery and buildings resilient shaft and ISO 10846-3
couplings, power
supply cables
Frequency range 1 Hz to f f to f Direct method: see 1 Hz to f
UL 2 3 UL
of validity under ISO 10846-2;
f dependent on test rig; f typically (but not f typically (but not
UL 2 UL
typically (but not limited limited to) between Indirect method: see limited to) < 200 Hz
to) 300 Hz < f < 500 Hz 20 Hz and 50 Hz. For under ISO 10846-3
UL
f is dependent both on
UL
very stiff mountings
test rig and on test
f > 100 Hz.
element properties;
f typically 2 kHz to
5 kHz, but dependent
on the test rig
Translational 1, 2 or 3 1, 2 or 3 1, 2 or 3 1, 2 or 3
components
Rotational none informative annex informative annex none
components
4 dB 4 dB
Expanded To be estimated To be estimated
measurement according to according to
(considered as the (considered as the
uncertainty for ISO/IEC Guide 98-3 ISO/IEC Guide 98-3
upper limit) upper limit)
95 % coverage
probability
NOTE Within coinciding frequency ranges of validity, and within the uncertainty ranges of the methods, the direct method, the
indirect method and the driving point method yield the same result.

Further guidance is given in Clauses 5 and 6.
5 Theoretical background
5.1 Dynamic transfer stiffness
This clause explains why the dynamic transfer stiffness is most appropriate to characterize the vibro-acoustic
transfer properties of resilient elements for many practical applications. It also describes special situations
where other vibro-acoustic properties, not covered in ISO 10846, would also be necessary.
4 © ISO 2008 – All rights reserved

ISO 10846-1:2008(E)
The dynamic transfer stiffness, as defined in 3.7, is determined by the elastic, inertia and damping properties
of the resilient element. Describing the test results in terms of stiffness properties allows for compliance with
data of static and/or low-frequency dynamic stiffness, which are commonly used. The additional importance of
inertial forces (i.e. elastic wave effects in the isolators) makes the dynamic transfer stiffness at high
frequencies more complex than at low frequencies. At low frequencies, only elastic and damping forces are
important. Because in general the modulus of elasticity and the damping properties are only weakly
dependent on frequency in this range, this holds also for the low-frequency dynamic stiffness.
NOTE For many resilient elements, static stiffness and low-frequency dynamic transfer stiffness are different.
In principle, the dynamic transfer stiffness of vibro-acoustic resilient elements is dependent on static preload,
temperature and relative humidity. In the following theory, linearity, as defined in 3.10, is assumed. See
Annex D for further information.
Relationships between the dynamic transfer stiffness and other quantities are listed in Annex A. These
relationships imply that, for the actual performance of the tests, only practical considerations will determine
whether displacements, velocities or accelerations are measured. However, for presentation of the results in
agreement with the other parts of ISO 10846, appropriate conversions may be needed.
5.2 Dynamic stiffness matrix of resilient elements
5.2.1 General concept
A familiar approach to the analysis of complex vibratory systems is the use of stiffness – compliance – or
transmission matrix concepts. The matrix elements are basically special forms of frequency-response
functions; they describe linear properties of mechanical and acoustical systems. On the basis of the
knowledge of the individual subsystem properties, corresponding properties of assemblies of subsystems can
be calculated. The three matrix forms mentioned above are interrelated and can be readily transformed
[5]
amongst themselves . However, only stiffness-type quantities are specified in ISO 10846 for the
experimental characterization of resilient elements under static preload.
The general conceptual framework for the specified characterization of resilient elements is shown in Figure 1.

Figure 1 — Block diagram of source/isolators/receiver system
The system consists of three blocks, which respectively represent the vibration source, a number n of isolators
and the receiving structures. A point contact is assumed at each connection between source and isolator and
between isolator and receiver. To each connection point, a force vector F containing three orthogonal forces
3)
and three orthogonal moments and a displacement vector u containing three orthogonal translational
components and three orthogonal rotational components are assigned. In Figure 1, just one component of
each of the vectors F , u , F and u is shown. These vectors contain 6n elements, where n denotes the
1 1 2 2
number of isolators.
To show that the blocked transfer stiffness, defined in 3.7 as dynamic transfer stiffness, is suitable for isolator
characterization in many practical cases, the discussion will proceed from the simplest case of unidirectional
vibration to the multidirectional case for a single isolator.

3) Linear algebra: a vector is a linear array of elements.
ISO 10846-1:2008(E)
5.2.2 Single isolator, single vibration direction
For unidirectional vibration of a single vibration isolator, the isolator equilibrium may be expressed by the
following stiffness equations:
F = k u + k u (1)
1 1,1 1 1,2 2
F = k u + k u (2)
2 2,1 1 2,2 2
where
k and k are driving point stiffnesses when the isolator is blocked at the opposite side (i.e. u = 0,
1,1 2,2 2
u = 0, respectively);
k and k are blocked transfer stiffnesses, i.e. they denote the ratio between the force on the
1,2 2,1
blocked side and the displacement on the driven side. k = k for passive isolators,
1,2 2,1
because passive linear isolators are reciprocal.
Due to increasing inertial forces, k and k become different at higher frequencies. At low frequencies, only
1,1 2,2
elastic and damping forces play a role, making all k equal.
i,j
NOTE 1 These equations are for single frequencies. F and u are phasors and k are complex quantities.
i i i,j
The matrix form of Equations (1) and (2) is
F = Ku (3)
with the dynamic stiffness matrix
⎡⎤kk
1,1 1,2
K= (4)
⎢⎥
kk
2,1 2,2
⎣⎦
For excitation of the receiving structure via the isolator
F
k= − (5)
t
u
where k denotes the dynamic driving point stiffness of the termination. The minus sign is a consequence of
t
the convention adopted in Figure 1.
From Equations (2) and (5) it follows that
k
2,1
F = u (6)
k
2,2
1 +
k
t
Therefore, for a given source displacement u , the force F depends both on the isolator driving point dynamic
1 2
stiffness and on the receiver driving point dynamic stiffness. However, if |k | < 0,1|k |, then F approximates
2,2 t 2
the so-called blocking force to within 10 %, i.e.
FF ≈ = u (7)
k
2,1
22, b 1
Because vibration isolators are only effective between structures of relatively large dynamic stiffness on both
sides of the isolator, Equation (7) represents the intended situation at the receiver side. This forms the
background for the measurement methods of ISO 10846. Measurement of the blocked transfer stiffness (or a
directly related function) for an isolator under static preload is easier than measurement of the complete
6 © ISO 2008 – All rights reserved

ISO 10846-1:2008(E)
stiffness matrix (or the complete transfer matrix). Moreover, it forms the representative isolator characteristic
under the intended circumstances.
NOTE 2 In cases where the condition |k | << |k | is not fulfilled, Equation (6) also shows that k and k need to be
2,2 t 2,2 t
known to predict F for a given source displacement u .
2 1
5.2.3 Single isolator, six vibration directions
If forces and motions at each interface can be characterized by six orthogonal components (three translations,
three rotations), the isolator may be described as a 12-port, Reference [11]. The matrix form of the 12
dynamic force equations is equal to Equation (3), where now
uF
uF==, (8)
{} { }
uF
are the vectors of six displacements, six angles of rotation, six forces and six moments. The 12 × 12 dynamic
stiffness matrix may be decomposed into four 6 × 6 submatrices
KK
⎡⎤1,1 1,2
K= (9)
KK
⎢⎥
2,1 2,2
⎣⎦
where
K and K are (symmetric) matrices of the driving point stiffnesses;
1,1 2,2
K and K are the blocked transfer stiffness matrices.
1,2 2,1
The symmetry of the dynamic stiffness matrix in Equation (3) implies that these transfer matrices equal the
transpose of each other.
Again, if the receiver has relatively large driving point dynamic stiffnesses compared to the isolator, the forces
exerted on the receiver approximate the blocking forces:
F≈=FKu (10)
22,b 2,11
Therefore, the blocked transfer stiffnesses are appropriate quantities to characterize vibro-acoustic transfer
properties of isolators, and also in the case of multidirectional vibration transmission.
5.3 Number of relevant blocked transfer stiffnesses
In general, the blocked transfer stiffness matrix K of a single isolator contains 36 elements. However,
2,1
structural symmetry causes most elements to be zero. The most symmetrical shapes (a circular cylinder or a
square block) have 10 non-zero elements, i.e. five different pairs (see Annex B and Reference [11]).
In practical situations, the number of elements relevant for characterization of the vibro-acoustic transfer is
usually even smaller than the number of non-zero elements. In many cases, it will be sufficient to take into
account only one, two or three diagonal elements for translation vibration, i.e. for only one vibration direction
(often vertical) or for two or three perpendicular directions (see Annex C for further discussion). For these
translational directions, measurement methods will be defined in ISO 10846-2, ISO 10846-3, ISO 10846-4 and
ISO 10846-5.
For some special cases, rotational degrees of freedom also play a significant role (see Annex C). Although it
is not considered as a subject for standardization in ISO 10846, reference is made in 6.3.5 to literature that
describes how rotational elements may be handled in the same way as the translational elements.
ISO 10846-3 has an informative annex relevant to this subject.
ISO 10846-1:2008(E)
5.4 Flanking transmission
The model shown in Figure 1 and of Equations (1) to (10) is correct under the assumption that the resilient
elements form the only transfer path between the vibration source and the receiving structure. In practice,
there may be mechanical or acoustical parallel transmission paths which cause flanking transmission. For any
measurement method of isolator properties, the possible interference of such flanking with proper
measurements has to be minimized.
5.5 Loss factor
The objective of ISO 10846 is to standardize measurements of the frequency-dependent dynamic transfer
stiffnesses k of resilient elements. Certain users of ISO 10846 also will be interested in the damping
2,1
properties of isolators. However, ISO 10846 does not standardize the measurement of damping properties of
isolators because this would become overly complex. Nevertheless, in ISO 10846-2, ISO 10846-3,
ISO 10846-4 and ISO 10846-5, descriptions are given of how phase data of the complex dynamic transfer
stiffness k can be optionally used to give information about the damping properties. The discussion in this
2,1
subclause is given as background information for the procedures.
For the purposes of the discussion, it is sufficient to consider the case of 5.2.2, i.e. a single isolator and a
single vibration direction. Because only measurements with a blocked output side are considered in
ISO 10846, the phasor Equations (1) and (2) are reduced to
F = k u (11)
1 1,1 1
F = k u (12)
2 2,1 1
At low frequencies, where inertial forces play no role, there is a simple relationship between the phase angle
of the dynamic transfer stiffness and the damping properties of the resilient element. At these low frequencies,
the frequency-dependent stiffness can be approximated by
k ≈ k ≈ k (13)
1,1 2,1
This complex low-frequency dynamic stiffness can be written as
k = k (1+jh) (14)
where k denotes the real part. The frequency-dependent loss factor h in Equation (14) characterizes the
damping of the resilient element at low frequencies (see 3.8).
The relationship between the loss factor and the phase angle ϕ of k is given by
h = tan ϕ (15)
Therefore, the loss factor of a resilient element can be estimated according to
h = tan ϕ (16)
2,1
where ϕ is the phase angle of the dynamic transfer stiffness k .
2,1 2,1
The following points should be kept in mind.
a) The measurement of loss factors, using Equation (16), is sensitive to imperfections in the blocked output
condition u = 0. In Reference [18], correction procedures are described. The measurement of small loss
factors is also sensitive to phase measurement uncertainties (Reference [12], pp. 216-218).
b) For higher frequencies, where the approximations of Equation (13) are no longer valid, it is no longer
correct to use Equation (16) as a characterization of the damping properties of the resilient element.
8 © ISO 2008 – All rights reserved

ISO 10846-1:2008(E)
Although there are no simple and strict criteria for when this occurs, a rather sudden change of the slope
of η with increasing frequency is usually a good indication that Equation (16) can no longer be used.
6 Measurement principles
6.1 Dynamic transfer stiffness
The dynamic transfer stiffness is dependent on frequency. In addition, it is also dependent on static preload
and, in many cases, on temperature. It may also be dependent on relative humidity. Three methods are in use
to obtain the appropriate test data. Because they are complementary with respect to their strong and weak
points, they are all covered in ISO 10846.
The direct method requires the measurement of input displacement (velocity, acceleration) and blocking
output force.
The indirect method uses a measurement of vibration transmissibility (for displacement, velocity or
acceleration). To obtain the blocking output force, the isolator is terminated with a mass which provides a
large dynamic stiffness. In a specified frequency range, the product of the measured displacement and the
known-point dynamic stiffness of the termination should provide a good approximation of the blocking force.
The driving point method for determination of the transfer stiffness is used in test rigs in which the dynamic
force on a resilient element with a blocked output side can only be measured on the input side. The stiffness
resulting from measuring input displacement (velocity, acceleration) and input force, is the dynamic driving
point stiffness. Only at low frequencies, where the driving point stiffness and the transfer stiffness are equal,
this method can be used for determination of the dynamic transfer stiffness. Although the direct method for
measuring the dynamic transfer stiffness has a wider frequency for valid measurements than the driving point
method, including those at low frequencies, the latter is covered by ISO 10846 as well. In this way, owners of
(often expensive) test rigs for driving point stiffness measurements, are enabled to use their facilities for
determination of the low-frequency dynamic transfer stiffness as well.
The basic features of these three methods and the general requirements for their proper use are described in
this part of ISO 10846. Detailed requirements are specified in ISO 10846-2, ISO 10846-3, ISO 10846-4 and
ISO 10846-5.
6.2 Direct method
6.2.1 Basic test set-up
The basic principle for the measurement of the dynamic transfer stiffness is shown in Figure 2.
The isolator under test is placed between a vibration exciter on the input side and a rigid termination on the
output side. A dynamic force transducer is placed between the isolator and the rigid termination. Often it will
be necessary to insert force-distribution plates. These serve to approximate point contact conditions and
unidirectional motion. For example, in the case of a large isolator flange supported by a small force transducer
only, the flange vibration and therefore the dynamic transfer stiffness may deviate significantly from that in
practice. For large isolators with a high static preload, stability requirements may make it necessary to
measure the force with a number of force transducers.
The dynamic transfer stiffness is determined as
F
(17)
ku=< for 2,1
u
ISO 10846-1:2008(E)
Key
1 hydraulic actuator (static preload and dynamic excitation)
2 moveable traverse
3 columns
4 test element
5 force measurement system
6 rigid foundation
Figure 2 — Example of a typical test set-up for the direct method
6.2.2 Measurement quantities
The dynamic quantities to be measured are the force and either the displacement, velocity or acceleration.
6.2.3 Measurement under static preload
Because the dynamic transfer stiffness may be heavily dependent on static load, tests should be provided
under nominal static load conditions. Often special test rigs are needed to apply such loads. Combined static
preloading and vibration is typically applied using a hydraulic actuator on top. However, test rigs with
separated components for preloading and for vibration excitation are also considered in ISO 10846.
6.2.4 Frequency limitations of the direct method
The frequency range of validity of the direct method is mainly determined by the test rig properties. One
limitation is determined by the actuator bandwidth. Another limitation is often determined by the occurrence of
flanking transmission at high frequencies through the frame which is used to apply the static preload. The
fundamental frame mode, which usually causes serious problems, is determined by the mass of the traverse
and the longitudinal stiffness of the vertical columns. A typical upper frequency of 300 Hz < f < 500 Hz is
UL
mentioned in Table 1. These values are reported by owners of test rigs with a static load capacity up to
100 kN (see Reference [10]). Of course, for smaller and more compact rigs this upper limit would move to
higher frequencies. For example, for small-size resilient elements with small preloads, valid measurements
have been made up to several kilohertz, using very simple test set-ups.
However, generally speaking, the indirect method (see 6.3) gives better possibilities with respect to high
frequency measurements. The indirect method gives less flanking transmission because the test isolator is
dynamically uncoupled from the load frame.
10 © ISO 2008 – All rights reserved

ISO 10846-1:2008(E)
6.2.5 Directions of vibration
Although Figure 2 presents an example for stiffness measurement in the normal load direction, the direct
method can be applied for translational and rotational vibration in all directions. In ISO 10846-2 stiffness
measurements for three perpendicular translations are standardized. Use of the direct method for rotational
vibration is not considered in ISO 10846.
6.3 Indirect method
6.3.1 Basic test arrangement
The basic principle for the measurement of blocked transfer stiffness is illustrated by the examples given in
Figure 3.
The resilient element under test is fitted between two rigid masses.
The mass on the input side of the element has a dual function:
⎯ its rigidity is used to provide point contact conditions;
⎯ it may also be used to obtain unidirectional excitation in different directions (see ISO 10846-3, ISO 10846-4
and ISO 10846-5).
The mass on the output side also has a dual function:
⎯ its rigidity is used for point contact conditions on the receiver side of the isolator;
⎯ its mass and rotational inertias should be large enough to form a high dynamic stiffness termination for all
excitation components of the isolator. Therefore, the six natural frequencies of the mass/spring system
formed by combination of the test element and mass m , should be well below the frequency range of
interest (see discussion below). The forces exerted by the isolator on the mass are then approximately
equal to the blocking forces. These can be derived from the accelerations of the mass on the output side.
The displacements of the masses are denoted by u and u . The ratio u /u is usually called (displacement)
1 2 2 1
transmissibility. It is equal to the corresponding velocity and acceleration ratio.
The relationship between the dynamic transfer stiffness and the displacement transmissibility is found by
using Newton's law. Therefore,
F u
≈≈ −   for f >> (18)
(2πf ) f
km
2,1 2
uu
where f is the eigenfrequency of the mass/spring system formed by m and the test element [and, as in
0 2
Figure 3 b), by the auxiliary isolators].
Equation (18) uses the assumption of Equation (7), i.e. that F is approximately equal to the blocking force.
6.3.2 Measurement quantities
The dynamic quantity to be measured is either the displacement, velocity or acceleration.
6.3.3 Measurement under static preload
6.3.3.1 Principle of applying preload
Figure 3 shows basic principles for test rigs in which a static preload can be applied.
...