ISO 10813-4:2022

INTERNATIONAL ISO
STANDARD 10813-4
First edition
2022-04
Vibration generating machines —
Guidance for selection —
Part 4:
Equipment for multi-axial
environmental testing
Générateurs de vibrations — Lignes directrices pour la sélection —
Partie 4: Équipement pour les essais environnementaux multi-axiaux
Reference number
© ISO 2022
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ii
Contents Page
Foreword .v
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Requirements for multi-axial environmental tests . 2
4.1 Multi-axial vibration test motivation . 2
4.2 Test waveforms . 3
4.3 Types of multi-axial environmental testing . 3
4.3.1 General . 3
4.3.2 Parallel thrust testing . . 3
4.3.3 Bi-axial vibration testing . 3
4.3.4 Tri-axial vibration testing . 4
4.3.5 Six-degrees-of-freedom vibration testing . 4
4.3.6 Other multi-degrees-of -freedom testing . 4
5 Multi-axial vibration test equipment .4
5.1 Types of multi-axial vibration test equipment . 4
5.1.1 General . 4
5.1.2 Parallel thrust equipment . 4
5.1.3 Bi-axial linear vibration equipment . 4
5.1.4 Tri-axial linear vibration equipment . 6
5.1.5 Six-degrees-of-freedom test equipment . 6
5.1.6 Other multi-axial test equipment . 8
5.2 Coordinate system . 8
5.3 Typical configurations for multi-axial testing . 8
6 Main components of multi-axial test equipment .10
6.1 Exciter . 10
6.2 Table . 11
6.3 Connectors .12
6.3.1 General .12
6.3.2 Spherical connector .12
6.3.3 Planar connector . 14
6.3.4 Orthogonal linear bearing set . 15
6.3.5 Drive rod . 16
6.3.6 Other connectors . . . 17
6.4 Other components . 17
7 System parameters.18
7.1 General . 18
7.2 Number of exciters . 18
7.3 Number of total, linear and angular degrees of freedom . 18
7.4 Maximum displacement . 19
7.5 Maximum velocity . 19
7.6 Maximum acceleration . 19
7.7 Maximum angular displacement . 19
7.8 Maximum angular velocity . 20
7.9 Maximum angular acceleration .20
7.10 Frequency range . 21
7.11 Parasitic motion . 21
7.11.1 General . 21
7.11.2 Harmonic distortion . . 21
7.11.3 Non-uniformity ratio .22
7.11.4 Transverse motion . 22
iii
7.12 Maximum payload . 23
7.13 Maximum torque . 23
7.14 Table suspension stiffness .23
8 Selection procedures .23
8.1 General .23
8.2 Determination of the exciter and connector numbers . 24
8.3 Determination of exciter types . 24
8.3.1 General . 24
8.3.2 Test waveform . 24
8.3.3 Frequency range .25
8.3.4 Maximum displacement, velocity, and acceleration . 25
8.3.5 Maximum force . 25
8.3.6 Validation of the proposed selection . 26
8.3.7 Other factors to be considered . 26
Annex A (informative) Examples of selections .27
Bibliography .34
iv
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 on 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 the following
URL: www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 108, Mechanical vibration, shock and
condition monitoring, Subcommittee SC 6, Vibration and shock generating systems.
A list of all parts in the ISO 10813 series can be found on the ISO website.
v
Introduction
Selection of a suitable vibration generating system is an urgent problem as one needs to purchase new
test equipment or to update the equipment already at one's disposal to perform a certain test or to
choose from among the equipment proposed by a test laboratory or even a laboratory itself which offers
its service to carry out such a test. A problem like this can be resolved only if a number of factors are
considered simultaneously, as follows:
— type of test to be carried out (environmental testing, normal and/or accelerated, dynamic structural
testing, diagnosis, calibration, etc.);
— requirements to be followed;
— test conditions (single or multiple excitation, one mode of vibration or combined vibration, single or
combined test, for example, dynamic plus climatic, etc.);
— objects to be tested.
This document deals only with equipment to be used for multi-axial environmental testing, and
procedures of the selection are predominant to meet the requirements of this testing.
Because the multi-axial environmental test system is composed of more than one exciter, ISO 10813-1
should be used along with this document to select the proper exciters. It is presumed in this document
that the system to be selected will be able to drive the object under test up to a specified level. In order
to generate an excitation without undesired motions, a suitable control system should be used, however
selection of a control system lays beyond the scope of this document.
It should be emphasized that vibration generating systems are complex machines, so the correct
selection always demands a certain degree of engineering judgement. As a consequence the purchaser,
when selecting the vibration test equipment, may resort to the help of a third party. In such a case, this
document can help the purchaser to ascertain if the solution proposed by the third party is acceptable
or not. Designers and manufacturers can also use this document to assess the market environment.
vi
INTERNATIONAL STANDARD ISO 10813-4:2022(E)
Vibration generating machines — Guidance for selection —
Part 4:
Equipment for multi-axial environmental testing
1 Scope
This document gives guidance for the selection of vibration generating equipment for multi-axial
environmental testing, depending on the test requirements.
Multi-axial environmental test equipment dealt with in this document refers to a vibration test system
having controlled vibration of more than one degree of freedom, including linear vibration and angular
vibration. In this document, one or more exciter per desired degree of freedom is supposed.
The guidance covers such aspects of selection as
— number, type and models of exciters,
— number, type and models of connectors,
— system configuration, and
— some components.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 2041, Mechanical vibration, shock and condition monitoring — Vocabulary
ISO 10813-1, Vibration generating machines — Guidance for selection — Part 1: Equipment for
environmental testing
ISO 15261, Vibration and shock generating systems — Vocabulary
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 2041 and ISO 15261 and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at http:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
exciter
vibration generator
excitation source where vibratory forces are generated
3.2
table
platform on which specimens or fixtures are mounted
3.3
multi-exciter system
vibration generating system which includes two or more exciters (3.1) and a control system to
coordinate the motion
3.4
connector
device used to transmit the excitation force from exciters (3.1) to the table (3.2) or specimens with the
capability of decoupling the linear motions between exciters (3.1)
3.5
spherical connector
connector (3.4) with spherical joints
Note 1 to entry: Normally spherical connector has one or two spherical joints (see Figure 7).
3.6
planar connector
connector (3.4) having planar restriction which is capable of moving in two orthogonal axes in that
plane
Note 1 to entry: Some planar connectors also have another single-degree-of-freedom (1-DOF) rotational motion
in the plane.
3.7
drive rod
stinger
rod with a large length-diameter ratio, stiff in the longitudinal direction and flexible in the transverse
direction
3.8
parasitic motion
undesired motion of the table (3.2) that occurs when multi-axial excitation is carried out over the table
(3.2)
3.9
guidance system
mechanical device used to guide the exciter (3.1) to move in the axial direction, providing transverse
motion restraint to the exciter (3.1)
4 Requirements for multi-axial environmental tests
4.1 Multi-axial vibration test motivation
In the real world, pure single axis vibration does not exist, meaning that the real vibration environment
is multi-axial. However due to test equipment restrictions, multi-axial vibration testing is mainly
conducted one axis after another sequentially, which has different impacts on the specimens than
multi-axial simultaneous vibration tests. It is reported that some devices failed in the real multi-
axial environment after single axis vibration testing was conducted with no abnormities observed.
Therefore, to simulate the real vibration environment and help discover the product malfunction
rationale due to multi-axial vibration, the need to conduct a real multi-axial vibration testing has been
growing dramatically.
[4][5]
The most common reasons to conduct a multi-axial vibration test are listed below :
— Distributed multi-axial vibration or shock energy is applied over the specimen in a controlled
manner without relying on the dynamics of the specimens for such distribution.
— Multi-axial testing can be selected when the specimen has a high slenderness ratio for energy
distribution considerations.
— Multi-exciter system is selected to increase the thrust force in order to achieve the desired vibration
level for large and heavy specimens.
— Some multi-axial vibration test systems are constructed to increase the overall test efficiency
because the tests of different axes can be conducted simultaneously rather than sequentially.
— Multi-axial vibration testing is conducted on inertial measurement units which are subject to
linear and angular vibration and the measuring accuracy is highly dependent on the multi-axial
environment.
— Multi-axial vibration testing is conducted in several directions rotationally or translationally to
meet test criteria or to reproduce in-service measurement data, such as automotive or earthquake
simulations.
— Multi-axial vibration testing can be selected to avoid the need to design and fabricate a very
expensive fixture that may be used only once.
— Multi-axial vibration testing can be selected to provide a compensating force to counteract large
overturning moments, which may occur during testing of tall structures, such as satellites with
several meters of height of centre of gravity.
4.2 Test waveforms
Multi-axial vibration testing mainly deals with the following waveforms:
— wide-band random;
— time history waveform replication.
NOTE Sinusoidal testing, including swept and fixed frequency sinusoidal testing, is not common in practice
for multi-axial configuration, but is achievable.
4.3 Types of multi-axial environmental testing
4.3.1 General
Typical multi-axial environmental vibration testing includes the following types.
4.3.2 Parallel thrust testing
Parallel thrust testing is used to excite one specimen at multiple points in parallel directions. The
purpose is to simulate the real multi-excitation parallel working environment. Typical tests include
automobile vibration testing through four wheels under independent excitations and missile vibration
testing through dual excitation points.
4.3.3 Bi-axial vibration testing
The purpose of bi-axial vibration testing is to excite the specimen from two orthogonal directions. It
is a simplified condition of tri-axial vibration testing, which is suitable when the specimen is firmly
constrained in one direction and therefore the vibration in that direction has little impact. The two
orthogonal directions can be two horizontal directions or one horizontal and one vertical direction.
4.3.4 Tri-axial vibration testing
The purpose of tri-axial vibration testing is to excite the specimen from three orthogonal directions
to simulate the actual tri-axial vibration environment for most real-world objects when rotational
excitations are not considered.
4.3.5 Six-degrees-of-freedom vibration testing
The purpose of six-degrees-of-freedom (6-DOF) vibration testing is to simulate a complete 6-DOF
spatial vibration of a specimen, including three-degrees-of-freedom (3-DOF) of linear vibration and
3-DOF of angular vibration. It is useful for specimens which are sensitive to angular vibration such as
inertial measurement units.
4.3.6 Other multi-degrees-of -freedom testing
Depending on conditions of the actual vibration environment, any number of degrees of freedom
(DOFs), but no less than 2 and no more than 6 per excitation point, may be required to conduct the test.
5 Multi-axial vibration test equipment
5.1 Types of multi-axial vibration test equipment
5.1.1 General
In order to meet various multi-axial vibration testing requirements, many kinds of test equipment have
been developed. Typical types of multi-axial vibration test equipment are listed in 5.1.2 to 5.1.6.
5.1.2 Parallel thrust equipment
In order to produce the force required for a test which cannot be satisfied by single exciters or to adapt to
testing slender specimens, multiple exciters are aligned in parallel. The exciters can be controlled in or
out of synchronization or completely independently. Angular vibration can be generated when exciters
are driven at different amplitudes or phases. The selection of an amplitude and phase synchronized
multi-exciter test system can be considered as the selection of a single vibration generator (see
ISO 10813-1), and is therefore not included in this document. Figure 1 shows an example of a parallel
thrust configuration in which a slender specimen is excited vertically by two independent exciters
at two excitation points with connectors decoupling motion contradictions brought about by exciter
asynchrony. A suspension device is applied to offset the specimen mass.
5.1.3 Bi-axial linear vibration equipment
Bi-axial linear vibration equipment is composed of two exciters in orthogonal coordinates. Linear
vibration testing in two orthogonal directions can be generated simultaneously and angular vibration
test cannot be performed. Figure 2 shows an example of a bi-axial linear vibration configuration, in
which two exciters are arranged in a vertical/horizontal manner. The table is linked with the two
exciters through the two connectors. Adapters can be employed when necessary to couple the table
with the connectors.
NOTE There are occasions when two exciters are not available or it is too expensive to construct a real bi-
axial test system. “Bi-axial” testing can be conducted by a one exciter configuration, in which the axis of the
exciter is at a specific angle, i.e. 45°, with respect to the two concerning axes. This method is essentially a single
[3]
axis test but can be taken as a synchronized bi-axial test as well. See IEC 60068-3-3 for a detailed description of
this method.
Key
1 exciter 1 4 suspension
2 connector 1 5 connector 2
3 specimen 6 exciter 2
Figure 1 — Example of parallel thrust equipment
Key
1 exciter 1 5 connector 2
2 connector 1 6 exciter 2
3 table 7 pedestal
4 adaptor
Figure 2 — Example of bi-axial linear vibration equipment
5.1.4 Tri-axial linear vibration equipment
Tri-axial linear vibration equipment is composed of many exciters in three orthogonal coordinates.
Simultaneous rectilinear vibrations in three orthogonal directions can be generated and angular
vibration test cannot be performed. Figure 3 shows an example of a tri-axial linear vibration
configuration, in which three exciters are arranged in a Cartesian coordinate. In this example, 6 dual
sphere connectors are used to decouple the table motion and restrain unwanted motions. Air spring
isolations are placed between the equipment and the ground to reduce vibration transmission to the
laboratory.
Key
1 exciter 1 5 table
2 exciter 2 6 connectors 3’ and 3’’
3 connectors 1’ and 1’’ 7 exciter 3
4 connectors 2’ and 2’’ 8 pedestal
Figure 3 — Example of three-exciters in orthogonal coordinate configuration
NOTE There are occasions when more than two exciters are not available or it is too expensive to construct a
real tri-axial test system. “Tri-axial” testing can be conducted by two exciter configurations, in which one exciter
is vertically assigned and the other is horizontally assigned. This method is essentially a bi-axial test but can be
taken as a synchronized tri-axial test as well. See IEC 60068-3-3 for a detailed description of this method.
5.1.5 Six-degrees-of-freedom test equipment
The 6-DOF test equipment is composed of no less than six exciters. At least two exciters are required
to act in parallel to generate an angular vibration. The basic motion 6-DOF equipment can generate
includes linear vibration in the three orthogonal axes and three angular vibrations about the orthogonal
axes. By controlling the basic motion properly, spatial in-axis or out-of-axis translational and rotational
vibration can be generated.
Typical 6-DOF test systems can be configured as follows:
— System composed of 6 exciters in orthogonal coordinate with three exciters in the vertical direction,
other three exciters in horizontal directions (two in X axis, one in Y axis), shown in Figure 4.
— System composed of 8 exciters in orthogonal coordinate with four exciters in the vertical direction,
other four exciters in horizontal directions (two for each axis), shown in Figure 5.
Key
1 exciter 1 6 connector 3 11 connector 6
2 exciter 2 7 exciter 3 12 exciter 5
3 connector 1 8 connector 4 13 exciter 6
4 connector 2 9 exciter 4 14 pedestal
5 table 10 connector 5
Figure 4 — Example of a 6-DOF vibration system composed of 6 exciters and 6 connectors
Key
1 exciter 1 7 exciter 4 13 connector 7
2 exciter 2 8 connector 5 14 connector 8
3 connector 1 9 table 15 exciter 8
4 connector 2 10 exciter 5 16 exciter 7
5 exciter 3 11 connector 6 17 pedestal
6 connector 3 12 exciter 6
NOTE Connector 4 is hidden.
Figure 5 — Example of a 6-DOF vibration system composed of 8 exciters and 8 connectors
NOTE The exciters can be any type in practice although the examples given in Figures 1 to 5 take
electrodynamic vibration generators as exciters.
5.1.6 Other multi-axial test equipment
Other multi-axial test equipment can be constructed to meet special testing requirements.
There are also some special multi-axial test systems. For instance, a system in which the coordinate
plane of the exciters and the coordinate plane of the table are neither parallel nor perpendicular can
generate a multi-axial testing environment in accordance with a special axis system. For example, a
Stewart platform is a typical 6-DOF motion platform, which is composed of 6 exciters arranged with a
special angle, neither parallel nor perpendicular, with the table coordinates.
NOTE Consult manufacturers for special multi-axial system requirements.
5.2 Coordinate system
See Figure 6.
Key
1 table
X, Y horizontal axes
Z vertical axis
α rotation about the X axis
β rotation about the Y axis
γ rotation about the Z axis
O centre point on the surface of the table in geometry
NOTE The centre of gravity of the table (point C) is not shown in the figure. Axes X, Y, Z form a Cartesian
coordinate system.
Figure 6 — Coordinate system of a multi-axial system
5.3 Typical configurations for multi-axial testing
Typical configurations of a multi-axial vibration test system can be found in Table 1. The “Conf. Code”
is unique to every configuration so that the code can be used to represent the arrangement of exciters.
Table 1 — Typical configuration of multi-axial vibration test system
Conf. Graphical rep-
Description N N N N
t l a e
a
Code resentation
C1 Two exciters in parallel. 2 1 1 2
C2 Three exciters in parallel. 2-DOF of angular vibra- 3 1 2 3
tion can be achieved when exciters are driven out
of phase.
C3 Four exciters in parallel. 2-DOF of angular vibra- 3 1 2 4
tion can be achieved when exciters are driven out
of phase.
C4 Two exciters in orthogonal directions, horizontal- 2 2 0 2
ly assigned.
C5 Two exciters in orthogonal directions, one hori- 2 2 0 2
zontally and one vertically assigned.
C6 Three exciters in orthogonal directions. 3 3 0 3
b
C7 One exciter in Y axis, providing linear motion 6 3 3 6
along Y axis; Two exciters in X axis, providing lin-
ear motion along X axis and rotation about Z axis;
Three exciters in Z axis, providing linear motion
in Z axis and rotation about X and Y axes.
Key
N : Number of total DOFs (see 7.3).
t
N : Number of linear DOFs (see 7.3).
l
N : Number of angular DOFs (see 7.3).
a
N : Number of exciters (see 7.2).
e
a
The graphical representation is an abbreviated view of the multi-axial vibration test equipment looking upward from
the bottom. The connectors are not shown in this representation. The definition of the elements used in the graphical
representation is as follows:
A horizontal exciter, including its associated connector.
A vertical exciter, including its associated connector.
The table, fixture or specimen from the bottom view.
b
Axes X, Y, Z are according to Figure 6.
Table 1 (continued)
Conf. Graphical rep-
Description N N N N
a t l a e
Code resentation
C8 One exciter in Y axis, providing linear motion 6 3 3 6
along Y axis; Two exciters in X axis, proving linear
motion along X axis and rotation about Z axis;
Three exciters in Z axis, providing linear motion
in Z axis and rotation about X and Y axes.
C9 One exciter in Y axis, providing linear motion 6 3 3 7
along Y axis; Two exciters in X axis, providing lin-
ear motion along X axis and rotation about Z axis;
Four exciters in Z axis, providing linear motion in
Z axis and rotation about X and Y axes.
C10 Two exciters each in X and Y axes, providing linear 6 3 3 8
motion along X and Y axes and rotation about Z
axis; Four exciters in Z axis, providing linear mo-
tion in Z axis and rotation about X and Y axes.
C11 Two exciters each in X and Y axes, providing linear 6 3 3 8
motion along X and Y axes and rotation about Z
axis; Four exciters in Z axis, providing linear mo-
tion in Z axis and rotation about X and Y axes.
C12 Four exciters in X and Y axis, providing linear mo- 6 3 3 12
tion along X and Y axis and rotation about Z axis;
Four exciters in Z axis, providing linear motion in
Z axis and rotation about X and Y axis.
Key
N : Number of total DOFs (see 7.3).
t
N : Number of linear DOFs (see 7.3).
l
N : Number of angular DOFs (see 7.3).
a
N : Number of exciters (see 7.2).
e
a
The graphical representation is an abbreviated view of the multi-axial vibration test equipment looking upward from
the bottom. The connectors are not shown in this representation. The definition of the elements used in the graphical
representation is as follows:
A horizontal exciter, including its associated connector.
A vertical exciter, including its associated connector.
The table, fixture or specimen from the bottom view.
b
Axes X, Y, Z are according to Figure 6.
6 Main components of multi-axial test equipment
6.1 Exciter
The most common types of exciters being used for multi-axial environmental testing are electrodynamic
vibration generators and servo-hydraulic vibration generators.
Typically, electrodynamic vibration generators are suitable for higher frequencies with low waveform
deformation, whereas servo-hydraulic vibration generators are suitable for long stroke and low
frequency test conditions. Refer to ISO 10813-1 for detailed characteristics and selection procedures of
electrodynamic vibration generators and servo-hydraulic vibration generators.
Other forms of exciters exist, such as mechanical vibration generators, electric servo cylinders or
linear motors, which are not typical components of multi-axial vibration test systems. Selection of such
exciters is not included in this document. Users may consult manufacturers regarding specific test
requirements.
6.2 Table
The table is a platform on which the specimens or fixtures are mounted. The forces of the exciters
merge in the table and are then transmitted to the specimens or fixtures. The table should be designed
using modal analysis and optimization methods, with the aim of making the table low in mass and high
in resonance frequency. This will make the table capable of working over a broader frequency range
without consuming much vibration force. The table must be constructed in such a manner as to avoid
undesired motions, particularly to be resistant to flexural deformation. An example of typical table
parameters is given in Table 2.
Exciters coupled to the table normally provide a static suspension force. In some situations, extra
suspension may be required. Typical situations include: 1) The load capacity of the table provided by
exciters cannot satisfy the loading requirement of the test specimen; 2) The exciters cannot provide
sufficient linear or rotational stiffness (see 7.4) to the table which may incur test failure.
Typical suspension solutions include the following: 1) air spring support (including air bags in a
hydraulic cylinder); 2) steel spring support; 3) elastic cable hanging; 4) rubber. For example to increase
the stiffness in the lateral direction for the case shown in Figure 3, springs (air spring or steel spring)
can be affixed opposite of the two horizontal exciters providing a lateral squeezing force to the table.
NOTE 1 There are situations where no table is needed in a multi-axial vibration system and specimens
or fixtures are linked directly with connectors or exciters. For example, in Figure 1, no table is used and the
connector is connected with the fixture.
NOTE 2 There are situations where exciters are installed inside the table as the table has a hollow structure
with the outer faces functioning as mounting interfaces.
Table 2 — Example of typical table parameters for multi-axial vibration test systems
[1]
Maximum frequency
Surface dimension Mass
f
max
length (mm) × width (mm) kg
Hz
500 × 500 30 1 000
600 × 600 60 800
800 × 800 120 500
1 000 × 1 000 200 400
1 200 × 1 200 300 300
1 500 × 1 500 500 250
2 000 × 2 000 1 000 150
3 000 × 3 000 4 300 100
NOTE 1 The values listed in the table are general estimations and given as an example. Consult manufacturers for specific
parameters.
NOTE 2 The values listed in the table are given when using magnesium as the material of the table because magnesium is
dominant in making key moving structures due to its high stiffness and low density. Other materials can be employed in
manufacturing the table such as aluminium; the mass and resonant frequencies should be calculated accordingly.
NOTE 3 Height of the table is not given in the table because it is heavily associated with the design of the table depending
on connector type, dimensions and other factors.
6.3 Connectors
6.3.1 General
As the driving motion of each exciter differs in amplitude, phase or direction, rigid connections between
the exciters and the table would result in a solid assembly with the exciters and table incapable of
moving in any direction at all. Connectors are the mechanical device used to connect the table and the
exciters, flexible in certain directions in order to decouple the motion between the exciters. Normally
one connector brings in 2 degrees to 5 degrees of freedom to the system.
Connectors mainly include the following types.
6.3.2 Spherical connector
Spherical connectors can have one or two spheres. One single sphere connector has one spherical
joint (shown in Figure 7 a), providing 3 DOFs of rotation and incapable of moving in the translational
direction. Plate A and plate B in Figure 7 are connecting interfaces used to couple the two objects in
relative motion, such as exciter and table. For single sphere connectors, the spherical joint is connected
rigidly with Plate A and the coupling joint is connected rigidly with Plate B. A double sphere connector
has two spherical joints (shown in Figure 7 b), providing 3 DOFs of rotation and 2 DOFs of translational
motion, which is a good choice for decoupling multi-axial motion conflicts. The sphere connection
between the spherical joint and the coupling joint creates 3 DOFs of rotation at the connection surface
by preloading and lubricating the interaction surface.
a)  Single sphere connector b)  Double sphere connector
Key
1 plate A 5 plate A
st
2 spherical joint 6 the 1 spherical joint
3 coupling joint 7 coupling joint
nd
4 plate B 8 the 2 spherical joint
9 plate B
[ ]
Figure 7 — Typical designs of a spherical connector 6
NOTE Single sphere connectors can serve as the decoupling component in such a way that they are connected
to each end of an actuator, i.e. servo-hydraulic actuator. This usage has the same decoupling utility as double
sphere connectors. In this document, the use of double sphere connectors can be replaced by the use of two
linked single sphere connectors.
Classified by lubrication methods, there are normally mechanical spherical connectors and hydrostatic
spherical connectors used for multi-axial test systems. Mechanical spherical connectors have simpler
structures, but the friction force is relatively higher causing a high force loss and high transverse
motion in the table performance. Hydrostatic spherical connectors, having the quality of low friction
and high frequency transmissibility, are used widely in decouple multi-axial vibration motion.
Double sphere connectors have transverse motion capabilities as illustrated in Figure 8. Plates A and B
have relative motion in a transverse direction relative to the exciter axis. In Figure 8, it can be seen that
when the spheres rotate by an angle θ, the transverse displacement of the connector is Dl=⋅sinθ . The
C
connector gets shorter in the vertical direction by Dl=⋅ 1c− osθ . This indicates that when selecting
()
L
double sphere connectors, the displacement of the exciters is not equal to the displacement of the table
in one particular axis with the difference being D . When θ is small, D could be neglected in practice.
L L
Key
1, 4 plate A
2, 3 plate B
Figure 8 — Transverse displacement of dou
...