ISO 21940-2:2017

INTERNATIONAL ISO
STANDARD 21940-2
First edition
2017-05
Mechanical vibration — Rotor
balancing —
Part 2:
Vocabulary
Vibrations mécaniques — Équilibrage des rotors —
Partie 2: Vocabulaire
Reference number
ISO 21940-2:2017(E)
©
ISO 2017

---------------------- Page: 1 ----------------------
ISO 21940-2:2017(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, 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
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved

---------------------- Page: 2 ----------------------
ISO 21940-2:2017(E)

Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Mechanics . 1
3.2 Rotor systems . 3
3.3 Unbalance . 5
3.4 Balancing . 7
3.5 Balancing machines . 9
Annex A (informative) Illustrated terminology for balancing machines .12
Bibliography .21
Alphabetical index .21
© ISO 2017 – All rights reserved iii

---------------------- Page: 3 ----------------------
ISO 21940-2:2017(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 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: w w w . i s o .org/ iso/ foreword .html.
The committee responsible for this document is Technical Committee ISO/TC 108, Mechanical vibration,
shock and condition monitoring, Subcommittee SC 2, Measurement and evaluation of mechanical vibration
and shock as applied to machines, vehicles and structures.
This first edition of ISO 21940–2 cancels and replaces ISO 1925:2001, which has been technically
revised. All terms and definitions formerly contained in different balancing standards have been
reviewed and compiled in this document.
A list of all parts in the ISO 21940 series can be found on the ISO website.
iv © ISO 2017 – All rights reserved

---------------------- Page: 4 ----------------------
INTERNATIONAL STANDARD ISO 21940-2:2017(E)
Mechanical vibration — Rotor balancing —
Part 2:
Vocabulary
1 Scope
This document defines terms on balancing. It complements ISO 2041, which is a general vocabulary on
mechanical vibration and shock.
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:
— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
NOTE An illustrated terminology for balancing machines is provided in Annex A.
3.1 Mechanics
3.1.1
principal axis of inertia
one of three mutually perpendicular axes intersecting each other at a given point about which the
products of inertia of a solid body are zero
Note 1 to entry: In balancing (3.4.1), the term principal axis of inertia is used to designate the central principal
axis of inertia (of the three such axes) most nearly coincident with the shaft axis (3.2.7) of the rotor.
[SOURCE: ISO 2041:2009, 1.34, modified — converted to singular and the notes to entry have been
changed.]
3.1.2
speed
angular velocity of a rotor
Note 1 to entry: Speed is measured in revolutions per unit time or in angle (in radians) per unit time.Note 2 to
entry: The quantities most frequently used for specifying speed are
n rotational speed measured in revolutions per minute;
f rotational frequency measured in revolutions per second;
Ω angular velocity measured in radians per second.
© ISO 2017 – All rights reserved 1

---------------------- Page: 5 ----------------------
ISO 21940-2:2017(E)

3.1.3
resonance speed
DEPRECATED: critical speed
DEPRECATED: resonant speed
characteristic speed at which resonances of a system are excited
Note 1 to entry: In the context of balancing (3.4.1), a resonance speed is related only to the once-per-revolution
component of vibration.
[SOURCE: ISO 2041:2009, 2.85, modified — the notes to entry have been changed.]
3.1.4
rigid-body-mode resonance speed
resonance speed (3.1.3) of a rotor at which flexure of the rotor can be neglected
3.1.5
flexural resonance speed
resonance speed (3.1.3) of a rotor at which flexure of the rotor cannot be neglected
3.1.6
service speed
angular velocity at which a rotor operates in its final installation or environment
3.1.7
balancing speed
angular velocity at which rotor balancing (3.4.1) is performed
3.1.8
axis of rotation
instantaneous line about which a body rotates
3.1.9
rigid body mode
mode shape of a rotor corresponding to a rigid-body-mode resonance speed (3.1.4) for a given
support system
3.1.10
flexural mode
mode shape of a rotor corresponding to a flexural resonance speed (3.1.5) for a given support system
3.1.11
shape function of the nth flexural mode
ϕ (z)
n
mathematical expression for the deflection shape of the rotor in the corresponding flexural mode
(3.1.10) normalized so that the maximum deflection is unity
Note 1 to entry: Frequently, it is assumed that the modes are mutually orthogonal and the system is axially
symmetric. This is not applicable in all cases.
3.1.12
modal amplification factor
M
n
ratio of the magnitude of the modal vibration displacement vector to the magnitude of the modal
eccentricity for the nth flexural mode (3.1.10)
Note 1 to entry: Modal amplification factor is a non-dimensional quantity. It is expressed for the nth mode as
2
Ω ω
()
n
M =
n
2
2 2
2
 
14−+ΩΩωωζ
() ()
nnn
 
 
2 © ISO 2017 – All rights reserved

---------------------- Page: 6 ----------------------
ISO 21940-2:2017(E)

where
Ω is the angular velocity expressed in radians per second;
ω is the undamped natural angular frequency expressed in radians per second;
n
ζ is the modal damping ratio (3.1.13).
n
Note 2 to entry: The modal amplification factor at the flexural resonance speed (3.1.5) is called “modal sensitivity”.
3.1.13
modal damping ratio
ζ
n
measure of the damping effect on the nth flexural mode (3.1.10)
3.2 Rotor systems
3.2.1
rigid behaviour
rotor where the flexure caused by its unbalance (3.3.1) distribution can be neglected with respect to
the agreed unbalance tolerance (3.4.12) at any speed up to the maximum service speed (3.1.6)
Note 1 to entry: A rotor that behaves as rigid under one set of conditions [e.g. service speed (3.1.6), initial unbalance
(3.3.10) and unbalance tolerances (3.4.12)] may not behave as rigid under another set of conditions.
3.2.2
flexible behaviour
rotor where the flexure caused by its unbalance (3.3.1) distribution cannot be neglected with respect to
the agreed unbalance tolerance (3.4.12) at any speed up to the maximum service speed (3.1.6)
Note 1 to entry: Flexible behaviour includes shaft-elastic behaviour (3.2.3), settling behaviour (i.e. unbalance
indication irreversibly changes after the first run-up) and component-elastic behaviour (i.e. unbalance indication
reversibly changes with speed due to displacement of rotor components other than the shaft).
3.2.3
shaft-elastic behaviour
rotor where the elastic flexure due to modal unbalances (3.3.16) cannot be neglected with respect to the
agreed unbalance tolerances (3.4.12)
Note 1 to entry: Shaft-elastic behaviour of a rotor is a subset of flexible behaviour (3.2.2).
3.2.4
journal
part of a rotor that is supported radially or guided by a bearing in which it rotates
3.2.5
journal axis
mean straight line joining the centroids of cross-sectional contours of a journal (3.2.4)
3.2.6
journal centre
intersection of the journal axis (3.2.5) and the radial plane of the journal (3.2.4) where the resultant
transverse bearing force acts
3.2.7
shaft axis
line joining the journal centres (3.2.6) which follows the deflected shape of the rotor due to gravity or
any other constant force
3.2.8
inboard rotor
rotor that has its centre of mass located between the journals (3.2.4)
© ISO 2017 – All rights reserved 3

---------------------- Page: 7 ----------------------
ISO 21940-2:2017(E)

3.2.9
outboard rotor
rotor that has its centre of mass located other than between the journals (3.2.4)
3.2.10
mass eccentricity
radial distance between a centre of mass and the shaft axis (3.2.7)
Note 1 to entry: See also specific unbalance (3.3.15).
3.2.11
slow-speed runout
real or apparent deflection measured on the rotor surface at a slow speed (3.1.2) where no vibration is
caused by unbalance (3.3.1)
Note 1 to entry: Depending upon the transducer used, a slow-speed runout can contain mechanical, magnetic or
electrical components.
3.2.12
fitment
component of a rotor which has to be mounted on a shaft, a balancing mandrel (3.5.14) or a balancing
adapter so that its unbalance (3.3.1) can be determined
EXAMPLE Couplings, pulleys, pump impellers, blower fans and grinding wheels.
3.2.13
spigot
type of interface used in the coupling of rotor components to maintain concentricity
3.2.14
half-key
key used in balancing (3.4.1), having the unbalance (3.3.1) value of that portion of the final (full) key
which occupies either the shaft keyway or the fitment (3.2.12) keyway in the final assembly
Note 1 to entry: See Figure 1.
1
Key
1 half-key for fitment
2 half-key for shaft
Figure 1 — Contoured half-key set
4 © ISO 2017 – All rights reserved

---------------------- Page: 8 ----------------------
ISO 21940-2:2017(E)

3.3 Unbalance
3.3.1
unbalance
condition that exists in a rotor when vibration force or motion is imparted to it and its bearings from
centrifugal forces of mass eccentricities (3.2.10)
3.3.2
unbalance mass
mass whose centre is at a radial distance from the shaft axis (3.2.7)
3.3.3
unbalance vector
vector whose magnitude is the amount of unbalance (3.3.4) and whose direction is the angle of
unbalance (3.3.5)
3.3.4
amount of unbalance
product of the unbalance mass (3.3.2) and the radial distance of its centre of mass from the shaft
axis (3.2.7)
3.3.5
angle of unbalance
polar angle at which an unbalance mass (3.3.2) is located with reference to the given rotating coordinate
system, fixed in a plane perpendicular to the shaft axis (3.2.7) and rotating with the rotor
3.3.6
static unbalance
component of the unbalance (3.3.1) that corresponds to a parallel misalignment of the central principal
axis of inertia (3.1.1) of the rotor with respect to the shaft axis (3.2.7)
Note 1 to entry: The amount of the static unbalance is equal to the product of the total mass of the rotor and the
radial distance of its centre of mass from the shaft axis.
3.3.7
moment unbalance
component of the unbalance (3.3.1) that corresponds to an inclined central principal axis of inertia
(3.1.1) intersecting the shaft axis (3.2.7) at the centre of mass
Note 1 to entry: The dimension of a moment unbalance is mass times length squared.
Note 2 to entry: This condition can be produced by two unbalance vectors (3.3.3) with equal amounts and
opposing directions, acting in two different planes perpendicular to the shaft axis, which thereby constitute a
couple unbalance (3.3.8).
3.3.8
couple unbalance
two unbalance vectors (3.3.3) with equal amounts and opposing directions, acting in two different
planes perpendicular to the shaft axis (3.2.7)
Note 1 to entry: A couple unbalance is an alternative representation of a moment unbalance (3.3.7) with the
amount of each of the two unbalance vectors calculated by dividing the amount of moment unbalance by the
distance between the two planes of the couple unbalance.
3.3.9
dynamic unbalance
state of unbalance (3.3.1) that corresponds to the central principal axis of inertia (3.1.1) having any
inclined and offset position relative to the shaft axis (3.2.7)
Note 1 to entry: This condition can be produced by adding a couple unbalance (3.3.8) and a static unbalance (3.3.6)
to an unbalance-free rotor.
© ISO 2017 – All rights reserved 5

---------------------- Page: 9 ----------------------
ISO 21940-2:2017(E)

Note 2 to entry: This condition can be produced equivalently by two unbalance vectors (3.3.3) acting in two
different planes perpendicular to the shaft axis.
3.3.10
initial unbalance
unbalance (3.3.1) of any kind that exists in a rotor before balancing (3.4.1)
3.3.11
residual unbalance
unbalance (3.3.1) of any kind that remains in a rotor after balancing (3.4.1)
3.3.12
resultant unbalance
U
r
vector sum of all unbalance vectors (3.3.3) distributed along the rotor
3.3.13
resultant moment unbalance
P
r
vector sum of the moments of all the unbalance vectors (3.3.3) distributed along the rotor with respect
to an arbitrarily selected plane perpendicular to the shaft axis (3.2.7)
3.3.14
resultant couple unbalance
C
r
pair of two unbalance vectors (3.3.3) of equal magnitude acting in opposite directions in two arbitrarily
selected planes perpendicular to the shaft axis (3.2.7) thereby constituting a moment unbalance (3.3.7)
equivalent to the resultant moment unbalance (3.3.13)
3.3.15
specific unbalance
e
amount of unbalance (3.3.4) divided by the mass of the rotor
Note 1 to entry: The specific unbalance calculated with the amount of static unbalance (3.3.6) is numerically
equivalent to the mass eccentricity (3.2.10).
3.3.16
nth modal unbalance
U
n
unbalance (3.3.1) distribution which only affects the nth flexural mode (3.1.10) of a rotor and
support system
3.3.17
equivalent nth modal unbalance
U
ne
minimum single unbalance (3.3.1) equivalent to the nth modal unbalance (3.3.16) in its effect o
...