ISO 21940-14:2026

International
Standard
ISO 21940-14
Second edition
Mechanical vibration — Rotor
2026-09
balancing —
Part 14:
Procedures for assessing balance
errors
Vibrations mécaniques — Équilibrage des rotors —
Partie 14: Modes opératoires d'évaluation des erreurs
d'équilibrage
Reference number
© ISO 2026
All rights reserved.
This ISO publication is protected by copyright and is owned by ISO and/or its licensors.
The content of this ISO publication is provided under licence, not sold. Use is subject to the applicable licence terms issued by ISO,
an ISO member body, or an authorized third-party distributor.
Except as required for implementation or expressly permitted by a separate licence, no part of this ISO publication may be
reproduced, distributed, modified, used, or made available in any form or by any means – electronic or mechanical, including
photocopying, scanning, recording, or posting on internal or external digital platforms.
Any use beyond the scope of the granted rights is prohibited and may result in legal action.
ISO copyright office
CP 401 • CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Balance error sources . 2
4.1 General .2
4.2 Examples of systematic errors .2
4.3 Examples of randomly variable errors .3
4.4 Examples of scalar errors .3
5 Balance error assessment . 3
5.1 General .3
5.2 Balance errors caused by balancing equipment and instrumentation .3
5.3 Balance errors caused by component radial and axial runout .4
5.4 Balance errors caused by deviation of the rotor configuration on the balancing machine
from the configuration at service .5
5.5 Assessment of balancing operation errors .5
5.6 Experimental assessment of randomly variable and scalar errors .6
5.6.1 General .6
5.6.2 Procedure .6
5.7 Experimental assessment of systematic errors .6
6 Combined error evaluation . 7
7 Balance criteria . 8
8 Accounting for measurement errors in the balance quality verification process. 9
Annex A (informative) Error examples, their identification and evaluation .10
Bibliography .18

iii
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 document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
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 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 second edition cancels and replaces the first edition (ISO 21940-14:2012), which has been technically
revised. It also incorporates the Amendment ISO 21940-14:2012/Amd.1:2022.
The main changes are as follows:
— the extension of the term “error” to "deviations" of the rotor’s state of assembly on the balancing machine
from the fully assembled rotor in service.
A list of all parts in the ISO 21940 series can be found on the ISO website.
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
Introduction
[1]
The balance quality of a rotor is assessed in accordance with the requirements of ISO 21940-11 or
[2]
ISO 21940-12 by measurements taken on the rotor. These measurements can contain errors which
originate from a number of sources. Where those errors are significant, they should be taken into account
when defining the required balance quality of the rotor.
[1] [2]
ISO 21940-11 and ISO 21940-12 do not consider balancing errors in detail. Therefore this document
gives examples of typical errors that can occur and provides recommended procedures for their evaluation.

v
International Standard ISO 21940-14:2026(en)
Mechanical vibration — Rotor balancing —
Part 14:
Procedures for assessing balance errors
1 Scope
This document specifies the requirements for
— identifying errors in the unbalance measuring process of a rotor including all factors similar to errors in
their effect on the balancing precision,
— assessing the identified errors, and
— taking errors into account in preparation and realization of the balancing process and in the evaluation
of the residual unbalance.
For the main typical errors this document lists the methods for their reduction in Annex A.
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 21940-2, Mechanical vibration — Rotor balancing — Part 2: Vocabulary
ISO 21940-11:2016, Mechanical vibration — Rotor balancing — Part 11: Procedures and tolerances for rotors
with rigid behaviour
ISO 21940-21, Mechanical vibration — Rotor balancing — Part 21: Description and evaluation of balancing
machines
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 21940-2 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at http:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
balancing error
known or unknown variable quantity by which the actual balance condition of a rotor differs from the
intended balance condition
4 Balance error sources
4.1 General
Balancing machine balance errors can be classified into:
a) systematic errors, in which the magnitude and angle can be evaluated either by calculation or
measurement;
b) randomly variable errors, in which the magnitude and angle vary in an unpredictable manner over a
number of measurements carried out under the same conditions;
c) scalar errors, in which the maximum magnitude can be evaluated or estimated, but its angle is
indeterminate.
Depending on the manufacturing processes used, the same error can be placed in one or more categories. In
the balancing process scalar errors and randomly variable errors are dealt with similarly.
Examples of error sources which can occur are listed in 4.2, 4.3 and 4.4 and for a detailed discussion of some
of the these errors see Annex A.
4.2 Examples of systematic errors
Examples of systematic error sources on a balancing machine:
a) inherent unbalance in the drive shaft;
b) inherent unbalance in the mandrel;
c) radial and axial runout of the drive element on the rotor shaft axis;
d) radial and axial runout in the fit between the components to be balanced or in the balancing machine
mandrel (see 5.3);
e) lack of concentricity between the journals and support surfaces used for balancing;
f) radial and axial runout of rolling bearings which are not the service bearings and which are used to
support the rotor;
g) radial and axial runout of rotating races (and their tracks) of rolling service bearings fitted after
balancing;
h) unbalance due to keys and keyways;
i) residual magnetism in the rotor or mandrel;
j) reassembly errors;
k) balancing equipment and instrumentation errors;
l) differences between service shaft and balancing mandrel diameters;
m) universal joint related errors;
n) temporary bend in the rotor during balancing;
o) permanent bend in the rotor after balancing;
p) components detached from the rotor on the balancing machine with known unbalance and fixed angular
position on the rotor.
4.3 Examples of randomly variable errors
Examples of randomly variable error sources on a balancing machine:
a) loose parts;
b) entrapped liquids or solids;
c) distortion caused by thermal effects;
d) windage effects;
e) use of a loose coupling as a drive element;
f) transient bend in the horizontal rotor caused by gravitational effects when the rotor is stationary;
g) components detached from the rotor on the balancing machine with unknown unbalance and arbitrary
angular position on the rotor;
h) faulty reassembly of detached rotor components.
4.4 Examples of scalar errors
Examples of scalar error sources on a balancing machine:
a) changes in clearance at interfaces that are intended to be disassembled after the balancing process;
b) clearance in universal joints;
c) clearance on the mandrel or shaft;
d) design and manufacturing tolerances;
e) runout of the balancing machine support rollers if their diameters and the rotor journal diameter are
the same or have an integer ratio;
f) a nearby machine running at same speed;
g) components detached from the rotor on the balancing machine with known unbalance and arbitrary
angular position on the rotor.
5 Balance error assessment
5.1 General
In some cases, rotors are in balance by design, are uniform in material and are machined to such tight
tolerances that there is no need for balancing after manufacture. Where rotor initial unbalance exceeds the
[1] [2]
values given in ISO 21940-11 or ISO 21940-12 the rotor should be balanced.
When balancing a rotor, several sources of errors occur. The following considerations on errors in the
balancing process are valid both for rotors with rigid behaviour and rotors with flexible behaviour. Due to
the widely varying procedures for balancing flexible rotors, it is advisable to adopt the provision for errors
to the respective procedure and the importance of each mode shape under consideration on the rotor’s
running performance in service.
5.2 Balance errors caused by balancing equipment and instrumentation
Balance errors caused by balancing equipment and instrumentation can increase with the magnitude of
the unbalance present. By considering unbalance causes during the design stage, some error sources can
be completely eliminated (e.g. by combining several parts into one) or reduced (e.g. by specifying tighter
tolerances). It is necessary to weigh the cost incurred in tightening the specified tolerances against the

benefit of decreased unbalance. Where the causes of balance errors cannot be eliminated or reduced to
negligible levels, they should be mathematically evaluated.
5.3 Balance errors caused by component radial and axial runout
When a perfectly balanced rotor component is mounted eccentrically to the rotor shaft axis, the resulting
static unbalance of the component, , is given by Formula (1):
(1)
where
is the resulting static unbalance of the component, in g⋅mm;
is the mass of the component, in g;
is the eccentricity of the rotor component relative to the rotor shaft axis, in mm.
NOTE The mass m can be stated in kg, the eccentricity in µm, but the static unbalance remains in units of
g⋅mm.
The static unbalance of the component creates an identical static unbalance of the assembled rotor. An
additional moment unbalance results if the component is mounted eccentrically in a plane other than that
of the centre of mass of the rotor. The further the plane is from the centre of mass, the larger the moment
unbalance.
If a perfectly balanced component is mounted concentrically, but with its principal axis of inertia inclined to
the rotor shaft axis, a moment unbalance results (see Figure 1).
For a small inclination angle, , between the two axes, the resulting moment unbalance, is approximately
equal to the difference between their moments of inertia about the component x- and z-axes, multiplied by
the angle, (see Formula (2)):
(2)
where
is the resulting moment unbalance, in g·mm ;
is the moment of inertia about the transverse x-axis through the component centre of mass, in
g·mm ;
is the moment of inertia about the principal z-axis of the component, in g·mm ;
is the small angle between the component principal axis of inertia and the rotor shaft axis, in
radians.
Formula (2) is applicable only if the component is symmetric about its rotational axis and is therefore
particularly applicable to the balancing of disks on arbours.
The effects of radial and axial runout of a component mounted on the rotor can be calculated separately.
For rotors with rigid behaviour, the separate unbalance components can be allocated to the tolerance planes
and then added vectorially.
For rotors with flexible behaviour, a rigid balance quality could be maintained, but accumulated axial disk
runout errors (often described as skew) can lead to significant vibration due to the moment unbalance
generated by the skewed disk(s).

Key
1 rotor plane, perpendicular to the rotor shaft axis
2 component plane
X, Y rotor shaft transverse axis
Z rotor shaft axis
x, y component transverse axis
z component principal axis
angle between the component principal axis of inertia and the rotor shaft axis
Figure 1 — Coordinates of the rotor shaft and component axes, showing a component inclined to the
rotor shaft axis
5.4 Balance errors caused by deviation of the rotor configuration on the balancing machine
from the configuration at service
Due to process requirements or limitations of the balancing equipment available, it can be necessary
to deviate from the rotor configuration for which the permissible residual unbalance is specified (e.g.
dismounted bearings, fans, couplings or blades). The uncertainty of unbalance introduced by these
deviations shall be added to the error of measurement [see 4.2, list item p), 4.3, list item g), 4.3, list item h),
4.4, list item g)].
5.5 Assessment of balancing operation errors
The purpose of balancing is to produce rotors that are within specified limits of residual unbalance. To
ensure that the set limits have been met, errors shall be controlled and taken into account.
When a balancing machine is used, various error sources exist, e.g. the
a) type of rotor to be balanced,
b) tooling used to support or drive the rotor,
c) balancing machine support structure (e.g. machine bearings and cradles),
d) balancing machine sensing system, and
e) electronic and read-out system.
However, it is important that in those cases where the error is taken into account by calculation, both the
measured unbalance before correction and the corrected value should be reported.
The balancing machine used should be chosen and set up such that all its systematic errors are eliminated,
corrected or compensated. When balancing rotors with rigid behaviour at their balancing speed, the
requirements of ISO 21940-21 shall be met.

5.6 Experimental assessment of randomly variable and scalar errors
5.6.1 General
If significant randomly variable errors or scalar errors are suspected to exist it is necessary, where practical,
to carry out several measuring runs to assess their magnitude.
When carrying out measuring runs, it is important to ensure that the random errors are themselves
produced randomly in each run (e.g. by ensuring that the angular position of the rotor is different at the
start of each run).
The randomly variable error magnitude can be evaluated by applying common statistical techniques to the
measurement results obtained. However, in most cases, carrying out the procedure described in 5.6.2 is
adequate.
5.6.2 Procedure
Plot the measured vectors of residual unbalance or vibration and find the mean vector from all the runs
(see Figure 2). Draw the smallest circle about centre A to enclose all the points. The vector represents an
estimation of the measured residual unbalance or vibration and the radius of the circle an estimation of the
maximum possible error of each si
...