ISO 21940-14

• Abstract:

  This part of ISO 21940 specifies the requirements for the following: a) identifying errors in the unbalance measuring process of a rotor; b) assessing the identified errors; c) taking the errors into account. This part of ISO 21940 specifies balance acceptance criteria, in terms of residual unbalance, for both directly after balancing and for a subsequent check of the balance quality by the user. For the main typical errors, this part of ISO 21940 lists methods for their reduction in an informative annex.

• Status: Not Published
• ICS: 21.120.40 - Balancing and balancing machines
• Technical Committee: ISO/TC 108/SC 2 - Measurement and evaluation of mechanical vibration and shock as applied to machines, vehicles and structures
• Drafting Committee: ISO/TC 108/SC 2 - Measurement and evaluation of mechanical vibration and shock as applied to machines, vehicles and structures
• Current Stage: 6000 - International Standard under publication
• Start Date: 01-Sep-2026
• Completion Date: 12-Sep-2026

• Revises: ISO 21940-14:2012 - Mechanical vibration — Rotor balancing — Part 14: Procedures for assessing balance errors
• Effective Date: 10-Dec-2022
• Revises: ISO 21940-14:2012/Amd 1:2022 - Mechanical vibration — Rotor balancing — Part 14: Procedures for assessing balance errors — Amendment 1
• Effective Date: 10-Dec-2022

Overview

ISO 21940-14:2026 – "Mechanical Vibration - Rotor Balancing - Part 14: Procedures for Assessing Balance Errors" – provides standardized procedures for identifying, evaluating, and accounting for errors in rotor unbalance measurement processes. Part of the comprehensive ISO 21940 series, this standard addresses typical error sources encountered during rotor balancing, including systematic, randomly variable, and scalar errors. ISO 21940-14 establishes balance acceptance criteria in terms of residual unbalance both immediately after balancing and during subsequent balance quality checks, ensuring reliability and safety in mechanical vibration management.

Key Topics

• Types of Balance Errors
  • Systematic errors: Consistent, predictable errors such as drive shaft or mandrel unbalance, runout, or alignment issues.
  • Randomly variable errors: Unpredictable errors arising from loose parts, thermal distortion, or entrapped materials.
  • Scalar errors: Magnitude-evaluable errors with undetermined direction, often caused by assembly variances or manufacturing tolerances.
• Balance Error Sources
  • Errors linked to balancing equipment, mandrels, auxiliary tooling, fit clearances, machine bearings, unintentional magnetism, and more.
  • Effects of reassembly or deviations from the rotor’s service configuration.
• Assessment Procedures
  • Stepwise methods for measuring, plotting, and statistically assessing errors using multiple measurement runs and index balancing.
  • Techniques for distinguishing and quantifying systematic versus random and scalar errors.
• Combined Error Evaluation
  • Mathematical models for combining uncorrected errors to determine their potential impact on residual unbalance.
• Balance Acceptance Criteria
  • Guidelines to determine whether a rotor meets permissible residual unbalance limits by considering combined errors.
  • Decision-making process for accepting or rejecting rotors based on measurement uncertainty.

Applications

ISO 21940-14 is relevant in industries and operations where precision rotor balancing is critical for machinery and system reliability, such as:

• Industrial machinery: Ensures correct balancing of pumps, turbines, fans, compressors, and other rotating machines to minimize mechanical vibration, reduce wear, and prevent premature failure.
• Automotive and aerospace engineering: Supports high-precision balancing in engines, rotors, and drive components, promoting both performance and safety.
• Power generation and utilities: Used for balancing generators, motors, and other rotational equipment to maintain efficient operation and compliance with maintenance protocols.
• Maintenance and field servicing: Provides maintenance engineers with standardized procedures for assessing balance errors during on-site or workshop repairs.
• Manufacturing and quality control: Integral for OEMs to validate that rotors meet specified tolerance grades before product release.

Adopting ISO 21940-14 improves confidence in balancing results, reduces operational risks, and provides verifiable documentation of compliance with internationally recognized standards.

Related Standards

For comprehensive control of rotor balancing and mechanical vibration, ISO 21940-14 should be used alongside key related standards, including:

• ISO 21940-2 - Mechanical vibration - Rotor balancing - Part 2: Vocabulary: Provides essential terminology used in rotor balancing standards.
• ISO 21940-11 - Mechanical vibration - Rotor balancing - Part 11: Procedures and tolerances for rotors with rigid behaviour: Defines procedures and tolerances specific to rigid rotors.
• ISO 21940-12 - Mechanical vibration - Rotor balancing - Part 12: Procedures and tolerances for rotors with flexible behaviour: Focuses on the requirements for flexible rotors.
• ISO 21940-21 - Mechanical vibration - Rotor balancing - Part 21: Description and evaluation of balancing machines: Specifies performance criteria and evaluation methods for balancing machines.

Implementing ISO 21940-14 as part of a complete vibration and rotor balancing strategy helps achieve higher reliability, operational safety, and quality assurance in mechanical systems across diverse industries.

FINAL DRAFT
International
Standard
ISO/FDIS 21940-14
ISO/TC 108/SC 2
Mechanical vibration — Rotor
Secretariat: DIN
balancing —
Voting begins on:
2026-07-06
Part 14:
Procedures for assessing balance
Voting terminates on:
2026-08-31
errors
Vibrations mécaniques — Équilibrage des rotors —
Partie 14: Modes opératoires d'évaluation des erreurs
d'équilibrage
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
Reference number
ISO/FDIS 21940-14:2026(en) © ISO 2026

FINAL DRAFT
ISO/FDIS 21940-14:2026(en)
International
Standard
ISO/FDIS 21940-14
ISO/TC 108/SC 2
Mechanical vibration — Rotor
Secretariat: DIN
balancing —
Voting begins on:
Part 14:
Procedures for assessing balance
Voting terminates on:
errors
Vibrations mécaniques — Équilibrage des rotors —
Partie 14: Modes opératoires d'évaluation des erreurs
d'équilibrage
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
© ISO 2026
IN ADDITION TO THEIR EVALUATION AS
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
or ISO’s member body in the country of the requester.
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland Reference number
ISO/FDIS 21940-14:2026(en) © ISO 2026

ii
ISO/FDIS 21940-14:2026(en)
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. 8
Annex A (informative) Error examples, their identification and evaluation . 9
Bibliography .18

iii
ISO/FDIS 21940-14:2026(en)
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
ISO/FDIS 21940-14:2026(en)
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
FINAL DRAFT International Standard ISO/FDIS 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 acutal balance condition of a rotor differs from the
intended balance condition
ISO/FDIS 21940-14:2026(en)
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.
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 component 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 element 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.
ISO/FDIS 21940-14:2026(en)
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 narrow
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 decreased
tolerances). It is necessary to weigh the cost incurred in tightening the specified tolerances against the

ISO/FDIS 21940-14:2026(en)
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 distance 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).

ISO/FDIS 21940-14:2026(en)
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.

ISO/FDIS 21940-14:2026(en)
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
...

ISO/DISFDIS 21940-14
ISO/TC 108/SC 2
Secretariat: DIN
Date: 2026-05-11xx
Mechanical vibration — Rotor balancing —
Part 14:
Procedures for assessing balance errors
Vibrations mécaniques — Équilibrage des rotors —
Partie 14: Modes opératoires d'évaluation des erreurs d'équilibrage
DISFDIS stage
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ISO/FDIS 21940-14:2026(en)
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication
may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying,
or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO
at the address below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
E-mail: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
ISO/FDIS 21940-14:2026(en)
Contents
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 . 4
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 . 6
5.5 Assessment of balancing operation errors . 6
5.6 Experimental assessment of randomly variable and scalar errors . 6
5.7 Experimental assessment of systematic errors . 9
6 Combined error evaluation . 10
7 Balance criteria . 11
8 Accounting for measurement errors in the balance quality verification process . 11
Annex A (informative) Error examples, their identification and evaluation . 13
Bibliography . 23

iii
ISO/FDIS 21940-14:2026(en)
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/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
ISO/FDIS 21940-14:2026(en)
Introduction
The balance quality of a rotor is assessed in accordance with the requirements of ISO 21940-11 or 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.
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
ISO/FDIS 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 terminologicalterminology 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 acutal balance condition of a rotor differs from the
intended balance condition
ISO/FDIS 21940-14:2026(en)
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.
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 component 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 element 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;
ISO/FDIS 21940-14:2026(en)
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 narrow
tolerances that there is no need for balancing after manufacture. Where rotor initial unbalance exceeds the
values given in ISO 21940-11 or ISO 21940-12 the rotor should be balanced.
Field Code Changed
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
ISO/FDIS 21940-14:2026(en)
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 decreased
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, 𝑈𝑈𝑼𝑼 , is given by Formula (1):
s s
��⃗��⃗
𝑈𝑈𝑼𝑼 =𝑚𝑚 ·𝑒𝑒⃗𝒆𝒆�⃗ (1)
s s
where
��⃗��⃗
𝑈𝑈𝑼𝑼 is the resulting static unbalance of the component, in g⋅mm;
s s
𝑚𝑚 is the mass of the component, in g;
𝑒𝑒⃗𝒆𝒆�⃗ 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 𝑈𝑈𝑼𝑼 remains in units of g⋅mm.
s s
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 distance 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, Δ𝛾𝛾, between the two axes, the resulting moment unbalance, 𝑃𝑃𝑷𝑷 is approximately
r r
equal to the difference between their moments of inertia about the component x- and z-axes, multiplied by the
angle, Δ𝛾𝛾 (see Formula (2)):
�⃗��⃗
𝑃𝑃𝑷𝑷 ≈ (𝐼𝐼 −𝐼𝐼 )Δ𝛾𝛾 (2)
r r 𝑥𝑥 𝑧𝑧
where
�⃗��⃗ 2
𝑃𝑃𝑷𝑷 is the resulting moment unbalance, in g·mm ;
r r
𝐼𝐼 is the moment of inertia about the transverse x-axis through the component centre of mass, in g·mm ;
𝑥𝑥
𝐼𝐼 is the moment of inertia about the principal z-axis of the component, in g·mm ;
𝑧𝑧
Δ𝛾𝛾 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.
ISO/FDIS 21940-14:2026(en)
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
ISO/FDIS 21940-14:2026(en)
2 component plane
X, Y rotor shaft transverse axis
Z rotor shaft axis
x, y component transverse axis
z component principal axis
Δ𝛾𝛾 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 hg).
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).
ISO/FDIS 21940-14:2026(en)
The randomly variable error magnitude can be evaluated by applying standard 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 OA from all the runs
�����⃗
(see Figure 2). Draw the smallest circle about centre A to enclose all the points. The vector OA 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 single reading. The uncertainty of these results is usually diminished by
increasing the number of runs carried
...