ISO 21940-12:2016
(Main)Mechanical vibration — Rotor balancing — Part 12: Procedures and tolerances for rotors with flexible behaviour
Mechanical vibration — Rotor balancing — Part 12: Procedures and tolerances for rotors with flexible behaviour
ISO 21940-12:2016 presents typical configurations of rotors with flexible behaviour in accordance with their characteristics and balancing requirements, describes balancing procedures, specifies methods of assessment of the final state of balance, and establishes guidelines for balance quality criteria. ISO 21940-12:2016 can also serve as a basis for more involved investigations, e.g. when a more exact determination of the required balance quality is necessary. If due regard is paid to the specified methods of manufacture and balance tolerances, satisfactory running conditions can be expected. ISO 21940-12:2016 is not intended to serve as an acceptance specification for any rotor, but rather to give indications of how to avoid gross deficiencies and unnecessarily restrictive requirements. Structural resonances and modifications thereof lie outside the scope of this part of ISO 21940. The methods and criteria given are the result of experience with general industrial machinery. It is possible that they are not directly applicable to specialized equipment or to special circumstances. Therefore, in some cases, deviations from this part of ISO 21940 are possible.
Vibrations mécaniques — Équilibrage des rotors — Partie 12: Modes opératoires et tolérances pour les rotors à comportement flexible
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 21940-12
First edition
2016-04-01
Mechanical vibration — Rotor
balancing —
Part 12:
Procedures and tolerances for rotors
with flexible behaviour
Vibrations mécaniques — Équilibrage des rotors —
Partie 12: Modes opératoires et tolérances pour les rotors à
comportement flexible
Reference number
ISO 21940-12:2016(E)
©
ISO 2016
---------------------- Page: 1 ----------------------
ISO 21940-12:2016(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2016, 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 2016 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 21940-12:2016(E)
Contents Page
Foreword .v
Introduction .vii
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Fundamentals of dynamics and balancing of rotors with flexible behaviour .2
4.1 General . 2
4.2 Unbalance distribution . 2
4.3 Mode shapes of rotors with flexible behaviour . 2
4.4 Response of a rotor with flexible behaviour to unbalance . . 3
4.5 Aims of balancing rotors with flexible behaviour . 4
4.6 Provision for correction planes . 5
4.7 Coupled rotors . 5
5 Rotor configurations. 5
6 Procedures for balancing rotors with flexible behaviour at low speed .7
6.1 General . 7
6.2 Selection of correction planes . 8
6.3 Service speed of the rotor . 8
6.4 Initial unbalance . 8
6.5 Low-speed balancing procedures . 8
6.5.1 Procedure A — Single-plane balancing . 8
6.5.2 Procedure B — Two-plane balancing . 8
6.5.3 Procedure C — Individual component balancing prior to assembly . 9
6.5.4 Procedure D — Balancing subsequent to controlling initial unbalance . 9
6.5.5 Procedure E — Balancing in stages during assembly . 9
6.5.6 Procedure F — Balancing in optimum planes .10
7 Procedures for balancing rotors with flexible behaviour at high speed .10
7.1 General .10
7.2 Installation for balancing .10
7.3 Procedure G — Multiple speed balancing .11
7.3.1 General.11
7.3.2 Initial low-speed balancing .11
7.3.3 General procedure .11
7.4 Procedure H — Service speed balancing .13
7.5 Procedure I — Fixed speed balancing.14
7.5.1 General.14
7.5.2 Procedure .14
8 Evaluation criteria .14
8.1 Choice of criteria .14
8.2 Vibration limits in the balancing machine .15
8.2.1 Overview .15
8.2.2 General.15
8.2.3 Special cases and exceptions .15
8.2.4 Factors influencing machine vibration .15
8.2.5 Critical clearances and complex machine systems.16
8.2.6 Permissible vibrations in the balancing machine .16
8.3 Residual unbalance tolerances .17
8.3.1 Overview .17
8.3.2 General.17
8.3.3 Limits for low-speed balancing .17
8.3.4 Limits for multiple speed balancing .18
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ISO 21940-12:2016(E)
9 Evaluation procedures .18
9.1 Evaluation procedures based on vibration limits .18
9.1.1 Vibration assessed in a high-speed balancing machine .18
9.1.2 Vibration assessed on a test facility .19
9.1.3 Vibration assessed on site .19
9.2 Evaluation based on residual unbalance tolerances .20
9.2.1 General.20
9.2.2 Evaluation at low speed .20
9.2.3 Evaluation at multiple speeds based on modal unbalances .20
9.2.4 Evaluation at service speed in two specified test planes .21
Annex A (informative) Cautionary notes concerning rotors when installed in-situ .23
Annex B (informative) Optimum planes balancing — Low-speed three-plane balancing .24
Annex C (informative) Conversion factors .26
Annex D (informative) Example calculation of equivalent residual modal unbalances .27
Annex E (informative) Procedures to determine whether a rotor shows rigid or
flexible behaviour .30
Annex F (informative) Method of computation of unbalance correction .32
Bibliography .33
iv © ISO 2016 – All rights reserved
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ISO 21940-12:2016(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 meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical
Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is 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 21940-12 cancels and replaces ISO 11342:1998, which has been technically
revised. The main changes are deletion of the terms and definitions which were transferred to
ISO 21940-2 and deletion of former Annex F which is a duplication of a part of D.1. It also incorporates
the Technical Corrigendum ISO 11342:1998/Cor.1:2000.
ISO 21940 consists of the following parts, under the general title Mechanical vibration — Rotor balancing:
1)
— Part 11: Procedures and tolerances for rotors with rigid behaviour
2)
— Part 12: Procedures and tolerances for rotors with flexible behaviour
3)
— Part 13: Criteria and safeguards for the in-situ balancing of medium and large rotors
4)
— Part 14: Procedures for assessing balance errors
5)
— Part 21: Description and evaluation of balancing machines
1) Revision of ISO 1940-1:2003 + Cor.1:2005, Mechanical vibration — Balance quality requirements for rotors in a
constant (rigid) state — Part 1: Specification and verification of balance tolerances
2) Revision of ISO 11342:1998 + Cor.1:2000, Mechanical vibration — Methods and criteria for the mechanical
balancing of flexible rotors
3) Revision of ISO 20806:2009, Mechanical vibration — Criteria and safeguards for the in-situ balancing of medium
and large rotors
4) Revision of ISO 1940-2:1997, Mechanical vibration — Balance quality requirements of rigid rotors — Part 2:
Balance errors
5) Revision of ISO 2953:1999, Mechanical vibration — Balancing machines — Description and evaluation
© ISO 2016 – All rights reserved v
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ISO 21940-12:2016(E)
6)
— Part 23: Enclosures and other protective measures for the measuring station of balancing machines
7)
— Part 31: Susceptibility and sensitivity of machines to unbalance
8)
— Part 32: Shaft and fitment key convention
The following part is under preparation:
9)
— Part 2: Vocabulary
6) Revision of ISO 7475:2002, Mechanical vibration — Balancing machines — Enclosures and other protective
measures for the measuring station
7) Revision of ISO 10814:1996, Mechanical vibration — Susceptibility and sensitivity of machines to unbalance
8) Revision of ISO 8821:1989, Mechanical vibration — Balancing — Shaft and fitment key convention
9) Revision of ISO 1925:2001, Mechanical vibration — Balancing — Vocabulary
vi © ISO 2016 – All rights reserved
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ISO 21940-12:2016(E)
Introduction
The aim of balancing any rotor is to achieve satisfactory running when installed in-situ. In this context,
“satisfactory running” means that not more than an acceptable magnitude of vibration is caused by the
unbalance remaining in the rotor. In the case of a rotor with flexible behaviour, it also means that not
more than an acceptable magnitude of deflection occurs in the rotor at any speed up to the maximum
service speed.
Most rotors are balanced in manufacture prior to machine assembly because afterwards, for example,
there might be only limited access to the rotor. Furthermore, balancing of the rotor is often the stage
at which a rotor is approved by the purchaser. Thus, while satisfactory running in-situ is the aim, the
balance quality of the rotor is usually initially assessed in a balancing machine. Satisfactory running
in-situ is, in most cases, judged in relation to vibration from all causes, while in the balancing machine,
primarily, once-per-revolution effects are considered.
This part of ISO 21940 classifies rotors in accordance with their balancing requirements and establishes
methods of assessment of residual unbalance.
This part of ISO 21940 also shows how criteria for use in the balancing machine can be derived from
either vibration limits specified for the assembled and installed machine or unbalance limits specified
for the rotor. If such limits are not available, this part of ISO 21940 shows how they can be derived from
ISO 10816 and ISO 7919 if desired in terms of vibration, or from ISO 21940-11, if desired in terms of
permissible residual unbalance. ISO 21940-11 is concerned with the balance quality of rotating rigid
bodies and is not directly applicable to rotors with flexible behaviour because rotors with flexible
behaviour can undergo significant bending deflection. However, in this part of ISO 21940, methods are
presented for adapting the criteria of ISO 21940-11 to rotors with flexible behaviour.
There are situations in which an otherwise acceptably balanced rotor experiences an unacceptable
vibration level in situ, owing to resonances in the support structure. A resonance or near resonance
condition in a lightly damped structure can result in excessive vibratory response to a small unbalance.
In such cases, it can be more practicable to alter the natural frequency or damping of the structure rather
than to balance to very low levels, which might not be maintainable over time (see also ISO 21940-31).
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INTERNATIONAL STANDARD ISO 21940-12:2016(E)
Mechanical vibration — Rotor balancing —
Part 12:
Procedures and tolerances for rotors with flexible
behaviour
1 Scope
This part of ISO 21940 presents typical configurations of rotors with flexible behaviour in accordance
with their characteristics and balancing requirements, describes balancing procedures, specifies
methods of assessment of the final state of balance, and establishes guidelines for balance quality
criteria.
This part of ISO 21940 can also serve as a basis for more involved investigations, e.g. when a more
exact determination of the required balance quality is necessary. If due regard is paid to the specified
methods of manufacture and balance tolerances, satisfactory running conditions can be expected.
This part of ISO 21940 is not intended to serve as an acceptance specification for any rotor, but rather to
give indications of how to avoid gross deficiencies and unnecessarily restrictive requirements.
Structural resonances and modifications thereof lie outside the scope of this part of ISO 21940.
The methods and criteria given are the result of experience with general industrial machinery. It is
possible that they are not directly applicable to specialized equipment or to special circumstances.
Therefore, in some cases, deviations from this part of ISO 21940 are possible.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
10)
ISO 1925 , Mechanical vibration — Balancing — Vocabulary
ISO 2041, Mechanical vibration, shock and condition monitoring — Vocabulary
11)
ISO 21940-11 , Mechanical vibration — Rotor balancing — Part 11: Procedures and tolerances for rotors
with rigid behaviour
ISO 21940-14, Mechanical vibration — Rotor balancing — Part 14: Procedures for assessing balance errors
ISO 21940-32, Mechanical vibration — Rotor balancing — Part 32: Shaft and fitment key convention
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 1925 and ISO 2041 apply.
10) To become ISO 21940-2 when revised.
11) To be published.
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ISO 21940-12:2016(E)
4 Fundamentals of dynamics and balancing of rotors with flexible behaviour
4.1 General
Rotors with flexible behaviour normally require multiplane balancing at high speed. Nevertheless,
under certain conditions, a rotor with flexible behaviour can also be balanced at low speed. For high-
speed balancing, two different methods have been formulated for achieving a satisfactory state of
balance, namely modal balancing and the influence coefficient approach. The basic theory behind both
of these methods and their relative merits are described widely in the literature and therefore, no
further detailed description is given here. In most practical balancing applications, the method adopted
is normally a combination of both approaches, often incorporated into a computer package.
4.2 Unbalance distribution
The rotor design and method of construction can significantly influence the magnitude and distribution
of unbalance along the rotor axis. Rotors may be machined from a single forging or they may be
constructed by fitting several components together. For example, jet engine rotors are constructed by
joining many shell, disc and blade components. Generator rotors, however, are usually manufactured
from a single forging, but will have additional components fitted. The distribution of unbalance may
also be significantly influenced by the presence of large unbalances arising from shrink-fitted discs,
couplings, etc.
Since the unbalance distribution along a rotor axis is likely to be random, the distribution along two
rotors of identical design will be different. The distribution of unbalance is of greater significance in a
rotor with flexible behaviour than in a rotor with rigid behaviour because it determines the degree to
which any flexural mode is excited. The effect of unbalance at any point along a rotor depends on the
mode shapes of the rotor.
The correction of unbalance in transverse planes along a rotor other than those in which the unbalance
occurs can induce vibrations at speeds other than that at which the rotor was originally balanced. These
vibrations can exceed specified tolerances, particularly at, or near, the flexural resonance speeds. Even
at the same speed, such correction can induce vibrations if the flexural mode shapes in-situ differ from
those dominating during the balancing process.
Rotors should be checked for straightness, and where necessary corrected prior to high-speed
balancing, since a rotor with an excessive bend or bow will result in a compromise balance, which can
lead to poor performance in service.
In addition, some rotors which become heated during operation are susceptible to thermal bows which
can lead to changes in the unbalance. If the rotor unbalance changes significantly from run to run, it
might be impossible to balance the rotor within tolerance.
4.3 Mode shapes of rotors with flexible behaviour
If the effect of damping is neglected, the modes of a rotor are the flexural principal modes and, in the
special case of a rotor supported in bearings which have the same stiffness in all radial directions, are
rotating plane curves. Typical shapes for the three lowest principal modes for a simple rotor supported
in flexible bearings near to its ends are illustrated in Figure 1.
For a damped rotor and bearing system, the flexural modes can be space curves rotating about the shaft
axis, especially in the case of substantial damping, arising perhaps from fluid-film bearings. Possible
damped first and second modes are illustrated in Figure 2. In many cases, the damped modes can be
treated approximately as principal modes and, hence, regarded as rotating plane curves.
It is important to note that the form of the mode shapes and the response of the rotor to unbalances are
strongly influenced by the dynamic properties and axial locations of the bearings and their supports.
2 © ISO 2016 – All rights reserved
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ISO 21940-12:2016(E)
a) Typical rotor
P
3
b) First flexural mode
c) Second flexural mode
P
P
1
4
d) Third flexural mode
Key
P , P , P nodes
1 2 4
P antinode
3
Figure 1 — Simplified mode shapes for rotors with flexible behaviour on flexible supports
4.4 Response of a rotor with flexible behaviour to unbalance
The unbalance distribution can be expressed in terms of modal unbalances. The deflection in each mode
is caused by the corresponding modal unbalance. When a rotor rotates at a speed near a resonance
speed, it is usually the mode associated with this resonance speed which dominates the deflection of
the rotor. The degree to which large amplitudes of rotor deflection occur under these circumstances is
influenced mainly by the following:
a) the magnitude of the modal unbalances;
b) the proximity of the associated resonance speeds to the running speeds;
c) the amount of damping in the rotor and support system.
If a particular modal unbalance is reduced by the addition of a number of discrete correction masses,
then the corresponding modal component of deflection is similarly reduced. The reduction of the modal
unbalances in this way forms the basis of the balancing procedures described in this part of ISO 21940.
The modal unbalances for a given unbalance distribution are a function of the rotor modes. Moreover,
for the simplified rotor shown in Figure 1, the effect produced in a particular mode by a given correction
depends on the ordinate of the mode shape curve at the axial location of the correction: maximum
effect near the antinodes, minimum effect near the nodes. Consider an example in which the curves
of Figure 1 b) to d) are mode shapes for the rotor in Figure 1 a). A correction mass in plane P has the
3
maximum effect on the first mode, while its effect on the second mode is small.
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ISO 21940-12:2016(E)
A correction mass in plane P will produce no response at all on the second mode, but will influence
2
both the other modes.
Correction masses in planes P and P will not affect the third mode, but will influence both the
1 4
other modes.
a) First mode
b) Second mode
Figure 2 — Examples of possible damped mode shapes
4.5 Aims of balancing rotors with flexible behaviour
The aims of balancing are determined by the operational requirements of the machine. Before balancing
any particular rotor, it is desirable to decide what balance criteria can be regarded as satisfactory. In this
way, the balancing process can be made efficient and economical, but still satisfies the needs of the user.
Balancing is intended to achieve acceptable magnitudes of machinery vibration, shaft deflection and
forces applied to the bearings caused by unbalance.
The ideal aim in balancing rotors with flexible behaviour would be to correct the local unbalance
occurring at each elemental length by means of unbalance corrections at the element itself. This would
result in a rotor in which the centre of mass of each elemental length lies on the shaft axis.
A rotor balanced in this ideal way would have no static and moment unbalance and no modal
components of unbalance. Such a perfectly balanced
...
INTERNATIONAL ISO
STANDARD 21940-12
Second edition
Mechanical vibration — Rotor
balancing —
Part 12:
Procedures and tolerances for rotors
with flexible behaviour
Vibrations mécaniques — Équilibrage des rotors —
Partie 12: Modes opératoires et tolérances pour les rotors à
comportement flexible
PROOF/ÉPREUVE
Reference number
ISO 21940-12:2016(E)
©
ISO 2016
---------------------- Page: 1 ----------------------
ISO 21940-12:2016(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2016, 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 2016 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 21940-12:2016(E)
Contents Page
Foreword .v
Introduction .vii
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Fundamentals of dynamics and balancing of rotors with flexible behaviour .2
4.1 General . 2
4.2 Unbalance distribution . 2
4.3 Mode shapes of rotors with flexible behaviour . 2
4.4 Response of a rotor with flexible behaviour to unbalance . . 3
4.5 Aims of balancing rotors with flexible behaviour . 5
4.6 Provision for correction planes . 5
4.7 Coupled rotors . 5
5 Rotor configurations. 6
6 Procedures for balancing rotors with flexible behaviour at low speed .8
6.1 General . 8
6.2 Selection of correction planes . 8
6.3 Service speed of the rotor . 8
6.4 Initial unbalance . 9
6.5 Low-speed balancing procedures . 9
6.5.1 Procedure A — Single-plane balancing . 9
6.5.2 Procedure B — Two-plane balancing . 9
6.5.3 Procedure C — Individual component balancing prior to assembly . 9
6.5.4 Procedure D — Balancing subsequent to controlling initial unbalance . 9
6.5.5 Procedure E — Balancing in stages during assembly .10
6.5.6 Procedure F — Balancing in optimum planes .10
7 Procedures for balancing rotors with flexible behaviour at high speed .10
7.1 General .10
7.2 Installation for balancing .11
7.3 Procedure G — Multiple speed balancing .11
7.3.1 General.11
7.3.2 Initial low-speed balancing .12
7.3.3 General procedure .12
7.4 Procedure H — Service speed balancing .14
7.5 Procedure I — Fixed speed balancing.14
7.5.1 General.14
7.5.2 Procedure .14
8 Evaluation criteria .15
8.1 Choice of criteria .15
8.2 Vibration limits in the balancing machine .15
8.2.1 Overview .15
8.2.2 General.16
8.2.3 Special cases and exceptions .16
8.2.4 Factors influencing machine vibration .16
8.2.5 Critical clearances and complex machine systems.16
8.2.6 Permissible vibrations in the balancing machine .16
8.3 Residual unbalance tolerances .17
8.3.1 Overview .17
8.3.2 General.18
8.3.3 Limits for low-speed balancing .18
8.3.4 Limits for multiple speed balancing .18
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ISO 21940-12:2016(E)
9 Evaluation procedures .19
9.1 Evaluation procedures based on vibration limits .19
9.1.1 Vibration assessed in a high-speed balancing machine .19
9.1.2 Vibration assessed on a test facility .19
9.1.3 Vibration assessed on site .20
9.2 Evaluation based on residual unbalance tolerances .20
9.2.1 General.20
9.2.2 Evaluation at low speed .20
9.2.3 Evaluation at multiple speeds based on modal unbalances .21
9.2.4 Evaluation at service speed in two specified test planes .22
Annex A (informative) Cautionary notes concerning rotors when installed in-situ .23
Annex B (informative) Optimum planes balancing — Low-speed three-plane balancing .24
Annex C (informative) Conversion factors .26
Annex D (informative) Example calculation of equivalent residual modal unbalances .27
Annex E (informative) Procedures to determine whether a rotor shows rigid or
flexible behaviour .30
Annex F (informative) Method of computation of unbalance correction .32
Bibliography .33
iv PROOF/ÉPREUVE © ISO 2016 – All rights reserved
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ISO 21940-12:2016(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 meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical
Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is 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 of ISO 21940-12 cancels and replaces ISO 11342:1998, which has been technically
revised. The main changes are deletion of the terms and definitions which were transferred to
ISO 21940-2 and deletion of former Annex F which is a doublication of a part of D.1. It also incorporates
the Technical Corrigendum ISO 11342:1998/Cor.1:2000.
ISO 21940 consists of the following parts, under the general title Mechanical vibration — Rotor balancing:
1)
— Part 11: Procedures and tolerances for rotors with rigid behaviour
2)
— Part 12: Procedures and tolerances for rotors with flexible behaviour
3)
— Part 13: Criteria and safeguards for the in-situ balancing of medium and large rotors
4)
— Part 14: Procedures for assessing balance errors
5)
— Part 21: Description and evaluation of balancing machines
1) Revision of ISO 1940-1:2003 + Cor.1:2005, Mechanical vibration — Balance quality requirements for rotors in a
constant (rigid) state — Part 1: Specification and verification of balance tolerances
2) Revision of ISO 11342:1998 + Cor.1:2000, Mechanical vibration — Methods and criteria for the mechanical
balancing of flexible rotors
3) Revision of ISO 20806:2009, Mechanical vibration — Criteria and safeguards for the in-situ balancing of medium
and large rotors
4) Revision of ISO 1940-2:1997, Mechanical vibration — Balance quality requirements of rigid rotors — Part 2:
Balance errors
5) Revision of ISO 2953:1999, Mechanical vibration — Balancing machines — Description and evaluation
© ISO 2016 – All rights reserved PROOF/ÉPREUVE v
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ISO 21940-12:2016(E)
6)
— Part 23: Enclosures and other protective measures for the measuring station of balancing machines
7)
— Part 31: Susceptibility and sensitivity of machines to unbalance
8)
— Part 32: Shaft and fitment key convention
The following part is under preparation:
9)
— Part 2: Vocabulary
6) Revision of ISO 7475:2002, Mechanical vibration — Balancing machines — Enclosures and other protective
measures for the measuring station
7) Revision of ISO 10814:1996, Mechanical vibration — Susceptibility and sensitivity of machines to unbalance
8) Revision of ISO 8821:1989, Mechanical vibration — Balancing — Shaft and fitment key convention
9) Revision of ISO 1925:2001, Mechanical vibration — Balancing — Vocabulary
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ISO 21940-12:2016(E)
Introduction
The aim of balancing any rotor is to achieve satisfactory running when installed in-situ. In this context,
“satisfactory running” means that not more than an acceptable magnitude of vibration is caused by the
unbalance remaining in the rotor. In the case of a rotor with flexible behaviour, it also means that not
more than an acceptable magnitude of deflection occurs in the rotor at any speed up to the maximum
service speed.
Most rotors are balanced in manufacture prior to machine assembly because afterwards, for example,
there might be only limited access to the rotor. Furthermore, balancing of the rotor is often the stage
at which a rotor is approved by the purchaser. Thus, while satisfactory running in-situ is the aim, the
balance quality of the rotor is usually initially assessed in a balancing machine. Satisfactory running
in-situ is, in most cases, judged in relation to vibration from all causes, while in the balancing machine,
primarily, once-per-revolution effects are considered.
This part of ISO 21940 classifies rotors in accordance with their balancing requirements and establishes
methods of assessment of residual unbalance.
This part of ISO 21940 also shows how criteria for use in the balancing machine can be derived from
either vibration limits specified for the assembled and installed machine or unbalance limits specified
for the rotor. If such limits are not available, this part of ISO 21940 shows how they can be derived from
ISO 10816 and ISO 7919 if desired in terms of vibration, or from ISO 21940-11, if desired in terms of
permissible residual unbalance. ISO 21940-11 is concerned with the balance quality of rotating rigid
bodies and is not directly applicable to rotors with flexible behaviour because rotors with flexible
behaviour can undergo significant bending deflection. However, in this part of ISO 21940, methods are
presented for adapting the criteria of ISO 21940-11 to rotors with flexible behaviour.
There are situations in which an otherwise acceptably balanced rotor experiences an unacceptable
vibration level in situ, owing to resonances in the support structure. A resonance or near resonance
condition in a lightly damped structure can result in excessive vibratory response to a small unbalance.
In such cases, it can be more practicable to alter the natural frequency or damping of the structure rather
than to balance to very low levels, which might not be maintainable over time (see also ISO 21940-31).
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INTERNATIONAL STANDARD ISO 21940-12:2016(E)
Mechanical vibration — Rotor balancing —
Part 12:
Procedures and tolerances for rotors with flexible behaviour
1 Scope
This part of ISO 21940 presents typical configurations of rotors with flexible behaviour in accordance
with their characteristics and balancing requirements, describes balancing procedures, specifies
methods of assessment of the final state of balance, and establishes guidelines for balance quality criteria.
This part of ISO 21940 can also serve as a basis for more involved investigations, e.g. when a more
exact determination of the required balance quality is necessary. If due regard is paid to the specified
methods of manufacture and balance tolerances, satisfactory running conditions can be expected.
This part of ISO 21940 is not intended to serve as an acceptance specification for any rotor, but rather to
give indications of how to avoid gross deficiencies and unnecessarily restrictive requirements.
Structural resonances and modifications thereof lie outside the scope of this part of ISO 21940.
The methods and criteria given are the result of experience with general industrial machinery. It is
possible that they are not directly applicable to specialized equipment or to special circumstances.
Therefore, in some cases, deviations from this part of ISO 21940 are possible.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
10)
ISO 1925 , Mechanical vibration — Balancing — Vocabulary
11)
ISO 2041 , Mechanical vibration, shock and condition monitoring — Vocabulary
11)
ISO 21940-11 , Mechanical vibration — Rotor balancing — Part 11: Procedures and tolerances for rotors
with rigid behaviour
ISO 21940-14, Mechanical vibration — Rotor balancing — Part 14: Procedures for assessing balance errors
ISO 21940-32, Mechanical vibration — Rotor balancing — Part 32: Shaft and fitment key convention
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 1925 and ISO 2041 apply.
10) To become ISO 21940-2 when revised.
11) To be published.
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ISO 21940-12:2016(E)
4 Fundamentals of dynamics and balancing of rotors with flexible behaviour
4.1 General
Rotors with flexible behaviour normally require multiplane balancing at high speed. Nevertheless,
under certain conditions, a rotor with flexible behaviour can also be balanced at low speed. For high-
speed balancing, two different methods have been formulated for achieving a satisfactory state of
balance, namely modal balancing and the influence coefficient approach. The basic theory behind both
of these methods and their relative merits are described widely in the literature and therefore, no
further detailed description is given here. In most practical balancing applications, the method adopted
is normally a combination of both approaches, often incorporated into a computer package.
4.2 Unbalance distribution
The rotor design and method of construction can significantly influence the magnitude and distribution
of unbalance along the rotor axis. Rotors may be machined from a single forging or they may be
constructed by fitting several components together. For example, jet engine rotors are constructed by
joining many shell, disc and blade components. Generator rotors, however, are usually manufactured
from a single forging, but will have additional components fitted. The distribution of unbalance may
also be significantly influenced by the presence of large unbalances arising from shrink-fitted discs,
couplings, etc.
Since the unbalance distribution along a rotor axis is likely to be random, the distribution along two
rotors of identical design will be different. The distribution of unbalance is of greater significance in a
rotor with flexible behaviour than in a rotor with rigid behaviour because it determines the degree to
which any flexural mode is excited. The effect of unbalance at any point along a rotor depends on the
mode shapes of the rotor.
The correction of unbalance in transverse planes along a rotor other than those in which the unbalance
occurs can induce vibrations at speeds other than that at which the rotor was originally balanced. These
vibrations can exceed specified tolerances, particularly at, or near, the flexural resonance speeds. Even
at the same speed, such correction can induce vibrations if the flexural mode shapes in-situ differ from
those dominating during the balancing process.
Rotors should be checked for straightness, and where necessary corrected prior to high-speed
balancing, since a rotor with an excessive bend or bow will result in a compromise balance, which can
lead to poor performance in service.
In addition, some rotors which become heated during operation are susceptible to thermal bows which
can lead to changes in the unbalance. If the rotor unbalance changes significantly from run to run, it
might be impossible to balance the rotor within tolerance.
4.3 Mode shapes of rotors with flexible behaviour
If the effect of damping is neglected, the modes of a rotor are the flexural principal modes and, in the
special case of a rotor supported in bearings which have the same stiffness in all radial directions, are
rotating plane curves. Typical shapes for the three lowest principal modes for a simple rotor supported
in flexible bearings near to its ends are illustrated in Figure 1.
For a damped rotor and bearing system, the flexural modes can be space curves rotating about the shaft
axis, especially in the case of substantial damping, arising perhaps from fluid-film bearings. Possible
damped first and second modes are illustrated in Figure 2. In many cases, the damped modes can be
treated approximately as principal modes and, hence, regarded as rotating plane curves.
It is important to note that the form of the mode shapes and the response of the rotor to unbalances are
strongly influenced by the dynamic properties and axial locations of the bearings and their supports.
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ISO 21940-12:2016(E)
4.4 Response of a rotor with flexible behaviour to unbalance
The unbalance distribution can be expressed in terms of modal unbalances. The deflection in each mode
is caused by the corresponding modal unbalance. When a rotor rotates at a speed near a resonance
speed, it is usually the mode associated with this resonance speed which dominates the deflection of
the rotor. The degree to which large amplitudes of rotor deflection occur under these circumstances is
influenced mainly by the following:
a) the magnitude of the modal unbalances;
b) the proximity of the associated resonance speeds to the running speeds;
c) the amount of damping in the rotor and support system.
If a particular modal unbalance is reduced by the addition of a number of discrete correction masses,
then the corresponding modal component of deflection is similarly reduced. The reduction of the modal
unbalances in this way forms the basis of the balancing procedures described in this part of ISO 21940.
The modal unbalances for a given unbalance distribution are a function of the rotor modes. Moreover,
for the simplified rotor shown in Figure 1, the effect produced in a particular mode by a given correction
depends on the ordinate of the mode shape curve at the axial location of the correction: maximum
effect near the antinodes, minimum effect near the nodes. Consider an example in which the curves
of Figure 1 b) to d) are mode shapes for the rotor in Figure 1 a). A correction mass in plane P has the
3
maximum effect on the first mode, while its effect on the second mode is small.
A correction mass in plane P will produce no response at all on the second mode, but will influence
2
both the other modes.
Correction masses in planes P and P will not affect the third mode, but will influence both the other
1 4
modes.
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ISO 21940-12:2016(E)
P₁ P₂ P₃ P₄
a) Typical rotor
P
3
b) First flexural mode
P₂
c) Second flexural mode
P
P
1
4
d) Third flexural mode
Key
P , P , P nodes
1 2 4
P antinode
3
Figure 1 — Simplified mode shapes for rotors with flexible behaviour on flexible supports
a) First mode
b) Second mode
Figure 2 — Examples of possible damped mode shapes
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ISO 21940-12:2016(E)
4.5 Aims of balancing rotors with flexible behaviour
The aims of balancing are determined by the operational requirements of the machine. Before balancing
any particular rotor, it is desirable to decide what balance criteria can be regarded as satisfactory. In this
way, the balancing process can be made efficient and economical, but still satisfies the needs of the user.
Balancing is intended to achieve acceptable magnitudes of machinery vibration, shaft deflection and
forces applied to the bearings caused by unbalance.
The ideal aim in balancing rotors with flexible behaviour would be to correct the local unbalance
occurring at each elemental length by means of unbalance corrections at the element itself. This would
...
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