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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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 2016
© ISO 2016, Published in Switzerland
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ii © ISO 2016 – All rights reserved
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
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
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
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 PROOF/ÉPREUVE © ISO 2016 – All rights reserved
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).
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.
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 PROOF/ÉPREUVE © ISO 2016 – All rights reserved
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
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
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.
P₁ P₂ P₃ P₄
a) Typical rotor
P
b) First flexural mode
P₂
c) Second flexural mode
P
P
d) Third flexural mode
Key
P , P , P nodes
1 2 4
P antinode
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
4 PROOF/ÉPREUVE © ISO 2016 – All rights reserved
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 rotor would then run satisfactorily at all speeds in
so far as unbalance is concerned.
In practice, the unbalance can be distributed along the length of the rotor, but the balancing process
is usually achieved by adding or removing masses in a limited number of correction planes. Thus,
there is invariably some distributed residual unbalance after balancing, which is assumed to be within
tolerance for the affected mode shapes.
It is necessary to reduce vibrations or oscillatory forces caused by the residual unbalance to acceptable
magnitudes over the service speed range. Only in special cases is it sufficient to balance rotors with
flexible behaviour for a single speed. It should be noted that a rotor, balanced satisfactorily for a given
service speed range, can still experience excessive vibration if it has to run through a resonance speed
to reach its service speed. Therefore, for passing through resonance speeds, the allowable vibration
may be greater than that permissible at service speed.
Whatever balancing technique is used, the final goal is to apply unbalance correction distributions to
minimize the unbalance effects at all speeds up to the maximum service speed, including start up and
shut down and possible overspeed. In meeting this objective, it might be necessary to allow for the
influence of modes with resonance speeds above the service speed range.
4.6 Provision for correction planes
The exact number of axial locations along the rotor that are needed depends to some extent on the
particular balancing procedure which is adopted. For example, centrifugal compressor rotors are
sometimes balanced as an assembly in the end planes only after each disc and the shaft have been
separately balanced in a low-speed balancing machine. Generally, however, if the speed of the rotor
is influenced by n flexural resonance speeds, which possibly include resonance speeds above the
maximum service speed, then usually if low-speed balancing is carried out, n + 2 correction planes are
needed along the rotor, if not, n planes can be used.
An adequate number of correction planes at suitable axial positions shall be included at the design
stage. In practice, the number of correction planes is often limited by design considerations and in-situ
balancing by limitations on accessibility.
4.7 Coupled rotors
When two rotors are coupled together, the complete unit has a series of resonance speeds and mode
shapes. In general, these speeds are neither equal nor simply related to the resonance speeds of the
individual, uncoupled rotors. Moreover, the deflection shape of each part of the coupled unit need
not be simply related to any mode shape of the corresponding uncoupled rotor. Ideally, therefore,
the unbalance distribution along two or more coupled rotors should be evaluated in terms of modal
unbalances with respect to the coupled system and not to the modes of the uncoupled rotors.
For practical purposes, in most cases, each rotor is balanced separately as an uncoupled shaft and this
procedure normally ensures satisfactory operation of the coupled rotors. The degree to which this
technique is practicable depends, for example, on the mode shapes and the resonance speeds of the
uncoupled and coupled rotors, the distribution of unbalance, the type of coupling and on the bearing
arrangement of the shaft train. If further balancing in-situ is required, refer to Annex A.
5 Rotor configurations
Typical rotor configurations are shown in Table 1, their characteristics outlined and the recommended
balancing procedures listed. Table 1 gives concise descriptions of the rotor characteristics. Full
descriptions of these characteristics and requirements are given in the corresponding procedures in
Clauses 6 and 7. These procedures are listed in Table 2.
Sometimes, a combination of balancing procedures can be advisable. If more than one balancing
procedure could be used, they are listed in the sequence of increasing time and cost. Rotors of any
configuration can always be balanced at multiple speeds (see 7.3) or sometimes, under special
conditions, be balanced at service speed (see 7.4) or at a fixed speed (see 7.5).
Table 1 — Rotors with flexible behaviour
Recommended
Configuration Rotor characteristics balancing
a
procedure
Elastic shaft without
1.1 Discs
unbalance, rigid disc(s)
Single disc
— perpendicular to shaft
A; C
axis
— with axial runout B; C
Two discs
— perpendicular to shaft B; C
axis
— with axial runout
— at least one B + C, E
removable
— intergral G
More than two discs
— all discs removable,
B + C, D, E
except one
— integral G
Elastic shafts without
1.2 Rigid sections unbalances, rigid
sections
Single rigid section
— removable B; C; E
— integral B
Two rigid sections
— at least one removable B + C; E
— integral G
a
See Table 2 for explanations of procedures A to G; two additional balancing procedures H and I can be used under
special circumstances, see 7.4 and 7.5.
6 PROOF/ÉPREUVE © ISO 2016 – All rights reserved
Table 1 (continued)
Recommended
Configuration Rotor characteristics balancing
a
procedure
More (than two) rigid
sections
— all discs removable, B + C; E
except one
— integral G
Elastic shaft without
1.3 Discs and rigid sections unbalance, rigid discs
and sections
One each
— at least one part
B + C; E
removable
— integral G
More parts
— all discs removable,
B + C; E
except one
— integral G
Mass, elasticity and
1.4 Rolls unbalance distribution
along the rotor
— under special conditions F
(see 6.5.6)
— in general G
Flexible roll, rigid
1.5 Rolls and discs/rigid sections
discs, rigid sections
— discs/rigid sections
removable
— under special
conditions C + F; E + F
(see 6.5.6)
— in general G
— integral G
Mass, elasticity and
1.6 Integral rotor unbalance distribution
along the rotor
Main parts with
G
unbalances not detachable
a
See Table 2 for explanations of procedures A to G; two additional balancing procedures H and I can be used under
special circumstances, see 7.4 and 7.5.
Table 2 — Balancing procedures
Procedure Description Subclause
Low-speed balancing
A Single-plane balancing 6.5.1
B Two-plane balancing 6.5.2
C Individual component balancing prior to assembly 6.5.3
D Balancing subsequent to controlling initial unbalance 6.5.4
E Balancing in stages during assembly 6.5.5
F Balancing in optimum planes 6.5.6
High-speed balancing
G Multiple speed balancing 7.3
H Service speed balancing 7.4
I Fixed speed balancing 7.5
6 Procedures for balancing rotors with flexible behaviour at low speed
6.1 General
Low-speed balancing is generally used for rotors with rigid behaviour and high-speed balancing is
generally used for rotors with flexible behaviour. Procedures to determine whether a rotor shows rigid
or flexible behaviour are described in Annex E. However, with the use of appropriate procedures, it
is possible under some circumstances to balance rotors with flexible behaviour at low speed so as to
ensure satisfactory running when the rotor is installed in its final environment. Otherwise, rotors with
flexible behaviour require the use of a high-speed balancing procedure.
Most of the procedures explained in this subclause require some information regarding the axial
distribution of unbalance.
In some cases where a gross unbalance can occur in a single component, it can be advantageous to
balance this component separately before mounting it on the rotor, in addition to carrying out the
balancing procedure after it is mounted.
Certain rotors contain a number of individual parts which are mounted concentrically (e.g. blades,
coupling bolts, pole pieces). These parts can be arranged according to their individual mass or mass
moment to achieve some or all of the required unbalance correction described in any of the procedures.
If these parts need to be assembled after balancing, they should be arranged in balanced sets.
Some rotors are made of individual components (e.g. turbine discs). In these cases, it is important to
recognize that the assembly process can produce changes in the shaft geometry (e.g. shaft runout) and
further changes can occur during high-speed service.
6.2 Selection of correction planes
If the axial positions of the unbalances are known, the correction planes should be provided as closely
as possible to these positions. When a rotor is composed of two or more separate components that are
distributed axially, there can be more than two transverse planes of unbalance.
6.3 Service speed of the rotor
If the service speed range includes or is close to a flexural resonance speed, then low-speed balancing
methods should be used with caution.
8 PROOF/ÉPREUVE © ISO 2016 – All rights reserved
6.4 Initial unbalance
The process of balancing a rotor with flexible behaviour in a low-speed balancing machine is an
approximate one. The magnitude and distribution of initial unbalance are major factors determining
the degree of success that can be expected.
For rotors in which the axial distribution of initial unbalance is known and appropriate correction
planes are available, the permissible initial unbalance is limited only by the amount of correction
possible in the correction planes.
For rotors in which the distribution of the initial unbalance is not known, there are no generally
applicable low-speed balancing methods. However, sometimes the magnitude can be controlled by the
pre-balancing of individual components. In these cases, the low-speed initial unbalance can be used as
a measure of the distribution of unbalance.
6.5 Low-speed balancing procedures
6.5.1 Procedure A — Single-plane balancing
If the initial unbalance is principally contained in one transverse plane and the correction is made in
this plane, then the rotor is balanced for all speeds.
6.5.2 Procedure B — Two-plane balancing
If the initial unbalance is principally concentrated in two transverse planes and the corrections are
made in these planes, then the rotor is balanced for all speeds.
If the unbalance in the rotor is distributed within a substantially rigid section of the rotor and the
unbalance correction is also made within this section, then the rotor is balanced for all speeds.
6.5.3 Procedure C — Individual component balancing prior to assembly
Each component, including the shaft, shall be low-speed balanced before assembly in accordance with
ISO 21940-11. In addition, the concentricities of the shaft diameters or other locating features that
position the individual components on the shaft shall be held to close tolerances relative to the shaft
axis (see ISO 21940-14).
The concentricities of the balancing mandrel diameters or other locating features that position each
individual component on the mandrel shall likewise be held within close tolerance relative to the axis
of the mandrel. Errors in unbalance and concentricity of the mandrel can be compensated by index
balancing (see ISO 21940-14).
When balancing the components and the shaft individually, make due allowances for any unsymmetrical
feature such as keys (see ISO 21940-32) that form part of the complete rotor, but are not used in the
individual balancing of the separate components.
It is advisable to check by calculation the unbalance produced by assembly errors, e.g. eccentricities
and assembly tolerances to evaluate their effects. When calculating the effect of these errors on the
mandrel and on the shaft, it is important to note that the effect of the errors can be cumulative on the
final assembly. Procedures for dealing with such errors can be found in ISO 21940-14.
6.5.4 Procedure D — Balancing subsequent to controlling initial unbalance
When a rotor is composed of separate components that are balanced individually before assembly (see
6.5.3), the state of unbalance might still be unsatisfactory. Subsequent balancing of the assembly at low
speed is permissible only if the initial unbalance of the assembly does not exceed specified values.
If reliable data on shaft and bearing flexibility, etc. are available, analysis of response to unbalance
using mathematical models is useful to assess the unbalance correction distribution.
Experience has shown that symmetrical rotors that conform to the requirements above, but have an
additional central correction plane can be balanced at low speed with higher initial unbalances of the
assembly. Experience has shown that between 30 % and 60 % of the initial resultant, unbalance should
be corrected in the central plane.
For unsymmetrical rotors that do not conform to the configuration defined above, e.g. as regards
symmetry or overhangs, it might be possible to use a similar procedure using different percentages in
the correction planes based on experience.
However, in extreme cases, the initial shaft unbalance can be so large that some other method of
balancing the rotor is required, e.g. Procedure E.
6.5.5 Procedure E — Balancing in stages during assembly
The shaft shall first be balanced. The rotor shall then be balanced as each component is mounted,
correction being made only on the latest component added. This method avoids the necessity for
close control of concentricities of the locating diameters or other features that position the individual
components on the shaft.
If this method is adopted, it is important to ensure that the balance of the parts of the rotor already
treated is not changed by the addition of successive components.
In some cases, it can be possible to add two single-plane components at a time and perform two-plane
balancing on the assembly by using one correction plane in each of the two components. In cases where
several components form a rigid section, e.g. a sub-assembly or core section which is normally balanced
in two planes only, one such section can be added at a time and corrected by two-plane balancing.
6.5.6 Procedure F — Balancing in optimum planes
If, because of the design or method of construction, a series of rotors has unbalances that are distributed
uniformly along their entire len
...
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 2016
© 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
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ii © ISO 2016 – All rights reserved
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
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
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
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
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).
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.
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
a) Typical rotor
P
b) First flexural mode
c) Second flexural mode
P
P
d) Third flexural mode
Key
P , P , P nodes
1 2 4
P antinode
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
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
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 rotor would then run satisfactorily at all speeds in
so far as unbalance is concerned.
In practice, the unbalance can be distributed along the length of the rotor, but the balancing process
is usually achieved by adding or removing masses in a limited number of correction planes. Thus,
there is invariably some distributed residual unbalance after balancing, which is assumed to be within
tolerance for the affected mode shapes.
It is necessary to reduce vibrations or oscillatory forces caused by the residual unbalance to acceptable
magnitudes over the service speed range. Only in special cases is it sufficient to balance rotors with
flexible behaviour for a single speed. It should be noted that a rotor, balanced satisfactorily for a given
service speed range, can still experience excessive vibration if it has to run through a resonance speed
4 © ISO 2016 – All rights reserved
to reach its service speed. Therefore, for passing through resonance speeds, the allowable vibration
may be greater than that permissible at service speed.
Whatever balancing technique is used, the final goal is to apply unbalance correction distributions to
minimize the unbalance effects at all speeds up to the maximum service speed, including start up and
shut down and possible overspeed. In meeting this objective, it might be necessary to allow for the
influence of modes with resonance speeds above the service speed range.
4.6 Provision for correction planes
The exact number of axial locations along the rotor that are needed depends to some extent on the
particular balancing procedure which is adopted. For example, centrifugal compressor rotors are
sometimes balanced as an assembly in the end planes only after each disc and the shaft have been
separately balanced in a low-speed balancing machine. Generally, however, if the speed of the rotor
is influenced by n flexural resonance speeds, which possibly include resonance speeds above the
maximum service speed, then usually if low-speed balancing is carried out, n + 2 correction planes are
needed along the rotor, if not, n planes can be used.
An adequate number of correction planes at suitable axial positions shall be included at the design
stage. In practice, the number of correction planes is often limited by design considerations and in-situ
balancing by limitations on accessibility.
4.7 Coupled rotors
When two rotors are coupled together, the complete unit has a series of resonance speeds and mode
shapes. In general, these speeds are neither equal nor simply related to the resonance speeds of the
individual, uncoupled rotors. Moreover, the deflection shape of each part of the coupled unit need
not be simply related to any mode shape of the corresponding uncoupled rotor. Ideally, therefore,
the unbalance distribution along two or more coupled rotors should be evaluated in terms of modal
unbalances with respect to the coupled system and not to the modes of the uncoupled rotors.
For practical purposes, in most cases, each rotor is balanced separately as an uncoupled shaft and this
procedure normally ensures satisfactory operation of the coupled rotors. The degree to which this
technique is practicable depends, for example, on the mode shapes and the resonance speeds of the
uncoupled and coupled rotors, the distribution of unbalance, the type of coupling and on the bearing
arrangement of the shaft train. If further balancing in-situ is required, refer to Annex A.
5 Rotor configurations
Typical rotor configurations are shown in Table 1, their characteristics outlined and the recommended
balancing procedures listed. Table 1 gives concise descriptions of the rotor characteristics. Full
descriptions of these characteristics and requirements are given in the corresponding procedures in
Clauses 6 and 7. These procedures are listed in Table 2.
Sometimes, a combination of balancing procedures can be advisable. If more than one balancing
procedure could be used, they are listed in the sequence of increasing time and cost. Rotors of any
configuration can always be balanced at multiple speeds (see 7.3) or sometimes, under special
conditions, be balanced at service speed (see 7.4) or at a fixed speed (see 7.5).
Table 1 — Rotors with flexible behaviour
Recommended
Configuration Rotor characteristics balancing
a
procedure
Elastic shaft without
1.1 Discs
unbalance, rigid disc(s)
Single disc
— perpendicular to shaft
A; C
axis
— with axial runout B; C
Two discs
— perpendicular to shaft B; C
axis
— with axial runout
— at least one B + C, E
removable
— integral G
More than two discs
— all discs removable,
B + C, D, E
except one
— integral G
Elastic shafts without
1.2 Rigid sections unbalances, rigid
sections
Single rigid section
— removable B; C; E
— integral B
Two rigid sections
— at least one removable B + C; E
— integral G
More (than two) rigid
sections
— all discs removable, B + C; E
except one
— integral G
Elastic shaft without
1.3 Discs and rigid sections unbalance, rigid discs
and sections
One each
— at least one part
B + C; E
removable
— integral G
More parts
— all discs removable,
B + C; E
except one
— integral G
a
See Table 2 for explanations of procedures A to G; two additional balancing procedures H and I can be used under
special circumstances, see 7.4 and 7.5.
6 © ISO 2016 – All rights reserved
Table 1 (continued)
Recommended
Configuration Rotor characteristics balancing
a
procedure
Mass, elasticity and
1.4 Rolls unbalance distribution
along the rotor
— under special conditions F
(see 6.5.6)
— in general G
Flexible roll, rigid
1.5 Rolls and discs/rigid sections
discs, rigid sections
— discs/rigid sections
removable
— under special
conditions C + F; E + F
(see 6.5.6)
— in general G
— integral G
Mass, elasticity and
1.6 Integral rotor unbalance distribution
along the rotor
Main parts with
G
unbalances not detachable
a
See Table 2 for explanations of procedures A to G; two additional balancing procedures H and I can be used under
special circumstances, see 7.4 and 7.5.
Table 2 — Balancing procedures
Procedure Description Subclause
Low-speed balancing
A Single-plane balancing 6.5.1
B Two-plane balancing 6.5.2
C Individual component balancing prior to assembly 6.5.3
D Balancing subsequent to controlling initial unbalance 6.5.4
E Balancing in stages during assembly 6.5.5
F Balancing in optimum planes 6.5.6
High-speed balancing
G Multiple speed balancing 7.3
H Service speed balancing 7.4
I Fixed speed balancing 7.5
6 Procedures for balancing rotors with flexible behaviour at low speed
6.1 General
Low-speed balancing is generally used for rotors with rigid behaviour and high-speed balancing is
generally used for rotors with flexible behaviour. Procedures to determine whether a rotor shows rigid
or flexible behaviour are described in Annex E. However, with the use of appropriate procedures, it
is possible under some circumstances to balance rotors with flexible behaviour at low speed so as to
ensure satisfactory running when the rotor is installed in its final environment. Otherwise, rotors with
flexible behaviour require the use of a high-speed balancing procedure.
Most of the procedures explained in this subclause require some information regarding the axial
distribution of unbalance.
In some cases where a gross unbalance can occur in a single component, it can be advantageous to
balance this component separately before mounting it on the rotor, in addition to carrying out the
balancing procedure after it is mounted.
Certain rotors contain a number of individual parts which are mounted concentrically (e.g. blades,
coupling bolts, pole pieces). These parts can be arranged according to their individual mass or mass
moment to achieve some or all of the required unbalance correction described in any of the procedures.
If these parts need to be assembled after balancing, they should be arranged in balanced sets.
Some rotors are made of individual components (e.g. turbine discs). In these cases, it is important to
recognize that the assembly process can produce changes in the shaft geometry (e.g. shaft runout) and
further changes can occur during high-speed service.
6.2 Selection of correction planes
If the axial positions of the unbalances are known, the correction planes should be provided as closely
as possible to these positions. When a rotor is composed of two or more separate components that are
distributed axially, there can be more than two transverse planes of unbalance.
6.3 Service speed of the rotor
If the service speed range includes or is close to a flexural resonance speed, then low-speed balancing
methods should be used with caution.
6.4 Initial unbalance
The process of balancing a rotor with flexible behaviour in a low-speed balancing machine is an
approximate one. The magnitude and distribution of initial unbalance are major factors determining
the degree of success that can be expected.
For rotors in which the axial distribution of initial unbalance is known and appropriate correction
planes are available, the permissible initial unbalance is limited only by the amount of correction
possible in the correction planes.
For rotors in which the distribution of the initial unbalance is not known, there are no generally
applicable low-speed balancing methods. However, sometimes the magnitude can be controlled by the
pre-balancing of individual components. In these cases, the low-speed initial unbalance can be used as
a measure of the distribution of unbalance.
6.5 Low-speed balancing procedures
6.5.1 Procedure A — Single-plane balancing
If the initial unbalance is principally contained in one transverse plane and the correction is made in
this plane, then the rotor is balanced for all speeds.
6.5.2 Procedure B — Two-plane balancing
If the initial unbalance is principally concentrated in two transverse planes and the corrections are
made in these planes, then the rotor is balanced for all speeds.
If the unbalance in the rotor is distributed within a substantially rigid section of the rotor and the
unbalance correction is also made within this section, then the rotor is balanced for all speeds.
8 © ISO 2016 – All rights reserved
6.5.3 Procedure C — Individual component balancing prior to assembly
Each component, including the shaft, shall be low-speed balanced before assembly in accordance with
ISO 21940-11. In addition, the concentricities of the shaft diameters or other locating features that
position the individual components on the shaft shall be held to close tolerances relative to the shaft
axis (see ISO 21940-14).
The concentricities of the balancing mandrel diameters or other locating features that position each
individual component on the mandrel shall likewise be held within close tolerance relative to the axis
of the mandrel. Errors in unbalance and concentricity of the mandrel can be compensated by index
balancing (see ISO 21940-14).
When balancing the components and the shaft individually, make due allowances for any unsymmetrical
feature such as keys (see ISO 21940-32) that form part of the complete rotor, but are not used in the
individual balancing of the separate components.
It is advisable to check by calculation the unbalance produced by assembly errors, e.g. eccentricities
and assembly tolerances to evaluate their effects. When calculating the effect of these errors on the
mandrel and on the shaft, it is important to note that the effect of the errors can be cumulative on the
final assembly. Procedures for dealing with such errors can be found in ISO 21940-14.
6.5.4 Procedure D — Balancing subsequent to controlling initial unbalance
When a rotor is composed of separate components that are balanced individually before assembly (see
6.5.3), the state of unbalance might still be unsatisfactory. Subsequent balancing of the assembly at low
speed is permissible only if the initial unbalance of the assembly does not exceed specified values.
If reliable data on shaft and bearing flexibility, etc. are available, analysis of response to unbalance
using mathematical models is useful to assess the unbalance correction distribution.
Experience has shown that symmetrical rotors that conform to the requirements above, but have an
additional central correction plane can be balanced at low speed with higher initial unbalances of the
assembly. Experience has shown that between 30 % and 60 % of the initial resultant, unbalance should
be corrected in the central plane.
For unsymmetrical rotors that do not conform to the configuration defined above, e.g. as regards
symmetry or overhangs, it might be possible to use a similar procedure using different percentages in
the correction planes based on experience.
However, in extreme cases, the initial shaft unbalance can be so large that some other method of
balancing the rotor is required, e.g. Procedure E.
6.5.5 Procedure E — Balancing in stages during assembly
The shaft shall first be balanced. The rotor shall then be balanced as each component is mounted,
correction being made only on the latest component added. This method avoids the necessity for
close control of concentricities of the locating diameters or other features that position the individual
components on the shaft.
If this method is adopted, it is important to ensure that the balance of the parts of the rotor already
treated is not changed by the addition of successive components.
In some cases, it can be possible to add two single-plane components at a time and perform two-plane
balancing on the assembly by using one correction plane in each of the two components. In cases where
several components form a rigid section, e.g. a sub-assembly or core section which is normally balanced
in two planes only, one such section can be added at a time and corrected by two-plane balancing.
6.5.6 Procedure F — Balancing in optimum planes
If, because of the design or method of construction, a series of rotors has unbalances that are distributed
uniformly along their entire length (e.g. tubes), it can be possible by selecting suitable axial positions
of two correction planes to achieve satisfactory running over the entire speed range by low-speed
balancing. I
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