ISO 11342:1994

I NTERNAT ION AL IS0
STANDARD
First edition
1994-1 1-01
Mechanical vibration - Methods and
criteria for the mechanical balancing of
flexible rotors
Vibrations mécaniques - Méthodes et critères
Reference number
IS0 1 1342: 1 994(E)
IS0 11342:1994(E)
Contents
Page
Section 1 General . 1
1.1 Scope . 1
1.2 Normative references . 1
1.3 Definitions . 2
Section 2 Balancing methods . 3
2.1 Fundamentals of flexible rotor dynamics and balancing . 3
2.2 Classification . 6
2.3 Balancing of class 2 rotors . 9
2.4 Balancing of class 3, 4 and 5 rotors . 11
Section 3 Criteria . 15
3.1 Evaluation of final state of unbalance . 15
Choice of criteria . 17
3.2
3.3 Recommendations for vibration criteria in the balancing facility 17
3.4 Recommendations for establishing criteria for permissible residual
unbalance in specified correction planes . 19
Annexes
A Cautionary notes concerning multispan rotors on site . 21
B Low-speed three-plane balancing of class 2d rotors .,. 22
C Conversion factors . 23
D Experimental determination of equivalent modal residual
unbalances . 24
E Procedure to determine if a rotor is rigid or flexible . 25
F Examples of the use of conversion factors . 27
Method of computation of inbalance correction . 29
G
H Definitions from IS0 1925: 990 relating to flexible rotors . 30
O IS0 1994
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 CH-1 21 1 Genève 20 Switzerland
Printed in Switzerland
II
8 IS0 IS0 11342:1994(E)
J Bibliography . : . 31

Q IS0
IS0 11342:1994(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work
of preparing International Standards is normally carried out through IS0
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. IS0
collaborates closely with the International Eiectrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are
circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard IS0 1 1342 was prepared by Technical Committee
lSO/TC 108, Mechanical vibration and shock, Subcommittee SC 1, Bal-
ancing, including balancing machines.
This first edition of IS0 11342 cancels and replaces IS0 5406:1980 and
IS0 5343:1983.
Annexes A, B, C, D, E, F, G, H and J of this International Standard are for
information only.
The aim of balancing any rotor is satisfactory running when installed on
site. In this context "satisfactory running" means that no more than an
acceptable leve! of vibration is caused by the unbalance remaining in the
rotor. In the case of a flexible rotor, it also means that no more than an
acceptable magnitude of deflection occurs in the rotor at any speed up to
maximum service speed.
Most rotors are balanced by their manufacturers prior to machine as-
sembly because afterwards, for example, there may be only limited ac-
cess 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 on site is the aim, the balance quality of the rotor is usually initially
assessed in a balancing facility. Satisfactory running on site is in most
cases judged in relation to vibration from all causes, while in the balancing
facility primarily once-per-revolution effects are considered.
Section 2 of this International Standard classifies rotors into groups in ac-
cordance with their balancing requirements and establishes in Section 3
methods of assessment of residual unbalance.
This International Standard also shows in Section 3 how criteria for use in
the balancing facility may 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 International Standard shows
how they may be derived from IS0 10816-1 and parts 1 to 4 of IS0 7919,
if desired in terms of vibration, or from IS0 1940-1 if desired in terms of
permissible residual unbalance.
IS0 1940-1 is concerned with the balance quality of rotating rigid bodies
and is thus not directly applicable to flexible rotors because they may un-
dergo significant bending deflection. However, in subclauses 2.3 and 3.4
of this International Standard, methods are presented for adapting the
criteria of IS0 1940-1 to flexible rotors.
As this International Standard is complementary in many details to parts
1 and 2 of IS0 1940, it is recommended that, where applicable, they
should be considered together.

a
INTERNATIONAL STANDARD 0 IS0 IS0 11342:1994(E)
Mechanical vibration - Methods and criteria for the
mechanical balancing of flexible rotors
Section 1: General
a basis for more involved investigations, for example
1.1 Scope
when a more exact determination of the required
balance quality is necessary. if due regard is paid to
This International Standard classifies rotors into
the specified methods of manufacture and limits of
groups in accordance with their balancing require-
unbalance, satisfactory running conditions can most
ments, describes balancing procedures, specifies
probably be excepted.
methods of assessment of the final state of unbal-
ance, and gives guidance on balance quality criteria.
There are situations in which an otherwise acceptably
balanced rotor experiences an unacceptable vibration
All rotors are classified into those which can be bal-
level in situ, owing to resonances. A resonant or
anced by rigid rotor, modified rigid rotor, or high-speed
near-resonant condition in a lightly damped structure
(flexible rotor) balancing techniques.
can result in excessive vibratory response to a small
unbalance. In such cases, it may be necessary to alter
Two methods are specified for evaluating the balance
the natural frequency or damping of the structure
quality of a flexible rotor in a balancing facility before
rather than to balance to very low levels, which may
machine assembly: the first assesses the vibration
not be maintainable over time.
level, and the second assesses the rotor residual un-
0 balance. If the rotor balance tolerances suggested
The subject of structural resonances and modifica-
herein are achieved during correction in a balancing
tions thereof is outside the scope of this International
facility, the specified vibration limits of the assembled
Standard.
machine in service (see IS0 1081 6-1 and parts 1 to 4
of IS0 7919) will most probably be achieved. Accord- The methods and criteria given are the result of ex-
ingly, the criteria specified are those to be met when perience with general industrial machinery. They may
the rotor is tested in the balancing facility, but they not be directly applicable to specialized equipment or
are derived from those specified for the complete to special circumstances. Therefore, there may be
machine, when installed, or from values known to cases where deviations from this International Stan-
ensure satisfactory running of the rotor when it is in- dard may be necessary’).
stalled.
As in the case of parts 1 and 2 of IS0 1940, this 1.2 Normative references
International Standard is not intended to serve as an
acceptance specification for any rotor group, but The following standards contain provisions which,
rather to give indications of how to avoid gross through reference in this text, constitute provisions
deficiences and/or unnecessarily restrictive require- of this International Standard. At the time of publi-
ments. This International Standard may also serve as cation, the editions indicated were valid. A11 standards
1) Information on such exceptions is welcomed and should be communicated to the national standards body in the country
of origin for transmission to the secretariat of ISOflC 108.

based o-n this International Standard are encouraged steam turbine-generator sets.
to investigate the possibility of applying the most re-
IS0 791 9-3:-*), Mechanical vibration of non-
cent editions of the standards indicated below.
reciprocating machines - Measurements on rotating
Members of IEC and IS0 maintain registers of cur-
shafts and evaluation - Part 3: Guidelines for cou-
rently valid International Standards.
pled industrial machines
IS0 1 925: 1 990, Mechanical vibration - Balancing -
IS0 791 9-4:-2), Mechanical vibration of non-
Vocabulary.
reciprocating machines - Measurements on rotating
shafts and evaluation - Part 4: Guidelines for gas
IS0 1940-1 :I 986, Mechanical vibration - Balance
turbines.
quality requirements of rigid rotors - Part 1: Deter-
mination of permissible residual unbalance.
IS0 8821 : 1989, Mechanical vibration - Balancing -
Shaft and fitment key convention.
IS0 1 940-2:-*’, Mechanical vibration - Balance
quality requirements of rigid rotors - Part 2: Balance
IS0 1081 6-1 :-2), Mechanical vibration - Evaluation
errors.
of machine vibration by measurements on non-
- Part 1: General guidelines.
IS0 2041 :I 990, Vibration and shock - Vocabulary. rotating parts
IS0 2953:1985, Balancing machines - Description
1.3 Definitions
and evaluation.
For the purposes of this International Standard, the
IS0 791 9-1 :I 986, Mechanical vibration of non-
definitions relating to mechanical balancing given in
reciprocating machines - Measurements on rotating
IS0 1925 and many of the definitions relating to vi-
shafts and evaluation - Part 1: General guidelines
bration given in IS0 2041 apply.
IS0 791 9-2:-*), Mechanical vibration of non-
Definitions given in IS0 1925 relating to flexible rotors
reciprocating machines - Measurements on rotating
are given for information in annex H.
2) To be published.
Q IS0
IS0 11342:1994(E)
Section 2: Balancing methods
2.1.2 Flexible rotor mode shapes
2.1 Fund mental of flexible rotor
dynamics and balancing
If the effect of damping is neglected, the modes of a
rotor are the flexural principal modes and, in the spe-
cial case of a rotor supported in isotropic bearings, are
rotating plane curves. Typical curves for the three
2.1.1 Unbalance distribution
lowest principal modes for a simple rotor supported
in flexible bearings near to its end are illustrated in
The rotor design and method of construction can sig-
figure 1.
nificantly influence the magnitude and distribution of
For a damped rotor/bearing system, the flexural
unbalance along a rotor. Rotors may be machined
modes may be space curves rotating about the shaft
from a single forging or they may be constructed by
axis, especially in the case of substantial damping,
fitting several components together. For example, jet
arising perhaps from fluid-film bearings. A possible
engine rotors are constructed by joining many shell,
substantially damped second mode is illustrated in
disc and blade components. Generator rotors, how-
figure2. In many cases, the damped modes can be
ever, are usually manufactured from a single forging,
treated approximately as principal modes and hence
but will have additional components fitted. The distri-
regarded as rotating plane curves.
bution of unbalance may also be significantly influ-
enced by the presence of large local unbalances
It must be stressed that the form of the mode shapes
arising from shrink-fitted discs, couplings, etc.
and the response of the rotor to unbalances are
strongly influenced by the dynamic properties and
Since the unbalance distribution along a rotor is likely
axial locations of the bearings and their supports.
to be random, the distribution along two rotors of
identical design will be different. The distribution of
unbalance is of greater significance in a flexible rotor 2.1.3 Response of a flexible rotor to
than in a rigid rotor because it determines the degree
unbalance
to which any flexural mode of vibration is excited.
The unbalance distribution can be expressed in terms
Moreover, the effect of unbalance at any point along
of modal unbalances. The deflection in each mode is
a rotor depends on the bending deflection of the rotor
caused by the corresponding modal unbalance. When
at that point.
a rotor rotates at a speed near a critical speed, it is
The correction of unbalance in transverse planes
usually the mode associated with this critical speed
along a rotor, other than those in which the unbalance
which dominates the deflection of the rotor. The de-
occurs, may induce vibrations at speeds other than
gree to which large amplitudes of rotor deflection oc-
that at which the rotor was originally corrected. These
cur in these circumstances is determined by:
vibrations may exceed specified tolerances, particu-
larly at or near the flexural critical speeds.
a) the magnitude of the modal unbalances;
In addtion, some rotors which become heated during
b) the proximity of the associated critical speeds to
operation are susceptible to thermal distortions which the running speeds; and
can lead to changes in the unbalance. If the rotor un-
c) the amount of damping in the rotor/support sys-
balance changes significantly from run to run, it may
tem.
be impossible to balance the rotor within tolerance.
IS0 11342:1994(E)
Pl p, p3 PL
a) Typical rotor
p3
b) First flexural mode
c) Second flexural mode
d) Third flexural mode
NOTE - Pl to P4 are correction planes.
Figure 1 - Typical mode shapes for flexible rotors on flexible supports
figure1 a) in the plane P2 will produce no change in
If a particular modal unbalance is reduced by the ad-
response in the second mode. Similarly, a correction
dition of a number of discrete correction masses, then
mass attached in either plane Pl or P4 will not affect
the corresponding modal component of deflection is
the response in the third mode. Conversely, a cor-
similarly reduced. The reduction of the modal unbal-
ances in this way forms the basis of the balancing rection mass in plane P3 will produce the maximum
procedures described in this International Standard. effect on the first mode.
The modal unbalances for a given unbalance distri-
2.1.4 Aims of flexible rotor balancing
bution are a function of the flexible rotor modes.
Moreover the effect produced in a particular mode by
The aims of balancing are determined by the opera-
a given correction depends on the ordinate of the
tional requirements of the machine. Before balancing
mode shape curve at the axial location of the cor-
any particular rotor, it is desirable to decide what bal-
rection. Consider an example in which the curves of
ance criteria can be regarded as satisfactory. In this
figure 1 b) to 1 d) are mode shapes for the rotor in
way the balancing process can be made efficient and
figure 1 a). A correction mass attached to the rotor in
economic, but still satisfy the needs of the user.

IS0 11342:1994(E)
I
NOTE - OX, OY and OZ are fixed axes. OX' and OY' are axes rotating about OZ at speed o.
Figure 2 - Possible damped second-mode shape
I
I
Vibrations or oscillatory forces due to the residual un-
Balance criteria are specified to achieve the following:
balance must be reduced to acceptable magnitudes
I
a) acceptable values of machinery vibration and shaft over a range of speeds, including one or more critical
I
deflection; speeds. Only in special cases is it sufficient to balance
l
flexible rotors for a single speed. It should be noted
b) acceptable values of unbalance forces applied to
that a rotor, balanced satisfactorily for a given service
the bearings.
speed range, may still experience excessive vibration
if it has to run through a critical speed to reach its
e
The ideal aim in balancing flexible rotors would be to
service speed. Balancing a rotor according to its mode
correct the local unbalance occurring at each elemen-
shapes is not an end in itself. Whatever balancing
tal length by means of unbalance corrections at the
technique is used, the final goal is to apply unbalance
element itself. This would result in a rotor in which
correction distributions to minimize the unbalance ef-
the centre of mass of each elemental length lies on
fects up to the service speed, and possible over-
the shaft axis.
speed.
A rotor balanced in this ideal way would have no static
and couple unbalance and no modal components of
2.1.5 Provision for correction planes
unbalance. Such a perfectly balanced rotor would then
run satisfactorily at all speeds in so far as unbalance
Rotors are often balanced mode by mode. In this
is concerned.
process, correction masses are located along the
rotor, so that at each stage in the balancing procedure
in practice, the necessary reduction in the unbalance
the new correction masses do not significantly disturb
forces is usually achieved by adding or removing
modes already balanced.
masses in a limited number of correction planes.
The exact number of axial locations along the rotor
There will invariably be some distributed residual un-
that are needed for this process depends to some
balance after balancing.
extent on the particular balancing procedure which is
IS0 11342:1994(E) 0 IS0
adopted. For example, centrifugal compressor rotors
2.2.1 Class 1: Rigid rotors
are sometimes assembly-balanced in the end planes
A rotor is considered to be rigid when its unbalance
only, after each disc and the shaft have been separ-
can be corrected in any two (arbitrarily selected)
ately balanced in a low-speed balancing machine.
planes. After the correction, its residual unbalance
Generally, however, if the speed of the rotor ap-
does not change significantly (relative to the shaft
proaches or exceeds its nth critical speed, then at
axis) at any speed up to the maximum service speed
least II and commonly (n + 2) correction planes are
and when running under conditions which approxi-
needed along the rotor.
mate closely to those of the final supporting system.
An adequate number of correction planes at suitable
Rotors of this type can be corrected by rigid-rotor
axial positions should be included at the design stage.
balancing methods (see IS0 1940-1 1.
In practice, the number of correction planes is often
limited by design considerations and in field balancing
2.2.2 Class 2: Quasi-rigid rotors
by limitations on accessibility.
A rotor that cannot be considered rigid but that can
be balanced using modified rigid-rotor balancing tech-
2.1.6 Rotors coupled together
niques is considered to be a quasi-rigid rotor.
Class 2 rotors are subdivided (see table 1) into:
When two rotors are coupled together, the complete
unit will have a series of critical speeds and mode
a) rotors in which the axial distribution of unbalance
shapes. In general, these speeds are neither equal to
is known (classes 2a, 2b, 2c and 2d; also class 2e
nor simply related to the critical speeds of the indi-
in which the axial distribution is partly known);
vidual, uncoupled rotors. Moreover, the deflection
shape of each part of the coupled unit need not be
b) rotors in which the axial distribution of unbalance
simply related to any mode shape of the correspond-
is not known (classes 2f, 2g and 2h).
ing uncoupled rotor. In theory, therefore, the unbal-
ance distribution along two or more coupled rotors
The subdivision of class 2 rotors shows the many
should be evaluated in terms of modal unbalances
reasons why rotors can often be balanced satisfac-
with respect to the coupled system and not to the
torily at low speed as rigid rotors even though they
modes of the uncoupled rotors.
are flexible. Some rotors will fit into more than one
category of the subdivision.
For practical purposes, it is often necessary that each
rotor be balanced separately as an uncoupled shaft.
In many cases, this procedure will ensure satisfactory 2.2.3 Class 3: Flexible rotors
operation of the coupled rotors. The degree to which
A rotor that cannot be balanced using modified rigid-
this technique is practicable depends, for example, on
rotor balancing techniques but instead requires the
the mode shapes and the critical speeds of the un-
use of high-speed balancing methods is considered to
coupled and coupled rotors, and the distribution of
be a flexible rotor.
un ba la nce.
Class 3 is subdivided (see table 1) because the bal-
If further balancing on site is required, reference
ancing techniques, criteria and bearing requirements
should be made to annex A.
may differ substantially for different rotors.
2.2.4 Class 4
2.2 Classification
A rotor that could fall into class 1, 2 or 3 but has in
For the purposes of this International Standard, rotors
addition one or more components that are them-
are divided into five main classes as shown in 2.2.1
selves flexible or flexibly attached is considered to be
to 2.2.5 and in tablel. Each class requires different
a class 4 rotor.
balancing techniques. A procedure to determine if a
rotor is rigid or flexible is given in annex E. A subdivision of class 4 rotors is indicated in 2.4.2.
0 IS0
IS0 11342:1994(E)
Table 1 - Classification of rotors
Class of
Description Example
rotor
I
A rotor whose unbalance can be corrected in any two (arbi-
Class 1:
trarily selected) planes so that after that correction, its unbal-
Rigid
ance does not change significantly at any speed up to
rotors
maximum service speed (see 2.2.1).
I Gear wheel
Class 2:
Quasi- A rotor that cannot be considered rigid but that can be balanced
rigid using modified rigid-rotor balancing techniques see (2.2.2).
rotors
Rotors in which the axial distribution of unbalance is known
4 rotor with a single transverse plane of unbalance, for exam-
Classe 2a Ae a single mass on a light flexible shaft whose unbalance can
)e neglected.
Grinding wheel
4 rotor with two transverse planes of unbalance, for example
:WO masses on a light shaft whose unbalance can be neg-
Class 2b
ected.
Grinding wheel with pulley
4 rotor with more than two transverse planes of unbalance.
Class 2c
Axial compressor rotor
Class 2d 4 rotor with uniformly or linearly varying unbalance
Printing press roller
A rotor consisting of a rigid mass of significant axial length
supported by flexible shafts whose unbalance can be neg-
Class 2e
+s!47-
lected.
Computer memory drum
Class of
Description Example
rotor
~~ ~ ~
Rotors in which the axial distribution of unbalance is not known
A symmetrical rotor (with two end correction planes) whose
maximum speed does not significantly approach second critical
Class 2f
speed, whose service speed range does not contain first criti-
cal speed, and which has a controlled initial unbalance.
Multistage centrifugal pump/compressor
A symmetrical rotor (with two end correction planes and a
central correction plane) whose maximum speed does not sig-
Class 29
nificantly approach second critical speed and which has a
controlled initial unbalance.
Hig-speed centrifugal pump/compressor
As unsymmetrical rotor which has a controlled initial unbalance
Class 2h
treated in a similar manner to a class 2f rotor.
I.P. steam turbine rotor
Class 3: A rotor that cannot be balanced using modified rigid-rotor bal-
ancing techniques but instead requires the use of high-speed
Flexible
balancing methods (see 2.2.3).
rotors
A rotor that, for any unbalance distribution, is significantly af-
WM------tW
Class 3a
fected by only the first mode unbalance. unu
Four-pole generator rotor
A rotor that, for any unbalance distribution, is significantly af-
Class 3b
fected by only the first and second mode unbalance.
Small two-pole generator rotor
A rotor significantly affected by more than the first and second
Class 3c
mode unbalance.
Large two-pole generator rotor
~
A rotor that could fall into class 1, 2 or 3 but has in addition one
or more components that are themselves flexible or flexibly
Class 4
attached (see 2.2.4).
Rotor with centrifugal switch
A rotor that could fall into class 3 but for some reason, for ex-
Class 5 ample economy, is balanced for one speed of operation only
(see 2.2.5).
High-speed motor
0 IS0
IS0 11342:1994(E)
2.3.3.1 Assembly of individually balanced
2.2.5 Class 5
components
A rotor that could fall into class 3 but in some cir-
Each component, including the shaft, should be indi-
cumstances is balanced for one speed of operation
vidually balanced as a rigid rotor in accordance with
only is considered to be a class 5 rotor. For rotors to
be treated as class 5, the conditions stated in 2.4.3 IS0 1940-1 before assembly. In addition, the fits and
shall be met. concentricities of the shaft diameters or other locating
features that position the individual components on
the shaft should be held to close tolerances.
2.3 Balancing of class 2 rotors
The fits and concentricities of the balancing mandrel
diameters or other location features that position each
2.3.1 General
individual component on the mandrel should likewise
be held within close tolerances relative to the shaft
Class 2 rotors are flexible rotors, however, they can
axis of the mandrel. Errors in unbalance and
be satisfactorily balanced at low speed by modified
concentricity of the mandrel may be compensated by
rigid-rotor balancing techniques. As such, they repre-
index balancing (see IS0 1940-1).
sent the borderline case between rigid rotors for
which low-speed balancing is sufficient and flexible
When balancing the components and the shaft indi-
rotors that demand the high-speed balancing proce-
vidually, due allowances should be made for any un-
dure given in 2.4.
symmetrical feature such as keys (see IS0 8821) that
A low-speed balancing machine generally measures form part of the complete rotor but are not used in the
only the dynamic unbalance of a rigid rotor. However, individual balancing of the separate components.
it is possible in some circumstances with the use of
It is advisable to check by calculation the unbalance
appropriate procedures to balance a flexible rotor at
produced by errors, such as eccentricities and as-
low speed so as to ensure satisfactory running when
sembly tolerances on the mandrel and on the shaft,
the rotor is installed in its final environment.
to evaluate their effects.
The amount of modal unbalance remaining in a rotor
When calculating the effect of these errors, it is im-
after low-speed balancing will depend on the mode
portant to note that the effect of the errors can be
shapes of the rotor and the axial positions of the un-
cumulative on the final assembly. Procedures for
balances relative to the correction planes used.
dealing with such errors can be found in IS0 1940-2.
2.3.2 Selection of correction planes
2.3.3.2 Sequential-assembly balancing
If the axial positions of the unbalances are known, the
correction planes should be provided as closely as
The shaft should first be balanced. The rotor should
possible to these positions. If the axial positions of the
then be balanced as each component is mounted,
unbalances are not known, then see 2.1.5 for general
correction being made only on the latest component
guidance.
added. This method avoids the necessity for close
control of concentricities of the locating diameters or
2.3.3 Rotors made up of individual
other features that position the individual components
components
on the shaft.
When a rotor is composed of separate components
If this method is adopted, it is important to ensure
that are distributed axially and mounted concentrically
that the balance of the parts of the rotor already
on a shaft, the adoption of one of the following pro-
treated is not changed by the addition of successive
cedures will considerably increase the probability that
components.
low-speed balancing is sufficient.
In some cases, it may be possible to add two single-
NOTE 1 Certain rotors in all classes contain a number of
plane components at a time and perform dynamic
individual components which are mounted concentrically
unbalance correction in those two components. In
(for example, blades, coupling bolts, pole pieces, etc.).
cases where several components form a short stiff
These components may be arranged according to their in-
unit or sub-assembly or core section that is normally
dividual mass or mass moment to achieve some or all of the
balanced in two planes only, one such unit or sub-
required unbalance correction described in any of the
assembly may be added at a time and corrected by
methods. If these components must be fitted or replaced
after balancing, they should be arranged in balanced sets. two-plane (dynamic) balancing.
IS0 11342:1994(E) 0 IS0
In some cases where a gross unbalance may occur in 2.3.6.2 Class 2b: Rotors with two transverse
a single component, it may be advantageous to bal-
planes of unbalance
ance this component separately before mounting it
on the rotor, in addition to carrying out the balancing If the initial unbalance is known to be wholly con-
procedure after it is mounted. tained in two transverse planes and the corrections
are made in these planes, then the rotors will be bal-
anced for all speeds.
2.3.4 Service speed of the rotor
In these circumstances, the unbalance can be
If the service speed range includes, or is close to, a measured and corrected by low-speed balancing as
flexural critical speed, then class 2 low-speed balanc- effectively as at service speed.
ing methods should only be used with caution.
2.3.6.3 Class 2c: Rotors with more than two
2.3.5 Initial unbalance
transverse planes of unbalance
The process of balancing a flexible rotor in a low-
When a rotor is composed of two or more separate
speed balancing machine is a compromise. The mag-
components that are distributed axially, it is likely that
nitude and distribution of initial unbalance is a major
there will be more than two transverse planes of un-
factor determining the degree of residual modal un-
balance. A satisfactory state of balance may be
balance that can be expected.
achieved by low-speed balancing, provided that the
methods of manufacture and the precautions sug-
For rotors in which the axial distribution of initial un-
gested in 2.3.3 are followed.
balance is known and appropriate correction planes
are available (classes 2a to 2e), the permissible initial
It is important to recognize that the assembly process
unbalance is limited only by the amount of correction
may produce changes in the shaft geometry (e.g.
possible in the correction planes. Methods of low-
shaft runout), and further changes may occur during
speed balancing of such rotors are given in 2.3.6.1 to
high-speed service.
2.3.6.5.
For rotors in which the actual distribution of the initial
2.3.6.4 Class 2d: Rotors with uniformly
unbalance is not known, there are no generally appli-
distributed or linearly varying unbalance
cable low-speed balancing methods. However, for
rotors of classes 2f to 2h, although the exact distri-
If, because of design or method of construction, a
bution of initial unbalance cannot be known, the
rotor has unbalances that are distributed uniformly
magnitude can be controlled by the prebalancing of
along its entire length (e.g. a tube), it may be possible
individual components. In these cases, the low-speed
by selecting suitable axial positions of two correction
initial unbalance can be used as a measure of the
planes to achieve satisfactory running over the entire
distribution of unbalance. The maximum initial unbal-
speed range by low-speed balancing. It is likely that
ance that can be tolerated will depend on the allow-
the optimum position of the two correction planes
able bearing load and the detail characteristics of the
producing the best overall running conditions can only
rotor. Balancing procedures for such rotors are given
be determined by experimentation on a number of
in 2.3.6.6 and 2.3.6.7.
rotors of similar type.
For a simple rotor system that satisfies the following
2.3.6 Balancing procedures for class 2 rotors
conditions:
2.3.6.1 Class 2a: Rotors with a single transverse
a) single-span rotor with no significant overhang,
plane of unbalance
b) uniform or linear distribution of unbalance,
If the initial unbalance is known to be wholly con-
tained in one transverse plane and the correction is c) uniform bending flexibility of rotor along its length,
made in this plane, then the rotor will be balanced for
d) symmetrical position of end correction planes
all speeds.
about midspan, and
In these circumstances, the unbalance can be cor-
rected by low-speed balancing as effectively as at
e) continuous service speeds below and not signifi-
service speed. cantly approaching second critical speed,
Q3 IS0
IS0 11342:1994(E)
the optimum position for the two correction planes is of the initial static unbalance should be corrected in
22 % of the bearing span inboard of each bearing. If the central plane.
correction in these planes does not produce satisfac-
For unsymmetrical rotors (class 2h) that do not con-
tory results, it may still be possible to balance the
form to the configuration defined in 2.3.6.6. (for ex-
rotor at low speed by utilizing correction planes in the
ample, as regards symmetry or overhangs), it may be
middle and at the rotor ends as shown in annex B.
possible to use a similar procedure and hence to ar-
To do this, it is necessary to assess what proportion
rive at the maximum permissible initial unbalance that
of the total initial unbalance is to be corrected at the
may be corrected satisfactorily at any given correction
centre plane.
plane.
However, in extreme cases, the permissible initial
2.3.6.5 Class 2e: Rotors with a rigid core
unbalance arrived at in this way may be too small to
If the unbalance in the rotor is known to be contained make this method of balancing practicable and in
wholly within a substantially rigid section of the rotor these cases some other method of balancing the rotor
and the unbalance correction is also made within this will have to be adopted, for example, sequential-
assembly balancing (2.3.3.2).
section, then the unbalance will be zero in all modes.
Such a rotor that has flexibility derived solely from its
flexible shaft can be balanced at low speed.
2.4 Balancing of class 3, 4 and 5 rotors
2.3.6.6 Class 2f Symmetrical rotors with
controlled initial unbalance (two end correction
2.4.1 Balancing procedures for class 3 rotors
planes)
2.4.1.1 General
When a rotor is composed of separate components
that are individually balanced before assembly, as
Traditionally, two different methods have been for-
outlined in 2.3.3.1, a satisfactory state of balance may
mulated for achieving a satisfactory state of balance,
be achieved in a low-speed balancing machine pro-
namely modal balancing and the influence coefficient
vided the initial unbalance of the assembled rotor
approach. The basic theory behind both of these
does not exceed specified tolerances.
methods and their relative merits are described widely
For such rotors, the axial distribution and magnitude
in the literature and therefore no further detailed de-
of unbalance of the complete assembly will not be
scription will be given here. In most practical balanc-
known. Since the maximum speed of this class of
ing applications, the method adopted will normally be
rotor does not significantly approach the second criti-
a combination of both approaches. The degree to
cal speed, the most unfavourable case that will occur
which the method is weighted to one or the other
with a given distribution of unbalance is when the in-
will be dependent on the particular circumstances.
@ dividual contributions of the assembled components
One such balancing method is described in 2.4.1.5.
to the resultant unbalance have the same angular
However, it should be recognized that for particular
position. The maximum initial unbalance that may be
cases some variation of the procedure may be used.
corrected in two planes will have to be determined
by experience.
2.4.1.2 Rotor supports
If realistic data on shaft and bearing flexibility, etc. are
For balancing purposes the rotor should be mounted
available, analysis of response to unbalance using
on suitable bearings. In some cases it is desirable that
mathematical models will be useful initially.
the bearing supports in the balancing facility are
chosen to provide similar conditions to those at site,
2.3.6.7 Class 2g and 2h rotors with controlled
so that the modes obtained during site operation will1
initial unbalance
be adequately represented during the balancing proc-
ess and hence reduce the necessity for subsequent
Experience has shown that symmetrical rotors (class
field balancing.
2g) that conform to the requirements given in
2.3.6.6, but have an additional central correction If the rotor to be balanced has an overhang of signifi-
plane, may be balanced at low speed as a rigid rotor, cant mass, or flexibility, that would normally be sup-
with a higher permissible initial unbalance for the ported when installed on site, it may be necessary to
complete rotor than the value arrived at in 2.3.6.6. provide an additional bearing (steady bearing) to limit
Experience has shown that between 30 % and 60 % its deflection during the balancing operation.
Q IS0
IS0 11342:1994(E)
2.4.1.3 Measuring system 2.4.1.5.2 Add a set of trial masses to the rotor,
which should be selected to produce a significant
Transducers should be positioned to measure shaft, vector change in vibration tor force) at the first flexural
bearing or support vibration or bearing force as balancing speed.
ppropriate. The system should be capable of measur-
If low-speed (rigid-rotor) balancing has been omitted,
ing the amplitude of the once-per-revolution compo-
the trial mass set usually comprises only one mass,
nent of the signal, together with the phase angle
which for rotors which are essentially symmetric
relative to some fixed angular reference on the rotor.
about midspan will be placed towards the middle of
Alternatively, it is possible to use a measuring system
the rotor.
which resolves the once-per-revolution measure-
ments into orthogonal components.
If low-speed balancing has been performed, then the
trial mass set will usually consist of masses located
It is recommended that the transducers and their
at three distinct correction planes. In this case, the
supports be selected such that they do not undergo
masses are proportioned so that the low-speed
resonant vibration at any test speed, to avoid errors
(rigid-rotor) balancing is not upset.
in interpretation of the unbalance response.
2.4.1.5.3 Run the rotor to the same speed and under
the same conditions as in 2.4.1.5.1, and record the
2.4.1.4 Low-speed (rigid-rotor) balancing
new readings of vibration (or force).
Experience has shown that it may be advantageous
to carry out rigid-rotor balancing at low speed, prior to
2.4.1.5.4 From the vectorial changes of the readings
balancing at higher speeds. This may be particularly
between 2.4.1.5.1 and 2.4.1.5.3, compute the rel-
advantageous for rotors significantly affected by only
evant influence coefficients at the first flexural bal-
the first flexural critical speed.
ancing speed. Hence, compute the magnitude and
angular position of the correction to be applied to
If desired, therefore, balance the rotor at low speed
cancel the effects of unbalance at the first flexural
when it is not affected by modal unbalances. Alterna-
balancing speed. Add this correction.
tively, this stage can be omitted by proceeding di-
rectly to 2.4.1.5.
NOTE 4 A graphical illustration of the vectorial sub-
traction underlying this calculation is shown in annex G.
NOTE 2 Low-speed balancing may avoid the need for
carrying out the procedure given in 2.4.1.5.10 .
The rotor should now run at any speed up to and
through the first flexural critical speed without any
significant amplification of vibration (or force). If this
2.4.1.5 High-speed (flexible-rotor) balancing is not the case, refine the correction or repeat the
procedure given in 2.4.1.5.1 to 2.4.1.5.4 using a new
All vibration (or force) measurements in this subclause balancing speed, possibly closer to the first flexural
relate to the once-per-revolution vectors. critical speed.
The procedure for high-speed (flexible-rotor) balancing
2.4.1.5.5 Run the rotor to some safe speed ap-
is given in 2.4.1.5.1 to 2.4.1.5.10.
proaching the second flexural critical speed. This will
be the second flexural balancing speed. Record
readings of vibration (or force) under steady-state
2.4.1.5.1 Run the rotor to some safe speed ap-
conditions at this speed.
proaching the first flexural critical speed. This will be
termed the first flexural balancing speed.
2.4.1.5.6 Add a set of trial masses to the rotor.
NOTE 3 For some rotor types (e.g. turbine rotors with
These should be located along the rotor, so that a
shrunk on stages, or generator rotors) it is advisable to
significant vector change in vibration (or force) is
make only preliminary corrections near the flexural critical
produced at the second flexural balancing speed,
speeds to get the rotor to its service speed, or overspeed,
without significantly affecting the first mode and, if
where components may move into their final position.
relevant, the low-speed balance.
Record the readings of vibration (or force) under
steady-state conditions. Before proceeding, it is es- 2.4.1.5.7 Run the rotor to the same speed as in
sential to confirm that the readings are repeatable. 2.4.1.5.5 and record the new readings of vibration (or
Several runs may be necessary for this purpose. force).
0 IS0 IS0 11342:1994(E)
2.4.1.5.8 From the vectorial changes in the readings
2.4.2 Balancing procedures for class 4 rotors
between 2.4.1.5.5 and 2.4.1.5.7, compute the influ-
ence coefficients at the second flexural balancing Rotors in this class may have a basic shaft and body
speed for this set of trial masses
...