ISO 11342:1998

INTERNATIONAL ISO
STANDARD 11342
Second edition
1998-04-15
Mechanical vibration — Methods and
criteria for the mechanical balancing of
flexible rotors
Vibrations mécaniques — Méthodes et critères pour l'équilibrage
mécanique des rotors flexibles
A
Reference number
Contents Page
1 Scope 1
2 Normative references 1
3 Definitions 2
4 Fundamentals of flexible rotor dynamics and balancing 2
5 Rotor configurations 6
6 Procedures for balancing flexible rotors at low speed 9
7 Procedures for balancing flexible rotors at high speed 12
8 Evaluation criteria 17
9 Evaluation procedures 22
Annexes
A (informative) Cautionary notes concerning rotors on site 26
B (informative) Optimum planes balancing — Low-speed three-plane balancing 27
C (informative) Conversion factors 29
D (informative) Calculation of equivalent mode residual unbalance 30
E (informative) Procedure to determine if a rotor is rigid or flexible 33
F (informative) Example — Permissible equivalent modal unbalance calculations 35
G (informative) A method of computation of unbalance correction 36
H (informative) Definitions from ISO 1925:1990 and ISO 1925:1990/Amd 1:1995 relating
to flexible rotors 37
I (informative) Bibliography 39
Tables
1 Flexible rotors 7
2 Balancing procedures 9
C.1 Suggested conversion factor ranges 29
Figures
1 Simplified mode shapes for flexible rotors on flexible supports 3
2 Examples of possible damped mode shapes 4
B.1 Graphical presentation for determination of H 28
D.1 Turbine rotor 30
D.2 Run-up curve — Before balancing 31
G.1 Vectorial effect of a trial mass set 36
©  ISO 1998
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ISO ISO 11342:1998(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee has
been established has the right to be represented on that committee. International organizations, governmental
and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
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 ISO 11342 was prepared by technical committee ISO/TC 108, Mechanical vibration
and shock, Subcommittee SC 1, Balancing, including balancing machines.
This second edition cancels and replaces the first edition (ISO 11342:1994), of which it constitutes a
technical revision.
Annexes A to I of this International Standard are for information only.
iii
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Introduction
The aim of balancing any rotor is to achieve satisfactory running when installed on site. 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 flexible rotor, 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
may 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 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.
This International Standard classifies rotors in accordance with their balancing requirements and establishes
methods of assessment of residual unbalance.
This International Standard also shows 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
ISO 10816 and ISO 7919 if desired in terms of vibration, or from ISO 1940-1 if desired in terms of
permissible residual balance. ISO 1940 is concerned with the unbalance quality of rotating rigid bodies and
is not directly applicable to flexible rotors because flexible rotors may undergo significant bending
deflection. However, in subclause 8.3 of this International Standard, methods are presented for adapting the
criteria of ISO 1940-1 to flexible rotors.
As this International Standard is complementary in many details to ISO 1940, it is recommended that, where
applicable, the two should be considered together.
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 resonant or near resonant condition in a lightly
damped structure can result in excessive vibratory response to a small unbalance. In such cases it may be
more practicable to alter the natural frequency or damping of the structure rather than to balance to very low
levels, which may not be maintainable over time. (See also ISO 10814.)
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INTERNATIONAL STANDARD  ISO ISO 11342:1998(E)
Mechanical vibration — Methods and criteria for the mechanical
balancing of flexible rotors
1 Scope
This International Standard presents typical flexible rotor configurations in accordance with their
characteristics and balancing requirements, describes balancing procedures, specifies methods of assessment
of the final state of unbalance, and gives guidance on balance quality criteria.
This International Standard may also be applicable to serve as a basis for more involved investigations, for
example when a more exact determination of the required balance quality is necessary. If due regard is paid
to the specified methods of manufacture and limits of unbalance, satisfactory running conditions can be
expected.
This International Standard is not intended to serve as an acceptance specification for any rotor, but rather to
give indications of how to avoid gross deficiencies and/or unnecessarily restrictive requirements.
The subject of structural resonances and modifications thereof is outside the scope of this International
Standard.
The methods and criteria given are the result of experience with general industrial machinery. They may not
be directly applicable to specialized equipment or to special circumstances. Therefore, there may be cases
1)
where deviations from this International Standard may be necessary .
2 Normative references
The following standards contain provisions, which, through reference in this text, constitute provisions of
this International Standard. At the time of publication, the editions indicated were valid. All standards are
subject to revision, and parties to agreements based on this International Standard are encouraged to
investigate the possibility of applying the most recent editions of the standards listed below. Members of IEC
and ISO maintain registers of currently valid International Standards.
ISO 1925:1990, Mechanical vibration — Balancing — Vocabulary
ISO 1940-1:1986, Mechanical vibration — Balance quality requirements of rigid rotors — Part 1:
Determination of permissible residual unbalance

1)
Information on such exceptions will be welcomed and should be communicated to the national standards body in
the country of origin for transmission to the secretariat of ISO/TC 108/SC1.
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ISO 1940-2:1997, Mechanical vibration — Balancing quality requirements of rigid rotors — Part 2:
Balance errors
ISO 2041:1990, Vibration and shock — Vocabulary
ISO 8821:1989, Mechanical vibration — Balancing — Shaft and fitment key convention
3 Definitions
For the purposes of this International Standard, the definitions relating to mechanical balancing given in
ISO 1925 and the definitions relating to vibration given in ISO 2041 apply.
NOTE —  Definitions from ISO 1925 relating to flexible rotors are given for information in annex H.
4 Fundamentals of flexible rotor dynamics and balancing
4.1 General
Flexible rotors normally require multiplane blancing at high speed. Nevertheless, under certain conditions a
flexible rotor 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 will be given here. In most practical
balancing applications, the method adopted will normally be 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 flexible rotor
than in a rigid rotor 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 may induce vibrations at speeds other than that at which the rotor was originally corrected. These
vibrations may exceed specified tolerances, particularly at, or near, the flexural critical speeds. Even at the
same speed such correction can induce vibrations if the flexural mode shapes on site differ from those
dominating during the balancing process.
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 may be
impossible to balance the rotor within tolerance.
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ISO ISO 11342:1998(E)
4.3 Flexible rotor mode shapes
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 curves 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/bearing system the flexural modes may 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 must be stressed 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.
NOTE —  P , P , and P are nodes. P is an antinode.
1 2 4 3
Figure 1 — Simplified mode shapes for flexible rotors on flexible supports
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Figure 2 — Examples of possible damped mode shapes
4.4 Response of a flexible rotor 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 critical speed, it is
usually the mode associated with this critical speed which dominates the deflection of the rotor. The degree
to which large amplitudes of rotor deflection occur in these circumstances is influenced mainly by:
a) the magnitude of the modal unbalances;
b) the proximity of the associated critical speeds to the running speeds; and
c) the amount of damping in the rotor/support system.
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ISO ISO 11342:1998(E)
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 International Standard.
The modal unbalances for a given unbalance distribution are a function of the flexible 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 1 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, whilst 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 modes.
1 4
4.5 Aims of flexible rotor balancing
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 satisfy 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 flexible rotors 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 couple 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 necessary reduction in unbalance is usually achieved by adding or removing masses in a
limited number of correction planes. There will invariably be some distributed residual unbalance after
balancing.
Vibrations or oscillatory forces caused by the residual unbalance must be reduced to acceptable magnitudes
over the service speed range. Only in special cases is it sufficient to balance flexible rotors for a single speed.
It should be noted that a rotor, balanced satisfactorily for a given service speed range, may still experience
excessive vibration if it has to run through a critical speed to reach its service speed. However, for passing
through critical 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 may be necessary to allow for the influence of
modes with critical speeds above the service speed range.
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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 assembly-
balanced in the end planes only, after each disc and the shaft have been separately balanced in a low-speed
th
balancing machine. Generally, however, if the speed of the rotor approaches or exceeds its n flexural
critical speed, then at least n and usually (n + 2) correction planes are needed along the rotor.
An adequate number of correction planes at suitable axial positions should be included at the design stage. In
practice the number of correction planes is often limited by design considerations and in-field balancing by
limitations on accessibility.
4.7 Rotors coupled together
When two rotors are coupled together, the complete unit will have a series of critical speeds and mode
shapes. In general, these speeds are neither equal to nor simply related to the critical 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 will normally ensure satisfactory operation of the coupled rotors. The degree to which this
technique is practicable depends, for example, on the mode shapes and the critical speeds of the uncoupled
and coupled rotors, and the distribution of unbalance and the type of coupling and on the bearing
arrangement of the shaft train.
If further balancing on site is required, reference should be made to annex A.
5 Rotor configurations
Typical rotor configurations are shown in table 1, their characteristics outlined, and the recommended
balancing procedures listed. The table gives concise descriptions of the rotor characteristics. Full
descriptions of these characteristics/requirements are given in the corresponding procedures in clauses 6
and 7. The procedures are listed in table 2.
Sometimes a combination of balancing procedures may be advisable. If more than one balancing procedure
could be used, they are listed in the sequence of increasing time/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).
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ISO ISO 11342:1998(E)
Table 1 — Flexible rotors
Recommended
Configuration Rotor characteristics
balancing
procedure
Elastic shaft without
1.1  Discs (see table 2)
unbalance, rigid disc(s)
(see next page
for key to
A-G)
Single disc
- perpendicular to shaft axis A; C
- with axial runout B; C
Two discs
- perpendicular to shaft axis B; C
- with axial runout
• at least one removable B + C, E
• integral G
More than two discs
- all (but one) removable B + C, D, E
- integral G
1.2  Rigid sections Elastic shafts without
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
section
- all (but one) removable B + C; E
- integral G
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Table 1 — Flexible rotors (concluded)
Recommended
Configuration Rotor characteristics
balancing
procedure
1.3  Discs and rigid sections Elastic shaft without
1)
(see table 2)
unbalance, rigid discs
and sections
One each
- at least one part B + C; E
removable
- integral G
More parts
- all (but one) removable B + C; E
- integral G
1.4  Rolls Mass, elasticity and
unbalance distribution
along the rotor
F
- under special conditions
G
- in general
1.5  Rolls and discs/rigid sections Flexible roll, rigid discs,
rigid sections
- discs/rigid
sections/removable
- under special
conditions C + F; E + F
-in general G
- integral G
1.6  Integral rotor Mass, elasticity and
unbalance distribution
along the rotor
Main parts with
unbalances not detachable G
1) A = Single-plane balancing E = Balancing in stages during assembly
B = Two-plane balancing F = Balancing in optimum planes
C = Individual component balancing prior to assembly G = Multiple speed balancing
Two additional balancing procedures H and I can be used in special circumstances, see 7.4 and 7.5.
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ISO ISO 11342:1998(E)
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 flexible rotors at low speed
6.1 General
Low-speed balancing is generally used for rigid rotors and high-speed balancing is generally used for
flexible rotors. However, with the use of appropriate procedures it is possible in some circumstances to
balance flexible rotors at low speed so as to ensure satisfactory running when the rotor is installed in its final
environment. Otherwise, flexible rotors require use of a high-speed balancing procedure.
Most of the procedures explained in this clause require some information regarding the axial distribution of
unbalance.
In some cases where a gross unbalance may occur in a single component, it may 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.
NOTE —  Certain rotors contain a number of individual parts which are mounted concentrically (for example blades,
coupling bolts, pole pieces, etc.). These parts may 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 may produce changes in the shaft geometry (e.g. shaft run out) and
further changes may occur during high-speed service.
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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 may 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 critical speed, then low-speed balancing methods
should only be used with caution.
6.4 Initial unbalance
The process of balancing a flexible rotor 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 actual 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
prebalancing 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 will be 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 will be 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 will be balanced for all speeds.
6.5.3 Procedure C — Individual component balancing prior to assembly
Each component, including the shaft, should be low-speed balanced before assembly in accordance with
ISO 1940-1. In addition, the concentricities of the shaft diameters or other locating features that position the
individual components on the shaft should be held to close tolerances relative to the shaft axis. (See
ISO 1940-2).
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ISO ISO 11342:1998(E)
NOTES
1  The concentricities of the balancing mandrel diameters or other location features that position each individual
component on the mandrel should likewise be held within close tolerance relative to the axis of the mandrel. Errors in
unbalance and concentricity of the mandrel may be compensated by index balancing (see ISO 1940-2).
2  When balancing the components and the shaft individually, due allowances should be made for any unsymmetrical
feature such as keys (see ISO 8821) that form part of the complete rotor but are not used in the individual balancing of
the separate components.
3  It is advisable to check by calculation the unbalance produced by balancing errors such as 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 1940-2.
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
(Procedure C), the state of unbalance may 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 will be useful.
Experience has shown that symmetrical rotors that conform to the requirements above but have an additional
central correction plane may 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, for example as regards
symmetry or overhangs, it may 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 may be so large that some other method of balancing
the rotor will have to be adopted, for example, Procedure E.
6.5.5 Procedure E — Balancing in stages during assembly
The shaft should first be balanced. The rotor should 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 may 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, for example a sub-assembly or core section which is normally
balanced in two planes only, one such section may 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 (for example, tubes), it may be possible by selecting suitable axial
positions of two correction planes to achieve satisfactory running over the entire speed range by low-speed
balancing. It is likely that the optimum position of the two correction planes producing the best overall
running conditions can only be determined by experimentation on a number of rotors of similar type.
For a simple rotor system that satisfies conditions a) to e) below, the optimum position for the two correction
planes is 22 % of the bearing span inboard of each bearing:
a) single-span rotor with end bearings;
b) uniform mass distribution with no significant overhangs;
c) uniform bending flexibility of the shaft along its length;
d) continuous service speeds not significantly approaching second critical speed;
e) uniform or linear distribution of unbalance.
If this correction method does not produce satisfactory results, it may still be possible to balance the rotor at
low speed by utilizing correction planes in the middle and at the rotor ends, as shown in annex B. To do this
it is necessary to assess what proportion of the total initial unbalance is to be corrected at the centre plane.
7 Procedures for balancing flexible rotors at high speed
7.1 General
Generally, high-speed balancing is required for flexible rotors. However, with the use of appropriate
procedures it is possible, in some circumstances, to balance flexible rotors at low speed (see clause 6).
7.2 Installation for balancing
For balancing purposes, the rotor should be mounted on suitable bearings. In some cases it is desirable that
the bearing supports in the balancing facility be chosen to provide similar conditions to those at site so that
the modes obtained during site operation will be adequately represented during the balancing process and
hence reduce the necessity for subsequent field balancing.
If a rotor has an overhung mass that would normally be supported when installed on site, a steady bearing
may be used to limit its deflection during the test.
If a rotor has an overhung mass that is not supported in any way when installed on site, it should also be left
unsupported during the test. However, it may be necessary in the early stage of balancing to provide support
with a steady bearing to enable a rotor to get safely to service speed or overspeed to allow the rotor
components to move into their final position.
Transducers should be positioned to measure shaft, bearing or support vibration or bearing force as
appropriate. The system shall be capable of measuring the once-per-revolution component of the signal. The
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ISO ISO 11342:1998(E)
measurement can be expressed either as an amplitude and a phase angle or in terms of orthogonal
components relative to some fixed angular reference on a rotor.
In some cases two vibration transducers may be installed 90° apart at the same transverse plane to permit
resolution of the transverse vibrations, when such resolution is required.
In all cases, there shall be no resonances of the transducer and/or mountings, which significantly influence
vibration measurement within the speed range of the test.
The output from all transducers should be read on equipment that can differentiate between the synchronous
component caused by unbalance, the slow-speed runout when significant, and other components of the
vibration.
The drive for a rotor should be such as to impose negligible restraint on the vibration of the rotor and
introduce negligible unbalance into the system. Alternatively, if known unbalance is introduced by the drive
system, then it should be compensated for in the vibration evaluation.
NOTE —  To establish that the drive coupling introduces negligible balance error, the coupling should be index
balanced as described in ISO 1940-2.
7.3 Procedure G — Multiple-speed balancing
This clause sets out the basic principles of high-speed balancing in a very simple form. The rotor is balanced
successively on a modal basis at a series of balancing speeds in turn, which are selected so that there is a
balancing speed close to each critical speed within the service speed range. There may also be a balancing
speed close to the maximum permissible test speed. In essence, each mode with a critical speed within the
service speed range is corrected in turn, followed by a final balance of the remaining (higher) modes at the
highest balancing speed.
The procedures used in practice may be packaged in the form of computer-aided balancing methods, which
permit automated or otherwise simplified techniques, for example, the influence coefficient method. In the
simplest versions, on-line computer-aided balancing will guide the operator through the process and will, for
example, perform the vector subtraction listed in 7.3.2.5, 7.3.2.9 and 7.3.2.10. In other cases, prior
knowledge of the relevant influence coefficients may be available which can be incorporated in the
computer-aided package so that tests with trial mass sets are not required. In appropriate circumstances,
vibration data for the unbalanced response can be safely acquired at several balancing speeds during one run
of the rotor, rather than at a single balancing speed, so that the necessary corrections for several modes can
be computed in one operation.
All vibration (or force) measurements in this clause relate to once-per-revolution components.
7.3.1 Initial low-speed balancing
Experience has shown that it may be advantageous to carry out initial balancing at low speed, prior to
balancing at higher speeds. This may be particularly advantageous for rotors significantly affected by only
the first flexural critical speed.
If desired, therefore, balance the rotor at low speed, when it is not affected by modal unbalances.
Alternatively, this stage can be omitted by proceeding directly to 7.3.2.
NOTE —  Low-speed balancing may avoid the need for carrying out the final balancing of the remaining (higher)
modes as described in 7.3.2.11.
©
7.3.2 General procedure
Throughout this procedure, correction planes should be chosen according to the relevant mode shapes. See
also clause 4.
7.3.2.1 The rotor should be run at some convenient low speed or speeds to remove any temporary bend. If
shaft measuring transducers are used, the remaining repeatable low-speed run-out values should be measured
and, where necessary, subtracted vectorially from any subsequent shaft measurements at the balancing
speeds.
7.3.2.2 Run the rotor to some safe speed approaching the first flexural critical speed. This will be termed the
"first flexural balancing speed".
Record the readings of vibration (or force) under steady-state conditions. Before proceeding, it is essential to
confirm that the readings are repeatable. Several runs may be necessary for this purpose.
7.3.2.3 Add a set of trial masses to the rotor, which should be selected and positioned along the rotor to
produce a significant vector change in vibration (or force) at the first flexural balancing speed.
If low-speed balancing has been omitted, the trial mass set usually comprises only one mass, which for rotors
which are essentially symmetrical about mid-span will be placed near the middle of the rotor span.
If low-speed balancing has been performed, then the trial mass set will usually consist of masses at three
distinct correction planes. In this case, the masses are proportioned so that the low-speed (rigid rotor)
balancing is not upset.
7.3.2.4 Run the rotor to the same speed and under the same conditions as in 7.3.2.2, and record the new
readings of vibration (or force).
7.3.2.5 From the vectorial changes of the readings between 7.3.2.2 and 7.3.2.4, compute the effect of the trial
mass set at the first flexural balancing speed. Hence compute the magnitude and angular position of the
correction to be applied to cancel the effects of unbalance at the first flexural balancing speed. Add this
correction.
NOTES
1  A graphical illustration of the vectorial subtraction underlying this calculation is shown in annex G.
2  In this description it is assumed that the effects on the measurements of unbalances in other modes can be
neglected or are eliminated by appropriate procedures.
The rotor should now run through the first flexural critical speed with acceptable vibration (or force). If this
is not the case, refine the correction or repeat the procedure in 7.3.2.2 to 7.3.2.5 using a new balancing speed,
possibly closer to the first flexural critical speed.
7.3.2.6 Run the rotor to some safe speed approaching the second flexural critical speed. This will be the
"second flexural balancing speed". Record readings of vibration (or force) under steady-state conditions at
this speed.
7.3.2.7 Add a set of trial masses to the rotor, which should be selected and positioned along the rotor to
produce a significant vector change in vibration (or force) at the second flexural balancing speed, without
significantly affecting the first mode and, if relevant, the low-speed balance.
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ISO ISO 11342:1998(E)
7.3.2.8 Run the rotor to the same speed as in 7.3.2.6 and record the new readings of vibration (or force).
7.3.2.9 From the vectorial changes in the readings between 7.3.2.6 and 7.3.2.8, compute the effect of the trial
mass set at the second flexural balancing speed for this set of trial masses. Use these values to compute a set
of correction masses which cancel the effects of unbalance at the second flexural balancing speed. Attach
this set of correction masses.
The rotor should now run through the first and second flexural critical speeds with acceptable vibration (or
force). If this is not the case, refine the correction or repeat the procedure in 7.3.2.6 to 7.3.2.9, using a
different balancing speed possibly closer to the second flexural critical speed. (See also notes in 7.3.2.5.)
7.3.2.10 Continue the above operations for balancing speeds close to each flexural critical speed in turn
within the permissible speed range. Each new set of trial masses should be chosen so that they have a
significant effect on the appropriate mode, but do not significantly affect the balance which has already been
achieved at lower speeds. The trial mass distribution can be obtained from experience or a computer
simulation. For each case, a set of correction masses should be computed and attached to the rotor. Each set
of correction masses will compensate for the unbalance at the current balancing speed.
7.3.2.11 If, after correction at all flexural balancing speeds, significant vibrations (or forces) still occur
within the service speed range, the procedure in 7.3.2.9 should be repeated at a balancing speed close to the
maximum permissible test speed. In this case, it may not be possible to magnify the effect of the remaining
(higher) modal unbalance components by running close to their associated flexural critical speeds.
NOTES
1  For some rotor types, for example turbine rotors with shrunk on stages or generator rotors, it is advisable to make
only preliminary corrections near the flexural critical speeds to get the rotor to its service speed or overspeed, where
components may move into their final position. For some rotors, it may be possible to run safely through some or all
of the critical speeds before completing the balancing. In that case, the number of runs required to determine the
influence coefficients can be reduced.
2  It should be noted that the method described above assumes that there is a linear relationship between the
unbalance vector and the vibration (or force) response vector. In certain cases this may not be so, particularly, for
example, where there is a high initial unbalance and the rotor is supported by fluid-film bearings. In these cases it may
be necessary to redetermine the effects of the trial mass sets as the vibration (or force) response vector is reduced in
magnitude.
3  As explained at the outset of 7.3, the high-speed balancing procedure is presented in a very simple form. In
particular, the flexural critical speeds are assumed to be sufficiently widely spaced so that the vibration measured at a
flexural balancing speed is predominantly in the mode associated with the corresponding critical speed. If two flexural
critical speeds are close together, then more refined procedures (which are beyond the scope of this simple outline)
are necessary to uncouple the individual modal components of vibration.
4  For machines that have axial asymmetry (in the support/bearing system), each mode (see figure 1) will split into
two modes, often of similar shape, with resonances appearing at different speeds. Reducing the unbalance in one of
these modes often reduces the unbalance in the other one too, avoiding the need to balance each mode separately.
7.4 Procedure H — Service-speed balancing
Some rotors that are flexible and pass through one or more critical speeds on their way up to service speed
may, under special circumstances, be balanced for one speed only (usually service speed). However, rotors
having critical speeds close to service speed or those coupled to other flexible rotors are excluded. In
general, these rotors should fulfil one or more of the following conditions:
a) the acceleration and deceleration up to and from service speed is so rapid that the amplitude of
vibration at the critical speeds will not build up beyond acceptable limits;
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b) the damping of the system is sufficiently high to keep vibrations at the critical speeds within
acceptable limits;
c) the rotor is supported in such a manner that objectionable vibrations are avoided;
d) a high level of vibration at the critical speeds is acceptable;
e) a rotor runs at service speed for such long periods that otherwise unacceptable starting/stopping
conditions can be tolerated.
A rotor that fulfils any of the above conditions may be balanced in a high-speed balancing machine or
equivalent facility at the speed at which it is determined that the rotor should be in balance.
If the rotor falls into category c) above, it is especially important that the stiffness of the balancing machine
support system be sufficiently close to site conditions to ensure that, at service speed in the balancing
facility, the predominant modes are the same as those that will be experienced at site.
Some consideration should be given to the axial correction mass distribution. It may be possible to choose
optimum axial positions for the correction planes so that two planes may be sufficient. This may produce a
minimum residual unbalance in the lower modes and thus minimize the vibrations when running through
critical speeds.
7.5 Procedure I — Fixed speed balancing
7.5.1 General
These rotors may have a basic shaft and body construction that either allows for low-
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