ISO 21940-11:2016

INTERNATIONAL ISO
STANDARD 21940-11
First edition
2016-11-15
Mechanical vibration — Rotor
balancing —
Part 11:
Procedures and tolerances for rotors
with rigid behaviour
Vibrations mécaniques — Équilibrage des rotors —
Partie 11: Modes opératoires et tolérances pour rotors à
comportement rigide
Reference number
ISO 21940-11:2016(E)
©
ISO 2016

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ISO 21940-11:2016(E)

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ISO 21940-11:2016(E)

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Pertinent aspects of balancing . 1
4.1 General . 1
4.2 Representation of the unbalance . 1
4.3 Unbalance effects . 2
4.4 Reference planes for unbalance tolerances . 2
4.5 Correction planes . 4
4.5.1 General. 4
4.5.2 Rotors which need one correction plane only . 4
4.5.3 Rotors which need two correction planes . 4
4.5.4 Rotors with more than two correction planes . 4
4.6 Permissible residual unbalance . 4
5 Similarity considerations . 5
5.1 General . 5
5.2 Permissible residual unbalance and rotor mass . 5
5.3 Permissible residual specific unbalance and service speed . 6
6 Specification of unbalance tolerances . 6
6.1 General . 6
6.2 Derivation of the unbalance tolerances . 6
6.3 Balance quality grade G . 7
6.3.1 Classification . 7
6.3.2 Special designs . 7
6.3.3 Permissible residual unbalance .10
6.4 Experimental evaluation .10
6.5 Unbalance tolerances based on bearing forces or vibrations .10
6.5.1 Bearing forces .10
6.5.2 Vibrations .11
6.6 Methods based on established experience .11
7 Allocation of permissible residual unbalance to tolerance planes .11
7.1 Single plane .11
7.2 Two planes .11
7.2.1 General.11
7.2.2 Limitations for inboard rotors .12
7.2.3 Limitations for outboard rotors .12
8 Allocation of unbalance tolerances to correction planes .13
8.1 General .13
8.2 Single plane .14
8.3 Two planes .14
9 Assembled rotors .14
9.1 General .14
9.2 Balanced as a unit .14
9.3 Balanced on component level .14
10 Accounting for errors in the verification of permissible residual unbalances .15
10.1 General .15
10.2 Unbalance tolerance .15
10.3 Combined error of unbalance measurements .15
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ISO 21940-11:2016(E)

10.4 Verification of the permissible residual unbalance .15
10.4.1 General.15
10.4.2 Unbalance readings within tolerance .16
10.4.3 Unbalance readings out of tolerance .16
10.4.4 Region of uncertainly .16
Annex A (informative) Example of the specification of permissible residual unbalance
based on balance quality grade G and allocation to the tolerance planes.17
Annex B (informative) Specification of unbalance tolerances based on bearing force limits .21
Annex C (informative) Specification of unbalance tolerances based on established experience .23
Annex D (informative) Rules for allocating unbalance tolerances from tolerance planes to
correction planes .25
Bibliography .28
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ISO 21940-11:2016(E)

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment,
as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the
Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword.html.
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 cancels and replaces ISO 1940-1:2003, which has been technically revised. The
main changes are deletion of the terms and definitions which were transferred to ISO 21940-2 and a
more pronounced explanation of the application of permissible residual unbalances for the processes
of balancing a rotor and verifying its residual unbalance. Information on specification of unbalance
tolerances based on vibration limits has been removed.
It also incorporates the Technical Corrigendum ISO 1940-1:2003/Cor 1:2005.
A list of parts in the ISO 21940 series can be found on the ISO website.
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ISO 21940-11:2016(E)

Introduction
Rotor balancing is a procedure by which the mass distribution of a rotor (or part or module) is checked
and, if necessary, adjusted to ensure the unbalance tolerance is met. This document covers the
balancing of rotors with rigid behaviour. A rotor is said to be rigid when the flexure of the rotor caused
by its unbalance distribution can be neglected with respect to the agreed unbalance tolerance at any
speed up to the maximum service speed. For these rotors, the resultant unbalance, and often moment
unbalance, are of interest, which when combined are expressed as a dynamic unbalance of the rotor.
The balancing machines available today enable residual unbalances to be reduced to very low limits.
Therefore, it is necessary to specify an unbalance quality requirement for a balancing task, as in most
cases it would not be cost-effective to reduce the unbalance to the limits of the balancing machine.
In addition to specifying an unbalance tolerance, it is necessary to consider the errors introduced by the
balancing process. This document takes into account the influence of these errors to distinguish clearly
between the specified permissible residual unbalance and the reduced residual unbalance values to be
achieved during the balancing process.
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INTERNATIONAL STANDARD ISO 21940-11:2016(E)
Mechanical vibration — Rotor balancing —
Part 11:
Procedures and tolerances for rotors with rigid behaviour
1 Scope
This document establishes procedures and unbalance tolerances for balancing rotors with rigid
behaviour. It specifies
a) the magnitude of the permissible residual unbalance,
b) the necessary number of correction planes,
c) the allocation of the permissible residual unbalance to the tolerance planes, and
d) how to account for errors in the balancing process.
NOTE In ISO 21940-14, the assessment of balancing errors is considered in detail. Fundamentals of rotor
balancing are contained in ISO 19499 which gives an introduction to balancing.
This document does not cover the balancing of rotors with flexible behaviour. Procedures and tolerances
for rotors with flexible behaviour are dealt with in ISO 21940-12.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 21940-2 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
4 Pertinent aspects of balancing
4.1 General
Rotor balancing is a procedure by which the mass distribution of a rotor is examined and, if necessary,
adjusted to ensure that the residual unbalance or vibration in service is within specified limits. It should
be noted that the vibration in service can originate from sources other than unbalance.
Rotor unbalance can be caused by design, material, manufacturing and assembly. Every rotor has an
individual unbalance distribution along its length, even in series production.
4.2 Representation of the unbalance
For a rotor with rigid behaviour, different vectorial quantities can be used to represent the same
unbalance as shown in Figure 1.
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ISO 21940-11:2016(E)

Figure 1 a) to c) shows different representations in terms of resultant unbalance and resultant couple
unbalance, whereas Figure 1 d) to f) shows different representations in terms of a dynamic unbalance
in two planes.
NOTE 1 The resultant unbalance vector can be located in any radial plane (without changing magnitude and
angle), but the associated resultant couple unbalance is dependent on the location of the resultant unbalance vector.
NOTE 2 The centre of unbalance is that location on the shaft axis for the resultant unbalance, where the
resultant couple unbalance is a minimum.
If single-plane balancing is sufficient (see 4.5.2) or when considerations are made in terms of resultant
unbalance and resultant couple unbalance (see 4.5.4), the representation in Figure 1 a) to c) is preferable.
In the case of typical two-plane considerations, the representation in Figure 1 d) to f) is advantageous.
4.3 Unbalance effects
Resultant unbalance and resultant moment unbalance (the latter can also be expressed as resultant
couple unbalance) have different effects on forces on the bearings and on the vibration of the machine.
In practice, therefore, both unbalances are often considered separately. Even if the unbalance is stated
as a dynamic unbalance in two planes, it should be noted that in most cases there is a difference in
effects if the unbalances predominantly form either a resultant unbalance or a resultant moment
unbalance.
4.4 Reference planes for unbalance tolerances
It is recommended to use reference planes to state the unbalance tolerances. For these planes, only the
magnitude of each residual unbalance needs to stay within the respective balance tolerance whatever
the angular position may be.
The aim of balancing is usually to reduce vibrations and forces transmitted through the bearings to
the environment. For the purposes of this document, the reference planes for unbalance tolerances are
taken to be the bearing planes. However, this use of bearing planes does not always apply.
NOTE For a component without a shaft (e.g. a disc shaped element), but where the final bearing positions are
known (or can be estimated), these planes can be used.
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ISO 21940-11:2016(E)

Unbalances in gram millimetres
a) Resultant unbalance b) Special case of a), namely c) Special case of a), namely
vector together with an resultant unbalance vector resultant unbalance vector
associated couple unbalance located at centre of mass CM located at the centre of
in the end planes (static unbalance), together unbalance CU
with an associated couple
unbalance in the end planes
d) Unbalance vector in each of e) Two 90° unbalance f) Unbalance vector in each of
the end planes components in each of the any two other planes
end planes
Key
CM centre of mass
CU centre of unbalance
l rotor length
NOTE For Figure 1 c), the associated couple unbalance is a minimum and lays in a plane orthogonal to the
resultant unbalance vector.
Figure 1 — Different representations of the same unbalance of a rotor with rigid behaviour
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ISO 21940-11:2016(E)

4.5 Correction planes
4.5.1 General
Rotors that are out of unbalance tolerance need correction. These unbalance corrections often cannot
be performed in the planes where the unbalance tolerances were set, but need to be performed where
material can be added, removed or relocated.
The number of necessary correction planes depends on the magnitude and distribution of the initial
unbalance, as well as on the design of the rotor, e.g. the shape of the correction planes and their location
relative to the tolerance planes.
4.5.2 Rotors which need one correction plane only
For some rotors, only the resultant unbalance is out of tolerance but the resultant moment unbalance is
in tolerance. This typically happens with rotors having a single disc, provided that
a) the bearing distance is sufficiently large,
b) the disc rotates with sufficiently small axial runout, and
c) the correction plane for the resultant unbalance is properly chosen.
After single-plane balancing has been carried out on a sufficient number of rotors, the largest residual
moment unbalance is determined and divided by the bearing distance, yielding a couple unbalance.
If, even in the worst case, the couple unbalance found this way is acceptable, it can be expected that
single-plane balancing is sufficient.
For single-plane balancing, the rotor does not need to rotate but, for sensitivity and accuracy reasons,
in most cases, rotational balancing machines are used.
4.5.3 Rotors which need two correction planes
If a rotor with rigid behaviour does not comply with the conditions specified in 4.5.2, the moment
unbalance needs to be reduced as well. In most cases, resultant unbalance and resultant moment
unbalance are assembled into a dynamic unbalance: two unbalance vectors in two planes; see
Figure 1 d).
For two-plane balancing, it is necessary for the rotor to rotate, since otherwise the moment unbalance
would remain undetected.
4.5.4 Rotors with more than two correction planes
Although all rotors with rigid behaviour theoretically can be balanced in two planes, sometimes more
than two correction planes are used, e.g.
a) in the case of separate corrections of resultant unbalance and couple unbalance, if the correction of
the resultant unbalance is not performed in one (or both) of the couple planes, and
b) if the correction is spread along the rotor.
In special cases, spreading the correction along the rotor can be necessary due to restrictions in the
correction planes (e.g. correction of crankshafts by drilling into the counterweights) or advisable in
order to keep the function and component strength.
4.6 Permissible residual unbalance
In the simple case of an inboard rotor for which the couple unbalance may be ignored (see 4.5.2), its
unbalance state can then be described as a single vectorial quantity, the unbalance, U.
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ISO 21940-11:2016(E)

To obtain a satisfactory running of the rotor, the magnitude of this unbalance, i.e. the residual unbalance,
U , shall not be higher than a permissible value, U :
res per
U ≤ U (1)
res per
More generally, the same applies to any type of a rotor with rigid behaviour, but then U covers the
per
resultant unbalance and the resultant moment unbalance, see also 5.2.
NOTE The SI unit for U is kg·m (kilogram metres), but for balancing purposes, more practical units are
per
g·mm (gram millimetres), kg·mm (kilogram millimetres) or mg·mm (milligram millimetres).
U is defined as the total tolerance in the plane of the centre of mass. In the case of two-plane
per
balancing, this tolerance shall be allocated to the tolerance planes (see Clause 7).
5 Similarity considerations
5.1 General
Some considerations on similarity can help in the understanding and calculation of the influences of
rotor mass and service speed on the permissible residual unbalance.
5.2 Permissible residual unbalance and rotor mass
In general, for rotors of the same type, the permissible residual unbalance, U , is proportional to the
per
rotor mass, m, as given in Formula (2):
U ~ m (2)
per
The ratio of U to the rotor mass, m, is the permissible residual specific unbalance, e , as given in
per per
Formula (3):
e = U /m (3)
per per
NOTE 1 The SI unit for U /m is kg·m/kg (kilogram metres per kilogram) or m (metres), but a more practical
per
unit is g·mm/kg (gram millimetres per kilogram), which corresponds to μm (micrometres) because many
permissible residual specific unbalances are between 0,1 µm and 10 µm.
NOTE 2 The term e is useful especially if geometric tolerances (e.g. runout, play) are related to unbalance
per
tolerances.
NOTE 3 In the case of a rotor with only a resultant unbalance (see 4.5.2), e is the distance of the centre of
per
mass from the shaft axis. However, in the case of a general rotor with both resultant unbalance and resultant
moment unbalance present, e is an artificial quantity containing the effects of the resultant unbalance as well
per
as of the resultant moment unbalance.
NOTE 4 There are limits for achievable residual specific unbalance, e , depending on the setup conditions in
per
the balancing machine (e.g. centring, bearings and drive).
NOTE 5 Small values of e can only be achieved in practice if the accuracy of shaft journals (roundness,
per
straightness, etc.) is adequate. In some cases, it can be necessary to balance the rotor in its own service bearings,
using belt-, air- or self-drive. In other cases, balancing needs to be carried out with the rotor completely assembled
in its own housing with bearings and self-drive, under service condition and temperature.
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ISO 21940-11:2016(E)

5.3 Permissible residual specific unbalance and service speed
For rotors of the same type, experience shows that, in general, the permissible residual specific
unbalance value, e , varies inversely with the service speed, n, of the rotor:
per
e ~ 1/n (4)
per
Differently expressed, this relationship is given in Formula (5):
e Ω = c (5)
per
where
Ω is the angular velocity of the service speed, in rad/s (radians per second), with
Ω = 2π n/(60 s/min) and the service speed, n, in r/min (revolutions per minute);
c is a constant.
This relationship follows also from the fact that for geometrically similar rotors running at equal
peripheral velocities, the stresses in the rotors and the bearing specific loads (due to centrifugal forces)
are the same. The balance quality grade G (see 6.3) is based on this relationship.
6 Specification of unbalance tolerances
6.1 General
The first step in the balancing process is to establish the magnitude of permissible residual unbalance
of the rotor and to allocate it to the tolerance plane(s). In order to meet these unbalance tolerances
reliably, reduced residual unbalance tolerances shall take account of errors as detailed in Clause 10.
NOTE 1 The ideal target value of the unbalance typically is zero (i.e. in a vector diagram, the unbalance
tolerance is the radius of the circular tolerance region around the origin).
NOTE 2 Sometimes the target unbalance has a specified quantity, given by amount and angle (e.g. removed
keys, asymmetric crank shafts, compensating shafts or rotational vibration exciter). In these cases, the unbalance
tolerance is the radius of a circle around the specified target unbalance vector.
6.2 Derivation of the unbalance tolerances
The magnitude of permissible residual unbalance can be determined by five different methods. The
methods are based on
a) balance quality grades, derived from long-term practical experience with a large number of
different rotors (see 6.3),
b) experimental evaluation of permissible residual unbalances (see 6.4),
c) limited bearing forces due to unbalance (see 6.5.1),
d)
...