Mechanical vibration -- Torsional vibration of rotating machinery

ISO 22266-1:2009 provides guidelines for applying shaft torsional vibration criteria, under normal operating conditions, for the coupled shaft system and long blades of a turbine generator set. In particular, these apply to the torsional natural frequencies of the coupled shaft system at line and twice‑line frequencies of the electrical network to which the turbine generator set is connected. In the event that torsional natural frequencies do not conform with defined frequency margins, other possible actions available to vendors are defined. ISO 22266-1:2009 is applicable to land-based steam turbine generator sets for power stations with power outputs greater than 50 MW and normal operating speeds of 1 500 r/min, 1 800 r/min, 3 000 r/min and 3 600 r/min, and to land-based gas turbine generator sets for power stations with power outputs greater than 50 MW and normal operating speeds of 3 000 r/min and 3 600 r/min. Methods currently available for carrying out both analytical assessments and test validation of the shaft system torsional natural frequencies are also described.

Vibrations mécaniques -- Vibration de torsion des machines tournantes

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Status
Published
Publication Date
19-Apr-2009
Current Stage
6060 - International Standard published
Start Date
24-Mar-2009
Completion Date
20-Apr-2009
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INTERNATIONAL ISO
STANDARD 22266-1
First edition
2009-05-01
Mechanical vibration — Torsional
vibration of rotating machinery —
Part 1:
Land-based steam and gas turbine
generator sets in excess of 50 MW
Vibrations mécaniques — Vibration de torsion des machines
tournantes —
Partie 1: Groupes électrogènes à turbines à vapeur et à gaz situés
sur terre et excédant 50 MW
Reference number
ISO 22266-1:2009(E)
ISO 2009
---------------------- Page: 1 ----------------------
ISO 22266-1:2009(E)
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© ISO 2009

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ii © ISO 2009 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 22266-1:2009(E)
Contents Page

Foreword............................................................................................................................................................ iv

Introduction ........................................................................................................................................................ v

1 Scope ..................................................................................................................................................... 1

2 Normative references ........................................................................................................................... 1

3 Terms and definitions........................................................................................................................... 2

4 Fundamentals of torsional vibration................................................................................................... 7

4.1 General................................................................................................................................................... 7

4.2 Influence of blades ............................................................................................................................... 8

4.3 Influence of generator rotor windings................................................................................................ 9

5 Evaluation.............................................................................................................................................. 9

5.1 General................................................................................................................................................... 9

5.2 Frequency margins............................................................................................................................... 9

5.3 Dynamic stress assessments............................................................................................................ 12

6 Calculation of torsional vibration...................................................................................................... 12

6.1 General................................................................................................................................................. 12

6.2 Calculation data .................................................................................................................................. 13

6.3 Calculation results.............................................................................................................................. 13

6.4 Calculation report ............................................................................................................................... 13

7 Measurement of torsional vibration.................................................................................................. 13

7.1 General................................................................................................................................................. 13

7.2 Method of measurement .................................................................................................................... 13

7.3 Measurement test report.................................................................................................................... 14

8 General requirements......................................................................................................................... 14

8.1 Set supplier responsibilities.............................................................................................................. 14

8.2 Guarantees .......................................................................................................................................... 14

8.3 Responsibilities .................................................................................................................................. 14

Annex A (informative) Torsional vibration measurement techniques ........................................................ 15

Annex B (informative) Examples of frequency margins relative to line and twice line frequencies

for shaft system modes that can be excited by torsional oscillations of the shaft..................... 21

Annex C (informative) Commonly experienced electrical faults ................................................................. 23

Bibliography ..................................................................................................................................................... 25

© ISO 2009 – All rights reserved iii
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ISO 22266-1:2009(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.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. 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.

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.

ISO 22266-1 was prepared by Technical Committee 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.

ISO 22266 consists of the following parts, under the general title Mechanical vibration — Torsional vibration of

rotating machinery:
⎯ Part 1: Land-based steam and gas turbine generator sets in excess of 50 MW
iv © ISO 2009 – All rights reserved
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ISO 22266-1:2009(E)
Introduction

During the 1970s, a number of major incidents occurred in power plants that were deemed to be caused by or

that were attributed to torsional vibration. In those incidents, generator rotors and some of the long turbine

blades of the low-pressure (LP) rotors were damaged. In general, they were due to modes of the coupled

shaft and blade system that were resonant with the grid excitation frequencies. Detailed investigations were

carried out and it became apparent that the mathematical models used at that time to predict the torsional

natural frequencies were not adequate. In particular, they did not take into account with sufficient accuracy the

coupling between long turbine blades and the shaft line. Therefore, advanced research work was carried out

to analyse the blade-to-discs-to-shaft coupling effects more accurately, and branch models were developed to

account properly for these effects in shaft system frequency calculations.

In the 1980s, dynamic torsional tests were also developed in the factory to verify the predicted dynamically

coupled blade-disc frequencies for the low-pressure rotors. These factory tests were very useful in identifying

any necessary corrective actions before the product went in service. However, it is not always possible to test

all the rotor elements that comprise the assembly. Hence, unless testing is carried out on the fully assembled

train on site, some discrepancy could still exist between the overall system models and the actual installed

machine.

There is inevitably some uncertainty regarding the accuracy of the calculated and measured torsional natural

frequencies. It is therefore necessary to design overall system torsional frequencies with sufficient margin

from the grid system frequencies to compensate for such inaccuracies. The acceptable margins will vary

depending on the extent to which any experimental validation of the calculated torsional frequencies is carried

out. The main objective of this part of ISO 22266 is to provide guidelines for the selection of frequency

margins in design and on the fully coupled machine on site.

In general, the presence of a natural frequency is only of concern if it coincides with an excitation frequency

within the margins defined in this part of ISO 22266 and has a modal distribution allowing energy to be fed into

the corresponding vibration mode. If either of these conditions is not satisfied, the presence of a natural

frequency is of no practical consequence, i.e. a particular mode of vibration is of no concern if it cannot be

excited. In the context of this part of ISO 22266, the excitation is due to variations in the electromechanical

torque, which is induced at the air gap of the generator. Any shaft torsional modes that are insensitive to these

induced excitation torques do not present a risk to the integrity of the turbine generator, regardless of the

value of the natural frequency of that mode (see 4.2 and 5.2).
© ISO 2009 – All rights reserved v
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INTERNATIONAL STANDARD ISO 22266-1:2009(E)
Mechanical vibration — Torsional vibration of rotating
machinery —
Part 1:
Land-based steam and gas turbine generator sets in excess
of 50 MW
1 Scope

This part of ISO 22266 provides guidelines for applying shaft torsional vibration criteria, under normal

operating conditions, for the coupled shaft system and long blades of a turbine generator set. In particular,

these apply to the torsional natural frequencies of the coupled shaft system at line and twice line frequencies

of the electrical network to which the turbine generator set is connected. In the event that torsional natural

frequencies do not conform with defined frequency margins, other possible actions available to vendors are

defined.
This part of ISO 22266 is applicable to

⎯ land-based steam turbine generator sets for power stations with power outputs greater than 50 MW and

normal operating speeds of 1 500 r/min, 1 800 r/min, 3 000 r/min and 3 600 r/min, and

⎯ land-based gas turbine generator sets for power stations with power outputs greater than 50 MW and

normal operating speeds of 3 000 r/min and 3 600 r/min.

Methods currently available for carrying out both analytical assessments and test validation of the shaft

system torsional natural frequencies are also described.
2 Normative references

The following referenced documents are indispensable for the application of this document. For dated

references, only the edition cited applies. For undated references, the latest edition of the referenced

document (including any amendments) applies.
1)
ISO 2041:— , Mechanical vibration, shock and condition monitoring — Vocabulary

ISO 2710-1, Reciprocating internal combustion engines — Vocabulary — Terms for engine design and

operation

ISO 2710-2, Reciprocating internal combustion engines — Vocabulary — Terms for engine maintenance

1) To be published. (Revision of ISO 2041:1990)
© ISO 2009 – All rights reserved 1
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ISO 22266-1:2009(E)
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 2041, ISO 2710-1 and ISO 2710-2

and the following apply.
3.1
set

assembly of one or more elements such as high-pressure, intermediate-pressure, low-pressure turbines and

generator and exciter elements
3.2
shaft system
fully connected assembly of all the rotating components of a set
NOTE 1 Figure 1 shows an example.

NOTE 2 When the torsional natural frequencies are calculated, it is the complete shaft system that is considered.

3.3
torsional vibration
oscillatory angular deformation (twist) of a rotating shaft system
3.4
torsional vibration magnitude

maximum oscillatory angular displacement measured in a cross section perpendicular to the axis of the shaft

system between the angular position considered and a given arbitrary reference position

3.5
natural frequency
frequency of free vibration of an undamped linear vibration system

NOTE 1 The same definition is given for natural frequency of a mechanical system in ISO 2041.

NOTE 2 It is usually not necessary to calculate the natural frequency for a damped system, which is

ωω= 1−η
where η is the damping ratio.
3.6
modal vector

relative magnitude for the whole section, where the system is vibrating at its associated natural frequency and

an arbitrary cross section of the system is chosen as a reference and given a magnitude of unity

3.7
torsional mode shape
shape produced by connecting the modal vector magnitudes at each section
3.8
vibratory node
point on a mode shape where the relative modal vector magnitude is equal to zero
3.9
natural mode of torsional vibration

torsional mode shape which is produced when the shaft is vibrating at its natural frequency

EXAMPLE First mode of vibration or one-node mode of vibration, second mode of vibration or two-node mode of

vibration.
NOTE Figure 2 shows examples.
2 © ISO 2009 – All rights reserved
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ISO 22266-1:2009(E)
3.10
excitation torque

torsional torque produced by the generator, exciter or driven components that excites torsional vibration of the

shaft system
3.11
harmonic
each term of the Fourier series of the excitation or response signal
3.12
all-in-phase mode

mode of vibration in which all blades in a particular row vibrate in phase with one another

NOTE When the rotor disc and the blades couple under dynamic conditions, the combined system produces several

new “all-in-phase” frequencies that are different from the individual disc and blade frequencies (see Figure 3). These

modes are often referred to as zero-nodal diameter or “umbrella” modes.
3.13
resonant speed
characteristic speed at which resonances of the shaft system are excited

EXAMPLE The shaft speed at which the natural frequency of a torsional vibration mode equals the frequency of one

of the harmonics of the excitation torques.
NOTE The same definition is given for resonant speed/critical speed in ISO 2041.
3.14
additional torsional stress

stress due to the torsional vibrations of a given excitation harmonic superimposed on the torsional stress

corresponding to the mean torque transmitted in the given section of the shaft system being considered

Key
1 high-pressure (HP) rotor
2 low-pressure (LP) rotor 1
3 blades
4 LP rotor 2
5 LP rotor 3
6 generator rotor
7 excitation torque applied
8 exciter
Figure 1 — Six-rotor steam turbine generator system
© ISO 2009 – All rights reserved 3
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ISO 22266-1:2009(E)
a) Second mode of vibration or two-node mode of vibration
b) Sixth mode of vibration or six-node mode of vibration
Figure 2 — Typical torsional mode shapes of the shaft system
4 © ISO 2009 – All rights reserved
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ISO 22266-1:2009(E)
Frequencies in hertz

a) Uncoupled frequencies of separated blade b) Coupled frequencies of blade-disc

and disc assembly
Rotor central axis.
Figure 3 — Schematic illustration of blade-disc dynamic coupling
3.15
synthesized torsional stress

dynamic torsional stress generated at a section of the shaft system given by the vector sum of all the

harmonics of the excitation torques, taking into account both the magnitude and phase of the stress generated

by each harmonic

NOTE 1 See Figure 4, in which the six upper plots show, for a particular point on the shaft, the time history of the

additional torsional stress for each of the first six excitation harmonics. The lowest plot is the combined effect of vectorially

adding all of the individual harmonics.

NOTE 2 Mean torque is not used when elaborating the synthesized torsional stress.

© ISO 2009 – All rights reserved 5
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ISO 22266-1:2009(E)
Key
X time, s
Y torsional stress
Figure 4 — Typical dynamic torsional stress
3.16
prohibited frequency range

frequency range over which the stress caused by the torsional vibration exceeds the stress value permitted for

continuous operation

NOTE Although continuous operation in this frequency range is forbidden, passing through it in transient operation is

permissible, provided that it offers no danger of accumulated damage to the shaft system.

6 © ISO 2009 – All rights reserved
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ISO 22266-1:2009(E)
4 Fundamentals of torsional vibration
4.1 General

Torsional vibrations in turbine generator shaft systems are most commonly excited by variations in

electromechanical torque induced at the air gap of the generator. When operating under ideal

steady-state conditions involving balanced three-phase currents and voltages, the effects of higher harmonics

are negligible and the electromagnetic torque applied to the rotor in the generator air gap is essentially a

constant, non-varying torque that transfers the turbine mechanical power through the generator and

electrically to the power system. Under such ideal conditions, there will typically be little or no rotor torsional

vibrations. Torsional vibrations occur as a result of transient or unbalanced steady-state power system

disturbances which act to induce variations in the generator air gap magnetic field and, hence, the torque.

Table 1 summarizes the typical components of air gap torque variations for various types of system

disturbances. The magnitudes of these components depend upon the nature and severity of each disturbance.

These disturbances can be categorized as transient and steady-state. In general, transient disturbances are

cleared after a short time, but steady-state disturbances can persist for extended periods. Further details of

various electrical faults that could occur in power plants are provided in Annex C.

Table 1 — Types of disturbances
Excite at
Excite at
Excite at line (between 0,1
twice line
Types of disturbances Step change
frequency and 0,9) of
frequency
line frequency
Transient:
Three phase fault × ×
Unbalanced fault × × ×
Synchronization out-of-phase × ×
Open transmission line (three phases) ×
Close transmission line (three phases) × ×
Single pole switching × ×
Transient sub-synchronous resonance (SSR) ×
Disturbances in the grid due to thyristor controlled
× ×
loads (e.g. variable speed electric motors)
Steady-state:
Line unbalance ×
Load unbalance ×
Steady-state sub-synchronous resonance (SSR) ×

Unbalanced fault can be either line-to-line, line-to-ground or twice line to ground short circuits. Such faults can be seen either on

the transmission system or more severely at the generator terminals.

Line unbalance: Unbalance in transmission line or system, for example, untransposed transmission lines.

Load unbalance: Unbalance of the electrical load of the system.
© ISO 2009 – All rights reserved 7
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ISO 22266-1:2009(E)

In summary, torsional excitation of turbine generator shaft systems is induced at the generator terminals due

to the following reasons:

a) unbalanced short circuits that produce unidirectional, line and twice line frequency transient torques;

b) out-of-phase synchronization of the unit to the grid, which could produce very high levels of unidirectional

and line frequency transient torques;
c) excitations from other sources, including
⎯ three-phase short circuits,
⎯ transmission line switching, and

⎯ load variations induced and transmitted by heavy-duty operating equipment (such as electric arc

furnaces) in the vicinity;

d) sub-synchronous resonance, which can occur if the generator is connected to long transmission lines and

could excite the sub-synchronous torsional modes. Simple lump mass-spring systems are used in grid

system stability studies to model these sub-synchronous frequencies and their mode shapes;

e) line or load unbalance resulting in negative sequence currents that produce torques at twice the line

frequency.

In view of the possible excitation from the electrical grid, it is necessary to design the overall system torsional

natural frequencies with regard to both the line and twice line system frequencies. For those modes that can

be excited by torsional oscillations of the generator and are evaluated to be critical to the integrity of the unit,

there shall be sufficient margin from both the line and twice line system frequencies. This is the primary

consideration for avoiding any torsional vibration issues on large turbine generators. The following steps are

usually taken into account when defining the margin:
⎯ calculation uncertainty due to inaccuracies of the mathematical models,
⎯ experimental validation of the torsional natural frequencies,

⎯ desired margin between shaft system natural frequencies and the excitation frequency,

⎯ any specified/experienced grid frequency excursions, and
⎯ operating temperature effects.

Mechanical parts that are connected to the main rotor body could participate in torsional vibration if not

adequately designed for strength or tuned away from grid frequencies. These parts include shrunk-on

couplings, coupling bolts and long steam turbine blades. Among them, blade dynamic behaviour in torsional

vibration is complex and is discussed in more detail below.
4.2 Influence of blades

The mode shapes of zero-nodal diameter natural frequencies of blade rows are such that all blades in a row

vibrate in phase with one another. The tangential component of such modes can therefore be excited by

torsional oscillations of the shaft system. In addition, modal interaction takes place between the blades, discs

and shaft system such that the resulting natural frequencies of the combined blade-disc-shaft system are

different from those of the uncoupled components (see Figure 3). It is important to note that for other blade

modes with non-zero-nodal diameters, different sectors of the blade row vibrate in anti-phase to those of

adjacent sectors and are therefore not excited by torsional oscillations of the shaft system.

8 © ISO 2009 – All rights reserved
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ISO 22266-1:2009(E)

For short- and medium-height blade rows (e.g. high-pressure and medium-pressure turbines, and the first

several rows of low-pressure turbines), the frequencies of the lowest zero-nodal diameter modes are generally

far away from the frequencies of interest for torsional analysis. Therefore, when calculating the natural

frequencies of the coupled shaft system, such blades can be considered as rigid and only their torsional

inertias need be taken into account when calculating the shaft system torsional natural frequencies.

For longer blades (such as the last and penultimate rows of the LP turbine or the first compressor stage), the

frequencies of the zero-nodal diameter modes can be within the range of, or sufficiently close to, the line

and/or the twice line frequency in order to significantly affect the resulting system modes, which can then

become critical as far as torsion is concerned. These modes interact with those of the shaft system in such a

way that additional coupled shaft system modes are introduced with various combinations of blade vibration in

phase and anti-phase with the shaft system. Under adverse conditions, such modes could amplify rotor/blade

stresses due to external torques arising from grid disturbances. Consequently, when calculating the natural

frequencies of the coupled shaft system and blades, it is necessary to model the long blades as branched

systems that fully replicate the zero-nodal diameter (all-in phase) modes of these blades.

The criterion for assessing whether the blades can be represented by their torsional inertia only, or as

branched systems, is as follows. If the lowest zero-nodal diameter mode of the blade row and disc (or rotor

section for drum type rotors) is less than 2,5 times the nominal line frequency of the electrical grid system (i.e.

125 Hz in countries where the nominal grid frequency is 50 Hz and 150 Hz in countries where the nominal grid

frequency is 60 Hz), consideration should be given to modelling the blade row as a branched system.

Otherwise, it is only necessary to lump the total inertia of a blade row at the appropriate point in the shaft

system model. In general, it could be required that the last stage LP blades (and in some cases, penultimate

stage LP blades) be modelled as branched systems.
4.3 Influence of generator rotor windings

Special knowledge of the generator rotor structural design is needed for modelling the stiffness effects of the

rotor body section with its copper windings and wedges.
5 Evaluation
5.1 General

This part of ISO 22266 provides two methods for the evaluation of the torsional vibration characteristics of

coupled shaft systems including the blades:

a) the maximum frequency margin between the calculated natural frequencies and the relevant electrical

grid system frequencies (see 5.2);

b) dynamic stress analysis to ensure that the peak stresses induced by the transient fault conditions listed in

Table 1 are satisfactory (see 5.3).

Stress analysis for steady-state fault conditions is only required if the frequency margins defined in 5.2 are not

achieved.

Further information regarding the calculation of torsional vibration is given in Clause 6.

5.2 Frequency margins

The objective is to provide criteria that ensure that there are no shaft system modes that can be excited by

torsional oscillations of the shaft within close proximity of the line and twice line excitation frequencies of the

electrical grid system. It should be noted that the shaft system frequencies and associated modes, which are

insensitive to induced torsional forces, are permitted within the frequency exclusion zone (see 5.3).

Calculations by the equipment supplier would indicate whether a mode is responsive or non-responsive to grid

excitations. The allowable torsional frequency margins are shown in Figure 5 and given in Table 2, and are

described in a) to g) below.
© ISO 2009 – All rights reserved 9
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ISO 22266-1:2009(E)

If tests/calculations are carried out at room temperature, the relevant upper and lower frequency limits should be

increased by the temperature correction factor F.
NOTE See Table 2 for the definition of A to E.
Figure 5 — Definition of torsional frequency exclusion zone

Table 2 — Margins at line and twice line frequencies for both 50 Hz and 60 Hz machines

Description Frequency margin
Allowable upper grid frequency deviation A1
Allowable lower grid frequency deviation A2
B Margin between maximum/minimum allowable grid frequency and resonance peak B
C Calculation uncertainty C

Reduction in calculation uncertainty if a full-speed (dynamic) shop test carried out on

D D
generator rotor and static shop test (e.g. modal testing) carried out on LP roto
...

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