Machine, Plant & Systems Monitor

• Torsional damping (brought about ex-

Calculation and measurement of clusively by material damping of the shaft)

is very low. Critical damping ratios of tor-
sional shaft modes are around 0.1% and
lower. Very low damping results in sharp

torsionals in large steam turbosets resonance peaks with amplification factors

higher than 300, allowing the natural fre-
quencies to be easily identified.
Torsional shaft vibration can be excited in large steam turbine generator sets by elec- • Torsional shaft vibrations can be neither
trical disturbance torques occurring in the active part of the generator, and because of felt nor heard.
the low torsional damping of the shaft trains, resonance can cause high torsional vi- • Torsional vibrations are practically in-
bration amplitudes. Some thermal power plant operators therefore require turbine gen- sensitive to changes in shaft train condi-
erator set vendors to provide experimental verification of the natural torsional shaft tions (for example, minor unbalance),
frequencies. This article by Josef Huster and Dr Lothar Eckert (ABB Power Genera- making torsional monitoring unsuitable
tion), and Frank Pohle (ABB Turbo Systems), looks at a new measurement technique, for qualified condition control of steam tur-
developed by ABB, which allows torsional vibration to be measured in just one selected bine trains.
measurement plane. With today’s highly sensitive sensors and modern measurement
data analysis equipment, the excitation caused by normal random disturbances in the
electrical grid provides sufficiently good results. All natural torsional frequencies in Dynamic properties
the range of interest are obtained with an accuracy of +/- 0.2 Hz and identified using
the calculated natural frequencies. The new measurement technique places no restric- The torsional vibration system is charac-
tions on normal power plant operation. terised by the distribution of mass mo-
ments of inertia as well as by its torsional
stiffness. The mass moment of inertia and
Large steam turbine generator sets rated resonance-free design at 1 and 2 times grid the torsional stiffness vary considerably
at 100 MW and higher consist of one or frequency. over the long steam-turbine shaft trains
more steam turbines (high-pressure, inter- • Simulate extreme electrical disturbances (Figure 1).
mediate-pressure and low-pressure) and a in order to prove the mechanical integrity Knowledge of the distribution of the mo-
turbo-generator, which are rigidly coupled of the shaft journals. ment of inertia and the torsional stiffness
together as a single shaft train; there is no helps in the interpretation of the torsional
Some utilities also ask for experimental
gearbox. The rated speed is equal to 1 or mode shapes of a turbine generator train.
verification of the natural torsional fre-
0.5 times the grid frequency, being depend- This information is also very useful for
quencies of the turbine generator trains in
ent on the frequency of the electrical grid defining modifications designed to tune a
thermal power plants.
(50 Hz or 60 Hz) and the number of gen- specific natural torsional frequency.
erator poles (2 or 4).
Torsional vibrations can be excited in the Large turbine generator
shaft trains of large steam turbine genera- Excitation of torsional
tors by electrical disturbance torques oc- trains
curring in the active part of the generator
vibration
Consideration has to be given to the fol-
with 1 and 2 times the grid frequency. The Torsional vibrations are excited in steam
lowing:
torque amplitudes can be high, for exam- turbine generator trains by electromagnetic
ple, during short-time faults, or remain low • Torsional vibrational motion is super-
field disturbances in the air gap of the gen-
over long operating periods. posed on the continuous rotation of the
erator. Selection of the right number of
rotor train. There is no link between the
Natural torsional frequencies which ap- stator and rotor turbine blades for one
torsional vibration system and non-rotat-
proach double the grid frequency (reso- blade stage excludes the possibility of dy-
ing parts, such as the casing.
nance) can cause damage to the steam tur- namic excitation being caused by the steam
bine blades (1, 2) because the torsional • Torsional vibrations in single-shaft flow.
shaft vibrations are excited by the nega- power trains are not coupled to
Torsional excitation can be subdivided into
tive-sequence current. lateral shaft vibrations. strong short-time and low long-time elec-
In view of this, it is standard practice at • Torsional displacement amplitudes are trical disturbance torques in the active part
ABB during the design of turbine genera- very small (< 0.002 rad, equivalent to < of the generator.
tor trains to: 0.1˚); dynamic torsional stresses in the shaft
• Calculate the natural torsional frequen- journal are therefore low during normal
cies and corresponding mode shapes for a operation. Strong, short-time
disturbance torques
These are caused by:
• short circuits in the electrical grid, trans-
former or generator stator windings; and
• synchronisation failure.
Strong, sudden dynamic excitation acts in
just fractions of a second (< 0.3 s). The
excitation frequency of the air-gap torque
Figure 1. Simplified torsional model, typical moment of inertia and torsional stiffness can be either the grid frequency in the case
distribution for a steam turbine generator train (HP = high pressure turbine; IP = of synchronisation failure, or 1 and 2 times
intermediate-pressure turbine; LP1 & LP2 = low-pressure turbines; GEN = generator; the grid frequency in the case of short cir-
EXC = exciter; k = stiffness; θ = mass moment of inertia). cuits. Its magnitude in each case depends

22
 March/April 1999

on the electrical properties of the genera-

tor, the transformer and the grid. The maxi-
mum torque caused by a fault may be as
high as eight times the nominal torque of
the unit. A line-to-line short circuit at the
generator terminals is considered as an
extreme electrical disturbance.

Low, long-time
disturbance torques
Excitation mechanisms are:
• Negative-sequence current, caused by
unbalanced loading of the three current
phases in the power system, causing an al-
ternating air-gap torque to act on the gen-
erator with double the grid frequency. The
allowed negative-sequence current is lim-
ited by international standards (3). Tor-
sional vibration caused by the allowed
negative-sequence current must be low if
train designs are to be free of resonance.
• Sub-synchronous resonance, which can Figure 3. Torsional model of a low-pressure steam turbine rotor.
occur if the generator is connected to long
transmission lines (for example, 1000 km
long) and may excite the lower torsional bine shaft train. Special know-how is blade row is separately modelled by means
modes (4). needed, for example, to model the active of a beam model with about 10 elements.
The dynamic air-gap excitation torque acts part of the generator with its copper wind- The beam model is linked to the torsional
uniformly over the length of the active part ing and wedges. model of the shaft.
of the generator. The effective excitation The number of degrees of freedom of the
of a mode shape depends on the mode coupled model is increased by the addi-
shape in the region of the active part of
Calculating natural tional degrees of freedom of the blade rows
the generator (Figure 2). torsional frequencies and considered.
mode shapes
Calculating torsional The natural torsional frequencies and
Case in point
vibrations mode shapes are calculated using the tor- The coupled shaft-blade model of a steam
sional model (Figure 3) described earlier. turbine shaft line with four
The mass moment of inertia and torsional Damping is not included because of the low
stiffness of the turbine generator train are modelled last-stage blade rows shows two
damping of the train. The free-free vibra-
described by means of approximately 200 additional pairs of coupled first blade
tion system has a rigid body mode at 0 Hz.
one-dimensional finite elements (FE) with modes. For one pair of these first blade
For each mode shape of higher natural fre-
linear shape functions (Figure 3). These FE modes the blade motion is in phase (M1
quency, the number of vibration nodes is
elements have constant properties over and M2) with the shaft torsional vibration;
increased. Typical groups of mode shapes,
their length (5). for the other pair it is in anti-phase (M3
for example, for a 700-MW steam turbine
and M4).
The mass moment of inertia and torsional generator, are shown in Figure 4 and in
stiffness are described for each element Table 1. Figure 6 shows the calculated shaft mode
separately in terms of the outer and inner shapes in a comparison with the uncou-
diameters for mass and stiffness. Young’s pled shaft train model and the coupled
modulus is applied as a function of the ac- Vibration’s influence shaft-blade model with the last two blade
tual element temperature. The turbine ro- rows of the low-pressure turbines.
The torsional vibrations in the turbine gen-
tor blades are modelled as an additional The coupling of the vibrations in the long
erator train are coupled to the vibration
mass moment of inertia. turbine blades with the torsional vibration
occurring in the long turbine rotor blades.
The accuracy of the results depends largely of the shaft train can be neglected due to
To investigate this phenomena, a coupled
on the quality of the modelling of the tur- the LP turbines having stiff, drum-type ro-
shaft-blade model is used in which each
tors of welded ABB design. Separate vibra-
tion designs for the rotor trains and long
turbine blades provide the required results.

Simulating electrical faults

To simulate a line-to-line short circuit at
the generator terminals, a dynamic distur-
bance torque is made to act on the active
Figure 2. Comparison of the effective excitation of different torsional mode shapes (a = part of the generator rotor during full-load
easily excited mode shape; b = difficult-to-excite mode shape; GEN = generator). operation. This disturbance torque M(t) is

23
 Machine, Plant & Systems Monitor

Mode shape ID Designation Description of mode shape

0 Rigid body mode No deformation of shaft train.

(black curve in Fig. 4)

1 to 3 Lower modes No torsional displacements visible

(green curves in Fig. 4) < = 30 Hz in stiff rotor bodies. Vibration nodes
between rotor bodies.

4 to 6 Rotor modes Torsional deformations visible in

(red curves in Fig. 4) = 30 Hz to individual rotors.
= 200 Hz

7 to 12 Higher modes Torsional deformations also occur

Figure 6. Shaft mode shapes of the
uncoupled shaft model (LHS) and coupled
(blue curves in Fig. 4) > = 200 Hz in stiff rotor bodies.
shaft-blade model (RHS) (f = frequency;
Table 1. Typical groups of torsional mode shapes. fG = grid frequency).

defined by the equations shown in the box

below (6, 7).

M(t) = Mst for t < 0

M(t) = MS/xd”{sin(ωt)-0.5sin(2ωt)} + Mst
for t ≥ 0
Where:
•Mst [Nm]: the static torque under full
load conditions;
•MS [Nm]: the torque based on apparent
power PS, MS = PS/ω0;
•ω0 [rad/s]: angular velocity; Figure 5. Uncoupled (100%) and coupled
•n [rpm]: the nominal speed; natural blade frequencies (M1-M4) (f =
•PS [VA]: apparent power, PS = PN/Cosφ; frequency).
•PN [W]: the rated power;
Figure 7. Simulated dynamic torsional
•ω [rad/s]: angular frequency;
stresses brought about by a line-to-line
•f [1/s]: electrical grid frequency; Figure 7 shows, as an example, the calcu-
short circuit at the generator terminals (MG
•Cosφ [-]: the power factor; lated time histories of torsional stresses due
= generator torque; t = time; t = torsional
•xd” [-]: the sub-transient reactance of to a line-to-line short circuit at the genera-
shaft stress; see Figure 1 for key to other
the generator; and tor terminals of a 600-MW steam turbine
notation).
•t [s]: time. generator. The maximum dynamic tor-
The maximum value for the term in the sional stress occurs in the shaft journal at
brackets in the second line ({…}) is 1.3, the driven end of the generator (element Torsional vibration
which occurs when ωt = 2π/3. number 503).
measurement
The objective of torsional vibration meas-
urement is to determine the natural fre-
quencies and classify the calculated mode
shapes of built steam turbine generator
trains for design verification. Torsional
measurement tests carried out on shaft
trains in power plants comprise the follow-
ing stages.
• Excitation of the torsional vibration of
the train – synchronisation failure with a
small phase displacement angle; ramp test,
solid line-to-ground fault; and random
excitation of the electrical grid.
Figure 4. • Measurement of the vibration response
Torsional model in measurement planes of the shaft train,
shapes (1-12) using toothed wheels (8); sensitive strain
for a 700 MW gauges fitted to the shaft journal; acceler-
steam turbine ometers mounted in the circumferential di-
generator (see rection; and laser technology (for future
Figure 1 for key applications)
to notation). • Identifying the torsional modes, based

24
 March/April 1999

on measured and calculated natural tor- stant in the upper speed range. This is due
sional frequencies to the ‘stiffening’ of the rotor windings and
ABB currently uses either sensitive four- wedges caused by the centrifugal force act-
arm strain gauges or accelerometers and ing on them as the speed increases. Agree-
telemetric signal transmission. Experience ment between the calculated natural tor-
with these methods has been very good. sional frequencies and the measured val-
ues is good, with differences of only about
3% being obtained.
Torsional measurement in In the following, a look is taken at meas-
urements carried out on turbine generator
the spin pit trains in thermal power plants under three
The torsional vibrations of a hydrogen- different kinds of excitation condition.
cooled 500 MVA turbo-generator in the
Figure 10. Calculated torsional mode
spin pit were measured using accelerometers
for the purpose of verifying the calculated
shapes (1-3) of a 500 MVA turbo-generator Torsional measurement
rotor (M = measurement plane).
natural torsional frequencies (Figures 8 & test with synchronisation
9). The shaft configuration in the spin pit
comprised an electrical drive, two-stage
ferent speeds and at short time intervals, failure
were transformed into amplitude spectra
gearbox, cardan shaft and the generator rotor.
for display in a Campbell diagram (Figure The unit was synchronised with the elec-
11). These spectra are collected as a func- trical grid with a small phase displacement
tion of the speed and are sorted in ascend- angle of about 5˚. This small electrical dis-
turbance caused the shaft train to be ex-
cited with a torsional impulse. The re-
sponding torsional vibrations fade away
after a fraction of a second (< 0.3 s). Only
the lower natural torsional frequencies re-
spond with detectable peaks in the ampli-
tude spectrum.
The machine tested using this procedure
was a 900-MW half-speed turbine genera-
tor train. The instrumentation was fixed
onto the shaft journal in the workshop.
Figure 8. A 500 MVA turo-generator Special attention was given to the fitting
equipped with two accelerometers at the Figure 11. Campbell diagram of measured of the rotating measuring devices, such as
hub of the axial fan. natural torsional frequencies for a 500 the strain gauges, wires and transmitters,
MVA turbo-generator rotor (a = vibration since they have to withstand high centrifu-
amplitudes; f = frequency; n = rotational gal forces (Figure 12).
speed). The measured amplitude spectra clearly
show the natural torsional frequencies up
ing order in the diagram. Campbell dia- to the single grid frequency. No significant
grams, in which the rotor speed is shown resonance peaks are visible in the upper fre-
along the abscissa and the frequency of quency range (Figure 13).
vibration as the ordinate, are commonly
used in analyses of blade dynamics. A small
vertical bar gives the amplitude of vibra- Ramp test
tion for a certain speed and vibration fre- The unit was disconnected from the elec-
quency. Only amplitudes of high magni- trical grid and a solid line-to-ground fault
tude are plotted, those of very low set up on the HV side of the generator (Fig-
Figure 9. A transmitter casing with magnitudes being neglected. ure 14). Afterwards, the generator rotor
integrated accelerometers. Three natural torsional frequencies of the was excited with a low excitation current,
generator rotor are found in the range up and the shaft train was run up slowly with
Figure 10 shows the calculated torsional to 250 Hz. The torsional frequencies in- steam. The dynamic torque produced in
mode shapes and the measurement plane. crease slightly with increasing rotor speed the generator air gap has a frequency equal
During the start-up with a low rotational in the lower speed range and remain con- to the rotating speed times the pole number
speed gradient, torsional vibrations were
excited by means of a mesh and pitch er-
ror in the gearbox.
Two accelerometers were mounted on the
fan hub at 0˚ and 180˚ of the circumfer-
ence. The measurement signals from these
accelerometers allowed compensation of
the lateral shaft vibration components. The
signals were transmitted by means of te-
lemetry to a data acquisition system, where
they were stored.
Figure 12. Four-arm strain gauge
The signals, which were measured at dif- bridge on a shaft journal.

25
 Machine, Plant & Systems Monitor

for the measurement plane that would en-

sure good signals of all the specified natu-
ral torsional frequencies (Figure 16a). The
non-rotating part of the telemetry system
consists of a receiver and the equipment
required to display, store and analyse the
data.
The graph in Figure 16b shows the meas-
ured amplitude spectrum. With the help
of the calculated natural torsional frequen-
cies and mode shapes it is possible to iden-
tify the measured natural frequencies. The
difference between the calculated and the
measured torsional frequencies was found
to be smaller than 3%.

Figure 13. FFT analysis of short-time steps. The test was conducted on a 900 MW half-
speed turbine generator train (a = vibration amplitudes; f = frequency; fG = grid frequency;
t = time; M1 & M2 = measurement planes; see Figure 1 for key to other notation).

of the machine. In this example, the speed is important to carefully monitor the tem-
of the shaft train (with a four-pole genera- perature of the generator windings during
tor) was increased and resonances of the this test.
natural torsional frequencies, correspond-
ing to four times the rotational speed, were
passed through. Torsional test with
The measured signals were transferred into random excitation from
the frequency domain by FFT and plotted
in the Campbell diagram (Figure 15). The the electrical grid
Figure 15. Campbell diagram for a 900
sharp resonance peaks at the natural tor- MW half-speed steam turbine generator (a
During normal operation, minor distur-
sional frequencies are clearly visible on the = vibration amplitudes; f = frequency; fR =
bances of the type commonly found in elec-
four times speed-line. The natural torsional natural frequency of train; fB = blade
trical grids produce continual, random
frequencies were measured at different frequencies; n = rotational speed; 1-4:
excitation of the natural torsional frequen-
speeds with different centrifugal force ef- multiples of speed).
cies of the turbine generator train. The
fects. Extrapolations were used to convert
measured signals are sampled over a pe-
the measured natural torsional frequencies
riod of 30 minutes or more. By averaging
to the rated speed.
some hundreds of FFTs, a final vibration Comparison of different
Curve veering is visible in the zoomed win- spectrum is obtained which contains all the test methods
dow in the Campbell diagram (Figure 15). natural torsional frequencies in the fre-
Natural blade frequencies, highly depend- quency range of interest. Table 2 compares different aspects of the
ent on the speed, cross a natural torsional various torsional measurement procedures
This test procedure was demonstrated by
frequency of the shaft. As has been ex- used in power plants. The method employ-
performing torsional measurements on a
plained, the first natural blade frequency ing random excitation from the electrical
600-MW half-speed turbine generator
is split into two pairs, which are clearly grid has been found to be highly efficient
train. The rotating part of the measuring
visible. and to yield good measurement results. For
equipment consists of strain gauges and te-
This test procedure allows excitation of the lemetry devices on one measurement plane. this reason, it is the method preferred by
specified natural torsional frequencies. It A location was selected on the shaft train ABB and the one currently used during the
design of turbine generator trains and for
experimental verifications.

Summary
By designing steam turbine trains with stiff,
ABB drum-type, welded LP rotors it is en-
sured that coupling of the blade vibrations
in large steam turbines to the torsional vi-
bration in the shaft train is negligible. Sepa-
rate vibration designs for the shaft trains
and long blades therefore provide adequate
Figure 14. Solid line-to-ground fault on the high voltage side of the generator (G = results. The natural torsional frequencies
generator stator, R,S & T = high voltage lines).

26
 March/April 1999

– Part 1: Rating and Performance, 10th

edition, 1996-11.
4. M. Canay: Subsynchronous resonance
– an explanation of the physical relationships.
Brown Boveri Rev 68 1981 (8/9) 348–357.
5. P. Schwibinger: Torsionsschwingungen
von Turbogruppen und ihre Kopplung mit
den Biegeschwingungen bei Getriebe-
Maschinen. VDI Progress Reports, Series
11: Schwingungstechnik No. 90,
Düsseldorf 1987
6. E. Wiedemann, W. Kellenberger:
Konstruktion elektrischer Maschinen.
Springer Verlag, Berlin, Heidelberg, New
York, 1967.
Figure 16. Calculated torsional mode shapes, 1-5, (a) and the amplitude spectrum
7. M. Canay: Drehmomentgleichungen
measured at the measurement plane M (b) (fG = grid frequency; a = vibration amplitudes;
und deren Gültigkeitsbereiche <em dash>
1-4: calculated natural frequencies.)
Einfluss auf mechanische Drehmomente in
der Welle einer Synchronmaschine. etz
calculated during the design phase differ brations in large steam turbine generator Archiv, vol. 8 (1986) no. 9, 325–330.
from the measured values by less than 3%. trains to be kept well under control.
8. P. Wutsdorff: Messung und Auswertung
Generally, the torsional vibrations excited
von Torsionsschwingungen an grossen
by normal random disturbances in the grid
can be measured by means of sufficiently References Dampfturbogruppen bei transienten
Betriebszuständen, VGB
sensitive strain gauges or accelerometers 1. K. Steigleder, E. Krämer: Coupled vi- Kraftwerkstechnik 64, no. 4, April 1984.
in just one measurement plane between the bration of steam turbine blades and rotors
LP turbine rotor and generator rotor, as- due to torsional excitation by negative se-
suming the availability of appropriate data Josef Huster or Dr Lothar Eckert, ABB
quence currents. American Power Confer-
acquisition systems. This procedure allows Power Generation Ltd, CH-5401 Baden,
ence, Chicago, April 24–26, 1989.
high-quality experimental verification of Switzerland; fax: +41-56-205-5605; e-
the specified natural torsional frequencies 2. D. Evans, H. Giesecke; E. Willman; P. mail: <josef.huster@chkra.mail.abb.com>;
(+/- 0.2 Hz) during normal operation in Moffitt: Resolution of torsional vibration e-mail: <lothar eckert @chkra.mail.abb.com>.
thermal power plants. issue for large turbine generators. Presented
at the Annual Meeting of the American
As measurements in actual thermal power This article is based on an article with the
Power Conference, April 19, 1995.
plants have demonstrated, the design meth- same titled which appears in ABB Review
ods available today allow the torsional vi- 3. EC 34-1: Rotating Electrical Machines 6/98.

Synchronisation failure with Ramp Test, Random excitation from

small displacement angle solid line-to-ground fault electrical grid
Measurement Four-arm strain gauge bridges Four-arm strain gauge Sensitive four-arm strain
bridges gauge bridges
Data transfer Telemetry Telemetry Telemetry
Preparation Synchronisation failure with Short circuit on high-voltage side None
on site small phase displacement of generator;
angle disconnection of some safety
devices on electrical side
Operating mode Unit ready to start operating Unit disconnected from Normal operation of unit
electrical grid
Duration of Approx 3 s 2 to 5 h; 30 min
measurement temperature in generator
winding have to be kept
below allowed levels
Total duration 30 min Unit needed for 2 to 3 Unit runs as normal.
of test days, during which time Test does not restrict
no electrical power is production of electric
produced power
Measured Only lower natural Natural frequencies below All natural frequencies
natural frequencies below grid four-times (4-pole generator) measured in normal operation;
frequencies frequency can be detected maximum rotational speed typical frequency range
measured at different speeds, currently about 150 Hz
have to be converted to rated speed (no limitation due to
measuring equipment)
Measurement ± 0.2 Hz ± 0.2 Hz ± 0.2 Hz
quality
Necessary work None Disconnected safety devices on None
electrical side need to be re-activated
Table 2. Important aspects of different measurement procedures.

27
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