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Assessment of fatigue damage in steam turbine shafting due to torsional

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Article  in  Strength of Materials · September 2011

DOI: 10.1007/s11223-011-9318-5

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Strength of Materials, Vol. 43, No. 5, September, 2011

SCIENTIFIC AND TECHNICAL SECTION

ASSESSMENT OF FATIGUE DAMAGE IN STEAM TURBINE SHAFTING

DUE TO TORSIONAL VIBRATIONS

A. P. Bovsunovskii UDC 621.165.65-192

We present a technique and results of fatigue damage evaluation of steam turbine shafting material
under conditions of torque vibrations occurring at turbogenerator abnormal modes of operation
(short circuit, random paralleling start, etc.). Combinations of loading parameters, which provide
the shafting limiting conditions, are identified.

Keywords: turbine shafting, torsional vibrations, fatigue damage, limiting state.

Introduction. In the analysis of vibration processes that occur in a steam turbine, the emphasis is usually
placed on the shaft lateral vibrations. Indeed, large-amplitude bending vibrations of the turbine rotors are generated
during the turbine acceleration and stop, when the shaft critical speeds are passed through. Meanwhile, torsional
vibrations of the turbine shaft, which arise in some operating modes of a turbogenerator, are equally critical and
sometimes are even more dangerous.
The danger of torsional vibrations is proved, in particular, by the burst of a steam turbine intermediate-
pressure rotor at Gallatin Power Plant (USA) in 1974, which was due to a crack growing for several years under
cyclic torsion conditions [1], as well as by the breakdown of Power Unit No. 3 of Kashira Power Plant in 2002 [2].
The risk that significant torsional vibrations of a shaft may be induced during a sudden generator short-circuit fault
was demonstrated by the analysis performed on a scaled-down model of a turbine-driven generator set [3].
Based on the investigation of the accident at Kashira Power Plant, the main causes of torsional vibrations of
the turbine shaft were found to include the following [2]:
(i) short-circuit fault mode;
(ii) cases of random paralleling start (coarse synchronization) of a turbogenerator;
(iii) dynamic instability of the turbogenerator–network system;
(iv) nonuniformity of the generator electric field.
However, despite the great potential danger of torsional vibrations in a shafting, these are never recorded for
steam turbines in operation. Consequently, there are no direct data on the level of torsional vibrations of a turbine
shaft during dynamic interaction with a generator. Therefore, nowadays the level of a shaft torsional vibrations and
the related level of fatigue damage in the rotor material under various dynamic actions of the generator on the turbine
shaft can be assessed only by modeling the said actions.
According to the existing practice, the evaluation of residual life of steam turbines is mostly based on an
analysis of the thermal stress state in the turbine rotor and casing and a study of degradation of mechanical properties
of their materials [4]. This methodology, however, disregards the fatigue damage in the turbine shaft due to its
torsional vibrations and therefore leads to significant errors in the assessment of real damage in the steam turbine
components.
Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine
(apbovsunovsky@gmail.com). Translated from Problemy Prochnosti, No. 5, pp. 5 – 20, September – October, 2011.
Original article submitted October 14, 2010.

0039–2316/11/4305–0487 © 2011 Springer Science+Business Media, Inc. 487

 Fig. 1. Mod. K-200-130 steam turbine.

From the standpoint of mechanical loading, the generator short-circuit fault or bringing the generator on-line
with coarse synchronization causes a short-time vigorous surge of a reactionary torque acting from the generator
end to the turbine shafting. The dynamic loading of this type is difficult to analyze and requires the use of some
numerical models [5]. Generally, the surge of the reactionary torque can be represented by three parameters:
magnitude, duration, and form. Amplitudes of various waveforms of the turbine torsional vibrations and fatigue
damage in the rotor material depend, to a certain extent, on these parameters.
In the general case, the material ability to resist alternating loads depends on a number of factors. As applied
to turbine rotors of thermal stations, these factors include a load ratio [6], high temperature [7], scale factor [8, 9],
stress concentration [9], nonuniformity of mechanical properties of steal in the rotor volume [10, 11], etc. They
should be allowed for, in order to achieve a reliable assessment of cyclic damage in a turbine shafting under vibration
conditions.
The objective of the present work was to study various possible cases of dynamic loading a turbine shaft,
which may occur during a sudden short-circuit fault of a generator or its random paralleling start, and to assess the
total fatigue damage level in a rotor material under the above loading conditions during the turbine operation.
Procedure of Calculation of Cyclic Damage in a Shafting under Torsional Vibrations. A Mod.
K-200-130 steam turbine is a complex mechanical system consisting of a high-pressure rotor (HPR), intermediate-
pressure rotor (IPR), low-pressure rotor (LPR), and a generator (Fig. 1 shows no generator). Induced vibrations in
this system, which arise due to a short surge of reactionary torque, were studied numerically with the K-200-130
turbine shafting being represented by a model in the form of a vibrating system with four degrees of freedom (Fig. 2).
The model was preset with inertial and stiffness properties of the shafting [5].
The full-load torques arising on the high-, intermediate-, and low-pressure cylinders, respectively, were
specified based on the turbine operating conditions: M h = 0.196 MN × m, M i = 0. 291 MN × m, and M l = 0.163
MN × m [5]. The full-load torque that acts between the turbine shafting and the generator is equal to a sum of the
above-mentioned moments M sum = 0. 65 MN × m. Hereinafter and in Fig. 2 M r denotes the amplitude of the
reactionary torque surge.
The torsional vibrations of this mechanical system were described by a set of four differential equations which
have the following matrix form
[ I ]{&&
j} + [ D ]{j& } + [ K ]{j} = {M }F ( t ), (1)

where [ I ] is the matrix of moments of inertia of the disks masses, [ D ] is the damping matrix, [ K ] is the stiffness
matrix, {M } is the moment vector, F ( t ) is the time function of a moment, and {j} is the vector of the disks turning
angles.
The method of solving set of equations (1) for the case of a short-term load was described earlier in [6]. The
emphasis in that publication was put on a study of vibrations in the most critical locations of the shafting: between

488
 Fig. 2. A model of a steam turbine shafting.

the LPR and the generator (Fig. 1, section 1), between the IPR and LPR (section 2), and between the HPR and IPR
(section 3).
The surge magnitude was taken equal to three and six full-load torques. The six-fold surge of the reactionary
torque simulated the short-circuit fault conditions of the generator, and the three-fold surge corresponded to bringing
the generator on-line with inaccurate synchronization. The surge waveform and duration were specified by the
function F ( t ) in the rectangular and biharmonic form (Fig. 3). The biharmonic waveform of the exciting force
during the sudden three-phase short-circuit fault of the generator follows from the publication [12] and is written as

F (t ) = 0. 046 + 0. 627 sin(wt ) - 0. 467 sin(2wt ), (2)

where w = 314 rad/s.
The model applicability was proved by a comparison between the results of calculations performed using a
finite-element model of the turbine (the model consisting of 50,000 elements) [5] and a shafting model with a large
number of concentrated masses and inertialless stiffnesses [13].
A short-time action of the reactionary torque surge on the mechanical system gives rise to a damped oscillating
process. The calculations assume a linear viscous damping; therefore, the damped oscillating process is described by
an exponential function of the form
t max = t a e - dft sin wt, (3)

where t a is the initial stress amplitude of the damped process, d is the logarithmic decrement that represents the
rate of decay of free vibrations, f and w are respectively the frequency and angular frequency of the shafting free
vibrations, and t is time.
The amplitude of the ith cycle of the damped process was found by the formula

t i max = t a e - d (1+ 4 i )/ 4 . (4)

The number of damaging load cycles in this process is governed by the vibration damping level in the
mechanical system. The dissipation of vibrational energy in a running shafting is due to energy losses in the material,
structural energy dissipation, and air damping associated with the interaction between the vibrating elements and the
air–steam media. Considering the difficulty of determining the damping characteristic of torsional vibrations for a
real turbine shafting, in model calculations its value was varied in the range d = 2–30% [13–15].
The cyclic strength calculation for the shaft was carried out by the linear damage summation theory (the
Palmgren–Miner hypothesis) [16, 17]. According to this theory, the fracture condition under block type loading is
written as
s n
å N i = 1, (5)
i = 1 if

489
 Fig. 3. Waveforms of the reactionary torque surges.

where ni is the number of cycles with a stress amplitude t i max , N if is the number of cycles to failure under cyclic
loading with a stress amplitude t i max , and s is the number of loading levels (blocks). Strictly speaking, the rate of
damage accumulation slightly grows with increasing number of loading cycles; in random loading this effect was
considered negligible and disregarded [18].
The functionalities of up-to-date computers make it possible to sum up damage at each loading cycles, i.e.,
to realize the case where the number of loading blocks s is equal to the number of deformation cycles. In doing so,
the cyclic damage in the material is assessed by the parameter

s
P= å Pi , (6)
i =1

where P i is the magnitude of damage in the material in the ith loading cycle.
The algorithm of finding the magnitude of damage in the material was as follows. First, we used formula (8)
to determine the stress amplitude in the ith cycle (starting from the first one) of damped vibrations, t i max . Then, for
this amplitude the number of cycles to failure N if was found by (5). The magnitude of damage in the material in
the ith vibration cycle is computed by the expression

1
Pi = . (7)
N if

This procedure was carried out sequentially for each of i cycles of damped vibrations. The computations
were stopped if the stress amplitude in the ith vibration cycle, t i max , turned out to be lower than the fatigue limit of
the rotor steel, t -1 .
In this work we took the fatigue curve for rotor steel 25Kh1M1FA which is used for the manufacture of
rotors for K-200-130 turbines shafting. This curve had been plotted for symmetrical torsion cycle conditions at 20°C
and approximated by a damped exponential of the form [14]

t max = h 0 + h p ( N ) c + h u ( N ) b , (8)

where h 0 , h p , and h è are the function coefficients (h 0 = 208. 3, h p = 3176. 229, and h u = 185,966.681), N is the
number of cycles to failure, and c and b are the exponents (c = -0. 3114, b = -0. 8348).

490
 The influence of operating factors (temperature, load ratio, and scale factor) typical of steam turbines on the
cyclic strength of 25Kh1M1FA steel was allowed for by means of correction coefficients as follows:

t max = K sc K a K t (h 0 + h p ( N ) c + h u ( N ) b ), (9)

where K sc is the coefficient representing the scale factor, K a is the coefficient allowing for the influence of the
mean stress, and K t is the temperature coefficient.
Based on the experimental evidence [9, 19], the coefficients K sc and K t were taken to be 0.58 and 0.78,
respectively. The coefficient K a was determined by the formula

t 2-1 - k 2 y 2t t 2m
Ka = . (10)
t -1

where t -1 = 230 MPa, k = 0.922, y t = 0.505 [14], and t m is the mean stress.
Results of Cyclic Damage Calculation for K-200-130 Turbine Shafting under Torsional Vibrations.
Generally, the stress in a shafting under torsional vibrations depends on the duration, waveform, and amplitude of the
reactionary torque surge as well as on the level of vibrations damping in the system. Figure 4 illustrates the effect of
the surge duration and waveform on the dynamic stresses that arise during the shafting free vibrations, i.e., after the
action of the reactionary torque M r has ceased; the reactionary torque was taken equal to the sum moment times
six, M r = 6 M sum . In case of a rectangular surge waveform, the surge duration t m was varied with an increment of
0.002 s, while for the biharmonic waveform the increment was 0.001 s. For each tm value we calculated at least 30
cycles of the shafting free vibrations over a time period of 1.5 s; out of these we chose the cycle with the largest
amplitude. Horizontal lines in Fig. 4 show also the levels of shear stresses corresponding to the ultimate strength and
fatigue limit of the rotor steel 25Kh1MFA at T = 20 and 500°C: t b = 500 and 390 MPa and t -1 = 230 and 160 MPa,
respectively.
Analysis of the calculated results given in Fig. 4 suggests that the influence of duration of rectangular and
biharmonic surges of the reactionary torque on the shear stresses is of complex quasi-periodic pattern. Almost at any
surge duration section 2 of the shafting is the most stressed one, while the stress amplitude in section 3 does not
exceed the fatigue limit of the rotor steel (Fig. 4). With a rectangular surge of the torque of the magnitude considered
and in some narrow intervals of its variation, in sections 1 and 2 (Fig. 4) there arise stresses which exceed the
ultimate strength of the rotor steel at high temperature. With other surge durations, the stresses are higher than the
torsional fatigue limit of the rotor steel within the turbine operating temperature range. Thus, depending on the
torque surge duration the vibrations induced by the surge may cause cyclic damage in the rotor material as well as
instantaneous fracture of the turbine shafting. In all likelihood, this was the case at Kashira Power Plant, where a
0.7-s short-circuit fault of the generator resulted in disastrous breakdown of the turbine shafting.
All other factors being equal, the rectangular surge of the reactionary torque is more dangerous than the
biharmonic one. It is seen from Fig. 4b that over almost entire range of durations of the biharmonic surge of the
reactionary torque the stresses do not exceed the ultimate strength of the rotor steel at elevated temperatures.
Figure 5 illustrates the development of vibration processes in the shafting sections at hand for the reactionary
torque surge duration t m = 0.02 s (with this surge duration the largest free vibrations arose in the shafting, Fig. 4a)
and for two levels of logarithmic decrement of the shafting vibrations. It is evident that this force action is capable of
exciting significant torsional vibrations in the shafting, with some cycle asymmetry. In this case, the number of
damaging cycles of vibration essentially depends on the vibration damping level in the system. Specifically, if the
logarithmic decrement of the shafting d = 30%, then in the loading case at hand there will arise only a few vibration
cycles with stresses in section 2, which will exceed the torsional fatigue limit of the rotor steel at 500°C (Fig. 5b). No
cyclic damage is observed in sections 1 and 3.
Similar behavior is observed also for the biharmonic surge of the reactionary torque. Under these conditions
the most dangerous surge is the one of duration t m = 0.19 s. Dynamic stresses that arise in sections 2 and 3 during

491
 a b
Fig. 4. Dynamic shear stresses in sections 1, 2, and 3 of the turbine shafting vs. the duration
of the rectangular (a) and biharmonic surge (b) of the reactionary torque.

a b
Fig. 5. Variation of shear stresses in sections 1, 2, and 3 of the turbine shafting during the rectangular
surge of the reactionary torque for the surge duration t m = 0.02 s (curve 4): (a) d = 0; (b) d = 30%.

the free vibrations are higher than the fatigue limit of the rotor steel only if there is no damping (Fig. 6a). With a high
damping level in the system, only one cycle of vibration in section 2 is a damaging cycle.
A conservative assessment of cyclic damage in a turbine rotor due to torsional vibrations of the shafting is
based on the consideration of the most damaging load cases which involve the reactionary torque surges of durations
whereby vibrations in various shafting sections reach the largest amplitude. In practice, the duration of the
reactionary torque surge during a generator short-circuit fault or bringing the generator on-line with inaccurate
synchronization is a random quantity. Thus, depending on the duration of the dynamic action of the generator on the
turbine shafting, it may result in either dangerous vibrations or some insignificant ones as, for example, in the case of
a rectangular surge of duration t m = 0.96 s (Fig. 4a).
Short-circuit fault of a generator is quite a rare phenomenon. On the other hand, the number of turbine starts
is limited to 2000 and every time the turbine is started there occurs at least one switching of the generator on-line,
which leads to a surge of the reactionary torque. The generator cannot always be brought on-line at the first try; this
depends on the operator skills. According to information from power plants, the number of such attempts can be as
large as seven. Consequently, the number of the reactionary torque surges causing torsional vibrations may exceed
2000. Even if a few dozens damaging cycles of vibrations were induced in such switch-on cases, a considerable
fatigue damage would be initiated in the turbine rotor over a service life of 20 years, the damage magnitude
depending on the reactionary torque parameters and vibration damping level in the system.

492
 a b
Fig. 6. Variation of shear stresses in sections 1, 2, and 3 of the turbine shafting during the biharmonic
surge of the reactionary torque for the surge duration t m = 0.19 s (curve 4): (a) d = 0; (b) d = 30%.

Below we will consider some cases of fatigue damage accumulation in a turbine shafting over a long period
of its operation; the cases will involve variation of the reactionary torque parameter within a real range.
The assessment of real cyclic damage in a turbine shafting over its operation period was based on an
assumption that the probability of the reactionary torque surge within the preset time range Dt m would be the same.
The range of variation of the surge duration was taken to be Dt m = 0.192 s for the rectangular surge and 0.5 s for the
biharmonic one. The increment of the surge duration within these ranges was t h = 0.001 s.
Using the model for each t m we computed the amplitude of maximum initial shear stresses t a in sections
1 and 2 of the shafting, the number of cycles of the damped vibration process i, whereby cyclic damage occurred in
the material, and the magnitude of cyclic damage in the rotor material P tm for the given surge duration. The
averaged magnitude of damage was determined by the formula

P av = P tm h, (11)

where h is the number of surges within the given time range (h = t m t h ), for which the magnitude of damage was
computed.
Tables 1–4 summarize the results of calculation of P av for rectangular and biharmonic surges of the
reactionary torque whose value was varied in the range M r = (2–12)M sum , for four damping levels. The tables show
also the quantity P -1
av , which denotes the number of times the generator was brought on-line with inaccurate
synchronization until the shafting reached its limiting state under the specified conditions.
A comparative analysis of the data given in Tables 1–4 has demonstrated that the rectangular surge of the
reactionary torque is more dangerous than the biharmonic one and that the extent of cyclic damage in the rotor
material is directly proportional to the magnitude of the torque and inversely proportional to the vibration damping
level in the system. According to the cyclic damage criterion for the shafting material, in most cases the number of
possible turbine starts until the shafting reach its limiting state exceeds the allowable 2000 starts. This implies that
over the turbine service life the cyclic damage due to torsional vibrations will not reach dangerous magnitudes. In
Tables 1–4, the dangerous levels of the reactionary torque are shown in brackets and the safe ones without brackets.
It is obvious that with the maximum damping level studied (d = 30%) only the rectangular surges of
significant magnitude turn out to be dangerous, while the biharmonic ones of any magnitude do not lead to the
limiting state.
With the lowest damping level considered (d = 2%) the limiting state in section 1 of the shafting is reached
with the rectangular surge magnitude M r > 3 M sum and the biharmonic surge M r > 8 M sum , while in section 2 the
same occurs when M r > 2 M sum and M r > 6 M sum . The surge magnitude above the six times total rated torque

493
 TABLE 1. Damage Estimation of Rotor Material in Shafting Section 1 (Fig. 1) for Rectangular Surge
of the Reactionary Torque (t m = 48 MPa)
M r M sum d = 2% d = 10% d = 20% d = 30%
Pav P-1
av
Pav P-1
av
Pav P-1
av
Pav P-1
av
2 0.000006 158,894 0.000002 552,115 0.000002 612,183 0.000001 684,698
3 0.000197 5081 0.000044 22,562 0.000026 38,647 0.000021 48,204
4 (0.000876) (1142) 0.000191 5244 0.000106 9478 0.000078 12,742
6 (0.004087) (245) (0.000869) (1150) 0.000467 2140 0.000334 2994
8 (0.009591) (104) (0.002020) (2322) (0.001074) (931) (0.000758) (1319)
10 (0.016999) (59) (0.003562) (281) (0.001881) (532) (0.001321) (757)
12 (0.025987) (39) (0.005426) (184) (0.002854) (350) (0.001996) (501)

TABLE 2. Damage Estimation of Rotor Material in Shafting Section 2 (Fig. 1) for Rectangular Surge
of the Reactionary Torque (t m = 61 MPa)
M r M sum d = 2% d = 10% d = 20% d = 30%
Pav P-1
av
Pav P-1
av
Pav P-1
av
Pav P-1
av
2 0.000245 4088 0.000055 18,248 0.000032 31,709 0.000025 40,097
3 (0.001672) (598) 0.000360 2777 0.000196 5093 0.000143 7014
4 (0.004564) (219) (0.000969) (1032) (0.000520) (1924) 0.000371 2698
6 (0.014157) (71) (0.002970) (337) (0.001571) (637) (0.001104) (905)
8 (0.027751) (36) (0.005790) (173) (0.003043) (329) (0.002126) (470)
10 (0.044424) (23) (0.009239) (108) (0.004837) (207) (0.003369) (297)
12 (0.063568) (16) (0.013191) (76) (0.006890) 145 (0.004788) (209)

TABLE 3. Damage Estimation of Rotor Material in Shafting Section 1 (Fig. 1) for Biharmonic Surge
of the Reactionary Torque (t m = 48 MPa)
M r M sum d = 2% d = 10% d = 20% d = 30%
Pav P-1
av
Pav P-1
av
Pav P-1
av
Pav P-1
av
2 0 ¥ 0 ¥ 0 ¥ 0 ¥
3 0 ¥ 0 ¥ 0 ¥ 0 ¥
4 0.000001 1539,526 0.000001 1987,301 0.000001 1950,678 0,0000004 2394,297
6 0.000039 25,491 0.000009 106,233 0.000007 152,217 0.0000060 169,522
8 0.000267 3752 0.000059 16,833 0.000034 29,287 0.0000270 36,805
10 (0.000812) (1232) 0.000177 5657 0.000098 10,200 0.0000720 13,818
12 (0.001722) (581) 0.000370 2701 0.000202 4960 0.0001460 6845

TABLE 4. Damage Estimation of Rotor Material in Shafting Section 2 (Fig. 1) for Biharmonic Surge
of the Reactionary Torque (t m = 61 MPa)
M r M sum d = 2% d = 10% d = 20% d = 30%
Pav P-1
av
Pav P-1
av
Pav P-1
av
Pav P-1
av
2 0 ¥ 0 ¥ 0 ¥ 0 ¥
3 0.000001 1537,301 0.000001 1971,635 0.000001 1628,788 0.0000004 2328,363
4 0.000013 75,442 0.000004 285,339 0.000003 340,038 0.0000030 389,297
6 0.000247 4053 0.000055 18,157 0.000032 31,528 0.0000250 40,263
8 (0.001003) (997) 0.000218 4595 0.000120 8335 0.0000880 11,323
10 (0.002391) (418) (0.000512) (1954) 0.000277 3608 0.0001990 5014
12 (0.004402) (227) (0.000935) (1070) (0.000502) (1994) 0.0003580 2793

494
 a b

c d

Fig. 7. The extent of damage in sections 1 (a, c) and 2 (b, d) of Mod. K-200-130 turbine shafting during
its service time vs. the magnitude of the rectangular (a, b) and biharmonic (c, d) surge of the reactionary
torque for various damping levels in the system: (1) d = 2%; (2) d =10%; (3) d = 20%; (4) d = 30%.

represents an unlikely loading scenario, while the surge magnitude exceeding two–three times rated torque may be
quite realistic during the turbine operation. Consequently, there is a strong probability that fatigue damage would
happen in the shafting material, a fatigue crack would be initiated and start growing with a rate depending on the
turbine operating conditions.
Figure 7 illustrates the damage in the shafting material over the specified service time, i.e., upon 2000
turbine starts, for various magnitudes of the rectangular and biharmonic surges of the reactionary torque and
vibration damping levels in the system. The extent of damage was determined by the formula

P S = 2000P av . (12)

Thus, one can assess the possible extent of fatigue damage in sections 1 and 2 of the turbine shafting for
various reactionary torque surge parameters and vibration damping levels in the system.
From the analysis of the data given in Fig. 7 it follows that in the case of the rectangular surge the limiting
state in the turbine shafting occurs at any damping level in the system and at relatively small surge magnitudes (the
last-mentioned thing applies primarily to section 2). In the case of the biharmonic surge, section 1 reaches its limiting
state only at the lowest damping level, and the fatigue damage in sections 1 and 2 takes place only at the reactionary
torque amplitudes M r > 4 M sum and M r > 3 M sum , respectively.
Figure 8 provides examples of fatigue damage calculations for the rotor material under torsional vibrations
induced when the generator is brought on-line with inaccurate synchronization (K is the number of times the
generator is brought on-line). It is evident that, in the case of the rectangular surge of a relatively small magnitude,

495
 a b
Fig. 8. The extent of damage in section 2 of Mod. K-200-130 turbine shafting during its service time
vs. the number of times the generator was brought on-line, in the case of the rectangular (a) and
biharmonic (b) surge of the reactionary torque for various damping levels in the system: (1) d = 2%;
(2) d =10%; (3) d = 20%; (4) d = 30%.

the fatigue damage is continuously accumulated in section 2 of the shafting and it reaches a critical extent at a small
damping level (Fig. 8a, curve 1). With the biharmonic surge of magnitude twice as large (M r = 6 M sum ) the critical
extent of damage cannot be reached at any damping levels studied; however, in all the cases, fatigue damage in the
material occurs at P S = 0.5 (Fig. 8b, curve 1).
Conclusions. Short-circuit fault of a generator or bringing it on-line with inaccurate synchronization
produce a short-term surge of the reactionary torque that acts from the generator end to the turbine shaft and excites
torsional vibrations of the shaft. The level of these vibrations depends on the reactionary torque surge parameters and
vibration damping level in the system. In the order of increasing hazard, the surge parameters are ranked as follows:
duration, magnitude, waveform.
With varying surge parameters, the turbine loading may follow different scenarios. When the turbine is
subjected to a sudden force action on the generator side, the shafting material experiences mainly the fatigue damage.
The extent of this damage depends on the waveform of the reactionary torque surge (from the standpoint of cyclic
damage in the rotor material, the rectangular surge is more dangerous than the biharmonic one), its magnitude (the
larger the surge magnitude, the greater the extent of fatigue damage), and the vibration damping level in the system
(the higher the damping level, the lower the torsional vibration amplitude and thus the smaller the extent of cyclic
damage in the material).
It has been demonstrated that fatigue damage may accumulate in a turbine shaft over a long period of
operation, the turbine shaft may reach its limiting state resulting in the shafting failure as was the case with Gallatin
Power Plant [1]. Meanwhile, a real assessment of fatigue damage in turbine components due to abnormal operating
conditions of a turbine-driven generator set still presents an outstanding question. It can be proved on the basis of
experimental data on the parameters of a reactionary torque surge and torsional vibrations in a turbine shafting,
which are usually obtained during vibration monitoring of a steam turbine under real operating conditions.

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496
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