SIngle Blade Broken _ Talcher

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turbine, and the diametral modes number (nD), see

[3] and [4]. In the high cycle fatigue failureanalysis, the vibratory stress due to the flow-

induced vibrations on the bladed disk is determined

in order to compare with the fatigue limit of the

material, [5], [6] and [7]. In this paper, oneproposes a numerical/experimental procedure to

analyse the low cycle fatigue problem.The computational mechanics procedure used

in this work consisted first in digitize a single blade

for obtaining a file with the geometric dimensions

and, secondly, to build a solid CAD model of the

blade. The CAD model was verified by comparingthe calculated and measured blade weights. This

model was analyzed using a finite element code in

order to obtain the natural frequencies and the

associated vibration modes of a single blade in a

free-free condition. A modal testing was also

performed and a numerical/experimentalcomparison was used to adjust the material

properties and the geometric dimensions.

In addition, a five blades grouped was

modeled considering the tie-wire and the shroudas

the elements used to connect the blades. In thiscase, another modal testing was performed and the

numerical/experimental comparison was made to

adjust the material properties introduced in the

computational model with the objective of

simulating the contact between the blade and the

tie-wire and the blades and the shroud. As shownin

several papers and reports, these elements can playa very important role in this type of analysis, [8]. A

combination of modal testing and finite element

analysis are the current procedure to accurately

predict the dynamic response of bladed disks in

turbo-machinery.

Finally, a fifth stage of the low-pressure

turbine model was built to solve the

eigenvalues/eigenvectors problem and the low

fatigue problem was investigated.

II. Modal analysis on a single blade

The purpose of this analysis is to adjust the

material properties and the geometric dimensions of

the blade in the numerical model, in order to fit the

modal testing measurements.

Figure 3 shows the blade configuration for the

modal testing in a free-free condition. The

instruments used for this purpose were a force

transducer B&K 8200, a shock hammer (coupled to

the force transducer), an accelerometer B&K 4344

and the LMS SCADAS III with a Fourier analysis

software. For the mode identification, accelerationswere obtained at 105 points on the blade.

Fig. 3. Experimental set for the modal analysis of a single

blade in a free-free condition

Figure 4 shows the first mode of vibration and

figure 5 shows the second mode of vibration of the

single blade in a free-free condition. In the

numerical model the medium size of the elements is

10 mm and the total number of elements is 14 313.

(a)

(b)

Fig. 4. First mode of the single blade: (a) numerical and

(b) experimental


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(a)

(b)Fig. 5. Second mode of the single blade: (a) numerical

and (b) experimental

TABLE I presents the numerical/experimental

results of the first seven modes of the modal

analysis of a single blade in a free-free condition.

Mode Numerical

(Hz)

Experimental

(Hz)

Error

(%)

1 162,8 166,9 -2,5

2 442,3 451,7 -2,8

3 524,6 547,2 -4,1

4 738,7 748,9 -1,4

5 1.112,0 1.077,2 3,2

6 1.212,0 1.166,1 3,9

7 1.448,0 1.457,7 -0,7

TABLE I Numerical/experimental results on a

single blade

III. Modal analysis on a five blades grouped

A tie-wire and a shroud, as seen in figure 6,

connect groups of four and five blades. The contact

problem between the blade and the tie-wire and the

blade and the shroud is analyzed by using a soft

material between them. So, the purpose of thisanalysis is to adjust the material properties,

introduced in these regions in the numerical model,

so that the numerical solution fits the experimental

results.

Fig. 6. Four and five bladed groups

The experimental set for the modal testing of a

five blades grouped is presented in figure 7. The

instruments used for this purpose were the same

used in the experimental setup in the modal testing

of the single blade test.

Fig. 7. Experimental set for the modal analysis of a five

blades grouped in a clamped-free condition

Figure 8 shows the first mode of the 5 blades

grouped in bending and figure 9 presents the

second mode of the 5 blades grouped in bending. In

the numerical model the medium size of the

elements is 7 mm on the blades, 4 mm on the

shroud, 3 mm on the tie-wire and 2 mm on the

material interface. The total number of elements

used in the model is 98 184.

shroud

tie-wire

root

bladeblade


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Fig. 8. First mode of the five blades grouped in bending

Fig. 9. Second mode of the five blades grouped inbending

TABLE II presents the numerical/experimental

results of the first eight modes of the modal

analysis of a five blades grouped, in a clamped-freecondition. Mode types are bending (B) and/or

torsion (T).

Numerical Experimental

Freq. (hz) Mode Freq. (hz) Mode Mode type

107,8 1 99,4 1 B

- - 142,3 2 B/T

172,7 2 148,5 3 B/T

213,6 3 210,7 4 B/T

- - 296,2 5 B/T

395,2 4 336,4 6 B/T

411,0 5 407,6 7 B/T

499,1 6 479,4 8 B/T

TABLE II. Numerical/experimental results on a fiveblades grouped

IV. Modal analysis of the fifth stage

The fifth stage of the low pressure turbine was

modeled in accordance with the results obtained in

the modal analysis on a single blade and on a fiveblades grouped. It is composed by 133 blades

divided in groups of four and five blades as shown

in figure 10 (five blades group in gray and four

blades group in black).

Fig. 10. Fifth stage model of the low pressure turbine

As found by Chyou in [3], one observes two

modal groups with a large modal density. In the

first modal group, blades are associated with first

mode of the blades grouped in bending (see figure8) and in the second modal group, blades are

associated with the second mode of the blades

group in bending (see figure 9).

TABLE III presents the first diametral modes

in the first group and TABLE IV presents the firstdiametral modes in the second group of the fifth

stage of the turbine turning at its operation speed of

3600 rpm.

The circunferencial modes are not excited by

the force acting on the blades due to steam flow, so

they are ignored in this analysis.

#1 1D 152,70 hz #2 1D 152,8 hz


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#3 2D 153,2 hz #4 2D 153,3 hz

#6 3D 154,1 hz #7 3D 154,4 hz

TABLE III. Diametral modes in the first modal group

#31 1D 184,4 hz #32 1D 184,4 hz

#33 2D 185,1 hz #34 2D 185,4 hz

#35 3D 185,9 hz #36 3D 186,2 hz

TABLE IV. Diametral modes in the second modal group

TABLE V shows the vibrations modes which

can cause the resonance of the fifth stage of theturbine at 3600 rpm due to the harmonics of the

operation speed and due to the diametral modenumber (nD).

Operation

speed(rpm)

Operation

speed (hz)

Harmonic/

Diametral modenumber (nD)

Frequency

(hz)

3600 60 1 60

3600 60 2 120

3600 60 3 180

TABLE V. Diametral modes in the second modal group

In observation of TABLE III, it is possible to

note that the frequencies in the first mode group are

approximately 150 hz, far from the second and the

third harmonics of the operation speed.

Nevertheless, in TABLE IV, it is observed that the

frequencies in the second mode group are

approximately 180 hz, near the third harmonic of

the operation speed.The two 3D diametral modes in the second

mode group 185,9 hz and 186,2 hz have a

deviation of 3,3% and 3,4% from the third

harmonic of the operation speed of the turbine,respectively. Orsagh and Roemer in [4] recommend

a value of 3% far from one of the harmonics to

assure an operation without resonance. Based on

this results, it is possible to conclude that in the

fifth stage of the low-pressure turbine there will be

no low cycle fatigue problem.


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V. Conclusions

In this work, the low cycle fatigue problem was

investigated on a fifth stage of the low-pressure

turbine in a thermoelectric power plant. Theprocedure for this study consisted initially in the

fitting of the computational model of a single blade

and a five blades grouped with experimental

measurements. Further, a computational model of

the complete fifth stage bladed disk was developed

and a modal analysis was performed. By analyzingthe harmonics of the operation speed and the

diametral modes of the bladed disk, it was

concluded that no resonance had occurred, so the

low cycle fatigue is not the root-cause of the

damage on the blades. This fact indicates that the

high cycle fatigue on the blades in the fifth stage of

the low-pressure turbine must be investigated.

References

[1] Dewey, R. P. and Rieger, N. F., 1985, Survey ofBlade Failures in Turbine-Generator Units.

Proceedings: Steam Turbine Blade Reliability

Seminar and Workshop, ed. By R. G. Brown and J.

F. Quilliam, EPRI CS-4001, pp. 2-61 ~ 2-78.

[2] Ortolano, R. J., 1991, Recent Case Histories in theInspection, Modification, and Repair of Steam

Turbine Blading. Proceedings, International Joint

Power Generation Conference, ASME PWR-Vol.13,

pp. 147-154.[3] Chyou, Y., 2000, Root-Cause Investigation on Blade

Failures in Steam Turbines From an Aspect of

Computational Mechanics. Proceedings of 2000

International Joint Power Generation Conference,

Miami, USA.

[4] Orsagh, R. F. and Roemer, M. J., 1994, Examinationof Successful Modal Analysis Techniques Used for

Bladed-Disk Assemblies. Technical Report, Impact

Technologies, New York.

[5] Fleeter, S., Zhou, C., Houstis, E. and Rice, J., 1998,Fatigue Life Prediction of Turbomachine Blading.

Technical Report, Lawrence Livermore National

Laboratory.

[6] Boven, R. and Lam, T. Management Strategy andTechnical Plan Used to Select, Qualify and Procure a

New 20.9 L-1 Stage Steam Turbine Bucket.

Proceedings of 2000 International Joint Power

Generation Conference, Miami Beach, Florida, July

23-26, 2000.

[7] Rao, J. S., Turbine Blade Life Estimation. AlphaScience International Ltd., 2000.

[8] Shiga, M., Vibration Characteristics of GroupedSteam Turbine Blades. JSME International Journal,

pp. 592-596, Series III, Vol. 32, No.4, 1989.

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