The quasi-modal reduction technique and finite element model (FEM) were used to construct an analytical model for the blade-rotor coupled torsional vibration of a steam turbine generator of the Matuura Power Station. A single rotor test was executed in order to evaluate umbrella vibration characteristics. Based on the single rotor test results and the quasi-modal procedure, the total rotor system was analyzed to predict coupled torsional frequencies. Finally, field measurement of the vibration of the last stage buckets was made, which confirmed that the double synchronous resonance was 124.2 Hz, meaning that the machine can be safely operated. The measured eigen values are very close to the predicted value. The single rotor test and this analytical procedure thus proved to be a valid technique to estimate coupled torsional vibration

Isii, Kuniyoshi

Murakami, Hideaki

Okabe, Akira

Otawara, Yasuhiko

English

NASA Technical Reports Server

FIELD TELEMETRY OF BLADE-ROTOR COUPLED TORSIONAL VIBRATION 
AT MATUURA POWER STATION NO. 1 UNIT 
Kuniyoshi l s i i  and Hideaki Murakami 
Thermal Power Department 
Kyushu E lec t r i c  Power Co., Inc. 
2-1-82, Watanabedouri , Chuo-ku, Fukuoka-shi 
Fukuoka-ken, Japan, 810 
Yasuhiko Otawara and Akira Okabe 
Steam Turbine Design Section 
Thermal Power Plant Design Department 
Hi tachi  Works, Hi tachi  Ltd.  
3-1-1, Saiwai-cho, Hitachi-shi 
Ibaraki-ken, Japan, 317 
At Matuura Power Station No.1 Unit, which is the 700MW coal fired plant of Kyushu Electric Corporation that 
started commercial operation on June 30, 1989, field telemetry of the last-stage bucket of the steam turbine is 
+ executed just after the first steaming in order to verify the blade-rotor (HP, lP, 2LP's, and Generator) coupled 
torsional vibration frequency, which is predicted to be near twice the line frequency. ' The measured frequency is 
different from the double synchronous frequency,and the steam turbine's reliable operation for the negative sequence 
current is confirmed. This paper reports the analytical procedure for prediction of coupled vibration incorporated 
with a single rotor test of blade-rotor coupled vibration at the manu~facturer's factory. It also compares the predicted 
value and the measured results. 
1 INTRODUCTION 
The effect of torsional excitation in a turbine generator system from the power line is an old but still ongoing 
topic because of the growing size of electrical networks and larger unit capacity. The electric disturbances which 
cause torsional excitation of the turbine generator include line accidents such as short circuits and faulty synchroni- 
zation. Since the mid 1970's, these matters have been widely discussed. A turbine generator was generally modeled 
as a lumped-mass and spring system. Dynamic simulations of the grid system and shaft system were executed in 
order to estimate the shaft torque. Stresses in the main journal bearings and coupling were analyzed by using the 
simulation results. (Ref.1) Finally, fatigue strength was evaluated for shaft life expectancy due to the power line 
transient. 
At the same time, the technology to monitor the torsional frequency of main shaft modes has developed. 
Generally, toothed gears are machined on each rotor to detect the phase differences between rotors by using a magnet 
pick-up. The differences in shaft twisting during operation were analyzed using FFT (Fast Fourier Transform) in 
order to find natural frequencies, mode shapes, and modal damping. 
These discussions have focused on the principle lower torsional vibration modes of the rotor system. From the 
late 19703, examinations of higher torsional frequency modes coupled with long buckets of low pressure turbines 
have been reported. The so-called umbrella modes are blade-disk coupled vibration. Since all blades mounted on a 
disk vibrate in the same direction and the disk vibrates with a zero nodal diameter in the case of an umbrella mode 
of blade-disk vibration, this mode is hardly excited by 
steam flow but can be excited by torsional excitation due Disk-Blade : 
to negative sequence currents from the power line. (Figure Blade : Tangential Vibration Umbrella Axial Vibration 
1) This frequency is a higher torsional mode, and f-4 
approaches different from the mere shaft system torsional 
analysis are required in order to accurately estimate the 4;: Torsional Vibration + ,I j 
higher torsional modes, because this problem is in the 
boundary between the blade-disk coupled vibration prob- 
lem and the rotor torsional vibration problem. I t 
-: 
In this paper, the analytical method will be reviewed , I 
, I  
and estimation of input data for the calculation of a 
blade-rotor coupled system will be made by measuring the Figure 1 Blade-disk-rotor coupled vibration 
https://ntrs.nasa.gov/search.jsp?R=19920005130 2020-03-24T07:05:37+00:00Z
umbrella mode of blade vibration coupled with a double-flow low pressure rotor of a 700MW steam turbine during 
manufacture. Then field telemetry of the last-stage buckets of a 700MW steam turbine a t  the Matuura P.S. was 
executed in order to verify the predicted values. The measured results were tabulated and compared with the 
calculated value. 
2 MODELING FOR ANALYSIS 
In a coupled shaft-blade system of a turbine generator shaft set, the shaft system and blade system correspond 
to a main system and to a subsystem, respectively. The main shaft system is more flexible than this subsystem. For 
example, The first torsional frequency of the shaft system is about 7 to 20Hz compared to the lowest umbrella 
frequency of blades which is about 50 to 150Hz. Therefore, the coupled model is obtained by combining the standard 
FEM beam model of the shaft main system with additional branches of a spring-mass model derived from the blade 
subsystem. A coupled model of the entire system is thus obtained. These additonal branches are  actually simple added 
nodal points with a mass connected to the boss of the shaft 
by a spring, one for each eigen mode of the blade system. Equivalent Reduced System 
In case of long blade vibration, two kinds of umbrella (2 Blade Eigenmodes) 
modes are generally considered for double synchronous 
& I *  
resonance a s  shown as in Figure 2. The equation of motion 
can be expressed in the following formula. (Ref.2) 
x32 * 
0 0 
@ k c *  k C q l  -kcq2 1 1 = meqz kc,, 0 Figure 2 Equivalent Reduced Model (2 Blade Modes) 0 keqz ~ 3 2  
where 
me,, = atq51tM3q51 =equivalent mass of 1st mode 
me,, =agq52tM3q52 =equivalent mass of 2nd mode 
k,,, = oTm,,, =equivalent spring of 1st mode 
k,,, = o,2meq, =equivalent spring of 2nd mode 
a,  = ltM3q5, /q5,'M3q5, = 1st coupling factor 
a, = l tM34, /~ , 'M3~,  =2nd coupling factor 
O denotes super imposing operation in FEM 
Nomenclature is as follows: 
X, : Absolute disp. vector of the main system 
x, : Absolute disp. of a bonding point 
x31 * : Absolute disp. vector of 1st equivalent mass 
x3,* : Absolute disp. vector of 2nd equivalent mass 
MI : Mass matrices ~f the main system (shaft) 
m, : Mass of a bonding point 
a m  : Residual mass attached to a bonding point 
M, : Mass matrices of the blade subsystem 
4 ,  : 1st eigen umbrella mode of an uncoupled blade 
subsystem 
q5, : 2nd eigen umbrella mode of an .uncoupled blade 
subsystem 
o,  : Natural frequency of the 1st eigen mode of an 
uncoupled blade subsystem 
o, : Natural frequency of the 2nd eigen mode of an  
uncoupled blade subsystem 
3 COUPLED VIBRATION CALCULATION 
3.1 Turbine Plant Description 
The Matuura Power Station is a coal fired 700MW 
power station. Its major specifications areshown inTable 1. 
The steam turbine is a tandem-compound type with 
four cylinders (high pressure turbine, intermediate pres- 
sure turbine, two double-flow low pressure turbine, a s  
shown in Picture 1.) 
Table 1 
The last-stage buckets of the low pressure turbine Picture 1 700MW Steam Turbine View 
16 
QRlGlNAk PAGE 
BLACK AND WHITE PW0TOGWAPC.r 
700,000kW 
2,30OTon/Hr 
Coal 
200m 
246kg/cmz 
538% deg 
566°C deg 
3600rpm 
778,000kVA 
25kV 
Characteristic Rated 
Boiler 
Turbine 
Generator 
Evaporation Quantity 
Fuel 
Stack Height 
Main Steam Pressure 
Main Steam Temperature 
Reheat Steam Temperature 
Speed 
Capacity 
Voltage 
are 33. 5 inches in length, and all blades are continuously connected with loose covers and sleeves for 360 degrees. 
This construction has very good structural damping and good vibration suppression characteristics for the steam 
force. The almost 20 years experience with this bucket design has shown its very high reliability. 
3.2 Modal quantity calculation of the blade 
Due to the pretwisted blade configuration, eigen modes vibrate in tangential and axial directions of the umbrella 
figure. The two modal masses and modes can be calculated by the differential mesh model of buckets incorporating 
the cover, sleeve, and dovetail configurations. The details of this procedure were reported by Matsusita et al. (Ref. 
3)After the eigenivalue problems of the last stage (L-0) and the Iast minus one (L-1) stage are solved independentIy, the 
two eigen modes, called the tangential and axial modes, are reduced to the equivalent additional masses, as shown 
in Figure 3. 
Concerning the L-0 blade, the equivalent masses of the tangential and axial modes comprise 46.1% and 46.3% 
of the polar moment of the total inertia of the blades, respectively. The residual polar moment of inertia, 7.6%, is 
attached to the boss of the last stage (L-0). In the same way, the L-1 stage is reduced, as shown in Figure 4. 
3.3 Single LP rotor test 
In order to calculate the coupled torsional frequency, it is necessary to first determine the uncoupled umbrella 
frequency of the blades. In the factory balancing pit, the LP rotor with blade vibration measuring equipment was 
excited by a torsional shaker during operation. Figure 5 shows the eigen frequency of the coupled umbrella mode of 
last-stage buckets near 120HZ. Since the measured result is a coupled frequency, the uncoupled frequency can be 
determined to match the measured results with the calcu- 
lated result. Table 2 compares the calculated uncoupled 
Elgen mode umbrella frequency and the corrected uncoupled umbrella 
, frequency. Table 3 shows the umbrella frequency coupled 
BLADE with the single LP rotor and the measured coupled fre- 
L-0 quency. Although the L-0 tangential umbrella mode has 
only one mode, the coupled mode with the single rotor 
splits into two modes. 
Figure 6 shows the mode configuration of a single rotor 
T s~de 
W 
V) 
Z 
2 
V) W
[L 
w 
BLADE n 4 
Calculated frequency 
Corrected frequency 
- Matuura P S NO.l Un~t ALP Rotor 
- 
- 
- 
107 4Hz 
- \r 
118.37Hz 
116.40Hz 
L-1 m 
0 
-I - 
. 
Elgen mode 
Figure 3 Coupled Model of LP turbine 
90 115 140 
FREQUENCY (Hz) 
Figure 5 Single rotor umbrella frequency 
Table 2 Uncoupled umbrella frequency near 120Hz 
(L-0 Tangential mode) 
Table 3 Coupled umbrella frequency near 120Hz 
Calculated frequency * 
107 40Hz 
121.57Hz 
Measured frequency 
107.40Hz 
121.50Hz 
* )  Calculat~on IS based on the corrected uncoupled fre- 
Figure 4 Equivalent Mass Distribution quency (116.4Hz) 
coupled with last-stage blades near 120Hz. In this figure, split modes correspond with the opposite twisting modes 
of the LP rotor and the blades, where both the turbine (T) and generator (G) side blades twist in the same direction. 
During the single rotor test, the resonance stress was measured by exciting the torsional exciter. Picture 2 shows the 
torsional exciter and how it was connected to  the LP rotor. Picture 3 shows the LP rotor in the test pit. The measured 
blade stress is about Ikg/mm2 per 5% negative sequence equivalent torque. This means that the stress due to 
torsional excitation is sufficiently lower than the material fatigue strength. 
3.4 Coupled frequency analysis of the rotor train 
Based on the single rotor test, the blade-rotor coupled torsional frequency of all rotors connected in a system 
was analyzed. The shaft system can be modeled by FEM and the blade subsystem can be added using the single rotor 
test result. 
Figure 7 shows the calculated modes and frequencies 
of blade-rotor coupled vibration near 120Hz. These results 
are very similar to the single rotor test, because the modes 
are chiefly related to the L-0 blades and LP rotor stiffness. 
The above results also show that there exist two 
similar modes for each coupled-split result, because there 
exists two LP rotors (ALP and BLP). Since the 120Hz 
nearest coupled mode (Mode No.8) is the ALP and L-0 
coupled frequency, it was decided to execute a single rotor 
test for the ALP rotor. 
4 FIELD MEASUREMENT OF COUPLED 
VIBRATION 
4.1 Measuring method 
In order to verify the coupled frequency under field 
CALC. FREQ. 107.40 (Hz) 
0.0 
CALC. FREQ. 121.57 (Hz) 
. . 
Picture 3 Single LP rotor test view 
0.0 
IMODE NO.] 61 CALC. FREQ. 107.81 (Hz) 
o.o+a- 
Figure 6 Mode configuration 
W 
-I <q I MODE NO. 1 7 1 CALC. FREQ. 108.94 (Hz) 
Picture 2 Torsional Exciter Figure 7 Blade-Shaft Coupled Torsional Modes 
- 
5 
a IMODE NO.181 CALC. FREQ. 121.67 (Hz) 
e 
ORIGINAL PAGE 
@LACK AND WHITE PHOTOGRAPH 
0.0 
2 
I- 
t a a 
5 
W 
a  MODE ~0 .191  CALC. FREQ. 121.97 (Hz) 
0.0 
conditions, it was decided to measure blade-rotor coupled vibration. Since the mode near the double synchronous 
frequency is the L-0 blade umbrella mode coupled with the shaft system, strain gauges to measure vibration were 
attached to the L-0 blades of both a ALP rotor and a BLP rotor. The output of the strain gauges was transmitted 
by a frequency modulation (FM) telemetry system to a receiving antenna. Figure 8 depicts the telemetry system. 
Picture 4 shows a transmitter and a receiving antenna under preparation. The transmitter and batteries were set in 
a balance weight slot of the last stage disk. The receiving antenna was set in a bearing cone of the LP casing. 
The test was executed just after initial steaming, considering strain gauge life under a steam flow. Under a no 
load condition, the turbine was slowly sped up and down near 6OHz and the shaft system was excited from a 
generator by a one phase grounding circuit at the high voltage side of the main transformer. Figure 9 shows the 
excitation circuit. The breaker between the main tranformer and the line was open. The measured signal was 
recorded and analyzed by FFT. 
4.2 Field test results 
Field test results are shown in Figures 10 and 11 for the ALP rotor and the BLP rotor, respectively. The 
resonance point with double synchronous frequency nearest to 120Hz is 124.2Hz in the ALP rotor. This frequency is 
far from twice the expected line frequency variation of 58.5-60.5Hz (117Hz-121Hz). 
The eigen frequencies of coupled umbrella modes are tabulated in Table 4. These measured values are also 
compared with the calculated values. Since the calculated values were incorporated in the single rotor test of the ALP 
rotor, the differences between the measured values and the analyzed results are smaller for modes dominated by the 
ALP rotor than those of the BLP rotor. From these results and the single rotor test results, it is necessary to confirm 
eiver Antenna 
El I Gauge I Transmitter Antenna Receiver Antenna 
, I".'. pq 
Recorder Analyzer 
LlNE 
4 I - 
Rotor I Test data acquisition Figure 9 Excitation Circuit 
facillty 
Figure 8 Telemetry System 
Picture 4 Telemetry Equipment 
I COUPLED FREOUENCY ! MODE 8 
Eigen 
Value DOUBLE SYNCHRONOUS 
RESONANCE 
DOUBLE / I SYNCHRONOUS 
/ 1 LlNE 
' (ROTOR SPEED X 2) i 
COUPLED FREQUENCY I MqDE 6 
107.3Hz Xn value 
60 65 
ROTOR SPEED (Hz) 
Figure 10 ALP rotor test results 
the umbrella frequency and equivalent spring of blades in order to get better accuracy. The input data for blades are 
one set, but four coupled modes are certain to be very accurate. This means that this analytical procedure (quasi- 
modal reduction technique? can be applied to estimate the shaft coupled umbrella frequency of an actual turbine 
shaft. 
COUPLED FREQUENCY Table 4 Eigen frequencies of test results 
DOUBLE SYNCHRONOUS 
RESONANCE 
- z 120 
> 
0 
z W 
3 
S 
CK u LED FREQUENCY 4.3 Evaluation at a rated load 
The test was executed under a no load condition. 
Table 5 shows a temperature comparison between the test 
condition and a rated load condition. The changes in 
rigidity of the rotor due to this temperature change effect 
are about 3% for a HP turbine, 4.5% for an IP turbine, and 
60 65 1.5% for a LP turbine. Since the coupled umbrella modes 
ROTOR SPEED (HZ) are mainly dominated by the L-0 buckets and the LP 
Figure 11 BLP rotor test results turbine, the change in coupled frequencies is small, as  
shown in Table 6. Especially, the coupled modes near 
120Hz do not change, because these two modes are basically the blade umbrella mode. 
Table 5 Temperature condition Table 6 Frequency change under a rated load 
Mode 
ALP 
BLP 
ALP 
BLP 
HP TB. Exhaust 218.6"C deg 296.9"C deg 
IP TB. Inlet 390.5"C deg 566.0"C deg 
IP TB. Exhaust 218.8'C deg 337.8'C deg 
LP TB. Exhaust 35.1"C deg 33.0"C deg 
5 CONCLUSION 
Difference 
Out-of-phase 
0.51Hz 
0.64Hz 
In-phase 
0.13Hz 
1.13Hz 
Measured 
107.3Hz 
108.3H.z 
121.8Hz 
123.1Hz 
Mode 
Out-of-phase 
ALP 
BLP 
In-phase 
ALP 
BLP 
The quasi-modal reduction technique and FEM model were used to construct an analytical model for the 
blade-rotor coupled torsional vibration of a steam turbine generator of the Matuura Power Station. A single rotor 
test was executed in order to evaluate umbrella vibration characteristics. Based on the single rotor test results and 
the quasi-modal procedure, the total rotor system was analyzed to predict coupled torsional frequencies. Finally, field 
measurement of the vibration of the last-stage buckets was made which confirmed that the double synchronous 
resonance is 124.2Hz, meaning that the machine can be safely operated. The measured eigen values are very close 
to the predicted value. The single rotor test and this analytical procedure thus proved to be a valid technique to 
estimate coupled torsional vibration. 
Calculated 
107.81Hz 
108.94Hz 
121.67Hz 
121.97Hz 
6 ACKNOWLEDGEMENT 
Measured under 
no load 
107.3Hz 
108.3Hz 
121.8Hz 
123.1Hz 
The authors would like to express their thanks to the engineers of Matuura Power Station of Kyushu Electric 
Power C., Inc., and field test crews of Hitachi Ltd.. 
Expected change under 
rated condition 
-0.2Hz 
-0.1Hz 
O.OHz 
O.OHz 
7 REFERENCES 
[l]  Watanabe, T., et  al. : Influence of High-speed Reclosing on Turbine Generators and the Shaft System, Hitachi 
Review, Vo1.27, No.1, PP.33-38 (1978) 
[2] Okabe, A., et  al. : COUPLED VIBRATION ANALYSIS: TORSIONAL VIBRATION O F  TURBINE-GENERATOR- 
BLADE COUPLED SYSTEM, T H E  1989 ASME DESIGN TECHNICAL CONFERENCES-12th BIENNIAL CONFER- 
ENCE ON MECHANICAL VIBRATION AND NOISE, Vol. 18-1, PP.135-140 (1989) 
[3] Matsushita, O., et a1 : Torsional Vibration Analysis of Turbine-Generator-Blade Coupled System, Proc. Am. 
Power Conf. Vol 41 (1989) (to be published) 


Field Telemetry of Blade-rotor Coupled Torsional Vibration at Matuura Power Station Number 1 Unit

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