ML20126M438

Torsiograph Tests of Emergency Diesel Generators,Divs 1 & 2,at Perry Nuclear Power Plant-Unit 1

ML20126M438
Person / Time
Site:	Perry
Issue date:	05/31/1985
From:	FAILURE ANALYSIS ASSOCIATES, INC.
To:
Shared Package
ML20126M432	List: ML20126M427 ML20126M438 ML20126M450
References
FAAA-85-4-1, NUDOCS 8506200333
Download: ML20126M438 (29)

Text

FaAA-85-4-1 QRCEI TORSIOGRAPH TESTS OF EERGENCY DIESEL GENERATORS, DIVISIONS 1 AND 2.,

AT PERRY NUCLEAR POER PLANT--UNIT 1 Prepared by Failure Analysis Associates l

l Prepared for TDI Diesel Generator Owners' Group l

l May 1985 l

l DR K

E

TABLE OF CONTENTS Page

1.0 INTRODUCTION

1 2.0 INSTRUMENTATION........................................................

1 3.0 PR0CEDURE..............................................................

1 3.1 Cali brati on and Inst rumentati on Run-i n............................ 2 3.2 Va ri abl e Speed, 0% Load Tests..................................... 3 3.3 Variable Load, Operating Speed Tests.............................. 3 3.4 St a rt u p / Coa st d own Tes t s........................................... 3 3.5 Post Test Data Veri ficat on and Cali brati on....................... 3 4.0 RESULTS................................................................

4 4.1 C a l i b rat i o n Dat a.................................................. 4 4.2 Va ri abl e S peed R esu l t s............................................ 6 4.3 Va ri ab l e Loa d R esu l t s............................................. 7 4.4 St a rt u p /Co a s t d own Res u l t s......................................... 8

5.0 CONCLUSION

S............................................................

9 REFERENCES..................................................................

9

1.0 INTRODUCTION

The purpose of the torsiograph test of the emergency diesel generator was to measure the angular displacements of the forward end of the crank-shaft.

These displacements were then used in conjunction with a dynamic torsional analysis of the crankshaft to assess the maximum stresses in the crankshaft.

Torsiograph tests were performed on diesel generators Unit 1 Division 1 (U101) and Unit 1 Division 2 (U1D2) at Perry Nuclear Power Plant.

Data were obtained during both steady-state and transient (startup and coast-down operation) conditions.

2.0 INSTRUMENTATION The instrumentation generally consisted of an tiBM Torsiograph, Signal Conditioner, Data Tape Recorder, Frequency Analyzer, Oscilloscope, Multimeter, and assorted interconnecting cables.

The specific instrumentation used is shown in Table 2.1.

3.0 PROCEDURE The torsiograph, which was attached to the front end of the crankshaft through an adapter plate supplied by the Perry plant, was used to measure angular displacements of the crankshaft relative to its mean rotational speed. The angular displacement signal from the signal conditioner was recor-ded on magnetic tape for further analysis to determine angular displacement components for each order.

Tests were conducted at several speeds under no-(

load conditions, and at several loads at operating speed.

In addition, fast starts were performed with predetermined crankshaft positions.

The torsio-l graph data was recorded continuously from startup through coastdown.

The spectrum analyzer was used to verify data integrity by determining harmonic components for each test condition.

The test was carried out for each diesel engine in the following five stages:

1

1.

Calibration and instrumentation run-in.

2.

Variable speed tests at 0% load.

3.

Variable load tests at rated speed.

4.

Startup and coastdown tests.

5.

Post test calibration.

3.1 Calibration and Instrumentation Run-in The torsiograph was mounted on the front end of the crankshaft using a rigid adapter plate.

The torsiograph was connected to the signal conditioner and the signal conditioner to the instrumentation recorder with the designated cables.

The signal conditioner was also connected to the spectrum analyzer and oscilloscope to monitor the torsiograph signals.

The following steps were completed to calibrate the instrumentation before and after testing:

1.

The recording equipment and cabling was calibrated by introducing a known signal into the signal conditioner connection and recording the signal.

2.

The calibration signal was verified by playing back the calibration recording.

3.

A field calibration of the torsiograph was completed following the manufacturer's instructions [1].

The field calibration signal was recorded.

4.

The field calibration signal was played back for verification.

After the calibration procedure was completed, the diesel engine was operated at no load for approximate'iy two to ten minutes while data was recor-ded.

The engine was then shut down while the recorded data was examined to verify the instrumentation and recording system operation.

The test documentation information in Table 3.1 was logged.

2

3.2 Variable Speed 0% Load Tests The engine was operated for two to five minutes at rated speed and no load. The speed was then adjusted using the mechanical governor to operate at speeds between 400 and 470 rpm. The engine was operated at each speed for two to ten minutes while the torsiograph output was recorded.

The output speeds and tape footage were recorded (Table 3.2).

3.3 Variable Load, Operating Speed Tests The engine was brought to operating speed.

The load was adjusted successively to operate at the following load conditions for five to ten minutes:

25%, 50%, 75%, 100%.

The load, current, speed, and tape footage were recorded (Table 3.3).

3.4 Startup and Coastdown Tests Transient data was recorded for each engine at four different startup positions and the four coastdowns from 450 rpm.

The startup and coastdown conditions monitored are the normal procedural fast starts and coastdowns in use at Perry.

The fast starts were performed with predetermined initial crankshaft positions at 180 degree intervals of crankshaft rotation to cover the full 720 degree firing cycle.

The positions are described in Table 3-4.

Once at the operating speed of 450 rpm the engine was allowed to coastdown.

No load was applied to the engine during this test.

The tape footage and run I.D.'s were recorded (Table 3.5).

3.5 Post Test Data Verification and Calibration Selected data records were played back to verify proper measurement and recording.

The calibration procedure outlined above was repeated and the signals recorded.

3

4.0 RESULTS

. 4.1 Calibration Data The pre and post test static calibration data are shown in Tables 4.1 and 4.2.

The torsiograph sensitivity was calculated as follows:

Teac Amp. Range mV/V)

Output,V)

Setu ng, 1W Torsiograph Sensitivity,

=

degree (Input, degrees)(

Tape Deck

)

Gain, V

/Vin The multiplication factors used in data reduction were calculated as follows:

Vibration (TapeDeck*)[ Amp. Range mV/V)

Ogtput,Vpk

Setting, 10Vpk Amplitude

=

Torstograph Tape Deck (degrees-pk) gyjy (Sensitivity, degree)(Gain,V

/ Vin) out mV/V where Amp. Range Setting = 20 10 Vpk Tape Deck Range Setting = 0.1 Vout / Vin Ch. 1 0.2 V

/ Vin Ch. 2 out Unit 1 - Division 1 From Table 4.1 for Channel 1, t

Torsiograph Sensitivity = (I'424)

= 4.747 i Oi14%

(.1) (6) degree For out put in VRMS (as in spectral plots) multiply by /2.

4

and for Channel 2, Torsiograph Sensitivity = II*

= 4.753 1 0.14%

d e

The sensitivities for the post test calibration were found to be 4.750 and mV/V 4.730 f r channels 1 and 2 respectively.

dem Multiplication factors for time domain response:

Ch 1.

Input, degrees-pk = (Output, Vpk)

(4.213 degrees-pk)

Ch 2.

Input, degrees-pk = (Output, Vpk)

(2.104 degrees-pk) and for frequency domain response:

Ch 1.

Input, degrees-pk = (Output, VRMS) ( 5.958 degrees-pk)

RMS Ch 2.

Input, degrees-pk = (Output, VRMS)

(2.975 d*9"*es-pk) y RMS Unit 1 - Division 2 From Table 4.1 for Channel 1, TorsiographSensitivity=([0

= 4.750 0.2%

dg e and for Channel 2, 5

Torsiograph Sensitivity = II*

= 4.730 ee ! 0.2%

d The sensitivities for the post test calibration were found to be 4.747 and 4.727 for channels 1 and 2 respectively.

d ree Multiplication factors for time domain response:

Ch 1.

Input, degrees-pk = (Output, Vpk) (4.211 degrees-pk)

Ch 2.

Input, degrees-pk = (Output, Vpk) (2.114 degres-pk) and for frequency domain response:

Ch 1.

Input, degrees-pk = (Output, VRMS) (5.955 WD RMS Ch 2.

Input, degrees-pk = (Output, VRMS) (2.990 degrees-pk)

RMS 4.2 Variable Speed Results The variable speed test was performed to determine the frequency of the first mode of the crankshaft torsional system.

The results of this test are shown in Table 4.3.

Figures 4.1 and 4.2 show that the 4th order critical speed is reached at about 436 rpm for each crankshaft.

Thus, the first natural frequency is 29.1 Hz.

This is in good agreement with the Holzer calculation of 29.2 Hz made by Delaval [2].

6

The amplitude of nominal shear stress may be estimated from the ampli-tude of free-end vibration by assuming that the shaft is vibrating in its first mode.

Under these conditions, the nominal shear stress in the number 8 crankpin journal and the number 9 main journal is 8596 psi per degree of free-end vibration [2]. Thus, the maximum amplitude of nominal shear stress during the variable speed test was 2923 psi for each crankshaft.

4.3 Variable Load Results The variable load test at rated speed was performed to determine the

~

amplitude of vibration and estimate the nominal shear stress as a function of load.

The results of this test are shown in Table 4.4.

Figures 4.3 and 4.4 show that the amplitude of vibration increases with load to a maximum of 0.54 degrees at 7000 kW.

The figures also show the response of the other major orders.

(

The amplitude of nominal Ghear stress may be estimated from the ampli-tude of f ree-end vibration by assuming that the shaft is vibrating in its first mode.

Under these conditions, the nominal shear stress in the number 8 crankpin journal and the number 9 main journal is 8596 psi per degree of free-end vibration [2].

Thus, the amplitude of nominal shear stress at full load is as follows:

Diesel Generator Nominal Torsional Stress at Full Load (7000 kW)

Single Order Combined Order Unit 1 - Division 1

?891 psi 4659 psi Unit 1 - Division 2 2020 psi 4642 psi DEMA [3] allowable S000 psi 7000 psi 7

v h..

4.4 Startup/Coastdown Results Coastdown For the coastdowns monitored, the response of the crankshaft was found to be repeatable in both shape and magnitude. The maximum peak-to-peak ampli-tude recorded was found to be 0.96 degrees and occurs at the 8th order critical speed of approximately 218 rpm.

The approximate length for a coastdown is 80 seconds.

An analytical model to predict the stress as a function of time during coastdown at each shaft section as well as the free-end rotational vibration was performed for the crankshaft at Perry. The analysis was performed using a cold compression curve with a peak pressure of 450 psi.

It was found that with a damping of 1.5 percent of critical modal damping in each mode, the maximum peak to peak response was 0.93 degrees which is in good agreement with that measured in the torsiograph test.

The maximum amplitude of nominal stress was found to be 3970 psi and occurred between cylinders No. 7 and No. 8 based on the analysis.

A comparison of the predicted and measured free-end amplitude time histories is shown in Figure 4-5.

The good comparison of dynamic features is readily apparent in these plots. The time occurrence of some features are shifted due to the assumed linear change of angular velocity with time in the analysis.

Startup The maximum peak-to-peak response for each of the four conditions tested in each engine is shown in Table 4.5 The mean maximum peak-to-peak response is 1.89 degrees for Unit 1 Division 1 and 1.84 degrees for Unit 1 Division 2.

For each engine the maximum peak-to-peak response for each condition tested varied within 9% of the mean maximum peak-to-peak response (except for the one start that had a poor quality signal). The duration of a fast start was found to be 6 seconds.

8

The analytical model was used to determine the stresses in the crank-shaft during startup for each of the four conditions tested. The analysis was performed using pressure-time data recorded during a fast start at another plant (Ref. (4)], and using damping of 2.5 percent of critical modal damping

~"

in each mode.

The analysis confirms that the effect of initial crankshaft position on the maximum peak-to-peak response is small.

The analysis indicates that the maximum amplitude of nominal stress for a typical fast start is 7650 psi and occurs between cylinders No. 7 and No.

8.

A comparison of the predicted and measured free-end amplitude time histories for a typical fast-start is shown in Figure 4-6.

l

5.0 CONCLUSION

S The following conclusions are made:

the first natural frequency of the torsional system for each e

engine was found to be approximately 29.1 Hz, and is in good agreement with Delaval Holzer calculations (2]. Thus the 4th order critical speed is 436 rpm.

for both Unit I diesel generators, the stresses in the crank-e shaft are below DEMA's [3] allowables for both single order and combined order response at full load (7000 kW) for steady-state operation, e

The coastdown transient response is repeatable and has a maximum peak-to-peak amplitude of approximately 0.96 degrees, which produces a maximum amplitude of nominal stress of 3970 psi.

A typical startup transient response produces a maximum peak-e to-peak response of 1.86 degrees.

Such a startup has a maximum amplitude of nominal stress of 7650 psi. This stress amplitude exists for only a few cycles on each startup.

e The results of the torsiograph test indicate that the crankshafts are adequate for their intended service at Perry nuclear Power Plant.

References 1.

HBM Operating Manual for Rotary Vibration Transducer, 160.03-1.0-1.0e.

9 l

2.

Yang, Roland, " Torsional and Lateral Critical Speed, Engine Numbers 75051/54 Delaval-Enterprise Engine Model DSRV-16-4, 7000 kW/9734 BHP at 450 RPM for Cleveland Electric Illuminating Co.,"

Delaval Engine &

Compressor Division, Oakland, California.

3.

Standard Practices for low and Medium Speed Stationary Diesel and Gas Engines, Diesel Engine Manufacturers Association, 6th ed.,1972, e

4.

" Evaluation of Transient Conditions on Emergency Diesel Generator Crankshafts at San Onofre Nuclear Generating Station Unit 1," FaAA 84-12-14, Revision 1.0, April 1985.

6 e

6 6

e 10

Table 2.1: EQUIPMENT LIST Equipment Equipment Model Serial FaAA l

Manufacturer Description No.

No.

ID No.

HBM Rotary Vibration BD 5 701 n/a Transducer HBM SKHz Carrier KWS 7073 72984 n/a Frequency Amp.

Teac Cassette Data MR-30 116404 00138 Recorder B&K Precision Sweep / Function 3020 89-11576 00119 Generator B&K Precision Dual Trace 40MHz 1540P 11400731 00118 Oscilloscope Hewlett Packard Dual Channel 3582A LO39823 FFT Analyzer HBM cable (connect n/a n/a n/a transducer to amplifier) n/a cable (connect n/a n/a n/a amplifier to tape deck) n/a cable (connect n/a n/a n/a tape deck monitor to Spectrum analyzer or oscilloscope)

Fluke Digital Multimeter 8060A 8396137 00128 Hewlett Packard Dual Channel 5423A 2040A00345 00124 FFT Analyzer Hewlett Packard Plotter 7225B 1206A01534 00122 11

l Table 3.1: TORSIOGRAPH TEST DOCUMENTATION Job Name:

Perry Torsiograph Test Date:

Job Number:

QRCEI Div. 1:

3/27/85 Location:

Perry Nuclear Power Plant Div. 2:

3/28/85 Cleveland Electric Illuminating Co.

Engine

Description:

Unit 1, Div. 1 Unit 1, Civ. 2 Transamerica Delaval Inc.

Transamerica Delaval Inc.

DSRV-16-4 DSRV-16-4 Serial No. 75051 Serial No. 75052 Notes:

Test Personnel:

Steve Riess FaAA Paul Johnston FaAA Tony Pusateri CEI Mark Hickman CEI 12

\\

Table 3.2: TORSIOGRAPH VARIABLE SPEED TEST Test Personnel:

Steve Riess, FaAA Date:

~~)N Paul Johnston, Fa' Div. 1:

3/27/85 Tony Pusateri, C' Div. 2:

3/28/85 Mark Hickman, Ci Unit 1 - Division 1 f

g Tape I.D.

itage Test Speed (RPM)

~~)

.44 400

-161 410 a-175 420

<9-190 430 k

QRCEl-1

.93-204 435 TORSIOGRAPH 207-216 440 TEST 222-230 450 242-250 460 262-271 470 278-289 425 Unit 1 - Division 2 Tape I.D.

Tape Footage Tape Speed (RPM)

ORCEI-2 177-186 400 TORSIOGRAPH 192-200 410 TEST 204-210 420 215-233 425 226-232 430 236-242 435 245-253 440 255-265 445 268-275 450 278-287 460 304-312 470 13 w.._.

<r Table 3.3: TORSIOGRAPH VARIABLE LOAD TEST Test Personnel:

Steve Riess, FaAA Date:

Paul Johnston, FaAA Div. 1:

3/27/85 Tony Pusateri, CEI Div. 2:

3/28/85 Mark Hickman, CEI Test Speed:

450 rpm Unit 1 - Division 1 Tape I.D.

Tape Footage Load (kW)

ORCEI-1 410-418 1750 (25%)

'd Torsiograph Test 427-435 3500 (50%)

s 442-448 5250 (75%)

460-510 7000 (100%)

Unit 1 - Division 2 Tape I.D.

Tape Footage load (kW)

QRCEI-2 361-369 1750 (25%)

l Torsiograph Test 379-387 3500 (50%)

397-405 5250 (75%)

423-432 7000 (100%)

14 I

I 1

P Table 3-4: PREDETERMINED INITIAL CRANKSHAFT POSITIONS FOR STARTUP TESTS Crankshaft Rotation Run I.D.

w.r.t.1 LB TDC Firing (degrees) 1 LB TDC firing 0*

7 LB TDC firing 180 8 LB TDC firing 360*

l 2 LB TDC firing 540*

i l

(

15

i l

l Table 3.5: STARTUP AW COASTDOW TESTS Test Personnel:

Steve Riess, FaAA Date:

Paul Johnston, FaAA Div. 1:

3/27/85 Tony Pusateri, CEI Div. 2:

3/28/85 Mark Hickman, CEI l

Unit 1 - Division 1 Tape ID Tape Footage Startup/Coastdown ID 1

555-566 Cylinder ILB TDC Firing QRCEI-1 566-581 Cylinder 7LB TDC Firing Torsiograph Test 581-595 Cylinder 8LB TDC Firing 595-611 Cylinder 2LB TDC Firing Unit 1 - Division 2 Tape ID Tape Footage Startup/Coastdown ID QRCEI-2 469-485 Cylinder ILB TDC Firing Torsiograph Test 485-500 Cylinder 2LB TDC Firing 500-517 Cylinder 7LB TDC Firing 517-534 Cylinder 8tB TDC Firing 16

Table 4.1: PRE TEST STATIC CALIBRATION Unit 1 - Division 1 Static Voltage Output Teac Range Setting HBM Signal Cond. Setting Input (Vdc)

(V/V)

(mV/V)

UB (degrees)

Ch. 1*

Ch. 2*

Ch. 1 Ch. 2 T6 V (V )

0

.005

.009

.1

.1 20 5

+3

.719

.726

.1

.1 20 5

0

.005

.010

.1

.1 20 5

-3

.705

.700

.1

.1 20 5

0

.003

.008

.1

.1 20 5

+3

.719

.726

.1

.1 20 5

0

.004

.010

.1

.1 20 5

-3

.705

.700

.1

.1 20 5

0

.002

.008

.1

.1 20 5

Unit 1 - Division 2 Static Voltage Output Teac Range Setting HBM Signal Cond. Setting Input (Vdc)

(V/V)

(mV/V)

UB (degrees)

Ch. 1*

Ch. 2*

Ch. 1 Ch. 2 f6 T (V )

0

.004

.008

.1

.1 20 5

+3

.722 721

.1

.1 20 5

0

.009

.013

.1

.1 20 5

-3

.703

.698

.1

.1 20 5

0

.006

.009

.1

.1 20 5

+3

.722

.721

.1

.1 20 C

0

.009

.010

.1

.1 20 5

-3

.704

.697

.1

.1 20 5

0

.006

.009

.1

.1 20 5

• t.002 Vdc 17

i Table 4.2: POST TEST STATIC CALIBRATION l

Unit 1 - Division 1 l

l Static Voltage Output Teac Range Setting HBM Signal Cond. Setting Input (Vdc)

(V/V)

(mV/V)

Ug (degrees)

Ch. 1*

Ch. 2*

Ch. 1 Ch. 2 ITT (V )

0

.011

.018

.1

.1 20 5

+3

.727

.730

.1

.1 20 5

0

.012

.020

.1

.1 20 5

-3

.698

.639

.1

.1 20 5

0

.011

.019

.1

.1 20 5

+3

.727

.730

.1

.1 20 5

0

.015

.021

.1

.1 20 5

-3

.697

.689

.1

.1 20 5

0

.012

.019

.1

.1 20 5

Unit 1 - Division 2 Static Voltage Output Teac Range Setting HBM Signal Cond. Setting Input (Vdc)

(V/V)

(mV/V)

UB (degrees)

Ch. 1*

Ch. 2*

Ch. 1 Ch. 2 10 V (V )

0

.014

.022

.1

.1 20 5

+3

.729

.733

.1

.1 20 5

0

.015

.022

.1

.1 20 5

-3

.695

.685

.1

.1 20 5

0

.014

.021

.1

.1 20 5

+3

.730

.734

.1

.1 20 5

0

.016

.024

.1

.1 20 5

-3

.695

.686

.1

.1 20 5

0

.013

.020

.1

.1 20 5

• t.002 Vdc 18

Table 4.3: VARIABLE SPEED RESPONSE Unit 1 - Division 1 Amplitude of free-end vibration (mil 11 degrees) for given speed (rpm)

Order 403 412 423 428 434 438 443 454 463 474 0.5 6

11 9

6 10 13 11 11 9

12 1.0 2

2 2

2 1

0 1

1 1

1 1.5 39 40 40 40 40 40 40 41 41 41 2.0 6

7 8

8 9

11 12 13 14 16 2.5 55 56 57 58 58 59 60 62 64 65 3.0 2

2 2

3 2

2 1

2 2

3 3.5 39 42 46 49 52 56 61 74 93 130 4.0 37 55 99 153 240 211 140 80 57 43 4.5 68 43 31 27 23 20 19 15 13 10 5.0 2

2 2

2 22 2

2 2

2 2

5.5 9

8 7

6 6

5 5

4 4

5 6.0 4

5 6

7 8

7 5

3 3

3 Total 170 170 210 260 340 290 240 230 230 240 Unit 1 - Division 2 Amplitude of free-end vibration (mil 11 degrees) for given speed (rpm)

Order 400 410 420 425 431 435 439 445 451 460 470 0.5 5

6 4

4 5

5 5

7 6

6 5

1.0 1

1 1

1 2

2 2

2 2

3 3

1.5 38 39 39 38 38 38 39 39 39 39 40 2.0 6

6 7

8 8

9 11 12 12 14 15 2.5 57 59 60 60 60 61 62 64 64 66 68 3.0 3

3 4

4 4

3 3

4 4

5 5

3.5 36 40 43 45 48 51 56 61 66 81 107 4.0 26 40 66 96 151 232 186 122 89 48 43 4.5 91 50 34 29 25 22 20 18 16 13 10 5.0 2

1 1

1 1

2 2

2 2

2 2

5.5 10 8

7 7

7 6

5 5

4 4

4 6.0 5

5 5

6 7

8 6

4 4

3 3

Total 185 165 160 200 255 340 270 235 215 205 230 19

Table 4.4: VARIABLE LOAD RESPONSE Unit 1-Division 1 Amplitude of free-end vibration (mil 11 degrees) for given load (kw)

Order 0

1750 3500 5250 7000 0.5 22 55 95 72 93 1.0 2

4 5

5 5

1.5 43 67 103 137 181 2.0 12 9

6 4

1 2.5 64 89 130 173 220 3.0 2

2 2

5 8

3.5 72 94 133 173 201 4.0 94 85 95 92 130 4.5 16 18 27 38 26 5.0 2

3 3

4 5

5.5 5

6 9

12 14 6.0 3

5 7

9 10 Total 225 273 368 417 542 Unit 1 - Division 2 Amplitude of free-end vibration (millidegrees) for given load (kw)

Order 0

1750 3500 5250 7K 0.5 7

6 13 34 55 1.0 3

3 3

3 1

1.5 41 64 98 138 184 2.0 11 8

5 5

7 2.5 68 96 138 185 235 3.0 4

7 8

7 4

3.5 69 93 129 172 205 4.0 88 69 80 133 141 4.5 15 19 29 41 52 5.0 1

1 1

2 1

5.5 5

6 10 12 14 6.0 4

6 8

11 12 Total 215 240 330 445 540 20

Table 4.5: STARTUP RESPONSE Maximum Peak-to-Peak Free-End Vibration Fast Start ID (degrees)

Unit 1 Unit 1 Division 1 Division 2 1 LB TDC Firing 2.39*

1.90 7 LB TDC Firing 1.80 1.68 8 LB TDC Firing 1.61 1.76 2 LB TDC Firing 1.75 2.00 t

• Torsiograph data for this test was determined from a noisy signal.

k -

l 21

)lll)!

I l'

lIllllllll1 08 4

d n

z O

e H

0 ee e

7 ed s 1 4

ro en9

.fm so2 np 1ft os os e p e :y n

r oei s sr c 0

i ef n e r n

6 sr or e e i gs r d u 4

vet p

s q

i di er e

oe D/

d

,i n r

r r

f si o2 C

1 p la

/

g l

t h1 0) t6n a

ot - r 5 m i9i u

T43t 4 p U8a n5t a

r r

emAN

(

fsb D

oii v

E es 0E sss 4P nei or 4S ptt ssf E

e a

N rrh I

as G

de ehe 0N esh 3 E p

t 4

sl ag enn lii bmm aou ins 0

r s

2 afa 4

Vo en

. do 1 ui

- tt 4ia 0

l r epb

' 1 rmi 4

uAv g*

i F

00 6

5 4

3 2

O4 0

0 O

O 0

3$.8P<oE> O2" wwEE EO W b

c y$eTi~

l l

flll

0.6 i

i i

i i

i i

e Total response S, 0.5 3

A 3-1/2 order response Natural frequency: 29.0 Hz

• g 9

g 0.4 e>

O2

• O.3 m

m II' E

E O 0.2 1

m O

3b

_a M

l

$ O.1 4:

^

^

i 1

lk I

0 400 410 420 430 440 450 460 470 460 ENGINE SPEED (rpm) in S

t!

Figure 4-2.

Variable speed response of Unit 1. Division 2.

t

• Amplitude of nominal shear stress is 8596 psi / degree of free-end vibration, assuming the shaft is vibrating in its first mode.

0.6 i

e Total response g

a 4th order response

.g 0.5 A 3-1/2 order response w

29 t-y 0.4 e>

O2y 0.3 W

W E

E b 0.2 5

3 0.1 x 1

0 O

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 GENERATOR LOAD (kw)

S T

Figure 4-3.

Variable load response of Unit 1, Division 1.

• Amplitude of nominal shear stress is 8596 psi / degree of free-end vibration, assuming the shaft is vibrating in its first mode.

l 00 0,

9 0

00, d

i 8

ne-.

ee ed ro 0

fm 0

=

0,

.ft i

2os 7

r nei oef i r sgs 0

iet 0

vdi i/

0, Din 6)

,si p

w 1

g k

6n t9i

(

=

i5t 0

D n8a 0

U r

A 0, O sb i

fii 5

L o

v s

R ess sei O

nr 0T ott psf 0 A s

a 0, R erh i

4E ras N

e dh e E

ash G

o t

e 0

ll ag s

0 enn e n 0,

lii s o np 3

bmm aou o s i ns

. pe r

s

. sr afa

. e Vo

. r 0

r p

e 0

en s rd

.d o er 0,

4ui e,d o

2 tt r

4ia

.o2 l r

/

epb

.h1 rmi t

143 0

uAv g*

0 i

. mA 0,

F i

1 b

O

,a 8

4 3

2 1

O 0

0 0

O 0

33 *getfe5 a*W Et $ wOgg:

4

,:T Yt -

lll lll l

I

l l

l 8

9 t

t I

i t

I 1

I t

l l

t i

I t

l l

t t

t i Le i

t I

f f

a.

f I

I I

I f

I I

f f

f I

t i

I t

1 I

I t

I I

t I

i i

i i

I ll I

f 9

I I

I I

t i

e i

i 1

e i

i t

i t

i a

e i

s T IME (S E C 0 N D $1 Figure 4-5.

Comparison of predicted and measured free-end amplitudes during a typical coastdown.

,i D>>

f OB Ut f

b I

.a

l l

1 1

I I

1 I

I I

l I

i l

i I

FREE-END AMPL1TUDE d,M $

l l hMk l h' f,h l I

(DECREES)

","l,"?ol7l,1,l^

wNj y' ' FIlIlgU I" ;" '

' ' Y l ]'iYl

^

~r

_i l

I I

I I

I I

I I

-2 l

l l

l l

l l

I I

2 I

l I

I I

i 1

1 I

I (DEGREES) k fg f l

}

ANALYTICAL MODEL l"

r > Jgig l

ll

-l

>i 2 LB TDC FIRING g

g g

-i 1

I I

I l

1

-2 l

I I

I I

I I

I I

f l

2 3

4 5

i TIME. (S E C 0 N D S)

Figure 4-6.

Comparison of predicted and measured free-end amplitudes.

FaAA-85-4-1

_ _ _ _