SHAFT LATERAL AND TORSIONAL VIBRATION RESPONSES TO … · 2011. 4. 6. · In this work, experimental results on the vibration measurements of rotor lateral and torsional vibration

June 2004 The Arabian Journal for Science and Engineering, Volume 29, Number 1C. 39

الخالصــة

تم في هذه الدراسة إعداد تجربة لمراقبة اهتزازات الريش والمحور الدّوار تحت تأثير اهتزازات إليجاد الترددات الطبيعية وأشكالها (ANSYS)وقد استخدم برنامج العناصر المحدودة . الّريش العشوائية

ت مراقبة اهتزازات الريش والمحور وخالل هذه التجربة، تّم. االهتزازية للجهاز الُمعد لهذه الدراسةالدوار بوساطة تثبيت مقاييس االنفعال على الريش والمحور الدوار وعن طريق تثبيت مقاييس تسارعية

وقد أظهرت نتائج هذه التجربة أن . على حوامل التثبيت ومحطة مقياس االنفعاالت االلتوائية للمحورباهتزازات الريش أآثر من االهتزازات المقاسة على االهتزازات االلتوائية للمحور تتأثر بوضوح

وبوجه أخص فإن اهتزازات الريش ذات الترددات المنخفضة تمثــّـل اهتزازات الريش . حوامل التثبيتوأخيرًا فإن . االنحنائية آما أن اهتزازات المحور االلتوائية تمثل الترددات االلتوائية المرآّبـة للمحور

دعم الثقـة في استخدام قياسات االهتزازات االلتوائية للتعرف على اهتزازات الريش، نتائج هذه الدراسة تاالهتزازات آما تلقي الضوء في الوقت نفسه على طبيعة التداخل بين االهتزازات االنحنائية للريش، و

.االلتوائية للمحور في حالة الترددات المنخفضة

SHAFT LATERAL AND TORSIONAL VIBRATION RESPONSES TO BLADE(S) RANDOM VIBRATION

EXCITATION B.O. Al-Bedoor*

Mechanical Engineering Department University of Jordan, P.O. Box 13568, Amman 11942, Jordan

Y. Al-Nassar† Mechanical Engineering Department, KFUPM Box 1876

L. Ghouti‡ Information and Computer Science Department, KFUPM Box 1128

and S.A. Adewusi and M. Abdlsamad Mechanical Engineering Department, KFUPM

* On leave from King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia e-mail: [email protected] † e-mail: [email protected] ‡ e-mail: [email protected]

B.O. Al-Bedoor, Y. Al-Nassar, L. Ghouti, S.A. Adewusi, and M. Abdlsamad

40 The Arabian Journal for Science and Engineering, Volume 29, Number 1C. June 2004

ABSTRACT

In this study, an experimental set-up for blades-shaft vibration monitoring under blade(s) random vibration excitation is used. The set-up natural frequencies and mode shapes are found using the ANSYS finite element package. The blades and shaft lateral and torsional vibration are monitored using blades strain-gages, bearing accelerometers and shaft torsional strain-gages stations. The results showed that the shaft torsional vibration measurement represents the blade(s) vibration more closely than the bearing accelerometers. In particular, the blades vibration at low frequencies corresponding to the blades bending and shaft torsional coupled modes is closely represented by the shaft torsional vibration signals. The results of this study increased the confidence in using the torsional vibration measurement for blades vibration identification and shed more light on the nature of coupling between the blade bending and shaft torsional vibration that occur at low frequencies.

Key words: Shaft, Torsional, Lateral, Vibration, Strain-Gages, Accelerometer, Coupling, Experimental, Blade(s), Natural Frequencies, Mode Shapes, Random Vibration.



SHAFT LATERAL AND TORSIONAL VIBRATION RESPONSES TO BLADE(S) RANDOM VIBRATION EXCITATION

1. INTRODUCTION

The majority of blades failures in rotating machinery are related to vibration generated fatigue stresses that put growing demands on monitoring blades vibration for design, evaluation, and diagnostics purposes. Blades are attached to the main rotor and interacting with the working fluid which means that they are excited by the working fluid and the main rotor vibrations. This situation makes the vibration measurement process and the identification of blades-related vibration problems a very difficult task. Newly reported and limited studies showed that the main rotor torsional vibration can give the blades vibration signature. An experimental study that shows a comparison between the shaft lateral and torsional vibration measurement under blades random vibration excitation is extremely necessary. Moreover, this experimental study is expected to contribute to the basic understanding of the interaction of blades–rotor systems.

Vibration measurement has been known as a powerful tool in machinery condition monitoring (Laws and Muszynska [1] and Vance [2]), that puts growing demands on developing reliable vibration measuring systems that sense and represent closely the machinery individual component vibration. The main rotor-bearing vibration systems have seen progress and helped in resolving many machinery problems such as the contribution of the eddy current probe in rotor–fluid instability problems. For general-purpose vibration measurement, accelerometers are the most popular vibration pick-ups that collect signals containing all rotor–bearing–housing dynamical behavior. When blades vibration information is required, the task becomes very complicated [3], as the blades are rotating and interacting with the working environment. To directly monitor blade vibration, strain-gages were used in many laboratory-testing studies [4–6]. Other techniques for blades vibration measurement were proposed; among these techniques is the use of Laser-doppler and optical methods [7–9], with some problems and limitations. Detailed discussion of the available methods for blade vibration measurement is reported by Al-Bedoor [10].

The approach of extracting blades vibration frequencies from the shaft torsional vibration was investigated experimentally in references [11–13]. The superiority of this approach to the lateral vibration approach, mainly, arose because torsional vibration is less affected by the boundary conditions than the lateral vibration. Muszynska et al. [14] have used the torsional vibration to identify rotor crack. They came up with an explanation for the sensitivity of torsional vibration that damping in torsional vibration modes is minimal. Al-Bedoor et al. [15] reported results and discussion of an experimental study on the measurement of blades free and forced vibration using the shaft torsional signals. The results showed that the torsional vibration signal reflect blades vibration up to a certain frequency after which the shaft torsional vibration has less sensitivity to blades vibration. This low sensitivity was related to the experimental set-up limitations and to the idealized single frequency excitation. Although the results of these experiments are promising, there was no comparison between the accelerometer and the shaft torsional vibration signals. Moreover, this study gave no attention to the random vibration of the blades that simulates more closely the fluid induced vibration. A recent theoretical model, Al-Bedoor et al. [16], showed that the blade vibration signature can be extracted from the shaft torsional vibration provided that an accurate and sensitive torsional vibration transducer is used. The model provided a tool for evaluating the sensitivity of shaft torsional vibration as related to the blade–disk–shaft combination of properties and what is known as the mistuning effect.

In this work, experimental results on the vibration measurements of rotor lateral and torsional vibration response due to blade random vibration excitation are reported and discussed. A test rig that is compromised of a changeable length shaft, a disk, and four blades has been manufactured. The natural frequencies and mode shapes of the test-rig are found, using the ANSYS finite element package. Strain-gages at two blades to measure blade-bending vibrations and three strain-gage stations are used to measure the shaft torsional vibration. The main rotor lateral vibration is measured using two accelerometers attached to the two bearing housings carrying the rotor. The signals are digitized using LabView and processed using the MATLAB package to find the frequency spectrums.



2. TEST-RIG DESCRIPTION

The test-rig whose schematic diagram shown in Figure 1(a) is composed of a rigid stand, two roller element bearings, shaft, and disk holding four blades. The dimensions and material properties of the shaft–disk–blade system are shown in Figure 1(b) and listed in Table 1, respectively. Moreover, a photograph that shows the test-rig and the measuring system is given in Figure 2. Three shaft lengths are used, as given in Table 1, to control the system torsional natural frequencies.

As a measuring system, two blades are equipped with full-bridge strain-gage stations located very close to the root of the blade to measure the blade bending vibrations, and three points on the shaft are equipped with a half-bridge strain-gages system at 45° alignment to measure torsional vibrations, as shown in Figure 1(b). The five measuring strain-gage stations’ results are connected to the signal conditioner (2310 Vishy) that powers the strain-gages, filters for noise signals, and amplifies the signals for further processing. The selected amplifier gain for all five channels is 1000 and the selected filter is the 10 KHz cut off frequency filter. The two accelerometer signals are passed through the conditioning units. The signals are taken to the DAQ of LabView for digitizing and then used in the MATLAB package for analysis. A schematic diagram of the measuring system and signal transmission arrangement is shown in Figure 3.

Table 1. Blade–Disk–Shaft Data.

Property Value

Blade material Steel (E=200 GPa, ρ̂ = 7850 kg/m3)

Blade length L 0.125 m

Blade cross section 2.54 × 0.16 cm

Blade mass per unit length, ρ 0.319 kg/m

Blade flexural rigidity, EI 0.173 N.m2

Disk Material Aluminum (E = 72 GPA, ρ̂ = 2700 kg/m3)

Disk Radius, RD 0.06 m

Disk width 0.04 m

Disk mass Md 1.22 kg

Disk moment of inertia, JD 2.2×10–3 kg.m2

Steel shaft G = 80 GPA

Shaft length (three lengths) L1 = 83.5 cm, L2 = 60.5 cm, L3 = 40.5 cm

Shaft diameter 1 cm

Torsional stiffness kT with L1 94 N.m/Rad

L2 130 N.m/Rad

L3 194 N.m/Rad



ShakerL

Blade-1 St-gage

Blade-2 St-gage

Shaft St-Gage 1Shaft St-Gage-2

Shaft St-Gage-3

ShakerL

Blade-1 St-gage

Blade-2 St-gage

Shaft St-Gage 1Shaft St-Gage-2

Shaft St-Gage-3

Figure 1. Schematic of the test-rig. (a) general view, (b) dimensions.

(a)

12

12.7

2.5

4

1

3

6 6 6

1 2 3

Fixedend

Sliding support2

Shaft Strain Gages

L

(b) DIMENSIONS IN CENTIMETERS

Accelerometer 2



Figure 3. Signal processing diagram.

Figure 2. Photograph of the test-rig and measuring system.

Shaker control

Signal conditioning

Shaker

Blade 1 Blade 2

Shaft Strain gages

LabViewDAQ

PC MATLAB/SIMULINK

Blade-1 Strain gageBlade-2 Strain gageShaft Strain gage-1Shaft Strain gage-2Shaft Strain gage-3

2310 Signal Conditioning Amplifier(Measurements Group)



3. RESULTS AND DISCUSSIONS

In a previous study [15], the blade vibration responses to distinct and sweeping frequency excitation were presented and discussed. This type of excitation represents an idealized condition in which the blade is excited at a single frequency. The more realistic excitation is the one that occurs due to signals with many frequencies, such as the excitation coming from fluid turbulence. Random vibration signals lend themselves to simulate such simultaneous multiple frequency excitations. The excited dynamic system will respond differently according to how close the excitation frequency is to the system natural frequencies. In addition, the random vibration excitation and the measurement of blades, shaft torsional vibration signals, and bearing vibration enable reliable comparison between shaft lateral and torsional vibration signals as measuring tools for the extraction of blade(s) vibration signature.

3.1. Natural Frequencies and Mode Shapes

To identify the experimental set-up natural frequencies and mode shapes, the ANSYS finite element package is used for three different lengths. The calculated natural frequencies are given in Table 2 and the associated mode shapes are given in Figures 4, 5, and 6 for three shaft lengths. As can be seen in Table 2 and Figures 4–6, the assembly has distinct vibration modes, such as the shaft-torsional, shaft-bending, blade-bending, and blade-torsional modes. In addition, the assembly has coupled modes of vibration between the shaft-bending, shaft-torsional, and blade bending.

3.2. Random Vibration Response

For the three different lengths of the shaft, blade 1 is excited by a random white noise shown in Figure 7. The vibration signals from blades 1 and 2, bearing accelerometers, and the three stations for the shaft torsional vibration measurement are collected and their spectrums are studied.

For shaft length L1 = 0.835 m, the vibration spectrums of blades 1 and 2 are shown in Figures 8 (a) and (b), respectively. As shown in Figure 8(a), blade 1 vibration occurs at frequencies of about 3 Hz, 17.5 Hz, 32.5 Hz, 125 Hz, and 300 Hz. Blade 2 spectrum, Figure 8(b), shows vibration at 12.5 Hz, 17.5 Hz, 40 Hz, 60 Hz, 75 Hz, and at higher frequencies with lower amplitudes. Now the spectrums of blades 1 and 2 can be considered as characteristic of the set-up blades vibration. The associated accelerometer spectrums are shown in Figures 9(a) and (b). The accelerometers spectrums show broad band spectrums and no frequency components less than 20 Hz that have the highest amplitudes in the blade spectrums. The shaft torsional strain-gages stations spectrums are shown in Figures 10(a), (b), and (c). The spectrum of strain-gages station 1, Figure 10(a), captured vibration at frequencies 20 Hz, 40 Hz, 125 Hz, 180 Hz, 220 Hz, 240 Hz, 260 Hz, 300 Hz, 420 Hz, 440 Hz, and 460 Hz. Torsional strain-gages station 2, Figure 10(b), shows vibration at frequencies of 3 Hz, 17.5 Hz, 30 Hz, 60 Hz, 70 Hz, 80 Hz, 120 Hz, 160 Hz, 220 Hz, 240 Hz, 300 Hz, 325 Hz, 340 Hz, 395 Hz, 420 Hz, and 475 Hz. Station 3’s spectrum, Figure 10(c), shows similar frequencies as station 1 spectrum, as given in Figure 10(a). Comparing the spectrums of the torsional stations in Figures 10 indicates that the position of the station makes a difference in the measurement sensitivity. The frequency contents of the five sensors’ signals are summarized in Table 3. Considering the frequency content shows that the torsional vibration signals represent the blade(s) vibration more than the accelerometer signals.

Similar spectrums for blades strain-gages, accelerometers and shaft torsional strain-gages are given in Figures 11–13 for the experiment when the shaft length is L2 = 0.605 m. Same behavior of distinct frequencies blade vibration and broad band accelerometers responses can be observed. The shaft torsional vibration signals spectrums, Figures 13, are shown to represent the blades vibration character more closely than the accelerometers spectrums. This observation can be seen in the frequency contents comparison given in Table 4. Towards having more reliable results, the experiment is further conducted for the shaft length L3 = 0.405 m. The spectrums of blades strain-gages signals, accelerometers signals, and shaft torsional strain-gages signals are given in Figures 14–16. The frequency contents of the five spectrums are given in Table 5. Same behavior can be observed as for the former two lengths experiments.

Considering the three experiments on the shaft lateral and torsional vibration measurement under blade random vibration excitation, one can observe the following:

(1) Blade 1 vibrated at distinct frequencies with the highest amplitude at low frequency, which is equivalent to the shaft torsional vibration natural frequency.



(2) Blade 2 vibrated at more frequencies than blade 1 due to its excitation at its base, that produced multiple responses and nonlinear behavior.

(3) Accelerometers showed broad band spectrums and do not represent blade(s) vibration closely. Moreover, accelerometers were not able to sense the blades vibration at low frequencies, even though this low frequency vibration has the highest amplitude.

(4) Shaft torsional vibration measurement showed distinct frequencies and represent blade(s) vibration closely. However, the location of the shaft torsional vibration strain-gages was shown to affect the sensitivity of measurement.

Table 2. ANSYS Simulation Natural Frequencies of the Experimental Setup.

L = 0.835 m L = 0.605 m L = 0.405 m Frequency

Hz Mode Frequency

Hz Mode Frequency

Hz Mode

2.85 Shaft torsion 2.8606 Shaft torsion 2.87 Shaft torsion 3.8284 Disk tilt 3.8323 Disk tilt 3.8357 Disk tilt 3.8284 Disk tilt 3.8323 Disk tilt 3.8357 disk tilt 27.695 Coupled shaft

torsion–blade 23.773 Shaft lateral 12.722 Shaft lateral

43.293 Shaft lateral 23.773 Shaft lateral 12.722 Shaft lateral 43.293 Shaft lateral 27.696 Coupled shaft

torsion–blade 27.697 Coupled shaft torsion–

blade 63.22 Blade 1st 63.059 Blade 1st 63.182 Blade 1st 63.256 Blade 1st 63.109 Blade 1st 63.22 Blade 1st 63.306 Blade 1st 63.22 Blade 1st 63.232 Blade 1st 71.155 Shaft lateral 79.043 Shaft lateral 79.717 Shaft lateral 71.155 Shaft lateral 79.044 Shaft lateral 79.717 Shaft lateral 131.06 Coupled 148.94 Coupled 147.93 Coupled 131.06 Coupled 148.94 Coupled 147.93 Coupled 166.86 Blade 2nd 166.86 Blade 2nd 166.86 Blade 2nd 237.81 Coupled shaft

lateral-blade 210.52 Coupled shaft

lateral-blade 223.16 Shaft lateral

237.83 Coupled shaft lateral-blade


223.16 Shaft lateral







385.99 Blade 3rd 385.99 Blade 3rd 385.99 Blade 3rd 392.4 Coupled shaft


lateral-blade 390.14 Coupled shaft lateral-

blade 393 Coupled shaft


lateral-blade 390.93 Coupled shaft lateral-

blade 445.53 Shaft lateral 416.84 Shaft lateral 437.16 Shaft lateral 445.53 Shaft lateral 416.84 Shaft lateral 437.16 Shaft lateral 512.45 Blade 4th 512.45 Blade 4th 512.45 Blade 4th 582.66 Coupled shaft

lateral-blade 651.16 Blade torsion 651.16 Blade torsion


651.16 Blade torsion 651.16 Blade torsion

651.16 Blade torsion 651.3 Blade torsion 651.32 Blade torsion 651.16 Blade torsion 651.3 Blade torsion 651.32 Blade torsion 651.33 Blade torsion 666.71 Shaft bending 722.39 Shaft bending 651.33 Blade torsion 666.79 Shaft bending 722.39 Shaft bending



Table 3. Frequency Contents for the White Noise Blade Excitation, Shaft Length L1.

Frequency contents Hz L1

White Noise

Blade 1 Blade 2 Accelerometer Shaft 1 Shaft 2 Shaft 3

3 12.5 20 20 17.5 20

17.5 17.5 25 125 37.5 105

32.5 37.5 30 185 47.5 125

125 57.5 35 225 55 145

300 75 55 247.5 77.5 187.5

80 65 307.5 82.5 227.5

85 75 350 97.5 247.5

105 80 372.5 102.5 272.5

125 90 385 125 310

250 95 432.5 155 350

335 110 452.5 177.5 372.5

372.5 120 472.5 185 432.5

387.5 155 200 437.5

407.5 180 225 452.5

430 185 247.5 475

440 225 285

445 285 297.5

452.5 300 307.5

460 330 315

335 330

350 335

435 347.5

440 407.5

490 432.5

440

475

485

495




Frequency contents

Frequency contents L2 White Noise


2.5 5 15 5 20 22.5

20 10 65 22.5 77.5 125

42.5 15 82.5 40 100 142.5

125 20 92.5 105 125 157.5

247.5 42.5 100 125 225 225

305 70 105 145 247.5 245

370 87.5 110 187.5 282.5 307.5

462.5 125 115 210 295 430

500 247.5 122.5 232.5 307.5 457.5

287.5 135 247.5 322.5 472.5

297.5 140 252.5 432.5

310 150 287.5 500

322.5 155 297.5

360 287.5 310

370 297.5 332.5

377.5 307.5 350

460 312.5 362.5

500 320 372.5

325 380

330 392.5

335 432.5

350 475

360 485

370

435

445

475

510




Frequency contents L3

White Noise


2.5 12.5 20 22.5 2.5 22.5

22.5 22.5 25 102.5 22.5 102.5

62.5 55 62.5 125 72.5 125

125 62.5 70 160 82.5 145

150 87.5 87.5 227.5 125 187.5

247.5 125 92.5 247 135 232.5

290 147.5 100 310 147.5 247.5

307.5 282.5 125 352.5 227.5 267.5

352.5 287.5 127.5 392.5 247.5 310

370 300 137.5 435 282.5 352.5

377.5 330 147.5 462.5 287.5 432.5

462.5 337.5 155 475 292.5 462.5

475 352.5 282.5 297.5 475

495 362.5 290 300

370 297.5 307.5

375 302.5 312.5

385 307.5 322.5

395 312.5 337.5

410 317.5 342.5

430 322.5 352.5

462.5 330 360

497.5 337.5 367.5

352.5 377.5

370 432.5

377.5 447.5

450 470

470 495

500


The Arabian Journal for Science and Engineering, Volume 29, Number 1C. June 200450

2.

85 H

z

3.

828

Hz

3.82

8 H

z

27

.695

Hz

43.2

93 H

z

43

.293

Hz

63.2

2 H

z

63

.256

Hz

63.3

05 H

z

71

.155

Hz

71

.155

Hz

131.

058

Hz

131.

058

Hz

166.

857

Hz

237.

811

Hz

1

X

Y Z

JUN 20 2004

13:06:12

DISPLACEMENT

STEP=1

SUB =6

FREQ=43.293

DMX =2.038

1

X

Y Z

JUN 20 2004

13:06:37

DISPLACEMENT

STEP=1

SUB =7

FREQ=63.22

DMX =5.652

1

X

Y Z

JUN 20 2004

13:06:56

DISPLACEMENT

STEP=1

SUB =8

FREQ=63.256

DMX =5.644

1

X

Y Z

JUN 20 2004

13:07:11

DISPLACEMENT

STEP=1

SUB =9

FREQ=63.306

DMX =5.646

1

X

Y

Z

JUN 20 2004

13:07:47

DISPLACEMENT

STEP=1

SUB =10

FREQ=71.155

DMX =4.537

1

X

Y Z

JUN 20 2004

13:08:36

DISPLACEMENT

STEP=1

SUB =11

FREQ=71.155

DMX =4.537

1

X

Y Z

JUN 20 2004

13:08:57

DISPLACEMENT

STEP=1

SUB =12

FREQ=131.058

DMX =1.933

1

X

Y Z

JUN 20 2004

13:09:19

DISPLACEMENT

STEP=1

SUB =13

FREQ=131.058

DMX =1.933

1

X

Y

Z

JUN 20 2004

13:09:41

DISPLACEMENT

STEP=1

SUB =14

FREQ=166.857

DMX =4.611

1

X

Y

Z

JUN 20 2004

13:09:57

DISPLACEMENT

STEP=1

SUB =15

FREQ=237.811

DMX =1.738

1

XYZ

JUN 20 2004

13:02:34

DISPLACEMENT

STEP=1

SUB =1

FREQ=2.85

DMX =2.57

1

X

Y

Z

JUN 20 2004

13:03:31

DISPLACEMENT

STEP=1

SUB =2

FREQ=3.828

DMX =2.576

1

X

Y

Z

JUN 20 2004

13:03:51

DISPLACEMENT

STEP=1

SUB =3

FREQ=3.828

DMX =2.576

1

X

Y

Z

JUN 20 2004

13:04:15

DISPLACEMENT

STEP=1

SUB =4

FREQ=27.695

DMX =3.692

1

X

Y

Z

JUN 20 2004

13:04:30

DISPLACEMENT

STEP=1

SUB =5

FREQ=43.293

DMX =2.038

Figu

re 4

(par

t). N

atur

al v

ibra

tion

mod

es o

f the

exp

erim

enta

l set

-up

with

Len

gth

L 1.


The Arabian Journal for Science and Engineering, Volume 29, Number 1C.June 2004 51

Figu

re 4

(con

t.) N

atur

al v

ibra

tion

mod

es o

f the

exp

erim

enta

l set

-up

with

Len

gth

L 1.

23

7.83

4 H

z

37

0.40

2 H

z

37

0.75

7 H

z

38

5.99

2 H

z

39

2.40

4 H

z

39

2.99

6 H

z

44

5.53

3 H

z

44

5.53

3 H

z

51

2.44

7 H

z

58

2.66

5 H

z

58

2.7

Hz

651.

162

Hz

651.

163

Hz

651.

329

Hz

651.

329

Hz

1

X

Y Z

JUN 20 2004

13:10:27

DISPLACEMENT

STEP=1

SUB =16

FREQ=237.834

DMX =1.738

1

X

Y Z

JUN 20 2004

13:10:48

DISPLACEMENT

STEP=1

SUB =17

FREQ=370.402

DMX =2.747

1

X

Y Z

JUN 20 2004

13:11:04

DISPLACEMENT

STEP=1

SUB =18

FREQ=370.757

DMX =2.656

1

X

Y Z

JUN 20 2004

13:11:24

DISPLACEMENT

STEP=1

SUB =19

FREQ=385.992

DMX =5.541

1

X

Y

Z

JUN 20 2004

13:11:45

DISPLACEMENT

STEP=1

SUB =20

FREQ=392.404

DMX =4.842

1

X

Y Z

JUN 20 2004

13:12:21

DISPLACEMENT

STEP=1

SUB =21

FREQ=392.996

DMX =4.904

1

X

Y Z

JUN 20 2004

13:12:51

DISPLACEMENT

STEP=1

SUB =22

FREQ=445.533

DMX =4.532

1

X

Y Z

JUN 20 2004

13:13:11

DISPLACEMENT

STEP=1

SUB =23

FREQ=445.533

DMX =4.532

1

X

Y Z

JUN 20 2004

13:13:37

DISPLACEMENT

STEP=1

SUB =24

FREQ=512.447

DMX =5.222

1

X

Y Z

JUN 20 2004

13:14:04

DISPLACEMENT

STEP=1

SUB =25

FREQ=582.665

DMX =2.024

1

X

Y Z

JUN 20 2004

13:14:21

DISPLACEMENT

STEP=1

SUB =26

FREQ=582.7

DMX =2.024

1

X

Y Z

JUN 20 2004

13:14:39

DISPLACEMENT

STEP=1

SUB =27

FREQ=651.162

DMX =7.196

1

X

Y Z

JUN 20 2004

13:14:52

DISPLACEMENT

STEP=1

SUB =28

FREQ=651.163

DMX =7.196

1

X

Y Z

JUN 20 2004

13:15:10

DISPLACEMENT

STEP=1

SUB =29

FREQ=651.327

DMX =7.169

1

X

Y Z

JUN 20 2004

13:15:38

DISPLACEMENT

STEP=1

SUB =30

FREQ=651.329

DMX =7.168



Figu

re 5

(par

t). N

atur

al v

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tion

mod

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f the

exp

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-up

with

Len

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L 2.

2.

86 H

z

3.

832

Hz

3.83

2 H

z

23

.773

Hz

23.7

73 H

z

27

.696

Hz

63.0

59 H

z

63

.109

Hz

79.2

2 H

z

79

.043

Hz

79

.044

Hz

148.

937

Hz

148.

937

Hz

166.

857

Hz

210.

516

Hz

1

X

Y

Z

JUN 20 2004

13:38:58

DISPLACEMENT

STEP=1

SUB =1

FREQ=2.861

DMX =2.57

1

X

Y

Z

JUN 20 2004

13:39:38

DISPLACEMENT

STEP=1

SUB =2

FREQ=3.832

DMX =2.557

1

X

Y

Z

JUN 20 2004

13:40:14

DISPLACEMENT

STEP=1

SUB =3

FREQ=3.832

DMX =2.557

1

X

Y

Z

JUN 20 2004

13:40:45

DISPLACEMENT

STEP=1

SUB =4

FREQ=23.773

DMX =3.45

1

X

Y

Z

JUN 20 2004

13:41:05

DISPLACEMENT

STEP=1

SUB =5

FREQ=23.773

DMX =3.45

1

X

Y Z

JUN 20 2004

13:41:41

DISPLACEMENT

STEP=1

SUB =6

FREQ=27.696

DMX =3.692

1

X

Y

Z

JUN 20 2004

13:42:02

DISPLACEMENT

STEP=1

SUB =7

FREQ=63.059

DMX =5.62

1

X

Y

Z

JUN 20 2004

13:42:21

DISPLACEMENT

STEP=1

SUB =8

FREQ=63.109

DMX =5.622

1

X

Y Z

JUN 20 2004

13:42:39

DISPLACEMENT

STEP=1

SUB =9

FREQ=63.22

DMX =5.652

1

X

Y Z

JUN 20 2004

13:42:57

DISPLACEMENT

STEP=1

SUB =10

FREQ=79.043

DMX =2.264

1

X

Y Z

JUN 20 2004

13:43:16

DISPLACEMENT

STEP=1

SUB =11

FREQ=79.044

DMX =2.264

1

X

Y Z

JUN 20 2004

13:43:30

DISPLACEMENT

STEP=1

SUB =12

FREQ=148.937

DMX =3.449

1

X

Y

Z

JUN 20 2004

13:43:49

DISPLACEMENT

STEP=1

SUB =13

FREQ=148.937

DMX =3.449

1

X

Y Z

JUN 20 2004

13:44:05

DISPLACEMENT

STEP=1

SUB =14

FREQ=166.857

DMX =4.611

1

X

Y Z

JUN 20 2004

13:44:18

DISPLACEMENT

STEP=1

SUB =15

FREQ=210.516

DMX =1.986



Figu

re 5

(con

t.). N

atur

al v

ibra

tion

mod

es o

f the

exp

erim

enta

l set

-up

with

Len

gth

L 2.

21

0.53

1 H

z

36

9.47

2 H

z

36

9.88

4 H

z

38

5.99

2 H

z

39

3.36

4 H

z

39

4.10

8 H

z

41

6.83

8 H

z

41

6.83

8 H

z

51

2.44

7 H

z

65

1.16

2 H

z

65

1.16

3 H

z

65

1.29

7 H

z

65

1.29

8 H

z

66

6.70

7 H

z

66

6.78

7 H

z

1

X

Y Z

JUN 20 2004

13:44:36

DISPLACEMENT

STEP=1

SUB =16

FREQ=210.531

DMX =1.986

1

X

Y Z

JUN 20 2004

13:45:01

DISPLACEMENT

STEP=1

SUB =17

FREQ=369.472

DMX =2.925

1

X

Y Z

JUN 20 2004

13:45:17

DISPLACEMENT

STEP=1

SUB =18

FREQ=369.884

DMX =2.841

1

X

Y Z

JUN 20 2004

13:45:38

DISPLACEMENT

STEP=1

SUB =19

FREQ=385.992

DMX =5.541

1

X

Y Z

JUN 20 2004

13:46:06

DISPLACEMENT

STEP=1

SUB =20

FREQ=393.564

DMX =4.758

1

X

Y

Z

JUN 20 2004

13:46:25

DISPLACEMENT

STEP=1

SUB =21

FREQ=394.108

DMX =4.82

1

X

Y Z

JUN 20 2004

13:46:38

DISPLACEMENT

STEP=1

SUB =22

FREQ=416.838

DMX =3.447

1

X

Y Z

JUN 20 2004

13:46:57

DISPLACEMENT

STEP=1

SUB =23

FREQ=416.838

DMX =3.446

1

X

Y

Z

JUN 20 2004

13:47:12

DISPLACEMENT

STEP=1

SUB =24

FREQ=512.447

DMX =5.221

1

X

Y

Z

JUN 20 2004

13:47:28

DISPLACEMENT

STEP=1

SUB =25

FREQ=651.162

DMX =7.166

1

X

Y

Z

JUN 20 2004

13:47:43

DISPLACEMENT

STEP=1

SUB =26

FREQ=651.163

DMX =7.166

1

X

Y

Z

JUN 20 2004

13:47:56

DISPLACEMENT

STEP=1

SUB =27

FREQ=651.297

DMX =7.177

1

X

Y

Z

JUN 20 2004

13:48:08

DISPLACEMENT

STEP=1

SUB =28

FREQ=651.298

DMX =7.178

1

XY Z

JUN 20 2004

13:48:26

DISPLACEMENT

STEP=1

SUB =29

FREQ=666.707

DMX =2.383

1XZ

JUN 20 2004

13:48:41

DISPLACEMENT

STEP=1

SUB =30

FREQ=666.787

DMX =2.383



2.

87 H

z

3.

835

Hz

3.83

6 H

z

12

.722

Hz

12.7

22 H

z

27

.697

Hz

63.1

82 H

z

63

.22

Hz

63.2

32 H

z

79

.717

Hz

79

.717

Hz

147.

925

Hz

147.

929

Hz

166.

857

Hz

223.

138

Hz

1

X

Y

Z

JUN 20 2004

13:55:34

DISPLACEMENT

STEP=1

SUB =1

FREQ=2.87

DMX =2.571

1

X

Y

Z

JUN 20 2004

13:55:50

DISPLACEMENT

STEP=1

SUB =2

FREQ=3.836

DMX =2.536

1

X

Y Z

JUN 20 2004

13:56:14

DISPLACEMENT

STEP=1

SUB =3

FREQ=3.836

DMX =2.536

1

X

Y Z

JUN 20 2004

13:56:31

DISPLACEMENT

STEP=1

SUB =4

FREQ=12.722

DMX =2.951

1

X

Y Z

JUN 20 2004

13:56:42

DISPLACEMENT

STEP=1

SUB =5

FREQ=12.722

DMX =2.951

1

X

Y Z

JUN 20 2004

13:57:04

DISPLACEMENT

STEP=1

SUB =6

FREQ=27.697

DMX =3.691

1

X

Y

Z

JUN 20 2004

13:57:23

DISPLACEMENT

STEP=1

SUB =7

FREQ=63.182

DMX =5.651

1

X

Y Z

JUN 20 2004

13:57:41

DISPLACEMENT

STEP=1

SUB =8

FREQ=63.22

DMX =5.652

1

X

Y Z

JUN 20 2004

13:57:55

DISPLACEMENT

STEP=1

SUB =9

FREQ=63.232

DMX =5.653

1

X

Y Z

JUN 20 2004

13:58:11

DISPLACEMENT

STEP=1

SUB =10

FREQ=79.717

DMX =2.95

1

X

Y Z

JUN 20 2004

13:58:25

DISPLACEMENT

STEP=1

SUB =11

FREQ=79.717

DMX =2.95

1

X

Y

Z

JUN 20 2004

13:58:50

DISPLACEMENT

STEP=1

SUB =12

FREQ=147.925

DMX =2.194

1

X

Y Z

JUN 20 2004

13:59:14

DISPLACEMENT

STEP=1

SUB =13

FREQ=147.929

DMX =2.194

1

X

Y

Z

JUN 20 2004

13:59:29

DISPLACEMENT

STEP=1

SUB =14

FREQ=166.857

DMX =4.611

1

X

Y Z

JUN 20 2004

13:59:46

DISPLACEMENT

STEP=1

SUB =15

FREQ=223.158

DMX =2.949

Figu

re 6

(par

t). N

atur

al v

ibra

tion

mod

es o

f the

exp

erim

enta

l set

-up

with

Len

gth

L 3.



22

3.15

8 H

z

33

8.10

8 H

z

33

8.28

5 H

z

38

5.99

2 H

z

39

0.14

1 H

z

39

0.93

Hz

437.

158

Hz

437.

158

Hz

512.

447

Hz

651.

162

Hz

65

1.16

3 H

z

65

1.31

8 H

z

65

1.32

Hz

722.

385

Hz

722.

385

Hz

1

X

Y Z

JUN 20 2004

14:00:00

DISPLACEMENT

STEP=1

SUB =16

FREQ=223.158

DMX =2.949

1

X

Y Z

JUN 20 2004

14:00:18

DISPLACEMENT

STEP=1

SUB =17

FREQ=338.108

DMX =2.453

1

X

Y Z

JUN 20 2004

14:00:33

DISPLACEMENT

STEP=1

SUB =18

FREQ=338.285

DMX =2.457

1

X

Y Z

JUN 20 2004

14:00:45

DISPLACEMENT

STEP=1

SUB =19

FREQ=385.992

DMX =5.541

1

X

Y Z

JUN 20 2004

14:01:05

DISPLACEMENT

STEP=1

SUB =20

FREQ=390.141

DMX =5.365

1

X

Y Z

JUN 20 2004

14:01:24

DISPLACEMENT

STEP=1

SUB =21

FREQ=390.93

DMX =5.384

1

X

Y Z

JUN 20 2004

14:01:40

DISPLACEMENT

STEP=1

SUB =22

FREQ=437.158

DMX =2.948

1

X

Y Z

JUN 20 2004

14:01:51

DISPLACEMENT

STEP=1

SUB =23

FREQ=437.158

DMX =2.948

1

X

Y

Z

JUN 20 2004

14:02:14

DISPLACEMENT

STEP=1

SUB =24

FREQ=512.447

DMX =5.22

1

X

Y

Z

JUN 20 2004

14:02:25

DISPLACEMENT

STEP=1

SUB =25

FREQ=651.162

DMX =7.166

1

X

Y Z

JUN 20 2004

14:02:38

DISPLACEMENT

STEP=1

SUB =26

FREQ=651.163

DMX =7.166

1

X

Y Z

JUN 20 2004

14:02:48

DISPLACEMENT

STEP=1

SUB =27

FREQ=651.318

DMX =7.168

1

X

Y Z

JUN 20 2004

14:03:01

DISPLACEMENT

STEP=1

SUB =28

FREQ=651.32

DMX =7.168

1

X

Y Z

JUN 20 2004

14:03:17

DISPLACEMENT

STEP=1

SUB =29

FREQ=722.385

DMX =2.947

1

X

Y

Z

JUN 20 2004

14:03:33

DISPLACEMENT

STEP=1

SUB =30

FREQ=722.385

DMX =2.947

Figu

re 6

(con

t.). N

atur

al v

ibra

tion

mod

es o

f the

exp

erim

enta

l set

-up

with

Len

gth

L 3.



Figure 7. Blade 1 white noise random excitation frequency spectrum.



(a)

(b)

Figure 8. Blades strain-gages signals spectrums, shaft length L1, (a) Blade 1 and (b) Blade 2.



(a)

(b)

Figure 9: Accelerometers vibration signals spectrums, shaft length L1, (a) Accelerometer 1 and (b) Accelerometer 2.



(a)

(b)

(c)

Figure 10: Shaft torsional strain gages signals spectrums, shaft length L1,

(a) Strain gage 1, (b) Strain gage 2, and (c) Strain gage 3.



(a)

(b)




(a)

(b)

Figure 12. Accelerometers vibration signals spectrums, shaft length L2, (a) Accelerometer 1 and (b) Accelerometer 2.



(a)

(b)

(c)

Figure 13. Shaft torsional strain-gages signals spectrums, shaft length L2,




(a)

(b)




(a)

(b)

Figure 15. Accelerometers vibration signals spectrums, shaft length L3, (a) Accelerometer 1 and (b) Accelerometer 2.



(a)

(b)

(c)

Figure 16: Shaft torsional strain gages signals spectrums, shaft length L3,




4. CONCLUSIONS

An experimental set-up for blades–shaft vibration monitoring under blade(s) random vibration excitation is used. The experimental set-up natural frequencies and mode shapes are found using the ANSYS finite element package. The blades and shaft lateral and torsional vibration are monitored using blades strain-gages, bearing accelerometers and shaft torsional strain-gages stations. The vibration signals are colleted using the LABVIEW and processed using the MATLAB package and the spectrums are analyzed and discussed. The results showed that the shaft torsional vibration measurement represent the blade(s) vibration more closely than the bearing accelerometers. In particular, the blades vibration at low frequencies corresponding to the blades–shaft torsional modes is closely represented by the shaft torsional vibration signals. The results of this study increased the confidence in using the torsional vibration measurement for blades vibration identification and shed more light on the nature of coupling between the blade bending and shaft torsional vibration that occur at low frequencies. Finally, further studies that address prototypes of machines and actual field testing are recommended.

ACKNOWLEDGMENTS

The authors acknowledge the support of King Fahd University of Petroleum (KFUPM), Dhahran, Saudi Arabia. This work is funded by KFUPM Research Office under project number ME/BLADE-VIBRATION/215.

REFERENCES

[1] W.C. Laws and A. Muszynska, “Periodic and Continuous Vibration Monitoring for Preventive/Predictive Maintenance of Rotating Machinery”, ASME Journal of Engineering for Gas Turbine and Power, 109 (1987), pp. 159–167.

[2] J.M. Vance, Rotor Dynamics of Turbo-Machinery. New York: John Wiley and Sons, Inc., 1988. [3] H.R. Simmons and A.J. Smalley, “Effective Tools for Diagnosing Elusive Turbo-Machinery Dynamics Problems in the Field”,

ASME Journal of Engineering for Gas Turbines and Power, 112 (1990), pp. 470–476. [4] A.V. Srinivasan and D.G. Cuts, “Measurement of the Relative Vibratory Motion at the Shroud Interfaces of a Fan”, ASME

Journal of Vibration, Acoustics, Stress and Reliability in Design, 106 (1984), pp. 189–197. [5] A.J. Scalzo, J.M. Allen, and R.J. Antos, “Analysis and Solution of a Non-Synchronous Vibration Problem in the Last Row

Turbine Blade of a Large Industrial Turbine”, ASME Journal of Engineering for Gas Turbines and Power, 108 (1986), pp. 591–598.

[6] Y.C. Fan, M.S. Ju, and Y.G. Tsuei, “Experimental Study on Vibration of a Rotating Blade”, ASME Journal of Engineering for Gas Turbines and Power, 116 (1994), pp. 672–677.

[7] R.A. Cookson and P. Bandyopadhyay, “A Fiber-Optic Laser-Doppler Probe for Vibration Analysis of Rotating Machines”, ASME Journal of Power, 102 (1980), pp.607–612.

[8] P. Nava, N. Paone, G.L. Rossi, and E.P. Tomasinin, “Design and Experimental Characterization of a Non-Intrusive Measurement System of Rotating Blade Vibration”, ASME Journal of Engineering for Gas Turbines and Power, 116 (1994), pp. 657–662.

[9] A.K. Reihardt, J.R. Kadambi, and R.D. Quinn, “Laser Vibrometery Measurements of Rotating Blade Vibrations”, ASME Journal of Engineering for Gas Turbines and Power, 117 (1995), pp. 484–488.

[10] B.O. Al-Bedoor, “Blade Vibration Measurement in Turbo-Machinery: The Current Status”, The Shock and Vibration Digest, in press.

[11] K.P. Maynard and M. Trethewey, “ On the Feasibility of Blade Crack Detection Through Torsional Vibration Measurements”, Proceedings of the 53rd Meeting of the Society for Machinery Failure Prevention Technology, Virginia Beach, VA, April 19–22, 1999, pp. 451–459.

[12] K.P. Maynard, M. Lebold, C. Groover, and M. Trethewey, “Application of Double Re-Sampling to Shaft Torsional Vibration Measurement for the Detection of Blade Natural Frequencies”, Proceedings of the 54th Meeting of the Society for Machinery Failure Prevention Technology, Virginia Beach, VA, May 1–4, 2000, pp. 87–94.

[13] K.P. Maynard and M. Trethewey, “Application of Torsional Vibration Measurement to Blade and Shaft Crack Detection in Operating Machinery”, Proceedings of the Maintenance and Reliability Conference, Gatlinburg, Tennessee, May 6–9, 2001.



[14] A. Muszynska, P. Goldman, and D.E. Bently, “Torsional/Lateral Vibration Cross-Coupled Responses Due to Shaft Anisotropy: A New Tool in Shaft Crack Detection”, Proceedings of the IMechE Conference on Vibrations in Rotating Machinery, C 432-090, Bath, UK, 1992, pp. 257–262.

[15] B.O. Al-Bedoor, L. Ghouti, S.A. Adewusi, Y. Al-Nassar, and M. Abdlsamad, “Experiments on the Extraction of Blade Vibration Signature from the Shaft Torsional Vibration Signals”, Journal of Quality in Maintenance Engineering, 9(2) (2003), pp.144–159.

[16] B.O. Al-Bedoor, “Model for the Extraction of Blade Vibration Signature from the Shaft Torsional Vibration Signal”, ASME Journal of Engineering for Gas Turbines and Power (submitted).

Paper Received 25 October 2003; Revised 30 August 2004; Accepted 13 October 2004.

Documents

SHAFT LATERAL AND TORSIONAL VIBRATION RESPONSES TO … · 2011. 4. 6. · In this work, experimental results on the vibration measurements of rotor lateral and torsional vibration