2

(Vibration Parameters)

1. (Vibration Amplitude)

1.1 (Definition of Vibration)

,

.

= (,

)

.

,

3 , .

2-1

.

2-1

.

Spring . (Neutral Position)

(Lower Limit) .

2 19

.

.

2-2

Pen ,

Strip Chart Recorder

2-2 .

1.2 (Harmonic Motion)

( 2-3).

.

(t) = sin t (1)

(t) :

:

:

. x(t)

. .

(t) = peak sin t (2)

2-3 .

T

(, ).

20 1

f 1/T /2 .

( = 1/ = 1/f = cycles/second)

t .

2-3 5 ms(510-3sec)

20 ms (4 5 ms). (1/2010-3)

50 , 50 . 60

.

2-3

1.3 (Vibration Amplitude)

1.3.1 (Vibration Displacement)

2-1

(1) . microns (1 micron =

0.001 ) mils (1 mil = 0.001 inch) .

1.3.2 (Vibration Velocity)

2-4 () .

.

(Zero).

.

Peak Velocity . /sec. peak

in/sec. peak , .

v(t) =dx(t)dt

(3)

2 21

2-4

1.3.3 (Vibration Acceleration)

.

. .

a(t) =dv(t)dt

=d2x(t)dt2

(4)

2-5 .

.

. .

Peak .

g's" Peak g

. g 980.665 /sec2 = 386.087 in/sec2 = 32.1739

ft/sec2 .

2-5

22 1

1.3.4 (Summary)

.

, , ,

.

x(t) = xpeaksint (5)

v = xpeakcost = vpeaksin[t +2] (6)

a(t) = -2xpeaksint = Apeaksin[t + ] (7)

2-6 90

180.

2-6 , ,

, ,

. ( )

.

,

(f) .

,

.

2-7 .

,

.

2 23

.

,

Severity ,

,

.

2-7 , ,

( ) ,

2-8 .

2-8

24 1

1.4 (Measurement Units)

. 2-9

.

2-9

RMS =2 2

Average =12 Peak

Peak-to-Peak = 2 Peak (8)

Peak = 1.414 RMS = 1.57 Average (9)

RMS = .707 peak = 1.11 Average (10)

Average = 0.9 RMS = 0.637 Peak (11)

Peak-to-Peak (Average)

1

.

Severity (RMS : Root Mean

Square) Peak Average Velocity Velocity RMS

(AC) RMS .

AC 0 (Peak Value) .

2 25

Peak

. RMS

. Velocity RMS

.

RMS Velocity 2 .

.

2-10 0.5 3

(In-phase) . Peak

Peak . 3 Severity

Peak

. RMS

3 12% .

2-11 3 (

) 2-10 Peak

50% .

2-11 Severity 2-10

1.5 . . Severity

. RMS .

2-10 3RPM Peak Velocity

RMS Velocity 12% .

26 1

2-11 3RPM Peak Velocity

1.5 RMS 12% .

2-12 Peak Velocity RMS .

1.5.

(A Comparison of Vibration Measurement Techniques)

1.5.1 (Introduction)

4050

.

? .

3 .

2 27

.

Rotor

Rotor Case

2

.

1.5.2

(General Factors Determining Bearing and Shaft Vibration)

( )

. .

2-13 .

.

,

, .

.

2-13

28 1

2-14

. . Oil

.

. (Casing)

.

2-14 Casing Shaft

2-15 () . Fan,

, , , .

.

.

.

,

.

2-15

2 29

1.5.3

(Reasons for Measuring Bearing Vibration)

Cap

.

.

Stud , Pick Up

Magnetic Base .

Pick Up 1 5.000

( 10 200 )

. 10 ,

. , ,

.

2-16 4500 rpm , ,

.

.

,

.

.

, , ,

, .

350,000 cpm

.

,

, .

2-17 .

30 1

2-16 ,

2 31

2-17

1.5.4

(Disadvantage of Measuring Bearing Vibration)

2-14 Mechanical Impedance

(Transmissibility = Shaft/Bearing Amplitude) ,

. 2-18 150

.

2-18 Shaft

32 1

3.812.5 ( 6.7)

.

.

.

. Pickup

Pickup

. ,

.

1.5.5

(Reasons for Measuring Relative Shaft Vibration)

2-19 Noncontact

Pickup . Pickup

.

, , .

.

( Pickup )

Misalignment

. .

2-19 Pickup

1.5.6

(Disadvantages of Measuring Relative Shaft Vibration)

, Blade

2 33

Sensitivity .

.

.

1.5.7

(Reasons for Measuring Absolute Shaft Vibration)

.

.

2-20 Shaft Rider

. Tip,

.

2-20 Shaft Rider Accessory

Pickup Pickup

. ,

.

Shaft Rider (Electrical Runout)

. Shaft Rider

.

34 1

1.5.8

(Disadvantages of Measuring Absolute Shaft Vibration)

.

, , .

().

Nodal Point .

Shaft Rider .

Probe

.

Probe Probe

.

.

.

.

2. (Vibration Frequency)

2.1 (Definition of Vibration Frequency)

2-21

(T) , (1/T)

. (cpm)

Hertz (1 Hertz = 60 cpm) .

2-21

2 35

2.2

(Information Provided by Vibration Frequency)

.

.

.

. ,

.

,

. Misalignment

Oil Whirl 1RPM .

2-22

.

.

. 1RPM

. 2RPM, 3RPM

. 1RPM 1 (First Harmonics)

.

.

. 1

RPM , .

.

.

36 1

2-22

2-23

.

2 37

2-23 ( )

38 1

2 39

2.3 (Vibration Spectrum)

2-27(c) .

2-2 .

.

.

.

. 2-24.

Pen

Servo Motor .

2-24

2-24

. 2-25

. (1RPM, 2RPM,

3RPM ) Oscilloscope

.

Oscilloscope .

Beam 2 .

2-26 .

40 1

tMAX( sec) =(60) (# FFT Lines)

FMAX=

(60) (Sample Size)(2.56) (FMAX )

tMAX(cpm) =(60) (# FFT Lines)

tMAX=

(60) (Sample Size)(2.56) (tMAX )

tMAX = Sampling( ) (sec)

Sample Size = Time Waveform Analog to

Conversion (400 Line FFT 1024

Sample )

FMAX = Maximum Spectral Frequency of Frequency Span (cpm)

2-25 Spectrum

2 41

2-26 Oscilloscope

X (sec min), Y (,

) .

.

. 2-24 2-27

Peak Peak .

(T) (F) (cpm, cps, Hertz) .

Fast Fourier Transform (FFT)

. FFT ( ) (

) Computer(Microprocessor) Transform. Fourier

2-25 ,

. 2-27

. (a) , (b)

, 3

.

, . 2-27(c)

.

( 2-27(a)) ( 2-27(c))

( ) ( )

. Spectrum .

Spectrum Signature FFT . Spectrum( )

42 1

(Discrete Frequency)

. 2-28

(a), -(b),

(c) FFT Spectrum .

(a)

(b)

3 . 3 , .

(c)

2-27

2-28 FFT Spectrum

Spectrum Peak

. ,

2 43

. Spectrum () 1,770 cpm

, (1RPM) 1,770 rpm ,

1RPM ,

, Blade Pass

.

3. (Vibration Phase)

3.1 (Definition of Vibration Phase)

3.1.1 (Vibration Phase)

.

(, Unbalance,

Misalignment, Eccentricity, Bent Shaft, Soft Foot, Cracked/Broken Gear Tooth,

Resonance, Loose Hold-Down Bolt ). 2 3RPM

. (1, 2, 3RPM)

.

. .

2

. 2-29 (In-Phase) 0

2 .

2-29 (0) 2

44 1

2-30 90 2 . Mass #2 Mass #1 1

1/4(90). Mass #2 Mass #1 90

(Phase Lag) .

2-30 90 2

2-31 (180) 2 .

Mass #1 Mass #2 .

2-31 (180) 2

2-32 .

1 2 0() 180

() .

2 45

2-32

3.1.2 (Relative Phase)

.

2-33

5 .

(mils, in/s, g's)

.

0 180 (Leading) (Lagging) .

3.1.3 (Absolute Phase)

Keyphasor (1 1 )

Positive Peak ( 2-382-40 ).

.

46 1

( )

.

(Lag Angle)

, 0 360 .

0

.

3.2 (Phase Measurements)

3 Strobo Light

Photocell Keyphasor

.

3.2.1 Strobe Light Method

Strobe Light Pickup Flash

Dial Flash,

.

2-34

2-35

2 47

Strobe Light (

) .

, .

Strobe Light ,

Strobe Light

.

3.2.2 Photocell Method

Tape Photocell Light

Beam , Strobe Light

Photocell .

2-36 Photocell

3.2.3 Keyphasor Method

Proximity Probe (-18 V-24 Vdc)

Radio Frequency , Field

Eddy Current . Probe Gap Radio

Frequency Eddy Current . Gap,

.

48 1

2-37 Proximity Probe

Proximity Probe Keyphasor (Shaft Reference Notch

Projection) Probe Keyphasor

Pulse (Keyphasor Pulse) . Keyphasor Pulse

Probe (Vibration) Positive Peak .

2-38 Keyphasor Probe

2-39 1 Blank

Spot Positive Peak.

Positive Peak. .

2-39 1

2 49

.

2. 1 (Keyphasor

Keyphasor )2 . Blank

Spot Positive Peak .

.

2-40 n