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Autorsk dlo v rmci projektu Rozvoj jazykovch kompetenc pracovnk VB-TUO: InterDV, registran slo projektu: CZ.1.07/2.2.00/15.0132

OSTRAVA 2012 ALENA BILOOV JAN BILO

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CONTENTS

LIST OF ABBREVIATIONS ............................................................................................... 7

FOREWORD ........................................................................................................................ 8

1 VIBRATION DIAGNOSTICS PRELIMINARY CONSIDERATIONS................. 10

1.1 Role of Maintenance ............................................................................................ 11

1.2 Maintenance Types .............................................................................................. 11

1.3 Diagnostics........................................................................................................... 13

1.4 Excitation Force and Vibration Response............................................................ 15

1.5 Basic Quantities Describing the Oscillatory Movement...................................... 18

1.6 Measured Quantities ............................................................................................ 21

2 VIBRATION MEASUREMENTS..............................................................................24

2.1 Analyzer ............................................................................................................... 24

2.2 Vibration Transducers.......................................................................................... 24

2.2.1 Displacement Transducers ........................................................................... 25

2.2.2 Velocity Transducers ................................................................................... 27

2.2.3 Accelerometers............................................................................................. 28

2.3 Vibration Measured on Non-Rotating Parts of a Machine (Absolute Vibration) 33

2.3.1 Selecting Measurement Points ..................................................................... 33

2.3.2 Criteria of Assessment according to ISO 10816.......................................... 34

2.4 Shaft Vibration..................................................................................................... 37

2.4.1 Proximity Probes Installation....................................................................... 38

2.4.2 Evaluation of Relative Vibration ................................................................. 40

2.4.3 Interpretation of the Proximity Probe Signal ............................................... 41

3 VIBRATION ANALYSIS (FREQUENCY ANALYSIS) .......................................... 45

3.1 Fourier Transform................................................................................................ 46

3.2 Aliasing Error (Stroboscopic Effect) ................................................................... 47

3.3 Leakage Error....................................................................................................... 48

3.4 Setting the Analyzer............................................................................................. 50

3.4.1 Number of Spectral Lines ............................................................................ 50

3.4.2 Number of Averages and Averaging ........................................................... 51

3.4.3 Starting Measurements................................................................................. 53

3.4.4 Time Synchronous Averaging ..................................................................... 54

3.5 Methods of Spectra Analysis ............................................................................... 55

3.5.1 Significant Frequencies................................................................................ 55

3.5.2 Reference Spectrum and Monitoring of Changes ........................................ 56

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3.5.3 Special Types of Cursors..............................................................................56

3.5.4 Waterfall Diagrams.......................................................................................57

3.5.5 Phase.............................................................................................................57

3.5.6 Applying Spectra and Phase Analysis to the Diagnostics of Machine Faults ...................................................................................................................... 60

4 DIAGNOSTICS OF COMMON ROTATING MACHINERY FAULTS ...................62

4.1 Unbalance .............................................................................................................63

4.1.1 Types of Unbalance......................................................................................63

4.1.2 Balancing on Balancing Machines ...............................................................65

4.1.3 Diagnostics of an Unbalance ........................................................................69

4.1.4 Field Balancing.............................................................................................72

4.2 Misalignment ........................................................................................................78

4.2.1 Alignment of Machines ................................................................................78

4.2.2 Diagnostics of Misalignment........................................................................82

4.3 Diagnostics of Rotor Systems Faults....................................................................82

4.3.1 Rotor Resonance...........................................................................................82

4.3.2 Orbit and Shaft Centerline............................................................................90

4.3.3 Rotor Rub .....................................................................................................91

4.4 Journal Bearings ...................................................................................................92

4.4.1 Principle of Journal Bearing Operation........................................................92

4.4.2 Principles of the Cylindrical Bearing Construction......................................93

4.4.3 Operational Problems of Cylindrical Bearings and Their Solving...............94

4.4.4 Elliptical Bearing..........................................................................................96

4.4.5 Other Types of Radial Bearings ...................................................................98

4.4.6 Faults of Journal Bearings - Wear, Excessive Clearance .............................99

4.4.7 Operational Problems of Machines Supported on Journal Bearings..........100

4.5 Rolling Element Bearings...................................................................................103

4.5.1 Rolling Bearing Design ..............................................................................103

4.5.2 Parameter for Assessing Rolling Bearing Condition..................................104

4.5.3 Types of Vibration Generated by Defective Rolling Bearings ..................105

4.5.4 Stages of Rolling Bearing Fault Development ...........................................108

4.5.5 Acceleration Envelope................................................................................109

4.5.6 Acceleration Envelope Spectra...................................................................111

REFERENCES ..................................................................................................................113

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LIST OF SYMBOLS

a acceleration [m s-2]

an, bn Fourier coefficients

cn Fourier coefficient (amplitude)

decay constant [s-1]

f frequency resolution [Hz]

f frequency [Hz]

fs sampling frequency [Hz]

fmax Nyquist frequency [Hz]

f(t) excitation force as a function of time [N]

F excitation force amplitude [N]

g acceleration of gravity ( 10 m s-2)

phase shift

F initial excitation force phase shift

n Fourier coefficient (phase)

k stiffness [kgs-2]

m mass [kg]

N number of time samples

t time [s]

T period, length of the time record [s]

v velocity [m/s], [mm/s]

x(t) displacement as a function of time [m], [mm], [m]

X displacement amplitude [m], [mm], [m]

xa amplitude (of an arbitrary quantity)

xRMS root mean square value (of an arbitrary quantity)

xmean mean value (of an arbitrary quantity)

xp-p peak-to-peak value (of an arbitrary quantity)

angular excitation frequency [s-1] (= [rad/s])

natural angular frequency of vibration [s-1]

damping ratio [-]

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LIST OF ABBREVIATIONS

A/D analog/digital

CW clockwise

CCW counter clockwise

CPM cycles per minute

SN Czech standard

FFT Fast Fourier Transform

MIMOSA Machinery Information Management Open Systems Aliance

ISO International Standard Organization

RMS Root Mean Square

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ACKNOWLEDGEMENT

This text was created with financial support of the European Social Fund in the scope of the project No CZ.1.07/2.2.00/15.0132. My preparati