كتاب The Simplified Handbook of Vibration Analysis - Volume 1

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The Simplified Handbook of Vibration Analysis
Volume 1: Introduction to Vibration Analysis Fundamentals
Arthur R. Crawford
President, ARC Associates
Senior Vibration Analyst, Computational Systems Incorporated
and
Steve Crawford
President, Crawford Communications

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Table of Contents
INTRODUCTION TO VIBRATION |. .
EARLY METHODS OF VIBRATION ANALYSIS
ELECTRONICS IN VIBRATION ANALYSIS
DIGITAL ANALYSIS OF VIBRATION SIGNATURES j
USES OF VIBRATION ANALYSIS
Certification
Potential Fault Analysis
Diagnostic Analysis
SYSTEM RESPONSE
I.0 A MECHANICAL SYSTEM
1.1 Mass
1.2 Spring
1.3 Damping
2.0 DEGREES OF FREEDOM
3.0 FORCING FUNCTIONS
4.0 CHARACTERISTICS OF VIBRATION
5.0 SINE WAVE PLOT OF PENDULUM MOTION
6.0 NATURAL FREQUENCY
7.0 DAMPING
8.0 FREE VS. FORCED VIBRATION
9.0 FORCED VIBRATIONS
10.0 PLOTTING FORCED VIBRATION
10.1 Amplification
II.0 RESONANCE AND DEGREES OF FREEDOM
12.0 SYSTEM OPERATING FREQUENCY VS. RESONANT FREQUENCY
12.1 Competition
12.2 Wear
12.3 Customer Demand
13.0 VECTOR REPRESENTATION OF VIBRATION
SUMMARY
TRANSDUCERS
1.0 TYPES OF TRANSDUCERS
LI Displacement Transducers
1.2 Velocity Transducers
1.3 Accelerometers
2.0 CONVERTING TRANSDUCER OUTPUT
3.0 OTHER TYPES OFTRANSDUCERS
SUMMARY
GENERAL ANALYSIS TECHNIQUES
1.0 OUTLINE TO VIBRATION PROBLEM SOLVmG
1.1 Identify the Problem
1.2 Gather Information About the Vibrating System
1.3 Determine the Possible Forcing Function(s)
1.4 Determine Where to Take Data and What Equipment to Use
1.5 Take Vibration Data
1.6 Analyze Vibration Data
1.7 Make Recommendations
SUMMARY
PHASE . . . . . . . .
1.0 MEASURING PHASE
1.1 Transducer Characteristics
2.0 SYSTEM RESPONSE AND PHASE
'2.1Finding theImbalance
2.2 Measuring Phase with a Strobe Light
2.3 Measuring Phase with a Reference Signal
3,0 CROSS CHANNEL TECHNIQUES
3.1 An Example of Cross Channel Analysis
4.0 OTHER CROSS CHANNEL CAPABILITIES
4.1 Transfer Functions
SUMMARY
FIELD BALANCING .
1.0 ADVANTAGES OF FIELD BALANCING
2.0 PRELIMINARIES TO FIELD BALANCING
3.0 SINGLE PLANE BALANCE
3.1 The Single Plane Balance Procedure
4.0 PLOTTING SINGLE PLANE BALANCE CORRECTION
5.0 MULTIPLE PLANE BALANCE
5.1 The Multiple Plane Balance Procedure
5.2 Single Plane Correction for Plane A
' 5.3MultiplePlaneSolution
6.0 CORRECTION WEIGHT SPLIT
6.1 The Weight Split Procedure
7.0 FOUR RUN BALANCE WITHOUT PHASE
7.1 Single Plane Balance Without Phase
8.0 PHASE READINGS USING A REFERENCE TRANSDUCER
SUMMARY
SHAFT ALIGNMENT
1.0 INTRODUCTION
2.0 TYPES OF MISALIGNMENT
3.0 ALIGNMENT PROCEDURES
3.1 The Face and Rim Method
3.2 The Reverse Dial Method
3.3 Other Methods
4.0 ALIGNMENT PREPARATION
4.1 Base Preparation
4.2 Soft Feet and Frame Twists
4.3 Tightening Machine Foot Bolts
4.4 Lifting and Moving the Machine
4.5 Piping Connections
4.6 Dial Indicator Sag
4.7 Thermal Growth
4.8 Calculating Machme Moves
5.0 VIBRATION FROM MISALIGNMENT
6.0 A SAMPLE ANALYSIS PROBLEM
SUMMARY
REFERENCES
APPENDIX A - APPROXIMATE HARDWARE WEIGHTS
GLOSSARY OF TERMS
Figure 1 - a one degree of freedom system (translational) |
Figure 2 - a one degree of freedom system (rotational)
Figure 3 - viewing pendulum motion
Figure 4 - defining pendulum motion
Figure 5 - plotting pendulum motion
Figure 6- labeling the pendulum plot
Figure 7- plotting a sine wave
Figure 8 - the relationship of velocity and displacement
Figure 9- the relationship of acceleration, velocity, and displacement
Figure 10 - a radian
Figure 11 - an underdamped system
Figure 12 - a critically damped system
Figure 13 - an overdamped system
Figure 14 - plotting a damped pendulum's movement
Figure 15 - a spring-mass system
Figure 16- amplitude vs. frequency response curve
Figure 17 - the amplification range
Figure 18 - system response curve for a new motor
Figure 19- the effect of wear on system response
Figure 20 - motion due to forcing function F(t)
List of Figures
Figure 21- the position of F(t) on x,y axes
Figure 22 - vector representation of an imbalance force
Figure 23 - vector addition
Figure 24 - vectors F*and Fm
Figure 25- the vector representation of Fc
Figure 26 - F(t) brings the system into equilibrium
Figure 27- F*, Fc, and Fm
Figure 28 - F(t) keeps the system in equilibrium
Figure 29 - frequency response and phase angle
Figure 30 - vector diagram of system running at Fr
Figure 31 - non-contact eddy current probe
Figure 32 - eddy current transducer DC offset voltage
Figure 33 - seismic velocity transducer
Figure 34 - compressive mode accelerometer
Figure 35 - shear mode accelerometer
Figure 36 - poorly machined spot faces
Figure 37 - response curves for stud mounting
Figure 38 - response curves for adhesive mounting
Figure 39 - response curves for magnet mounting
Figure 40 - response curves for hand-held accelerometers
Figure 41 - integration and double integration
Figure 42 - differentiation and double differentiation
Figure 43 - machine sketch for vibration analysis
Figure 44 - anti-friction bearing components
Figure 45 - sleeve bearing
Figure 46 - friction vs. RPM
Figure 47 - oil whirl
Figure 48 - bearing designs that prevent oil whirl
Figure 49 - peripheral velocity of two sheaves
Figure 50 - calculating belt length
Figure 51 - calculating gear ratios
Figure 52 - planetary gears \ i
Figure 53- planes for collecting vibration data
Figure 54 - determining total bearing motion
Figure 55 - time domain data taken on a fan
Figure 56 - frequency domain display of time domain data from Figure 55
Figure 57 - measuring transducer phase shift
Figure 58 - system response and phase characteristics
Figure 59 - system phase response and measurement
Figure 60 - positive and negative angles
Figure 61 - an unbalanced rotor
Figure 62 - impact directions
Figure 63 - an imbalance condition
Figure 64 - mechanical response at a degree of freedom
Table of ContentsFigure 65 - plotting a single plane balance solution 114
Figure 66 - determining correction weight split using polar paper 120
Figure 67 - solving four-run formulas on polaf paper 123
Figure 68 - phase between reference and vibration signals 124
'TV \ Figure69- types of misalignment
" Figure70-usingdialindicatorsforalignment I 129
Figure 71 - positions for taking dial indicator readings } 130
1Figure 72- the face and rim method j 131
8: Figure 73- length of subtended line segments | 131
y : ~ - Figure 74 - mounting the dial indicator on the bracket j 132
Figure 75 - the reverse dial method j 132
^ ' > Figure 76 - taking reverse dial readings off of a spool piece 133
Figure 77 - using dial indicators to check for a soft foot 134
Figure 78 - measuring indicator bracket sag | 136
jFigure 79- measuring thermal growth | 138
Figure 80 - vibration spectra of cooling pump before alignment 141
Figure 81 - vibration spectra after alignment 143
'6 ‘-V-~T-:Figure82-thegraphicsolutionforcoldalignment 144
List of Tables
Table 1- suggested alignment tolerances i 128
Table 2 - dial indicator readings on shim and fixed machine . .. 141
Table 3- machine movements necessary for cold alignment 142
Table 4 - measured thermal growth 142
Table 5 - machine movements necessary for hot alignment 142
Table 6 - UNC Hex Head Cap Screws . 150
Table 7 - UNC Socket Head Cap Screws 152
Table 8 - UNC Machine Screws | v 154
Table 9 - UNC Socket Head Set Screws ( 155 »
Table 10 - UNF Hex Head Cap Screws j 156
Table 11- UNF Socket Head Cap Screws 158
Table 11- UNF Socket Head Cap Screws (cont.) 159
Table 12 - UNF Machine Screws I 160
Table 13 - UNF Socket Head Set Screws

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