كتاب Vibration Analysis, Instruments, and Signal Processing
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 كتاب Vibration Analysis, Instruments, and Signal Processing

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تاريخ التسجيل : 01/07/2009
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مُساهمةموضوع: كتاب Vibration Analysis, Instruments, and Signal Processing    كتاب Vibration Analysis, Instruments, and Signal Processing  Emptyالثلاثاء 13 ديسمبر 2022, 1:40 am

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Vibration Analysis, Instruments, and Signal Processing
Jyoti Kumar Sinha

كتاب Vibration Analysis, Instruments, and Signal Processing  V_a_i_10
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Contents
Preface xi
About the Author xiii
1. Introduction .1
1.1 Introduction .1
1.2 Layout of the Chapters .2
1.2.1 Basic Theories and Analysis Methods 3
1.2.2 Instrumentations, Signal Processing, and
Experimental Methods 3
1.2.3 Combined Analysis and Experimental Methods 4
1.2.4 Case Studies 4
2. Single Degree of Freedom (SDOF) System .5
2.1 A Single Degree of Freedom (SDOF) System 5
2.2 Equation of Motion .5
2.2.1 Example 2.1: SDOF System .7
2.2.2 Example 2.2: A Massless Bar with a Tip Mass .7
2.2.3 Example 2.3: A Massless Bar with a Disc .8
2.3 Damped SDOF System .9
2.3.1 Equation of Motion for Free Vibration 9
2.3.2 Critically Damped System: Case 1: Limiting Case
When DF = 0 . 11
2.3.3 Overdamped System: Case 2: When DF ≥ 0 .12
2.3.4 Underdamped System: Case 3: When DF ≤ 0 13
2.4 Forced Vibration 15
2.4.1 The System Vibration Behavior 19
2.5 Summary 21
3. Introduction to Finite Element Modeling 23
3.1 Basic Concept .23
3.1.1 Degree of Freedom (DOF) 23
3.1.2 Concept of Node, Element, and Meshing in
the FE Model . 24
3.1.3 Element Mass and Stiffness Matrices for a Spring .25
3.2 Modeling Procedure for Discrete Systems 29
3.2.1 Example 3.1: Three-DOF System 29
3.2.2 Example 3.2: Another Three-DOF System . 31
3.3 Extension of FE Modeling Approach to Continuous Systems . 32
3.3.1 Example 3.3: A Simple Continuous System of Steel Bar . 32
3.3.2 Example 3.4: Beam Structure .33iv Contents
3.4 Element Mass and Stiffness Matrices 34
3.5 Construction of Global Mass and Stiffness Matrices . 37
3.6 Concept of the Formal FE Method .39
3.6.1 Element Shape Functions (ESFs) 40
3.6.2 Generalized Mass and Stiffness Matrices 40
3.7 FE Modeling for the Beam in Example 3.4 41
3.7.1 Applying Boundary Conditions (BCs) 42
3.7.1.1 Cantilever Condition at Node 1 .42
3.7.1.2 Simply Supported (SS) Beam at Nodes 1 and 3 .42
3.7.1.3 Clamped–Clamped (CC) Beam at Nodes 1
and 3 .43
3.8 Modal Analysis .43
3.8.1 Natural Frequencies and Mode Shape Estimation .44
3.8.2 Concept of Mode Shapes .46
3.9 Sensitivity of the Element Size 50
3.10 Damping Modeling 53
3.11 Summary 55
References .55
4. Force Response Analysis .57
4.1 Introduction .57
4.2 Direct Integration (DI) Method .58
4.2.1 Example 4.1: A SDOF System .59
4.2.2 Example 4.2: A Two-DOF System 61
4.2.3 Example 4.3: A Cantilever Beam .69
4.3 Mode Superposition (MS) Method .73
4.3.1 Example 4.4: A Two-DOF System 78
4.4 Excitation at the Base 86
4.5 Summary 89
Reference .89
5. Introduction to Vibration Instruments 91
5.1 Vibration Measurement 91
5.1.1 Typical Measurement Setups .92
5.1.2 Steps Involved in the Collection of Data 95
5.1.3 Instrument Calibration and Specifications 96
5.1.3.1 Specifications of Instruments/Sensors 97
5.2 Response Measuring Transducers 99
5.2.1 Sensor/Transducer Unit 99
5.3 Displacement Transducers . 100
5.3.1 Proximity or Eddy Current Probe . 101
5.3.2 Optical Sensor 102
5.4 Velocity Transducers 102
5.4.1 Seismometer . 102
5.4.2 Laser Sensor 106Contents v
5.5 Acceleration Transducers . 106
5.5.1 Technical Specifications of Accelerometer . 109
5.5.2 Accelerometer Mounting 110
5.6 External Excitation Instruments . 111
5.6.1 Instrumented Hammer . 111
5.6.2 Portable Shaker . 111
5.6.3 Payload Shaker . 112
5.7 Data Collection and Storage 114
5.7.1 Digital Data Tape Recorder 114
5.7.2 PC-Based Data Acquisition and Storage . 114
5.7.3 Precautions during Data Recording/Collection 115
5.8 Concept of Sampling Frequency, fs . 115
5.9 Aliasing Effect and the Selection of Sampling Frequency, fs 118
5.9.1 Effect of Different Sampling Frequencies 118
5.9.2 Observations . 121
5.10 DAQ Device Bit for ADC 122
5.10.1 Case 1: 2-Bit DAQ Device 123
5.10.2 Case 2: 16-Bit DAQ Device 126
5.10.3 Case 3: DAQ Card Bit, b = 8, FSIV = 10 V, Sd = 10/28 =
0.0391 V/bin 131
5.10.4 Summary of ADC 134
6. Basics of Signal Processing 137
6.1 Introduction . 137
6.2 Nyquist Frequency 137
6.3 Time Domain Signals . 137
6.4 Filtering 139
6.4.1 Low-Pass (LP) Filter . 140
6.4.2 High-Pass (HP) Filter . 140
6.4.3 Band-Pass (BP) Filter 140
6.5 Quantification of Time Domain Data . 142
6.5.1 RMS Value . 142
6.5.2 Example 6.1: RMS Computation 143
6.5.3 Crest Factor (CF) . 144
6.5.4 Kurtosis (Ku) . 144
6.5.5 Example 6.2: Comparison between CF and Kurtosis . 145
6.6 Integration of Time Domain Signals 146
6.6.1 Example 6.3: Data Integration 146
6.7 Frequency Domain Signal: Fourier Transformation (FT) . 148
6.7.1 Fourier Series 148
6.7.2 Limitations for Experimental Data . 150
6.7.3 Alternate Method . 150
6.7.4 Computation of Fourier Transform (FT) 151
6.7.5 Example 6.4: Importance of Segment Size on
FT Analysis . 152vi Contents
6.7.6 Leakage 154
6.7.7 Window Functions 157
6.8 Aliasing Effect . 160
6.9 Averaging Process for the Spectrum Computation . 165
6.9.1 Example 6.5: Averaged Spectrum 165
6.9.2 Concept of Power Spectral Density (PSD) 166
6.9.3 Example 6.6: Comparison of the Averaged Spectra
for the Signals with and without (i.e., No) Noise 168
6.9.4 Example 6.7: Averaged Spectrum for the
Noisy Signal .170
6.9.5 Concept of Overlap in the Averaging Process . 172
6.10 Short-Time Fourier Transformation (STFT) . 173
6.11 Correlation between Two Signals . 175
6.11.1 Cross-Power Spectral Density (CSD) 175
6.11.2 Frequency Response Function (FRF) 176
6.11.3 Ordinary Coherence 177
6.11.4 Example 6.8: FRF and Coherence 178
6.12 Experiments on a SDOF System . 180
References . 183
7. Experimental Modal Analysis . 185
7.1 Introduction . 185
7.2 Experimental Procedure 185
7.2.1 Impulsive Load Input Using the Instrumented
Hammer 186
7.2.2 Shaker Excitation . 186
7.3 Modal Test and Data Analysis 187
7.4 Example 7.1: Peak Pick Method . 188
7.4.1 Step 1: The Modal Testing Experiment . 189
7.4.2 Step 2: Computation of the Amplitude Spectrum,
FRF, and Coherence . 189
7.4.3 Step 3: Identification of Natural Frequency from
the FRF Plot . 191
7.4.4 Step 4: Mode Shape Extraction . 196
7.4.5 Step 5: Half-Power Point (HPP) Method for
Estimation Modal Damping . 196
7.5 Example 7.2: A Clamped–Clamped Beam . 198
7.5.1 Step 1: The Modal Testing Experiment . 198
7.5.2 Step 2: Computation of the Amplitude Spectra, FRFs,
and Coherences 200
7.5.3 Step 3: Natural Frequency Identification from
the FRF Plots .203
7.5.4 Step 4: Extraction of Mode Shapes 205
7.5.5 Step 5: Estimation Modal Damping 206Contents vii
7.6 Industrial Examples 207
7.6.1 Example 7.3: Sparger Tube 209
7.6.2 Example 7.4: Shutoff Rod Guide Tube . 210
7.6.3 Example 7.5: Horizontal Tank 214
7.7 Summary 217
References . 217
8. Finite Element Model Updating 219
8.1 Introduction . 219
8.2 Model Updating Methods .220
8.3 Gradient-Based Sensitivity Method .220
8.3.1 Steps Involved 221
8.3.2 Regularization 225
8.4 Example 8.1: A Simple Steel Bar 225
8.5 Example 8.2: An Aluminum Cantilever Beam . 231
8.6 Summary 233
References .233
9. A Simple Concept on Vibration-Based Condition Monitoring 235
9.1 Introduction .235
9.2 Operational Personnel 236
9.2.1 Rotating Machines .236
9.2.2 Reciprocating Machines 237
9.2.3 Piping . 237
9.2.4 Comparative Observations . 237
9.3 Plant Maintenance Engineers .238
9.4 Vibration Experts 238
9.5 Condition Monitoring of Rotating Machines 238
9.5.1 Type of Vibration Transducers . 240
9.5.2 Data Processing and Storage 241
9.6 Normal Operation Condition 242
9.6.1 Overall Vibration Amplitude . 242
9.6.2 Vibration Spectrum . 242
9.6.3 The Amplitude—Phase versus Time Plot 244
9.6.4 The Polar Plot .244
9.6.5 The Orbit Plot .244
9.7 Transient Operation Conditions . 246
9.7.1 The 3D Waterfall Plot of Spectra 246
9.7.2 The Shaft Centerline Plot 246
9.7.3 The Orbit Plot . 247
9.7.4 The Bode Plot 247
9.8 Instrumenting TG Sets for Condition Monitoring . 248
9.9 Types of Faults .250viii Contents
9.10 Identification of Faults 251
9.10.1 Mass Unbalance . 251
9.10.2 Shaft Bow or Bend . 252
9.10.3 Misalignment and Preloads . 252
9.10.4 Crack 253
9.10.5 Asymmetric Shaft 254
9.10.6 Shaft Rub .256
9.10.7 Fluid-Induced Instability 257
9.10.8 Mechanical Looseness .259
9.10.9 Blade Vibration .259
9.10.10 General Comments 260
9.11 Condition Monitoring for Other Rotating Machines . 261
9.11.1 Detection of Fault(s) in Antifriction Bearings 261
9.11.2 Characteristic Frequencies of a Ball Bearing . 262
9.11.3 Concept of Envelope Analysis .263
9.12 Field Balancing 264
9.12.1 Single Plane Balancing—Graphical Approach 265
9.12.1.1 Example 9.1 265
9.12.1.2 Example 9.2 267
9.12.2 Single Plane Balancing—Mathematical Approach . 267
9.12.3 Multiplane Balancing 272
9.13 Comments about Model-Based Fault Diagnosis (MFD) 273
References . 274
10. Case Studies .277
10.1 Introduction .277
10.2 Roles and Philosophy of Vibration Diagnostic
Techniques (VDTs) 277
10.3 Dynamic Qualification due to In-Service Load Condition . 278
10.4 Seismic Qualification 280
10.4.1 Shake-Table Method 280
10.4.2 Railway Track–Induced Vibration Method 280
10.4.3 Direct Use of In Situ Modal Data . 281
10.4.4 Updated FE Model Method 283
10.4.4.1 Experimental Setup and Modal Tests .283
10.4.4.2 Updated FE Model .284
10.4.4.3 The Reactor Conditions .285
10.4.4.4 Seismic Response Estimation .286
10.5 Machine Installation and Commissioning 286
10.5.1 High Vibration 287
10.5.2 Different Dynamic Behavior of Two Identical Pumps . 289
10.5.3 Frequent Failure . 292Contents ix
10.6 Aging Management for Machines and Structural
Components . 294
10.6.1 Structural Components: The Coolant Channels . 294
10.6.2 Machines . 298
10.6.2.1 A Centrifugal Pump 298
10.7 Summary 302
References .302


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