Vibration Analysis for Electronic Equipment

cover.jpg......Page 1
Front Matter......Page 2
Bibliography......Page 0
Preface......Page 5
List of Symbols......Page 7
Table of Contents......Page 9
1.1 Vibration Sources......Page 18
1.2 Definitions......Page 19
1.4 Degrees of Freedom......Page 20
1.6 Vibration Nodes......Page 22
1.7 Coupled Modes......Page 23
1.8 Fasteners......Page 24
1.9 Electronic Equipment for Airplanes and Missiles......Page 27
1.10 Electronic Equipment for Ships and Submarines......Page 30
1.11 Electronic Equipment for Automobiles, Trucks, and Trains......Page 32
1.13 Electronics for Computers, Communication, and Entertainment......Page 33
2.1 Single Spring-Mass System without Damping......Page 34
2.1.1 Sample Problem - Natural Frequency of a Cantilever Beam......Page 36
2.2 Single-Degree-of-Freedom Torsional Systems......Page 38
2.2.1 Sample Problem - Natural Frequency of a Torsion System......Page 39
2.3 Springs in Series and Parallel......Page 40
2.3.1 Sample Problem - Resonant Frequency of a Spring System......Page 42
2.4 Relation of Frequency and Acceleration to Displacement......Page 43
2.4.1 Sample Problem - Natural Frequency and Stress in a Beam......Page 44
2.5 Forced Vibrations with Viscous Damping......Page 47
2.6.1 Sample Problem - Relating the Resonant Frequency to the Dynamic Displacement......Page 51
2.7 Multiple Spring - Mass Systems without Damping......Page 53
2.7.1 Sample Problem - Resonant Frequency of a System......Page 54
3.2 Vibration Problems with Components Mounted High above the PCB......Page 56
3.2.1 Sample Problem - Vibration Fatigue Life in the Wires of a TO-5 Transistor......Page 57
3.3 Vibration Fatigue Life in Solder Joints of a TO-5 Transistor......Page 60
3.4 Recommendations to Fix the Wire Vibration Problem......Page 62
3.5.1 Sample Problem - Dynamic Forces and Fatigue Life in Transformer Lead Wires......Page 63
3.6 Relative Displacements between PCB and Component Produce Lead Wire Strain......Page 66
3.6.1 Sample Problem - Effects of PCB Displacement on Hybrid Reliability......Page 67
4.1 Natural Frequency of a Uniform Beam......Page 73
4.1.1 Sample Problem - Natural Frequencies of Beams......Page 77
4.2 Nonuniform Cross Sections......Page 81
4.2.1 Sample Problem - Natural Frequency of a Box with Nonuniform Sections......Page 85
4.3 Composite Beams......Page 86
5.1 Electronic Components Mounted on Circuit Boards......Page 92
5.2 Bent with a Lateral Load - Hinged Ends......Page 94
5.3 Strain Energy - Bent with Hinged Ends......Page 97
5.4 Strain Energy - Bent with Fixed Ends......Page 100
5.5 Strain Energy - Circular Arc with Hinged Ends......Page 107
5.6 Strain Energy - Circular Arc with Fixed Ends......Page 109
5.7 Strain Energy - Circular Arcs for Lead Wire Strain Relief......Page 111
5.7.1 Sample Problem - Adding an Offset in a Wire to Increase the Fatigue Life......Page 114
6.1 Various Types of Printed Circuit Boards......Page 120
6.2 Changes in Circuit Board Edge Conditions......Page 123
6.3 Estimating the Transmissibility of a Printed Circuit Board......Page 125
6.4 Natural Frequency Using a Trigonometric Series......Page 128
6.5 Natural Frequency Using a Polynomial Series......Page 133
6.5.1 Sample Problem - Resonant Frequency of a PCB......Page 137
6.6 Natural Frequency Equations Derived Using the Rayleigh Method......Page 139
6.7 Dynamic Stresses in the Circuit Board......Page 144
6.7.1 Sample Problem - Vibration Stresses in a PCB......Page 148
6.8 Ribs on Printed Circuit Boards......Page 149
6.9 Ribs Fastened to Circuit Boards with Screws......Page 154
6.11 Proper Use of Ribs to Stiffen Plates and Circuit Boards......Page 158
6.12 Quick Way to Estimate the Required Rib Spacing for Circuit Boards......Page 159
6.13 Natural Frequencies for Different PCB Shapes with Different Supports......Page 161
6.13.1 Sample Problem - Natural Frequency of a Triangular PCB with Three Point Supports......Page 166
7.1 Dynamic Coupling between the PCBs and Their Support Structures......Page 167
7.3 Description of Dynamic Computer Study for the Octave Rule......Page 171
7.5 The Reverse Octave Rule Must Have Lightweight PCBs......Page 172
7.5.1 Sample Problem - Vibration Problems with Relays Mounted on PCBs......Page 173
7.6 Proposed Corrective Action for Relays......Page 174
7.7 Using Snubbers to Reduce PCB Displacements and Stresses......Page 176
7.7.1 Sample Problem - Adding Snubbers to Improve PCB Reliability......Page 178
7.9 Properties of Material Damping......Page 179
7.10 Constrained Layer Damping with Viscoelastic Materials......Page 180
7.12 Problems with PCB Viscoelastic Dampers......Page 181
8.1 Introduction......Page 183
8.2 Estimating the Vibration Fatigue Life......Page 184
8.2.1 Sample Problem - Qualification Test for an Electronic System......Page 185
8.3 Electronic Component Lead Wire Strain Relief......Page 186
8.4 Designing PCBs for Sinusoidal Vibration Environments......Page 188
8.4.1 Sample Problem - Determining Desired PCB Resonant Frequency......Page 191
8.5 How Location and Orientation of Component on PCB Affect Life......Page 192
8.6 How Wedge Clamps Affect the PCB Resonant Frequency......Page 194
8.6.1 Sample Problem - Resonant Frequency of PCB with Side Wedge Clamps......Page 196
8.7 Effects of Loose PCB Side Edge Guides......Page 199
8.8 Sine Sweep through a Resonance......Page 202
8.8.1 Sample Problem - Fatigue Cycles Accumulated during a Sine Sweep......Page 204
9.2 Basic Failure Modes in Random Vibration......Page 205
9.3 Characteristics of Random Vibration......Page 206
9.4 Differences between Sinusoidal and Random Vibrations......Page 207
9.5 Random Vibration Input Curves......Page 209
9.6 Random Vibration Units......Page 210
9.7 Shaped Random Vibration Input Curves......Page 211
9.7.1 Sample Problem - Input RMS Accelerations for Sloped PSD Curves......Page 212
9.8 Relation between Decibels and Slope......Page 214
9.9 Integration Method for Obtaining the Area under a PSD Curve......Page 215
9.10.1 Sample Problem - Finding PSD Values......Page 217
9.11 Using Basic Logarithms to Find Points on the PSD Curve......Page 218
9.13 Gaussian or Normal Distribution Curve......Page 219
9.14 Correlating Random Vibration Failures Using the Three-Band Technique......Page 221
9.15 Rayleigh Distribution Function......Page 222
9.16 Response of a Single-Degree-of-Freedom System to Random Vibration......Page 223
9.16.1 Sample Problem - Estimating the Random Vibration Fatigue Life......Page 225
9.17 How PCBs Respond to Random Vibration......Page 231
9.18 Designing PCBs for Random Vibration Environments......Page 232
9.18.1 Sample Problem - Finding the Desired PCB Resonant Frequency......Page 235
9.19 Effects of Relative Motion on Component Fatigue Life......Page 237
9.19.1 Sample Problem - Component Fatigue Life......Page 238
9.20 It\'s the Input PSD That Counts, Not the Input RMS Acceleration......Page 239
9.21 Connector Wear and Surface Fretting Corrosion......Page 240
9.22 Multiple-Degree-of-Freedom Systems......Page 241
9.23 Octave Rule for Random Vibration......Page 242
9.23.1 Sample Problem - Response of Chassis and PCB to Random Vibration......Page 243
9.23.2 Sample Problem - Dynamic Analysis of an Electronic Chassis......Page 246
9.24 Determining the Number of Positive Zero Crossings......Page 248
9.24.1 Sample Problem - Determining the Number of Positive Zero Crossings......Page 250
10.1.1 Sample Problem - Determining the Sound Pressure Level......Page 251
10.2 Microphonic Effects in Electronic Equipment......Page 252
10.3 Methods for Generating Acoustic Noise Tests......Page 253
10.5 Determining the Sound Pressure Spectral Density......Page 255
10.6 Sound Pressure Response to Acoustic Noise Excitation......Page 256
10.6.1 Sample Problem - Fatigue Life of a Sheet-Metal Panel Exposed to Acoustic Noise......Page 257
10.7 Determining the Sound Acceleration Spectral Density......Page 262
10.7.1 Sample Problem - Alternate Method of Acoustic Noise Analysis......Page 263
11.1 Introduction......Page 265
11.2 Specifying the Shock Environment......Page 266
11.3 Pulse Shock......Page 268
11.4 Half-Sine Shock Pulse for Zero Rebound and Full Rebound......Page 269
11.4.1 Sample Problem - Half-Sine Shock-Pulse Drop Test......Page 270
11.5 Response of Electronic Structures to Shock Pulses......Page 274
11.6 Response of a Simple System to Various Shock Pulses......Page 275
11.8 Determining the Desired PCB Resonant Frequency for Shock......Page 277
11.8.1 Sample Problem - Response of a PCB to a Half-Sine Shock Pulse......Page 279
11.9 Response of PCB to Other Shock Pulses......Page 281
11.9.1 Sample Problem - Shock Response of a Transformer Mounting Bracket......Page 282
11.10.1 Sample Problem - Shipping Crate for an Electronic Box......Page 286
12.2 Different Types of Mounts......Page 317
12.3 Preliminary Dynamic Analysis......Page 320
12.4 Bolted Covers......Page 322
12.5 Coupled Modes......Page 325
12.6 Dynamic Loads in a Chassis......Page 328
12.7 Bending Stresses in the Chassis......Page 333
12.8 Buckling Stress Ratio for Bending......Page 335
12.9 Torsional Stresses in the Chassis......Page 337
12.10 Buckling Stress Ratio for Shear......Page 341
12.11 Margin of Safety for Buckling......Page 342
12.12 Center-of-Gravity Mount......Page 343
12.13 Simpler Method for Obtaining Dynamic Forces and Stresses on a Chassis......Page 345
13.1 Introduction......Page 347
13.2 Typical Tolerances in Electronic Components and Lead Wires......Page 348
13.2.1 Sample Problem - Effects of PCB Tolerances on Frequency and Fatigue Life......Page 349
13.3 Problems Associated with Tolerances on PCB Thickness......Page 350
13.4 Effects of Poor Bonding Methods on Structural Stiffness......Page 351
13.5 Soldering Small Axial Leaded Components on Through-Hole PCBs......Page 352
13.6 Areas Where Poor Manufacturing Methods Have Been Known to Cause Problems......Page 353
13.7 Avionic Integrity Program and Automotive Integrity Program (AVIP)......Page 355
13.8 The Basic Philosophy for Performing an AVIP Analysis......Page 357
13.9 Different Perspectives of Reliability......Page 360
14.1 Vibration Simulation Equipment......Page 363
14.3 Vibration Test Fixtures......Page 364
14.4 Basic Fixture Design Considerations......Page 365
14.5 Effective Spring Rates for Bolts......Page 367
14.6 Bolt Preload Torque......Page 369
14.7 Rocking Modes and Overturning Moments......Page 370
14.8 Oil-Film Slider Tables......Page 372
14.9 Vibration Fixture Counterweights......Page 373
14.11 Suspension Systems......Page 374
14.12 Mechanical Fuses......Page 375
14.13 Distinguishing Bending Modes from Rocking Modes......Page 376
14.14 Push-Bar Couplings......Page 377
14.15 Slider Plate Longitudinal Resonance......Page 381
14.16 Acceleration Force Capability of Shaker......Page 382
14.17 Positioning the Servo-Control Accelerometer......Page 383
14.18 More Accurate Method for Estimating the Transmissibility Q in Structures......Page 384
14.18.1 Sample Problem - Transmissibility Expected for a Plug-in PCB......Page 385
14.19 Cross-Coupling Effects in Vibration Test Fixtures......Page 386
14.20 Progressive Vibration Shear Failures in Bolted Structures......Page 387
14.21 Vibration Push-Bar Couplers with Bolts Loaded in Shear......Page 388
14.22 Bolting PCB Centers Together to Improve Their Vibration Fatigue Life......Page 390
14.23 Vibration Failures Caused by Careless Manufacturing Methods......Page 392
14.24 Alleged Vibration Failure That was Really Caused by Dropping a Large Chassis......Page 393
14.25 Methods for Increasing the Vibration and Shock Capability on Existing Systems......Page 394
15.2 Environmental Stress Screening Philosophy......Page 396
15.3 Screening Environments......Page 398
15.5 Things an Acceptable Screen are Not Expected to Do......Page 400
15.7 Preparations Prior to the Start of a Screening Program......Page 401
15.8 Combined Thermal Cycling, Random Vibration, and Electrical Operation......Page 404
15.10 Importance of the Screening Environment Sequence......Page 406
15.11 How Damage Can be Developed in a Thermal Cycling Screen......Page 407
15.12 Estimating the Amount of Fatigue Life Used up in a Random Vibration Screen......Page 409
15.12.1 Sample Problem - Fatigue Life Used up in a Vibration and Thermal Cycling Screen......Page 412
Bibliography......Page 418
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