Vibration analysis for electronic equipment.: 3rd

Preface xvii List of Symbols xix 1. Introduction 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 Vibration Sources Definitions Vibration Representation Degrees of Freedom Vibration Modes Vibration Nodes Coupled Modes Fasteners Electronic Equipment for Airplanes and Missiles Electronic Equipment for Ships and Submarines Electronic Equipment for Automobiles, Trucks, and Trains Electronics for Oil Drilling Equipment Electronics for Computers, Communication, and Entertainment 2. Vibrations of Simple Electronic Systems 2.1 Single Spring-Mass System Without Damping Sample Problem-Natural Frequency of a Cantilever Beam Sample Problem-Natural Frequency of a Torsion System Springs in Series and Parallel Sample Problem-Resonant Frequency of a Spring System Relation of Frequency and Acceleration to Displacement Sample Problem-Natural Frequency and Stress in a Beam Forced Vibrations with Viscous Damping Transmissibility as a Function of Frequency Sample Problem-Relating the Resonant Frequency to the Dynamic Displacement 2.2 Single-Degree-of-Freedom Torsional Systems 2.3 2.4 2.5 2.6 1 1 2 3 3 5 5 6 7 10 13 15 16 16 17 17 19 21 22 23 25 26 27 30 34 34 vii Viii CONTENTS 2.7 Multiple Spring-Mass Systems Without Damping Sample Problem-Resonant Frequency of a System 3 Component Lead Wire and Solder Joint Vibration Fatigue Life 3.1 3.2 3.3 3.4 3.5 3.6 Introduction Vibration Problems with Components Mounted High Above the PCB Sample Problem-Vibration Fatigue Life in the Wires of a TO-5 Transistor Vibration Fatigue Life in Solder Joints of a TO-5 Transistor Recommendations to Fix the Wire Vibration Problem Dynamic Forces Developed in Transformer Wires During Vibration Sample Problem-Dynamic Forces and Fatigue Life in Transformer Lead Wires Relative Displacements Between PCB and Component Produce Lead Wire Strain Sample Problem-Effects of PCB Displacement on Hybrid Reliability 4. Beam Structures for Electronic Subassemblies 4.1 Natural Frequency of a Uniform Beam Sample Problem-Natural Frequencies of Beams 4.2 Nonuniform Cross Sections Sample Problem-Natural Frequency of a Box with Nonuniform Sections 4.3 Composite Beams 5. Component Lead Wires as Bents, Frames, and Arcs 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Electronic Components Mounted on Circuit Boards Bent with a Lateral Load-Hinged Ends Strain Energy-Bent with Hinged Ends Strain Energy-Bent with Fixed Ends Strain Energy-Circular Arc with Hinged Ends Strain Energy-Circular Arc with Fixed Ends Strain Energy-Circular Arcs for Lead Wire Strain Relief Sample Problem-Adding an Offset in a Wire to Increase the Fatigue Life 36 37 39 39 39 40 43 45 46 46 49 50 56 56 60 64 68 69 75 75 77 80 83 90 92 94 97 CONTENTS 6 Printed Circuit Boards and Flat Plates 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 Various Types of Printed Circuit Boards Changes in Circuit Board Edge Conditions Estimating the Transmissibility of a Printed Circuit Board Natural Frequency Using a Trigonometric Series Natural Frequency Using a Polynomial Series Sample Problem-Resonant Frequency of a PCB Natural Frequency Equations Derived Using the Rayleigh Method Dynamic Stresses in the Circuit Board Sample Problem-Vibration Stresses in a PCB Ribs on Printed Circuit Boards Ribs Fastened to Circuit Boards with Screws Printed Circuit Boards With Ribs in Two Directions Proper Use of Ribs to Stiffen Plates and Circuit Boards Quick Way to Estimate the Required Rib Spacing for Circuit Boards Natural Frequencies for Different PCB Shapes with Different Supports Sample Problem-Natural Frequency of a Triangular PCB with Three Point Supports 7. Octave Rule, Snubbing, and Damping to Increase the PCB Fatigue Life 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 Dynamic Coupling Between the PCBs and Their Support Structures Effects of Loose Edge Guides on Plug-in Type PCBs Description of Dynamic Computer Study for the Octave Rule The Forward Octave Rule Always Works The Reverse Octave Rule Must Have Lightweight PCBs Sample Problem-Vibration Problems with Relays Mounted on PCBs Proposed Corrective Action for Relays Using Snubbers to Reduce PCB Displacements and Stresses Sample Problem-Adding Snubbers to Improve PCB Reliability Controlling the PCB Transmissibility with Damping Properties of Material Damping Constrained Layer Damping with Viscoelastic Materials Why Stiffening Ribs on PCBs are Often Better than Damping Problems with PCB Viscoelastic Dampers ix 103 103 106 108 111 116 120 122 127 131 132 137 141 141 142 144 149 150 150 154 154 155 155 156 157 159 161 162 162 163 164 164 X CONTENTS 8. Preventing Sinusoidal Vibration Failures in Electronic Equipment 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Introduction Estimating the Vibration Fatigue Life Sample Problem-Qualification Test for an Electronic System Electronic Component Lead Wire Strain Relief Designing PCBs for Sinusoidal Vibration Environments Sample Problem-Determining Desired PCB Resonant Frequency How Location and Orientation of Component on PCB Affect Life How Wedge Clamps Affect the PCB Resonant Frequency Sample Problem-Resonant Frequency of PCB with Side Wedge Clamps Effects of Loose PCB Side Edge Guides Sample Problem-Resonant Frequency of PCB with Loose Edge Guides Sine Sweep Through a Resonance Sample Problem-Fatigue Cycles Accumulated During a Sine Sweep 9. Designing Electronics for Random Vibration 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 Introduction Basic Failure Modes in Random Vibration Characteristics of Random Vibration Differences Between Sinusoidal and Random Vibrations Random Vibration Input Curves Sample Problem-Determining the Input RMS Acceleration Level Random Vibration Units Shaped Random Vibration Input Curves Sample Problem-Input RMS Accelerations for Sloped PSD Curves Relation Between Decibels and Slope Integration Method for Obtaining the Area Under a PSD Curve Finding Points on the PSD Curve Sample Problem-Finding PSD Values Using Basic Logarithms to Find Points on the PSD Curve Probability Distribution Functions 166 166 167 168 169 171 174 175 177 179 182 185 185 187 188 188 188 189 190 192 193 193 194 195 197 198 200 200 20 1 202 9.13 9.14 9.15 9.16 9.17 9.18 9.19 9.20 9.21 9.22 9.23 9.24 CONTENTS Gaussian or Normal Distribution Curve Correlating Random Vibration Failures Using the Three-Band Technique Rayleigh Distribution Function Response of a Single-Degree-of-Freedom System to Random Vibration Sample Problem-Estimating the Random Vibration Fatigue Life How PCBs Respond to Random Vibration Designing PCBs for Random Vibration Environments Sample Problem-Finding the Desired PCB Resonant Frequency Effects of Relative Motion on Component Fatigue Life Sample Problem-Component Fatigue Life It’s the Input PSD that Counts, Not the Input RMS Acceleration Connector Wear and Surface Fretting Corrosion Sample Problem-Determining Approximate Connector Fatigue Life Multiple-Degree-of-Freedom Systems Octave Rule for Random Vibration Sample Problem-Response of Chassis and PCB to Random Vibration Sample Problem-Dynamic Analysis of an Electronic Chassis Determining the Number of Positive Zero Crossings Sample Problem-Determining the Number of Positive Zero Crossings 10 Acoustic Noise Effects on Electronics 10.1 10.2 10.3 10.4 10.5 10.6 10.7 Introduction Sample Problem-Determining the Sound Pressure Level Microphonic Effects in Electronic Equipment Methods for Generating Acoustic Noise Tests One-Third Octave Bandwidth Determining the Sound Pressure Spectral Density Sound Pressure Response to Acoustic Noise Excitation Sample Problem-Fatigue Life of a Sheet-Metal Panel Exposed to Acoustic Noise Determining the Sound Acceleration Spectral Density Sample Problem-Alternate Method of Acoustic Noise Analysis xi 202 204 205 206 208 214 215 218 220 221 222 223 224 224 225 226 229 23 1 233 234 234 234 235 23 6 238 238 239 240 245 246 Xii CONTENTS 11. Designing Electronics for Shock Environments 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 11.12 11.13 11.14 11.1s 11.16 11.17 11.18 11.19 11.20 11.21 Introduction Specifying the Shock Environment Pulse Shock Half-Sine Shock Pulse for Zero Rebound and Full Rebound Sample Problem-Half-Sine Shock-Pulse Drop Test Response of Electronic Structures to Shock Pulses Response of a Simple System to Various Shock Pulses How PCBs Respond to Shock Pulses Determining the Desired PCB Resonant Frequency for Shock Sample Problem-Response of a PCB to a Half-Sine Shock Pulse Response of PCB to Other Shock Pulses Sample Problem-Shock Response of a Transformer Mounting Bracket Equivalent Shock Pulse Sample Problem-Shipping Crate for an Electronic Box Low Values of the Frequency Ratio R Sample Problem-Shock Amplification for Low Frequency Ratio R Shock Isolators Sample Problem-Heat Developed in an Isolator Information Required for Shock Isolators Sample Problem-Selecting a Set of Shock Isolators Ringing Effects in Systems with Light Damping How Two-Degree-of-Freedom Systems Respond to Shock The Octave Rule for Shock Velocity Shock Sample Problem-Designing a Cabinet for Velocity Shock Nonlinear Velocity Shock Sample Problem-Cushioning Material for a Sensitive Electronic Box Shock Response Spectrum How Chassis and PCBs Respond to Shock Sample Problem-Shock Response Spectrum Analysis for Chassis and PCB How Pyrotechnic Shock Can Affect Electronic Components Sample Problem-Resonant Frequency of a Hybrid Die Bond Wire 248 248 249 25 1 252 25 3 25 7 25 8 260 260 262 264 265 269 269 274 274 275 276 277 278 28 1 282 284 285 285 286 288 288 29 1 292 296 298 CONTENTS Xiii 12. Design and Analysis of Electronic Boxes 300 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12 12.13 Introduction Different Types of Mounts Preliminary Dynamic Analysis Bolted Covers Coupled Modes Dynamic Loads in a Chassis Bending Stresses in the Chassis Buckling Stress Ratio for Bending Torsional Stresses in the Chassis Buckling Stress Ratio for Shear Margin of Safety for Buckling Center-of-Gravity Mount Simpler Method for Obtaining Dynamic Forces and Stresses on a Chassis 13. Effects of Manufacturing Methods on the Reliability of Electronics 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 Introduction Typical Tolerances in Electronic Components and Lead Wires Sample Problem-Effects of PCB Tolerances on Frequency and Fatigue Life Problems Associated with Tolerances on PCB Thickness Effects of Poor Bonding Methods on Structural Stiffness Soldering Small Axial Leaded Components on Through- Hole PCBs Areas Where Poor Manufacturing Methods Have Been Known to Cause Problems Avionic Integrity Program and Automotive Integrity Program (AVIP) The Basic Philosophy for Performing an AVIP Analysis Different Perspectives of Reliability 14. Vibration Fixtures and Vibration Testing 14.1 Vibration Simulation Equipment 14.2 Mounting the Vibration Machine 14.3 Vibration Test Fixtures 14.4 Basic Fixture Design Considerations 14.5 14.6 Bolt Preload Torque Effective Spring Rates for Bolts 300 300 303 305 308 311 316 318 320 324 325 326 328 330 330 331 332 333 334 335 336 338 340 343 346 346 347 347 348 350 352 XiV CONTENTS 14.7 14.8 14.9 14.10 14.11 14.12 14.13 14.14 14.15 14.16 14.17 14.18 Sample Problem-Determining Desired Bolt Torque Rocking Modes and Overturning Moments Oil-Film Slider Tables Vibration Fixture Counterweights A Summary for Good Fixture Design Suspension Systems Mechanical Fuses Distinguishing Bending Modes from Rocking Modes Push-Bar Couplings Slider Plate Longitudinal Resonance Acceleration Force Capability of Shaker Positioning the Servo-Control Accelerometer More Accurate Method for Estimating the Transmissibility Q in Structures Sample Problem-Transmissibility Expected for a Plug-in PCB Vibration Testing Case Histories 14.19 Cross-Coupling Effects in Vibration Test Fixtures 14.20 Progressive Vibration Shear Failures in Bolted Structures 14.21 Vibration Push-Bar Couplers with Bolts Loaded in Shear 14.22 Bolting PCB Centers Together to Improve Their Vibration Fatigue Life 14.23 Vibration Failures Caused by Careless Manufacturing Methods 14.24 Alleged Vibration Failure that was Really Caused by Dropping a Large Chassis 14.25 Methods for Increasing the Vibration and Shock Capability on Existing Systems 15. Environmental Stress Screening for Electronic Equipment (ESSEE) 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 Introduction Environmental Stress Screening Philosophy Screening Environments Things an Acceptable Screen Are Expected to Do Things an Acceptable Screen Are Not Expected to Do To Screen or Not to Screen, That is the Problem Preparations Prior to the Start of a Screening Program Combined Thermal Cycling, Random Vibration, and Electrical Operation Separate Thermal Cycling, Random Vibration, and Electrical Operation 353 353 355 356 357 357 358 359 360 364 365 366 367 368 369 369 370 371 3 73 375 376 377 379 379 379 381 383 383 384 384 387 389 CONTENTS XV 15.10 Importance of the Screening Environment Sequence 389 15.11 How Damage Can Be Developed in a Thermal Cycling Screen 390 15.12 Estimating the Amount of Fatigue Life Used Up in a Random Vibration Screen 392 Sample Problem-Fatigue Life Used Up in Vibration and Thermal Cycling Screen 395 Bibliography 401 Index 405