Title Details

ANTHONY SOFRONAS, DEng, PE, has spent the past forty-five years troubleshooting field failures and designing machinery for ExxonMobil, General Electric, and the Bendix Corporation. He is currently a consultant to industry, presenting seminars worldwide under the aegis of his company Engineered Products. Dr. Sofronas has published many technical papers and articles, including a bimonthly column for Hydrocarbon Processing dedicated to engineering case histories. He is also the author of Analytical Troubleshooting of Process Machinery and Pressure Vessels (Wiley).

Preface xv

1 Introduction 1

Reference 4

2 Basics of Vibration 5

2.1 Spring–Mass Systems and Resonance 5

2.2 Case History: Combining Springs and Masses in a Steam Turbine Problem 9

2.3 Useful Questions to Ask Before Beginning a Vibration Analysis 12

2.4 Linear Spring Constants and Area Moments of Inertia 13

2.5 Vibrating Flat Plates 14

2.6 Two-Degree Tuned Vibration Absorber 16

2.7 Natural Frequencies of Pipes and Beams 19

2.8 Effect of Clearance on the Natural Frequency 19

2.9 Static Deflection and Pendulum Natural Frequency 21

2.10 Coupled Single-Mass Systems 23

References 25

3 Vibration-Measuring Methods and Limits 27

3.1 Important Frequencies 27

3.2 Campbell Diagrams 31

3.3 Case History: Systematic Procedure to Identify a Vibration Source 33

3.4 Vibration-Measuring Terms 34

3.5 Cascade Diagram 36

3.6 Shock Pulse Method 37

3.7 Measuring Transducers 38

3.8 Measurements: Time-Based, Bode, and Orbit Plots 40

4 Simple Analytical Examples 45

4.1 Determining Vibration Amplitude 45

4.2 Resonant and Off-Resonant Amplitudes 47

4.3 Case History: Transmitted Force and Isolation of a Roof Fan 49

4.4 Case History: Seal Failure Due to Misalignment of an Agitator Shaft 51

4.5 Case History: Structural Vibration 53

4.6 Case History: Production-Line Grinding Problem 54

4.7 Case History: Vehicle on Springs 57

4.8 Case History: Vibrating Cantilevered Components 58

4.9 Bump Test 60

4.10 Case History: Vibrating Pump Mounted on a Plate Deck 60

4.11 Case History: Misalignment Force 62

4.12 Case History: Vertical Pump Vibrations and Bearing Survival 64

4.13 Case History: Cause of Mysterious Movement on a Centrifuge Deck 67

4.14 Case History: Engine Vibration Monitoring Device 70

4.15 Case History: Natural Frequency of A Midsupport Vertical Mixer 72

4.16 Case History: Valve Float Analysis 73

References 75

5 Vibration-Based Problems and Their Sources 77

5.1 Fatigue Cracking 77

5.2 Fretting and Wear 79

5.3 Ball and Roller Bearing Failures 83

5.4 Bolt Loosening 84

5.5 Flow-Induced Vibration 86

5.5.1 Case History: Stack Vibration Induced by Wind 87

5.6 Excessive Noise 88

5.7 Pressure Pulsations 89

5.8 Mechanical Seal Chipping and Damage 90

5.9 Surging of Fans and Other Causes of Vibration 90

5.10 Vibration Due to Beats 92

5.11 The Slip-Stick Problem 92

5.12 Drive Belt Vibration 97

References 98

6 Causes of Vibrations and Solutions in Machinery 99

6.1 Rotating Imbalance 99

6.1.1 Case History: Motor Imbalance 100

6.2 Causes of Shaft Misalignment 102

6.2.1 Types of Misalignment 102

6.2.2 Thermal Offset 102

6.2.3 Acceptable Coupling Offset and Angular Misalignment 103

6.3 A Problem in Measuring Vibration on Large Machines 104

6.4 Causes of Pump Vibration 105

6.4.1 NPSH Problems and Cavitation 105

6.4.2 Suction Vortex 107

6.4.3 Off Best Efficiency Point 107

6.4.4 Vertical Pump Vibration 109

6.4.5 Pump Vibration Level Guidelines 111

6.5 Other Causes of Motor Vibration 111

6.5.1 Electrical Causes 111

6.5.2 Mechanical Cause 112

6.5.3 Motor Vibration-Level Guidelines 112

6.6 Causes of Gearbox Vibration 113

6.6.1 Cyclic External Reaction Loads 113

6.6.2 Tooth Breakage 113

6.6.3 Gearbox Vibration-Level Guidelines 114

6.6.4 Causes of Cooling Tower Fan System Vibration 114

6.6.5 Complex Gearbox Vibration Spectra 115

6.7 Types of Couplings for Alignment 116

References 120

7 Piping Vibration 121

7.1 Types of Piping Vibration Problems 121

7.2 Vibration Screening Charts and Allowable Limits 122

7.3 Case History: Water Hammer and Piping Impacts 123

7.4 Case History: Heat-Exchanger Tube Vibration 126

7.5 Case History: Useful Equations In Solving a Cracked Nozzle 128

7.6 Support and Constraint Considerations in Vibrating Services 130

7.7 Case History: Control Valve Trim Causing Piping Vibration 130

7.8 Vibration Observed and Possible Causes 131

7.9 Acoustical Vibration Problems 131

7.9.1 Case History: Compressor Acoustical Vibration Analysis 133

7.9.2 Case History: Tuning Using a Helmholz Resonator 134

7.9.3 Case History: Tuning Using Surge Volume 135

7.10 Two-Phase Flow and Slug Flow 136

7.11 Case History: U-Tube Heat-Exchanger Vibration 138

7.12 Crack Growth in a Flat Plate 139

References 140

8 Torsional Vibration 141

8.1 Torsional Vibration Defined 141

8.2 Case History: Torsional Vibration of a Motor–Generator–Blower 143

8.3 Case History: Engine–Gearbox–Pump 144

8.4 Case History: Internal Combustion Engine–Gearbox–Propeller 146

8.5 Case History: Effect of Changing Firing Order On Crankshaft Stress 152

8.6 Case History: Transient Power Surge Motor–Gearbox–Compressor 152

8.7 Case History: Vibratory Torque on the Gear of a Ship System 155

8.8 Torsional Spring Constants and Mass Moments of Inertia 157

8.9 Three-Mass Natural Frequency Simplification 158

8.10 Case History: Torsional Vibration of a Drill String 160

8.11 Case History: Effect of a Suddenly Applied Torsional Load 160

8.12 Sensitivity Analysis of a Two-Mass Torsional System 162

8.13 Case History: Engine Natural Frequency as a Continuous Shaft 163

8.14 Types of Torsionally Soft Couplings 164

8.15 Torsional Vibration Testing 168

8.16 Case History: Out-of-Synchronization Grid Closure 170

8.17 Operating Through a Large Torsional Amplitude 171

8.18 Case History: Engine Mode Shape as a Continuous Shaft 173

8.19 Holzer Method for Calculating Torsional and Linear Multimass Systems 174

8.20 Experimental Determination of Mass Moment of Inertia J 177

References 178

9 Turbomachinery Vibration 179

9.1 Unique Vibration Problems of Turbomachinery 179

9.1.1 The Rotor System 180

9.2 Lateral Vibrations of a Simplified System 181

9.2.1 A Simplified Rotor System 181

9.2.2 Compressor with High Stiffness Bearings 182

9.2.3 Critical Speed of a Rotor on Spring Supports 183

9.3 Allowable Shaft Displacement Guidelines 185

9.4 Compressor Surge and Rotor Vibration 185

9.5 Rigid and Flexible Rotor Balancing 187

9.6 Case History: Checking the Critical Speed of a Motor Rotor 190

9.7 Case History: Response of a Missing Blade on a Steam Turbine 192

9.8 Case History: Stepped Shaft Into Equivalent Diameter 195

9.9 Case History: Two-Diameter Rotor System 196

9.10 Hydrodynamic Bearing Stiffness 197

9.11 Rotor Dynamics of Pumps 201

References 202

10 Very Low Cycle Vibrations and Other Phenomena 203

10.1 Very Low Cycle Vibration Defined 203

10.2 Vessels In High-Cycle Service 204

10.3 Case History: Cracking of a Rotary Dryer 205

10.4 Phantom Failures: Some Failures are Very Elusive 207

10.5 Case History: Troubleshooting Gear Face Damage 208

10.6 Case History: Thermally Bowed Shaft and Vibration 210

10.7 Case History: Effect of Nonlinear Stiffness 212

10.8 Case History: Effect of Clearance on a Vibrating System 214

10.9 Case History: Fatigue Failure of a Crankshaft 215

10.10 Case History: Understanding Slip–Jerk During Slow Roll 218

10.11 Case History: Predicting the Crack Growth on a Machine 219

10.12 Case History: Bolt Loosening on Counterweight Bolts 222

10.13 Case History: Centrifuge Vibration 223

10.14 Case History: Crack Growth In a Gear Tooth 225

10.15 Case History: Vibration of a Rotor In Its Case 227

10.16 Case History: Gearbox Input Shaft Lockup 229

10.17 Case History: Troubleshooting a Roller Bearing Failure 231

10.18 Case History: Using Imprints to Determine Loads 232

10.19 Case History: Extruder BlowBack 235

10.20 Case History: Vibratory and Rotational Wear 239

10.21 Two-Mass System With Known and Unknown Displacement 241

10.22 Case History: Fiberglass Mixing Tank Flexing Vibration 241

References 243

11 Vibration Failures 245

11.1 Why Things Fail In Vibration 245

11.2 Case History: Spring Failure 246

11.3 Case History: Spline Fretting 247

11.4 Case History: Sheet Metal Vibration Cracking 248

11.5 Case History: Bearing Brinelling and False Brinelling 249

11.6 Case History: Crankshaft Failure 250

11.7 Case History: Brush Holder Wear 251

11.8 Case History: Cracking of a Vibrating Conveyor Structure 251

11.9 Case History: Failure of a Cooling Tower Blade Arm 252

11.10 Case History: Fatigue Failures at High Cyclic Stress Areas 254

11.11 Case History: Fatigue Failure of Shafts 254

11.12 Case History: Failure of a Steam Turbine Blade 257

11.13 Case History: Failure of a Reciprocating Compressor Slipper 258

11.14 Case History: Multiple-Cause Gear Failure 259

11.15 Case History: Loose Bolt Failures 259

11.16 Case History: Piston Failure in a Racing Car 262

11.17 Case History: Stop Holes For Cracks Don’t Always Work 262

11.18 Case History: Small Bearing Failure Due To Vibration 264

11.19 Appearance of Fatigue Fracture Surfaces 266

References 268

12 Metal Fatigue 269

12.1 Metal Fatigue Defined 269

12.2 Reduction of a Component’s Life When Subjected to Excessive Vibration 270

12.3 Case History: Special Case of Fatigue Potential 273

12.4 Metallurgical Examination 274

12.5 Taking Risks and Making High-Level Presentations 275

References 277

13 Short History of Vibration 279

References 282

Index 285

“The guide should be valuable in many sectors of industry, particularly to those new to industry or new to vibration analysis.”  (Chemical Engineering Progress, 1 May 2013)

“In all, this most recent Sofronas text is readable, practical and valuable throughout.”  (Process Machinery Consulting, 1 April 2013)