Case Histories in Vibration Analysis and Metal Fatigue for the Practicing Engineer

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 xv1 Introduction 1Reference 42 Basics of Vibration 52.1 Spring–Mass Systems and Resonance 52.2 Case History: Combining Springs and Masses in a Steam Turbine Problem 92.3 Useful Questions to Ask Before Beginning a Vibration Analysis 122.4 Linear Spring Constants and Area Moments of Inertia 132.5 Vibrating Flat Plates 142.6 Two-Degree Tuned Vibration Absorber 162.7 Natural Frequencies of Pipes and Beams 192.8 Effect of Clearance on the Natural Frequency 192.9 Static Deflection and Pendulum Natural Frequency 212.10 Coupled Single-Mass Systems 23References 253 Vibration-Measuring Methods and Limits 273.1 Important Frequencies 273.2 Campbell Diagrams 313.3 Case History: Systematic Procedure to Identify a Vibration Source 333.4 Vibration-Measuring Terms 343.5 Cascade Diagram 363.6 Shock Pulse Method 373.7 Measuring Transducers 383.8 Measurements: Time-Based, Bode, and Orbit Plots 404 Simple Analytical Examples 454.1 Determining Vibration Amplitude 454.2 Resonant and Off-Resonant Amplitudes 474.3 Case History: Transmitted Force and Isolation of a Roof Fan 494.4 Case History: Seal Failure Due to Misalignment of an Agitator Shaft 514.5 Case History: Structural Vibration 534.6 Case History: Production-Line Grinding Problem 544.7 Case History: Vehicle on Springs 574.8 Case History: Vibrating Cantilevered Components 584.9 Bump Test 604.10 Case History: Vibrating Pump Mounted on a Plate Deck 604.11 Case History: Misalignment Force 624.12 Case History: Vertical Pump Vibrations and Bearing Survival 644.13 Case History: Cause of Mysterious Movement on a Centrifuge Deck 674.14 Case History: Engine Vibration Monitoring Device 704.15 Case History: Natural Frequency of A Midsupport Vertical Mixer 724.16 Case History: Valve Float Analysis 73References 755 Vibration-Based Problems and Their Sources 775.1 Fatigue Cracking 775.2 Fretting and Wear 795.3 Ball and Roller Bearing Failures 835.4 Bolt Loosening 845.5 Flow-Induced Vibration 865.5.1 Case History: Stack Vibration Induced by Wind 875.6 Excessive Noise 885.7 Pressure Pulsations 895.8 Mechanical Seal Chipping and Damage 905.9 Surging of Fans and Other Causes of Vibration 905.10 Vibration Due to Beats 925.11 The Slip-Stick Problem 925.12 Drive Belt Vibration 97References 986 Causes of Vibrations and Solutions in Machinery 996.1 Rotating Imbalance 996.1.1 Case History: Motor Imbalance 1006.2 Causes of Shaft Misalignment 1026.2.1 Types of Misalignment 1026.2.2 Thermal Offset 1026.2.3 Acceptable Coupling Offset and Angular Misalignment 1036.3 A Problem in Measuring Vibration on Large Machines 1046.4 Causes of Pump Vibration 1056.4.1 NPSH Problems and Cavitation 1056.4.2 Suction Vortex 1076.4.3 Off Best Efficiency Point 1076.4.4 Vertical Pump Vibration 1096.4.5 Pump Vibration Level Guidelines 1116.5 Other Causes of Motor Vibration 1116.5.1 Electrical Causes 1116.5.2 Mechanical Cause 1126.5.3 Motor Vibration-Level Guidelines 1126.6 Causes of Gearbox Vibration 1136.6.1 Cyclic External Reaction Loads 1136.6.2 Tooth Breakage 1136.6.3 Gearbox Vibration-Level Guidelines 1146.6.4 Causes of Cooling Tower Fan System Vibration 1146.6.5 Complex Gearbox Vibration Spectra 1156.7 Types of Couplings for Alignment 116References 1207 Piping Vibration 1217.1 Types of Piping Vibration Problems 1217.2 Vibration Screening Charts and Allowable Limits 1227.3 Case History: Water Hammer and Piping Impacts 1237.4 Case History: Heat-Exchanger Tube Vibration 1267.5 Case History: Useful Equations In Solving a Cracked Nozzle 1287.6 Support and Constraint Considerations in Vibrating Services 1307.7 Case History: Control Valve Trim Causing Piping Vibration 1307.8 Vibration Observed and Possible Causes 1317.9 Acoustical Vibration Problems 1317.9.1 Case History: Compressor Acoustical Vibration Analysis 1337.9.2 Case History: Tuning Using a Helmholz Resonator 1347.9.3 Case History: Tuning Using Surge Volume 1357.10 Two-Phase Flow and Slug Flow 1367.11 Case History: U-Tube Heat-Exchanger Vibration 1387.12 Crack Growth in a Flat Plate 139References 1408 Torsional Vibration 1418.1 Torsional Vibration Defined 1418.2 Case History: Torsional Vibration of a Motor–Generator–Blower 1438.3 Case History: Engine–Gearbox–Pump 1448.4 Case History: Internal Combustion Engine–Gearbox–Propeller 1468.5 Case History: Effect of Changing Firing Order On Crankshaft Stress 1528.6 Case History: Transient Power Surge Motor–Gearbox–Compressor 1528.7 Case History: Vibratory Torque on the Gear of a Ship System 1558.8 Torsional Spring Constants and Mass Moments of Inertia 1578.9 Three-Mass Natural Frequency Simplification 1588.10 Case History: Torsional Vibration of a Drill String 1608.11 Case History: Effect of a Suddenly Applied Torsional Load 1608.12 Sensitivity Analysis of a Two-Mass Torsional System 1628.13 Case History: Engine Natural Frequency as a Continuous Shaft 1638.14 Types of Torsionally Soft Couplings 1648.15 Torsional Vibration Testing 1688.16 Case History: Out-of-Synchronization Grid Closure 1708.17 Operating Through a Large Torsional Amplitude 1718.18 Case History: Engine Mode Shape as a Continuous Shaft 1738.19 Holzer Method for Calculating Torsional and Linear Multimass Systems 1748.20 Experimental Determination of Mass Moment of Inertia J 177References 1789 Turbomachinery Vibration 1799.1 Unique Vibration Problems of Turbomachinery 1799.1.1 The Rotor System 1809.2 Lateral Vibrations of a Simplified System 1819.2.1 A Simplified Rotor System 1819.2.2 Compressor with High Stiffness Bearings 1829.2.3 Critical Speed of a Rotor on Spring Supports 1839.3 Allowable Shaft Displacement Guidelines 1859.4 Compressor Surge and Rotor Vibration 1859.5 Rigid and Flexible Rotor Balancing 1879.6 Case History: Checking the Critical Speed of a Motor Rotor 1909.7 Case History: Response of a Missing Blade on a Steam Turbine 1929.8 Case History: Stepped Shaft Into Equivalent Diameter 1959.9 Case History: Two-Diameter Rotor System 1969.10 Hydrodynamic Bearing Stiffness 1979.11 Rotor Dynamics of Pumps 201References 20210 Very Low Cycle Vibrations and Other Phenomena 20310.1 Very Low Cycle Vibration Defined 20310.2 Vessels In High-Cycle Service 20410.3 Case History: Cracking of a Rotary Dryer 20510.4 Phantom Failures: Some Failures are Very Elusive 20710.5 Case History: Troubleshooting Gear Face Damage 20810.6 Case History: Thermally Bowed Shaft and Vibration 21010.7 Case History: Effect of Nonlinear Stiffness 21210.8 Case History: Effect of Clearance on a Vibrating System 21410.9 Case History: Fatigue Failure of a Crankshaft 21510.10 Case History: Understanding Slip–Jerk During Slow Roll 21810.11 Case History: Predicting the Crack Growth on a Machine 21910.12 Case History: Bolt Loosening on Counterweight Bolts 22210.13 Case History: Centrifuge Vibration 22310.14 Case History: Crack Growth In a Gear Tooth 22510.15 Case History: Vibration of a Rotor In Its Case 22710.16 Case History: Gearbox Input Shaft Lockup 22910.17 Case History: Troubleshooting a Roller Bearing Failure 23110.18 Case History: Using Imprints to Determine Loads 23210.19 Case History: Extruder BlowBack 23510.20 Case History: Vibratory and Rotational Wear 23910.21 Two-Mass System With Known and Unknown Displacement 24110.22 Case History: Fiberglass Mixing Tank Flexing Vibration 241References 24311 Vibration Failures 24511.1 Why Things Fail In Vibration 24511.2 Case History: Spring Failure 24611.3 Case History: Spline Fretting 24711.4 Case History: Sheet Metal Vibration Cracking 24811.5 Case History: Bearing Brinelling and False Brinelling 24911.6 Case History: Crankshaft Failure 25011.7 Case History: Brush Holder Wear 25111.8 Case History: Cracking of a Vibrating Conveyor Structure 25111.9 Case History: Failure of a Cooling Tower Blade Arm 25211.10 Case History: Fatigue Failures at High Cyclic Stress Areas 25411.11 Case History: Fatigue Failure of Shafts 25411.12 Case History: Failure of a Steam Turbine Blade 25711.13 Case History: Failure of a Reciprocating Compressor Slipper 25811.14 Case History: Multiple-Cause Gear Failure 25911.15 Case History: Loose Bolt Failures 25911.16 Case History: Piston Failure in a Racing Car 26211.17 Case History: Stop Holes For Cracks Don’t Always Work 26211.18 Case History: Small Bearing Failure Due To Vibration 26411.19 Appearance of Fatigue Fracture Surfaces 266References 26812 Metal Fatigue 26912.1 Metal Fatigue Defined 26912.2 Reduction of a Component’s Life When Subjected to Excessive Vibration 27012.3 Case History: Special Case of Fatigue Potential 27312.4 Metallurgical Examination 27412.5 Taking Risks and Making High-Level Presentations 275References 27713 Short History of Vibration 279References 282Index 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)