Rotor and Structural Dynamics of Turbomachinery: A Practical Guide for Engineers and Scientists (Applied Condition Monitoring (11))

This book provides engineers and scientists with practical fundamentals for turbomachinery design. It presents a detailed analysis of existing procedures for the analysis of rotor and structure dynamics, while keeping mathematical equations to a minimum. Specific terminologies are used for rotors and structures, respectively, allowing the readers to clearly distinguish between the two. Further, the book describes the essential concepts needed to understand rotor failure modes due to lateral and torsional oscillations. It guides the reader from simple single-degree-of-freedom models to the most complex multi-degree-of-freedom systems, and provides useful information concerning steel pedestal stiffness degradation and other structural issues. Fluid-film bearing types and their dynamical behavior are extensively covered and discussed in the context of various turbomachinery applications. The book also discusses shaft alignment and rotor balancing from a practical point of view, providing readers with essential information to help them solve practical problems. As the main body of the book focuses on the diagnostics and description of case studies addressing the most pressing practical issues, together with their successful solutions, it offers a valuable reference guide, helping field engineers manage day-to-day issues with turbomachinery. Preface I 6 Preface II 8 Acknowledgements I 10 Acknowledgements II 12 Contents 13 1 Basics of Rotor and Structural Vibration 21 1.1 Introduction 21 1.2 General 21 1.3 Fundamentals of Rotor Dynamics in Turbo-Machinery 23 1.4 Why Rotor Dynamics Plays a Vital Role in Rotating Machinery Design? 24 1.5 Rotor Failure Modes 27 1.5.1 Torsional Vibration (Due to Rotor Twist). See Fig. 1.5 27 1.5.2 Lateral Vibration (Due to of Rotor Bending). See Fig. 1.6 29 1.6 Rotor Dynamics Versus Stationary Structural Dynamics 30 1.6.1 Structural Vibration Versus Rotor Whirl 31 1.6.2 Structural Natural Frequencies Versus Rotor Critical Speeds 31 1.6.3 Structural Mode Shapes Versus Rotor Whirl Motions 31 1.6.4 Structural Responses Versus Rotor Whirl Responses 31 1.6.5 Structural Excitation Versus Rotor Excitation Forces 32 1.6.6 Stability of Structures Versus Rotor Stability 33 1.7 Examples 33 1.7.1 Example-1 33 1.7.2 Example-2 35 1.7.3 Example-3 36 1.7.4 Example-4 37 1.8 Fluid-Film Stiffness 38 1.9 Forward and Backward Rotor Whirl Vectors 38 1.9.1 Split Critical Speeds of a Rotor 40 1.9.2 Construction of Whirl Plots 41 1.10 Closure 42 References 43 2 Mathematical Model 44 2.1 Introduction 44 2.2 General 44 2.3 Lateral (Bending) Rotor Dynamic Model 45 2.3.1 The Rotor Modeling 45 2.3.2 The Fluid-Film Bearing Modeling 46 2.3.3 Bearing Support Pedestal Modeling 46 2.3.4 Concrete Foundation Modeling 46 2.3.5 Steel Foundation Structures 47 2.4 Solution Methods 47 2.4.1 Transfer Matrix (TM) Approach 47 2.4.2 Two Dimensional Finite Element Formulation 50 2.4.3 Gyroscopic Effect in Rotor Systems 51 2.4.4 Asymmetric Stiffness Effects in Rotor Systems 52 2.5 Advanced Rotor Modeling Methods 54 2.5.1 Lateral Rotor Model 54 2.5.2 Mode-Frequency Analysis or Modal Analysis on Rigid Supports 58 2.5.3 Unbalance Response Calculations 59 2.5.4 Q-Factor Evaluation 60 2.5.4.1 An Important Note About Q-Factor Evaluations 61 2.5.5 Rotor Stability Calculations 61 2.6 Various Rotor Constructions 63 2.6.1 Mono-Bloc Rotor 63 2.6.2 Shrunk-on Disc Rotor 64 2.6.3 Welded Rotor 64 2.7 Rotor Mechanics 65 2.8 Torsional (Twist) Rotor Dynamics 66 2.8.1 Lumped Mass Model 67 2.8.2 Blade and Rotor Disc Frequency Coupling 68 2.8.3 Three-D Finite Element Model of a Bladed-Disc 69 2.8.4 Effects of Blade-Disc Coupling on Lateral Dynamics 71 2.8.5 Rotor Torsional Model 73 2.8.6 Three-D Torsional Modeling of Rotors 75 2.8.7 Modal Analysis 76 2.8.8 Steady-State Excitations 79 2.8.9 Positive and Negative Sequence Currents 80 2.8.10 Transient Excitations 82 2.8.11 Loss of Life Calculations 85 2.8.12 Out-of Phase Synchronization (OPS) 86 2.8.12.1 Sudden Impulse or Repetitive Industrial Loads Near Power Plants—Excites Sub-synchronous Modes 87 Line Switching and Resonance Due to Series Capacitor Compensated Transmission- Excites Sub-synchronous Modes 87 2.8.13 Sub-synchronous Excitations 87 2.8.14 Impact on Shaft Torque Due to Grid Events 88 2.9 Testing for Torsional Frequencies and Modes 89 2.9.1 Stationary Frequency Testing 89 2.9.2 Rotating Tests 90 2.10 Closure 91 References 91 3 Rotor-to-Structure Interaction 92 3.1 Introduction 92 3.2 General 92 3.3 Influence of Bearing Support Pedestal Stiffness on Rotor Critical Frequencies 93 3.3.1 Rigid Bearing Support Pedestals 93 3.3.2 Flexible Bearing Support Pedestals 95 3.3.3 Background on Flexible Bearing Support Pedestal Degradation 97 3.3.4 Pedestal Degradation Experience in Power Plants 99 3.4 First Rotor Mode or U-Rotor Mode 99 3.5 Second Rotor Mode or S-Rotor Mode 100 3.6 Rotor and Bearing Support Pedestal Modeling 101 3.7 Testing Methods 102 3.7.1 Electrical Shaker 103 3.7.2 Shaker Test Process 104 3.7.3 Shaker Test Spectrum Plots 105 3.7.4 Shaker Test Pedestal Stiffness Plots 105 3.8 Calculation of Lateral Frequencies Using Shaker Data 110 3.8.1 Mode Shapes of LP Rotor Systems Connected with an Extension Shaft 110 3.8.2 Finite Element Model and Results 112 3.9 Evaluation of Pedestal Degradation Condition 112 3.9.1 Primary Evaluation 112 3.9.2 Secondary Evaluation 113 3.9.3 Stiffening of Flexible Pedestals 113 3.10 Recommended Guide Lines (GL) to Assess Safe Operational Condition of Flexible Bearing Pedestals 113 3.10.1 Primary Assessment 113 3.10.2 Secondary Assessment 114 3.10.3 Inspections 114 3.10.4 Other Influences 115 3.10.5 Seasonal Changes in Condenser Pressure 115 3.10.6 Influences Due to Electrical Grid Events 116 3.10.7 Influences Due to Grout Degradation 116 3.11 Closure 116 References 117 4 Fluid-Film, Steam and/or Gas Seal Influences on Rotor Dynamics 118 4.1 Introduction 118 4.2 General 118 4.3 Bearing Types 120 4.4 Capabilities of Various Bearing Types 121 4.4.1 Fluid-Film Bearings 121 4.4.2 Rolling Element Bearings (Ball and Roller) 122 4.4.3 Magnetic Bearings 122 4.5 Plain Cylindrical Bearings 122 4.5.1 Hydrodynamic Film Formation 123 4.5.2 Journal Position in Oil Film 124 4.5.3 When Does a Bearing Need an Oil Lift? 125 4.5.4 Partial-Arc Bearings 126 4.5.5 Viscosity Pump Bearings 126 4.5.6 Common Construction Features on All Hydrodynamic Bearings 129 4.6 Elliptical Bearings 130 4.7 Axial Groove Type Bearings 131 4.8 Pressure Dam Bearings 131 4.9 Tilting-Pad Bearings 132 4.9.1 Leading Edge Groove (LEG) Bearings 134 4.9.2 Two-Pad Tilt Pad Bearings 136 4.9.3 Three-Pad Tilt Pad Bearings 137 4.9.4 Five-Pad Tilt-Pad Bearing 137 4.9.5 Six-Pad Tilt-Pad Bearings 138 4.10 Special Bearing Types 139 4.10.1 Squeeze-Film Dampers 139 4.10.2 Magnetic (Levitated) Bearings 140 4.11 Comparison of Bearing Types 142 4.12 Fluid-Film Bearing Theory 143 4.12.1 Oil Film Dynamic Coefficients 147 4.12.2 Bearing L/D Ratios 148 4.12.3 Oil Lift Pockets 150 4.13 Rotor Instability 151 4.13.1 Oil Whirl/Whip in Bearings 152 4.13.2 Steam Whirl 153 4.13.2.1 Analysis 156 4.13.3 Discussions of Self-excited Vibration 157 4.14 Thrust or Axial Bearings 157 4.14.1 How Are Thrust Bearings Built? 159 4.15 Symptoms of Issues in Fluid-Film Bearings: Journal (Radial) Bearings 161 4.16 Symptoms of Issues in Fluid-Film Bearings: Thrust (Axial) Bearings 163 4.17 Closure 163 References 164 5 Rotor Balancing: Concept, Modeling and Analysis 166 5.1 Introduction 166 5.2 General 166 5.3 Why do Rotors Need Balancing? 167 5.4 Basic Methods of Balancing 167 5.5 Rotor Classifications 168 5.5.1 Rigid Rotor 168 5.5.2 Flexible Rotor 169 5.5.3 Methods of Balancing 169 5.6 Practical Field Balancing of Turbine—Generator (T-G) Trains 170 5.6.1 Vibration Measurement 170 5.6.2 Various Vibration Components 174 5.6.3 Vibration Data Organization 177 5.6.4 Initial Data Required for Evaluation 177 5.6.5 Evaluation of Slow Roll Data (Static Imbalance of Shaft Run Out) 178 5.7 Natural Frequency, Mode Shapes and Critical Vibration 181 5.8 Actual Heavy Spot Angle Versus Indicated Heavy Spot Angle 182 5.8.1 Calculating Lag Angle to Mode Shape Relationship 184 5.8.2 Identifying Rotor Critical Speeds 186 5.8.3 Determining Static and Dynamic Imbalance Components 189 5.9 Balancing Analysis 192 5.9.1 Calculating Effect Coefficients and Lag Angles 204 5.9.2 Applying Effect Coefficients and Lag Angles to Balance 206 5.10 Balancing of Rotors with Shared Bearings 210 5.11 Rotor Systems with Clutch 211 5.12 Commonly Used Balance Weights 212 5.13 Closure 213 References 213 6 Rotor Train Alignment 215 6.1 Introduction 215 6.2 General 215 6.3 Turbine Assembly 216 6.4 Rotor Train Alignment 218 6.4.1 Coupling Gaps and Displacements 218 6.4.2 How are Coupling Displacements and Gaps Measured in the Field? 221 6.4.3 Coupling Alignment Data from Measured Readings 225 6.5 Two Different Philosophies of Rotor Alignments 226 6.5.1 Coupling Alignment Impacts: Shared Bearing System Versus Two Bearings System 226 6.5.2 Coupling Alignment for Two Bearings Per Rotor Supports 227 6.5.3 Alignment in Multi-span Rotor Systems 228 6.5.4 How Does Shaft Alignment Keep the Bending Stresses in Check? 229 6.6 Coupling Alignment for Shared Bearing Rotor Supports 229 6.7 General Guideline for Runout Measurements 230 6.8 Other Guidelines for Better Shaft Alignments 231 6.8.1 Galling in Coupling Bolts 231 6.8.2 Requirements of Spigot Clearances/Interferences 233 6.9 Other Shaft Alignment Methods 234 6.10 Closure 234 References 234 7 Condition Monitoring of Rotors 235 7.1 Introduction 235 7.2 General 235 7.3 Diagnostic Data and Tools 236 7.3.1 Shaft Relative Vibration (SRV) Measurement 237 7.3.2 Seismic Vibration (SV) Measurement of Structures 238 7.3.3 Shaft Absolute Vibration (SAV) Measurement 239 7.3.4 Bearing Metal Temperature Measurements 241 7.4 Load Variations 242 7.5 Pressure Variations 242 7.6 Diagnostic Data 242 7.6.1 Bode Plot 243 7.6.2 Polar Plot 244 7.6.3 Shaft Centerline Plot 246 7.6.4 Spectrum Plot 247 7.7 Frequency/Time Domain Plots 248 7.7.1 Spectrum Water Fall Plot 249 7.8 General Information 251 7.9 Torsional Shaft Vibration Measurement 253 7.9.1 Angular Velocity Measuring Methods in Shafts [6–8] 253 7.10 Operational Influences on Rotor Vibration 258 7.10.1 Closing of Rotor-Stator Clearances 258 7.10.2 Cylinder Distortion/Misalignment 260 7.10.3 Ingress of a Cooling Media Such as Cool Steam and/or Water Induction 261 7.10.4 Lube Oil Influences on Increased Rotor Vibration 262 7.11 Closure 268 References 269 8 Case Studies 270 8.1 Introduction 270 8.2 General 270 8.3 Description of a Problem for Test Case-1 271 8.3.1 Data Review 271 8.3.2 Simulation 273 8.3.3 Solution 274 8.4 Description of a Problem for Test Case-2 275 8.4.1 Data Review 275 8.4.2 Solution 277 8.5 Description of a Problem for Test Case-3 278 8.5.1 Data Review 278 8.5.2 Analyses 281 8.5.3 Solution 283 8.6 Description of a Problem for Test Case-4 284 8.6.1 Analyses: The Following Data Were Reviewed 284 8.6.2 Solution 285 8.7 Description of a Problem for Test Case-5 286 8.7.1 Analyses 286 8.7.2 Solution 288 8.8 Description of a Problem for Test Case-6 289 8.8.1 Data Analysis 289 8.8.2 Solution 291 8.9 Description of a Problem for Test Case-7 292 8.9.1 Data Analysis 292 8.9.2 Solution 293 8.10 Description of a Problem for Test Case-8 294 8.10.1 Analysis 294 8.10.2 Solution 295 8.11 Description of a Problem for Test Case-9 296 8.11.1 Data Analysis 296 8.11.2 Solution 297 8.12 Description of a Problem for Test Case-10 298 8.12.1 Historical Data Review 298 8.12.2 Field Measurements with Excessive Runout at the Coupling End 299 8.12.3 Concerns 299 8.12.4 Resolution 300 8.12.5 Conclusion 300 8.13 Description of a Problem for Test Case-11 301 8.13.1 Analysis 302 8.13.2 Thermal Stress Analysis 302 8.13.3 Metallurgical Findings 303 8.13.4 Conclusions 303 8.14 Closure 303 Appendix A: Behavioral Similarities Between a Structure and a Human Body 304 References 306 This book provides engineers and scientists with practical fundamentals for turbomachinery design. It presents a detailed analysis of existing procedures for the analysis of rotor and structure dynamics, while keeping mathematical equations to a minimum.Ӱecific terminologies are used for rotors and structures, respectively, allowing the readers to clearly distinguish between the two.Ƶrther, the book describes the essential concepts needed to understand rotor failure modes due to lateral and torsional oscillations. It guides the reader from simple single-degree-of-freedom models to the most complex multi-degree-of-freedom systems, and provides useful information concerning steel pedestal stiffness degradation and other structural issues. Fluid-film bearing types and their dynamical behavior are extensively covered and discussed in the context of various turbomachinery applications. The book also discusses shaft alignment and rotor balancing from a practical point of view, providing readers with essential information to help them solve practical problems.s the main body of the book focuses on the diagnostics and description of case studies addressing the most pressing practical issues, together with their successful solutions, it offers a valuable reference guide, helping field engineers manage day-to-day issues with turbomachinery

By: Donald E. Bently with Charles T. Hatch.  Edited by: Bob Grissom

OVERVIEW

A practical course in the fundamentals of machinery diagnostics for anyone who works with rotating machinery, from operator to manager, from design engineer to machinery diagnostician.

This comprehensive book thoroughly explains and demystifies important concepts needed for effective machinery malfunction diagnosis:

(A) Vibration fundamentals: vibration, phase, and vibration vectors.

(B) Data plots: timebase, average shaft centerline, polar, Bode, APHT, spectrum, trend XY, and the orbit.

(C) Rotor dynamics: the rotor model, dynamic stiffness, modes of vibration, anisotropic (asymmetric) stiffness, stability analysis, torsional and axial vibration, and basic balancing.

Modern root locus methods (pioneered by Walter R. Evans) are used throughout this book.

(D) Malfunctions: unbalance, rotor bow, high radial loads, misalignment, rub and looseness, fluid-induced instability, and shaft cracks.

Hundreds of full-color illustrations explain key concepts, and several detailed case studies show how these concepts were used to solve real machinery problems.

A comprehensive glossary of diagnostic terms is included.

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Maximize uptime! Sharpen your machinery diagnostic and troubleshooting skills.-- An up-to-date, hands-on single-source diagnostic guide for process machinery.-- How to use software tools to evaluate machinery behavior.-- 45 detailed case studies describing problem definition, investigation, analytical technique and corrective solutions.This is a single source reference for process machinery diagnostics and troubleshooting. It includes usable computations, analytical procedures, definitions, fundamental machinery behavior, static and dynamic measurements, data acquisition and processing, data interpretation and field problem-solving techniques.The book begins with fundamental concepts of mechanical motion, and expands these basic models into acceptable simulations of real machines. Steam and gas turbines, gear boxes, centrifugal and reciprocating compressors, motors and generators are each analyzed from multiple perspectives. The text describes common malfunctions, plus unusual excitations and failure mechanisms. It is extensively illustrated, and contains detailed examples with sample calculations -- along with 45 case histories that cover entire scenarios, from problem definition through corrective solutions. "This reference/text demonstrates that the design and geometry of gears, and the measuring and processing of noise and vibration information are logical, and can be investigated without a detailed knowledge of mathematics or complex computations - focusing on problems of design, metrology, development, and troubleshooting when noise and vibration occur."--BOOK JACKET. "Written primarily for industrial engineers who are either buying-in or designing, manufacturing, and inspecting gears and encounter noise trouble or must measure unknown quantities, Gear Noise and Vibration describes the overall path of vibration from mesh to final sound ... suggests ways for making improvements at the most economical stage ... and more."--Jacket "This reference/text demonstrates that the design and geometry of gears, and the measuring and processing of noise and vibration information are logical, and can be investigated without a detailed knowledge of mathematics or complex computations - focusing on problems of design, metrology, development, and troubleshooting when noise and vibration occur.". "Written primarily for industrial engineers who are either buying-in or designing, manufacturing, and inspecting gears and encounter noise trouble or must measure unknown quantities, Gear Noise and Vibration describes the overall path of vibration from mesh to final sound ... suggests ways for making improvements at the most economical stage ... and more."--BOOK JACKET. Front Matter ....Pages i-xx Basics of Rotor and Structural Vibration (Raj Subbiah, Jeremy Eli Littleton)....Pages 1-23 Mathematical Model (Raj Subbiah, Jeremy Eli Littleton)....Pages 25-72 Rotor-to-Structure Interaction (Raj Subbiah, Jeremy Eli Littleton)....Pages 73-98 Fluid-Film, Steam and/or Gas Seal Influences on Rotor Dynamics (Raj Subbiah, Jeremy Eli Littleton)....Pages 99-146 Rotor Balancing: Concept, Modeling and Analysis (Raj Subbiah, Jeremy Eli Littleton)....Pages 147-195 Rotor Train Alignment (Raj Subbiah, Jeremy Eli Littleton)....Pages 197-216 Condition Monitoring of Rotors (Raj Subbiah, Jeremy Eli Littleton)....Pages 217-251 Case Studies (Raj Subbiah, Jeremy Eli Littleton)....Pages 253-289 Examining the fundamentals of machinery diagnostics for those working with rotating machinery, this volume prepares engineers, researchers, and students for the future of rotor dynamics and bearing technology, especially pressurized bearings. Demystifying important concepts in the diagnosis of machinery malfunction, it serves as an essential reference for anyone who works with rotating machinery, from operator to manager and from design engineer to machinery diagnostician. The book features hundreds of full color illustration explaining key concepts, numerous detailed case histories demonstrating actual solutions to machinery problems, and a comprehensive glossary of diagnostic terms. A guide to the application of engineering principles in the diagnosis and correction of malfunction of a wide range of machinery which operates within the heavy process industries. Fifteen chapters discuss dynamic motion, rotor mode shapes, bearings and supports, analytical rotor modeling, transducer and dynamic signal characteristics, data acquisition and processing, common malfunctions, unique behavior, rotor balancing, alignment, maintenance and monitoring, and diagnostic methodology. Annotation c. by Book News, Inc., Portland, Or. Specific, practical guidance for every individual involved with solving process machinery problems. The single source reference for explanations of fundamental machinery behavior, static and dynamic measurements, plus data acquisition, processing and interpretation. A variety of lateral and torsional analytical procedures, and physical tests are presented and discussed. This Work Demonstrates That The Design And Geometry Of Gears And The Measuring And Processing Of Noise And Vibration Information Are Logical, And Can Be Investigated Without A Detailed Knowledge Of Mathematics Or Complex Computations. It Focuses On Problems Of Design, Metrology, Development And Troubleshooting When Noise And Vibration Occur.