CONTENTS. 5 BALANCING OF MACHINERY Scope Introduction Balancing Machines Balancing Procedures

Transcription

1 CONTENTS 1 OVERVIEW Introduction Organization Standard Paragraphs Definitions and References Fundamental Concepts Of Rotating Equipment Vibrations LATERAL ROTORDYNAMICS 2.1 Introduction Rotor Bearing System Modeling Rotor Modeling Methods and Considerations Support Stiffness Effects Journal Bearing Modeling Seal Types and Modeling Elements of a Standard Rotordynamics Analysis Machinery Specific Considerations API Testing and Results Standard Paragraph Sections for Lateral Analysis STABILITY ANALYSIS Introduction Rotor Modeling Journal Bearings Seals Excitation Sources Support Stiffness Effects Experience Plots Machinery Specific Considerations Solving Stability Problems Indentifying Fluid Induced Instabilities Stability of Testing Machinery Standard Paragraph Sections for Stability Analysis SP6.8.5 SP TORSIONAL ANALYSIS Introduction and Scope Modeling Machinery Specific Modeling Considerations Reciprocating Machinery Torsional Analysis Calculations Torsional Excitation Sources from Rotating Machinery Fatigue Analysis Contents of a Torsional Report Field Testing to Determine Torsional Response Torsional Lateral Vibration Coupling API Document Paragraphs on Torsional Vibration BALANCING OF MACHINERY Scope Introduction Balancing Machines Balancing Procedures v

2 Figures 1-1 Simple Mass-spring-damper System Amplitude Ratio Versus Excitation Frequency (Rotation Speed) Phase Angle Versus Excitation Frequency Response of a Spring-mass System to Transient (Stable) Response of a Spring-mass System to Transient (Unstable) Jeffcott Form for Rotor Model Simplified Model of a Beam-type Rotating Machine Simplified Model of a Beam-type Rotating Machine with Damping Spring-Mass-Damper Model of Beam Type Rotating Machine Synchronous Response of Beam Type Machine for Various Shaft Stiffness Values Schematic of a Lumped Parameter Rotor Model D Finite Element Model of a Complex Geometry Rotating Component Elastic Modulus vs. Temperature Rotor Model Cross-section of an Eight-Stage 12 MW (16,000 HP) Steam Turbine Turboexpander with Curvic Coupling Fits Turbocompressor with Rabbet and Curvic Coupling Fits Modeling of Curvic Coupling Joints Train Lateral Model Train Lateral Guideline Diagram (W jnl = Static Bearing Reaction) Train Lateral Mode Shapes Equivalent Coupling Model Steam Turbine Support Schematic Journal Bearing Fluid Film and Flexible Support Model Single Degree of Freedom Flexible Support Model Dynamic Stiffness Analysis Diagram Exhaust End Dynamic Compliance Plots Steam End Test Stand Response Exhaust End Test Stand Response Exhaust End Constant Stiffness Support Model Steam End Dynamic Compliance Support Model Steam End Analytical Results, Dynamic Compliance Model Journal Bearing Hydrodynamic Film Two Axial Groove Bearing Spring Stiffness Journal Bearing Stiffness and Damping Pressure Dam Bearing Pressure Dam Bearing Top and Bottom Pads Elliptical Bearing Offset Half Bearing Taper Land Bearing with Three Tapered Pockets Multi-Lobe Bearing with Three Preloaded, Offset Lobes Pad Tilting Pad Bearing Schematic Zero Preloaded Pad Preloaded Pad Negative Preloaded Pad Stiffness and Damping vs. Preload and Bearing Clearance, 4-pad Bearing Stiffness and Damping vs. Preload and L/D Ratio, 4-pad Bearing Lund s Data vs. Experimental Jones and Martin Data vs. Experimental Actual Test Stand Response, 3-axial Groove Bearings Analytically Predicted Response Actual Test Stand Response, 4-pad Tilting Pad Bearings Analytically Predicted Response, Various Bearing Designs Induction Motor Test Stand Response, Tilting Pad Bearings vi

3 2-45 Induction Motor Analytical Response, Tilting Pad Bearings Induction Motor Analytical Response, Elliptical Bearings Induction Motor Test Stand Response, Elliptical Bearings Oil Bushing Breakdown Seal Pressures Experienced by the Outer Floating Ring Seal Mid-span Rotor Unbalance Response of a High Pressure Centrifugal Compressor for Different Suction Pressures at Start-Up Mechanical (Contact) Shaft Seal Liquid-film Shaft Seal with Cylindrical Bushing Liquid-film Shaft Seal with Pumping Bushing Compressor Labyrinth Seals Typical Turbine Shaft Seal Arrangement HP End Honeycomb Seal Pocket Damper Seal Segmented-ring Shaft Seal Self-acting Gas Seal Swirl and Thrust Brakes Used in High-Pressure Compressors [27] Measured Natural Frequency and Damping Showing a Drop of the First Bending Mode of the Shaft [27] Change in First Critical Speed Frequency Due to Influential Gas Seals Change in Separation Margin From Unbalance Response Calculation Labyrinth Seal Bulk Flow Control Volume Approaches Undamped Critical Speed Map Mode Shape Examples for Soft and Stiff Bearings Relative to Shaft Typical Undamped Modes Shapes for a Between Bearing Machine with Different Values of Support Stiffness Typical Bode Plot for Asymmetric System with Split Critical Speeds Example Compressor with Probes Rotated to True Horizontal and Vertical Evaluating Amplification Factors (AFs) from Speed-amplitude Bode Plots Rotor Response Shape Plots in 2D and 3D Form Motion of a Stable System Undergoing Free Oscillations Motion of an Unstable System Undergoing Free Oscillations Steam Turbine Support Schematic Typical Resultant Bearing Load Vector Including Partial Admission Steam Forces Resolution of Partial Admission Forces into Journal Bearing Reactions Gear Set Gear Force Schematic Gear Load Angles at Partial and Full Load Accumulated Pitch Error Chart FCC Expander Critical Speed Map FCC Expander Cross-section FCC Expander Rotor-bearing-support Model Axial Compressor Rotor Construction: Disc-on-shaft Shrink Fit Axial Compressor Rotor Construction: Stacked Discs with Tie Bolts Axial Compressor Rotor Construction: Drum Rotor with Studs Axial Compressor Rotor Construction: Drum Rotor with Tie Bolts Typical Multi-stage Compressor Soft Support Undamped Mode Shapes Multi-stage Compressor Stiff Support Undamped Mode Shapes Multi-stage Compressor Typical Unbalance Distributions for Multi-Stage Compressors Unbalance Response of 1st and 3rd Critical Speeds Rotor Response 4500 rpm Unbalance Response of 2nd Critical Speed Rotor Response 12,800 rpm Typical Overhung Compressor vii

4 2-97 Overhung Compressor Assembly a Soft Support Undamped Mode Shapes Overhung Compressor b Stiff Support Undamped Mode Shapes Overhung Compressor Undamped Critical Speed Map Overhung Compressor Typical Unbalance Distribution Overhung Compressors Impeller Unbalance Response Overhung Compressor Rotor Response Shape at 4,300 rpm Coupling Unbalance Response Overhung Compressors Typical Pinion Rotors from an Integrally Geared Compressor Pinion Rotor Model Integrally Geared Compressor Typical Rigid and Flexible Body Mode Shapes & Unbalances Used to Excite Each Baseline Vibration Reading (Graphically) Readings After the Addition of the Unbalance Weight Influence of the Unbalance Weight Bode Plot for Eight-Stage Compressor Unbalance Weight Influence (... Predicted Test) Bode Plot for Three-Stage Compressor Unbalance Weight Influence (. Predicted Test) Bode Plot of Example # Unbalance Weight Influence (.Predicted Test) SP-1 Rotor Response Plot SP-2 Undamped Critical Speed Map SP-3 Typical Mode Shapes Definition of Log Dec Based on Rate of Decay Stability Analysis Flow Chart Fixed Geometry Bearing Schematic High-Speed, Lightly-Loaded, Unstable Bearing Low-Speed, Heavily-Loaded, Stable Bearing Bearing-Induced Shaft Whip and Oil Whirl Frequency Spectrum, Power Turbine Test, 3-Axial Groove Bearings Rotor Bearing System Stability, Power Turbine N = 5,000 rpm Frequency Spectrum, Power Turbine Test, Double Pocket Bearings Frequency Dependent Stiffness and Damping Full Coefficient vs. Synchronous Reduced Tilting Pad Bearing Stability Sensitivity Waterfall Showing Self-excited Instability High Speed Balance Vacuum Pit Oil Atomization Resulting in Subsynchronous Vibration Single Housing Orifice Design Resulting in Subsynchronous Vibration Button Spray Design Resulting in Subsynchronous Vibration Spray Bar Evacuated Housing Design Squeeze Film Damper Schematic Typical End Seal Arrangements Axial Pressure Profiles of Various Damper Arrangements [Enrich, 10] Squeeze Film Damper Coefficients vs. Eccentricity Ratio: Short Bearing Theory (Cavitated) [Enrich, 10] Idealization of Bearing-damper-support Characteristics O-ring Supported Squeeze Film Damper Schematic Mechanical Arc Spring Supported Squeeze Damper Squeeze Film Damper Stability Map Re-excitation of Rotor First Critical from Oil Seal Excitation Rotor Tracking Instability from Low-pressure Oil Seal Test Rotor Tracking Instability from Distorted Oil Seal Lip Contact Area Typical Configuration for the Last Stage of a Series Flow Compressor Showing the Impeller Eye Seal, the Inter Stage Seal and a Typical Balance Piston Seal Typical Shunt Line Schematic to Reduce Entry Swirl viii

5 3-30 Typical Swirl Brake Schematic to Reduce Entry Swirl Compressor on Full Load Test: With Inert Gas Showing no Instability at Rotor First Critical Frequency, With Process Gas Showing Instability from Balance Piston Excitation, [5,20] Honeycomb Seal Arrangement Comparison of Honeycomb and Hole Pattern Seals Various Hole Pattern Surface Areas Relative to Honeycomb Pocket Seal Arrangement Blade Forces Due to Centerline Displacement Shrink Fit Internal Friction and Shaft Material Hysteresis Destabilizing Force Dry Friction Rub Backward Whirl Excitation Entrapped Fluid Cross-Coupled Force Differential Heating at Bearing Journal for Synchronous Forward Whirl Simple Bearing Support Model System for Measuring Support Compliance Horizontal Dynamic Compliance of the Bearing Supports Experimental Flexible Rotor with Flexible Supports Predicted Response at the Rotor Center with and without Bearing Support Predicted Response at the Bearings with and without Bearing Support Models Predicted and Measured Stability Threshold with and without Bearing Support Models Sood s General Rotor Stability Criteria Sood/Fulton Empirical Stability Criteria Kirk s Compressor Design Map Sheffield s Compressor Experience Using Fulton s Criteria Steam Turbine Leakage Path Aerodynamic Labyrinth Seal Forces Typical Resultant Bearing Load Vector Including Partial Admission Steam Forces Resolution of Partial Admission Forces into Journal Bearing Reactions FCC Expander Critical Speed Map FCC Expander Cross-section FCC Expander Rotor-bearing-support Model Axial Compressor Rotor Construction: Disk-on-shaft Shrink Fit Axial Compressor Rotor Construction: Stacked Disks with Tie Bolts Axial Compressor Rotor Construction: Drum Rotor with Studs Axial Compressor Rotor Construction: Drum Rotor with Tie Bolts High-speed Gearbox Pressure Dam Pinion Bearing High-speed Gearbox Pressure Dam Bull Gear Bearing Typical Multi-stage High-pressure Centrifugal Compressor Rotor Overhung Compressor Rotor Pinion Rotors from an Integrally Geared Compressor Forces Exerted on a Whirling Shaft Mode Shapes for Various Support/Rotor Stiffnesses Half Spectrum Plot Fluid Induced Instability Orbit Plots Shaft Centerline Plot Typical Subsynchronous Rub Orbits Forward Precession Vibration Reverse Precession Vibration Full Spectrum Reverse Precession of 0.5X Calculating Logarithmic Decrement from Test Data SP-4 Typical Plot of Applied Cross-coupled Stiffness vs. Log Decrement SP-5 CSR Plot to Determine Analysis Level Process Compressor Cross-Section Gas Injection Compressor Cross-Section Sheet 3-1 Modified Alford s Force Processor Compressor ix

6 Sheet 3-2 Modified Alford s Force Gas Injection Compressor Process Compressor Stability Plot Gas Injection Compressor Stability Plot Process and Gas Injection Compressors on Experience Plot Diagram of a Shaft Undergoing Torsional Elastic Deflection Side View of a Typical Motor/Gear/Compressor Train Modeling a Typical Motor/Gear/Compressor Train Schematic Lumped Parameter Model for the Motor/Gear/Compressor Train Side View of a Typical Steam Turbine Driven Compressor Train Modeling a Typical Steam Turbine Drive Compressor Train Schematic Lumped Parameter Model for the Steam Turbine Driven Compressor Train Typical Non-linear Stiffness vs. Torque for an Elastomeric Coupling A Typical Twin-Pinion Integrally-geared Centrifugal Compressor That Should be Modeled as a Branched System Effective Penetration of a Smaller Diameter Shaft Section into a Larger Diameter Shaft Section Examples of Shrunk on Sleeves With and Without Relieved Fits A Reduced Moment Gear Coupling A Marine-style Diaphragm Coupling A Reduced Moment Disc Coupling Coupling Spacer Torsional Stiffness Model Two Mass Torsional System with Damping An Elastomeric Hybrid Coupling (w/disc Type) Temperature Dependent Shear Modulus Curve Cross-sectional View of a Parallel Shaft Speed Increaser Torsional Model of a Parallel Shaft Speed Increaser Cross-section of the Shaft Under the Windings of a Typical Induction Motor View of Typical Screw Compressor Rotor Pair Typical System Model of a Dry Screw Compressor Train Typical System Model of a Flooded Compressor Train Portion of a Typical Crankshaft Throw Finite Element Models Used to Calculate Torsional Stiffness of Crankshaft Sections Untuned Damper Campbell Diagram for a Motor-gear-compressor System Campbell Diagram for a Steam Turbine Driven Compressor System Torsional Mode Shapes for a Typical Motor-gear-compressor Train Torsional Mode Shapes for a Typical Motor-gear-compressor Train (Continued) Campbell Diagram for a Motor-gear-compressor Train After Tuning Torsional Mode Shapes for a Typical Steam Turbine Driven Compressor Train rd Torsional Natural Frequency of a Motor-gear-compressor System st Torsional Natural Frequency of a Motor A Typical Magnification Factor Plot of a Torsional Synchronous Response Analysis Transient Torsional Motor Fault Analysis Plot Speed Torque Curve for a Synchronous Motor Plot of Synchronous Motor Transient Response Analysis With Motor Torque Shaft Torques, Motor Speed And Torque Dependent Damping of an Elastomeric Coupling Crossover Points on Torque Residual Curves Transient Torque Associated with a Single Line to Line to Line Fault High Cycle Fatigue for Continuous Excitation Sources Plot of a Shaft Operating Stress as a Function of Shaft Operating Speed Transient Torsional Simulation of a Synchronous Motor-Driven Compressor Train Typical Speed Torque Curve for a Synchronous Motor with Laminated Pole Construction Typical Speed Torque Curve for a Synchronous Motor with Solid Pole Construction Displacement Measurement Considerations x

7 4-47 Torsional Measurements Using a Toothed Wheel and Sensors Torsional Vibration Measurements with a Laser Unbalance Expressed as the Product of Weight and Distance Static Unbalance Couple Unbalance Quasi-Static Unbalance Dynamic Unbalance Unbalance Distribution Resolution ISO Unbalance Tolerance Guide for Rigid Rotor Shaft Centerline Unbalance Orbits (Based on ISO and API Standards) Unbalance Versus Speed for API Limits and Balance Machine Limit (Calculated at w=1 pound) Applicable Speed Ranges for Hard-bearing and Soft-bearing Balancing Machines Fit Eccentricity Related Unbalance Unbalance Correction to Fit Eccentricity Initial Reading of the Index Balancing Method Indexed Component Relative to the Shaft Vector Representation of R 11 and R Results of Adding and Subtracting Vectors R 11 and R SP-6 Rotor Response Plot SP-7 Undamped Critical Speed Map SP-8 Typical Mode Shapes SP-9 Typical Plot of Applied Cross-coupled Stiffness vs. Log Decrement SP-10 Level I Screening Criteria Tables 2-1 Typical Units for Material Properties Computer Model Generated for the Eight-stage Steam Turbine Rotor General Synchronous Behavior and Requirements of Oil and Gas Seals Rotordynamic Characteristics of Axial Compressors Summary of the Results of the Tests Formula for Squeeze Film Damper Stiffness and Damping Coefficients Rotordynamic Characteristics of Axial Compressors Level I Stability Results for Process and Gas Injection Compressor Minimum Log Decrement for Gas Injection Compressor Penetration Factors for Selected Shaft Step Ratios Comparison of Exact and Approximate Results for Torsional Rigidity (Simple Geometric Cross-sectional Shapes) Relationship Between Balancing Machine Pedestal Stiffness, Rotor Weight and Operating Speed (for one manufacturer) xi