Mechanical and Fluids Engineering. Rotordynamics Tutorial: Theory, Practical Applications and Case Studies

Transcription

1 Mechanical and Fluids Engineering Gas Turbine Technology Center Southwest Research Institute Rotordynamics Tutorial: Theory, Practical Applications and Case Studies Dr. J. Jeffrey Moore Southwest Research Institute

2 Goal for this Tutorial To Familiarize The Attendee with The Basic Concepts Of Rotordynamics, API Requirements, Analysis and Design Techniques, and Vibration Behavior

3 Overview Rotordynamics Theory Rotordynamic Analysis of Turbomachinery API Requirements Transducers and Instrumentation Types of Vibration Data Example Vibration Phenomena

4 Rotordynamic Theory Rotordynamics is the study of the dynamics of rotating equipment Types of Dynamics: Lateral Torsional Structural/Foundation

5 Rotordynamic Theory Single Degree of Freedom Theory M X&& + C X& + K X = F(t) F( t) ωn = K = K M Meω 2 cos ωt Natural Frequency C 2 X ( t) = Meω A( ω) cos( ωt + φ) A( ω) = M 2 1 ( 2 2 ) 2 2 ω ω ( Cω) 1 Cω φ( ω) = tan 2 2 m( ωn ω ) n F(t) M X(t) Jeffcott Rotor

6 Rotordynamic Theory Bode Plot - Amplitude Light Damping More Damping ω=ω n Imbalance

7 Rotordynamic Theory Bode Plot - Phase More Damping Light Damping 0 ω=ω n

8 Rotordynamic Theory Solving Resonance Problems Move natural frequency away from excitation frequency Increasing or decreasing stiffness Increasing or decreasing mass Reduce the excitation magnitude Balancing Add damping to the system Improved bearing design Squeeze film dampers Change the excitation frequency Change rotation speed

9 Rotordynamic Theory Gyroscopic Effects Important with overhung disks Eg. Single-stage overhung compressor Gyroscopic forces: C xθ = I p ω Creates radial damping force due to rotation velocity Forward critical speeds increase with speed (gyroscopic stiffening effect) Backward critical speeds decrease with speed Causes rotors to whirl rather than translate Natural Frequency, Hz Simple Overhung Disk Rotor Shaft1 1 0 Bearings Rotordynamic Damped Natural Frequency Map Overhung Disk Example Rotor Speed, rpm 5 10 Forward Backward Shaft1 12

10 Rotordynamic Theory Modeling Turbomachinery Continuous system modeled by a system of springs and masses formulated using either finite element or transfer matrix methods Results in following system of equations: && [ M ] X [ C] X + [ K] X = F(t) + & Similar form as the single degree of freedom Use Matrix solution techniques to solve for natural frequencies, unbalance response, and stability

11 Rotordynamic Theory Stability Analysis Unstable Stable A Rotor System Is Unstable When The Destabilizing Forces Exceed Stabilizing (Damping) Forces

12 Rotordynamic Theory Stability Analysis Damping is a Stabilizing Influence Destabilizing Forces Arise from Cross-Coupling Effects that Generate Forces in the Direction of Whirl Cross-Coupled Stiffness Yields a force in the Y- direction for a displacement in the X Sources include: fixed arc bearings, floating ring oil seals, labyrinth seals, impeller/turbine stages Fx=-K xy Y Y Fy=K yx X X

13 Rotordynamic Theory Stability Calculated by Solving the Eigenvalue Problem: [ M ] X&& + [ C] X& + [ K ] X = { 0} Eigenvalues of the form: s = - ζω n + i ω d Imaginary part gives the damped natural frequency Real part gives the damping ratio (ζ), or stability Logarithmic decrement (log dec) is related by: δ = 2πζ 1 ζ 2 Instability characterized by subsynchronous vibration near the first whirling frequency that rapidly grows to a large amplitude bounded only by rotor/stator rubbing Can be brought on by small changes in load, pressure, or speed.

14 Rotordynamic Theory Evaluation Using Log Dec(rement) Neutrally Stable Linear Vibration X N-1 X N Rotor Vibration δ = L X X n-1 n = n 0 Unstable Undesirable δ < 0 Stable δ > 0 Desirable

15 Rotordynamic Modeling Rotordynamic Modeling 2 nd Section Break the series of smaller segments at diameter steps Components like impellers, couplings, thrust disks do not add shaft stiffness are modeled as added mass Stations added at bearings centerlines Division Wall Seal Gas Flow Path Second Section Gas Balance Seal 1 st Section Sample 10-Stage Compressor Model Typical High Pressure Centrifugal Compressor haft Shaft1 79 Reference: Moore, J.J., Soulas, T.S., 2003, Damper Seal Comparison in a High-Pressure Re-Injection Centrifugal Compressor During Full-Load, Full-Pressure Factory Testing Using Direct Rotordynamic Stability Measurement, Proceedings of the DETC 03 ASME 2003 Design Engineering Technical Conference, Chicago, IL, Sept. 2-6, 2003

16 Rotordynamic Modeling Shaft Radius, meters Shaft Rotordynamics Shaft FE Model 5 Coupling Impellers DGS Stage Centrifugal Compressor SWRI Model - Nom Brngs Bearings Balance Drum Red = Structural Green = Added Mass 65 Thrust Disk Shaft Axial Location, meters

17 Rotordynamic Modeling Journal Bearing Cross-Coupling Oil wedge causes a horizontal movement from a vertical load (cross-coupling) Non-symmetric Pressure Profile

18 Rotordynamic Modeling [ ] + = + t h hu x z p h z x p h x μ Journal Bearing Modeling Solution to the Reynolds equation provides the pressure profile on the pad Assuming small perturbation results in 1 st order equations that yield rotordynamic coefficients (Kxx, Kxy, etc.)

19 Rotordynamic Modeling Common Bearing Types Load Load Journal Radius R Bearing Groove Bearing Plain Cylindrical Bearing Clearance (C) Elliptical Bearing C = Clearance m = Preload Groove Load Bearing Bearing Housing Clearance (C) Most Stable Bearing Tilting Shoe Clearance C Pivot 4-Axial Groove Bearing Tilting Pad Bearing Load Between Pads

20 Rotordynamic Modeling Journal Bearing Modeling Plain journal bearings are the least stable Elliptic and Axial Groove bearings introduce preload that improves the stability Tilt-Pad bearings possess essentially no crosscoupling since the pads can pivot Most commonly used bearing in high speed turbomachinery More expensive than fixed pad designs Necessary when operating at speeds well above (> 3X) first critical speed Many parameters can be adjusted to achieve desired stiffness and damping properties Preload, L/D, Clearance, Offset, Pad orientation

21 Rotordynamic Modeling Undamped Critical Speed Map First six natural frequencies calculated for varying bearing support stiffness Undamped Critical Speed Map 10-Stage Centrifugal Compressor SWRI Model - Nom Brngs Critical Speed, cpm nd Critical Speed 1 st Critical Speed MCOS 1.0E E E E E E E+12 Bearing Stiffness, N/m Intersection between bearing stiffness curve and mode curve is the undamped critical speed

22 Rotordynamic Modeling 1 st Critical Speed Mode Shape Intersection between bearing stiffness curve and critical speed curve represents critical speed Cylindrical mode with flexibility Undamped C.S. Mode Shape Plot 10-Stage Centrifugal Compressor SWRI Model - Nom Brngs forward backward Critical Speed, cpm Undamped Critical Speed Map 10-Stage Centrifugal Compressor SWRI Model - Nom Brngs E E E E E E E+12 Bearing Stiffness, N/m 2 nd Critical Speed 1 st Critical Speed f= cpm K= N/m

23 Rotordynamic Modeling 2 nd Critical Speed Mode Shape Undamped Critical Speed Map 10-Stage Centrifugal Compressor SWRI Model - Nom Brngs Conical Mode with Flexibility Undamped C.S. Mode Shape Plot 10-Stage Centrifugal Compressor SWRI Model - Nom Brngs forward backward Critical Speed, cpm E E E E E E E+12 Bearing Stiffness, N/m 2 nd Critical Speed 1 st Critical Speed f= cpm K= N/m

24 Rotordynamic Modeling API Requirements Critical speeds separated from operating speed range Separation margin function of amplification factor SM 2 = =Unbalance Amount: UB = 4W N 1 AF 1.5 Unbalance Configuration 1 st Mode 2 nd Mode Reference: API 617, 7 th Edition, Axial and Centrifugal Compressors and Expander-compressors for Petroleum, Chemical and Gas Industry Services, American Petroleum Institute, July, 2002.

25 Rotordynamic Modeling Unbalance Response Example First critical speed excited by mid-span unbalance Second critical speed excited by quarter-span unbalance Damping increased 2 nd critical speed from to rpm Separation margins meet API requirements for 1 st critical speed No separation margin required for 2 nd critical speed since AF < 2.5 Response, microns pk-pk Response, microns pk-pk st Critical Speed Rotordynamic Response Plot Rotor Speed, rpm Rotordynamic Response Plot 2 nd Critical Speed Operating Speed Operating Speed NC1=4060 rpm AF1=5.84 NC2=15000 rpm AF2= Rotor Speed, rpm

26 Close Clearance Components Journal Bearing Labyrinth Seal Honeycomb Seal Oil Seal Impeller

27 Rotordynamic Modeling Honeycomb Seal Damping Test Data vs. Predictions Damper seals like honeycomb seals provide substantial damping Damping increases with increasing pressure differential Ceff - Y-Direction 5000 Re (H) (N/m) Frequency (Hz) Reference: Camatti, M., Vannini, G., Fulton, J.W., Hopenwasser, F., 2003, Instability of a High Pressure Compressor Equipped with Honeycomb Seals, Proc. of the Thirty-Second Turbomachinery Symposium, Turbomachinery Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station, Texas.

28 Rotordynamic Modeling Aero Cross-Coupling Arises from Impellers of Centrifugal Compressors Most Common Method version of Wachel Equation ( K ) XY i ( N S ) i Mole Weight ( Horsepower ) i 63,000*, j ρ D = 10 RPM * D * h ρ CFD Methods Have Been Developed j= 1 i i S j Show good correlation to experimental data for pump impellers

29 Rotordynamic Modeling Stability Analysis First Forward Whirling Mode at Maximum Continuous Speed Log Decrement = (no seal effects or cross-coupling) No aero cross-coupling or seal effects included Damped Eigenvalue Mode Shape Plot 10-Stage Centrifugal Compressor SWRI Model - Nom Brngs forward backward f= cpm d=.1494 logd N=12000 rpm

30 Rotordynamic Modeling Stability map shows sensitivity to destabilizing cross-coupling at rotor mid-span Rotor would be unstable without seal effects Damper seal greatly improves stability 2 Stability Map Log Dec E+00 2.E+07 4.E+07 6.E+07 8.E+07 1.E+08 1.E With Seals No Seals API Kxy Mid-span Kxy (N/m)

31 Rotordynamic Modeling Measured Log Decrement in Centrifugal Compressor Shows damper seal effectiveness Log Dec increases as discharge pressure increases A smooth seal was tested to simulate a plugged-up seal Log Dec Smooth Seal - Test Smooth Seal - Prediction Hole Pattern - Test Hole Pattern - Prediction Division Wall Seal Leakage Increasing Smooth Seal - Test Smooth Seal - Prediction Hole Pattern - Test Hole Pattern - Prediction Discharge Pressure (psia) Discharge Pressure (psia) Reference: Moore, J.J., Soulas, T.S., 2003, Damper Seal Comparison in a High-Pressure Re-Injection Centrifugal Compressor During Full-Load, Full-Pressure Factory Testing Using Direct Rotordynamic Stability Measurement, Proceedings of the DETC 03 ASME 2003 Design Engineering Technical Conference, Chicago, IL, Sept. 2-6, 2003

32 Rotordynamic Modeling Foundation Support Effects Industrial Gas Turbine Casing/Rotor Model Finite element casing model coupled to rotor model Casing and foundation flexibility had a great effect on location of critical speeds Lowers critical speeds Increases amplification factor According to API 617, if the foundation flexibility is less than 3.5 times the bearing stiffness, then a foundation model should be included.

33 Review of Transducers Transducer Types Proximity Probe Measures Relative Shaft Displacement (static and dynamic) Most Common Most Applicable to Fluid Film Bearings Subject to Electromechanical Runout (false vibration) Velocity Transducer Measures Absolute Casing Motion Types: magnetic coil or integrating accelerometer Indicates dynamic force transmitted to casing Function of flexibility of casing Vibration severity independent of frequency Not usually used on compressors due to low motion of massive casing

34 Review of Transducers Transducer Types Cont. Accelerometers Typically used in higher frequency measurement Not usually used on compressors due to low motion of massive casing Severity a function of frequency Typically used with rolling element bearing (eg. Aeroderivative gas turbines) and on gearboxes

35 Types of Vibration Instrumentation Overall Level / Vibration Monitor Provides machinery protection Overall vibration level only No detailed information Waveform/Orbit Oscilloscope Good for viewing vibration data in real time Orbit shape shows symmetry in system Round=symmetric Shows transient data (impacts, bursts, etc.)

36 Types of Vibration Instrumentation Fast Fourier Transform (FFT s) Spectrum Analyzer Breaks down complex waveform into frequency components Characterize vibration: Subsynchronous - < running speed Synchronous = running speed Supersynchronous > running speed Can display multiple spectra in time to make waterfall plot Shows how vibration changes in time or during transient events

37 Types of Vibration Instrumentation Waterfall Plot Courtesy of: Memmott, E.A., 1992, Stability of Centrifugal Compressors by Application of Tilt Pad Seals, Damper Bearings, and Shunt Holes, Proceedings of the Institute of Mechanical Engineers, IMechE , 7-10 September, 1992.

38 Types of Vibration Instrumentation Tracking Filter Provides amplitude and phase at running speed and multiples of running speed Used to generate Bode plots DC Data Amplitude/Phase vs Speed (Bode and Polar plot formats) Shows Critical Speed Locations Used for balancing Used to indicate rubs and changes in system behavior Shows shaft position (for proximity probes) Used to characterize external loads on bearings Can indicate misalignment issues

39 Example Vibration Phenomena Faulty Instrumentation Can result in random vibration (amplitude and frequency) Check for: Loose connections Mis-wired leads Damaged probes Loose transducer mounting Probe or probe housing resonance Incorrect transducer or signal conditioning Accelerometer resonant frequency (use low pass filter) Wrong proximity probe cable length Calibrate instrumentation if suspect

40 Example Vibration Phenomena Unbalance High synchronous vibration (1X) Vibration increases with speed squared More rapid near critical speeds Phase angle constant at constant speed and steadystate conditions Can be balanced out if suitable balance planes exist

41 Example Vibration Phenomena Critical Speed in the Operating Speed Range High sensitivity to unbalance Can be caused by: worn bearings, loose foundation, poor initial design Operating Speed Amplitude Speed (rpm)

42 Example Vibration Phenomena Rotordynamic Instability Frequency < Running speed (subsynchronous) Usually does not track with speed Frequency at a natural frequency (usually first mode) Close to but not equal to the first critical speed Amplitude can grow suddenly with small changes in operating condition Can be destructive (wiped seals, bearing, etc.) Results when destabilizing forces exceed stabilizing ones Cross-coupled forces > Damping forces Analytically shown when log dec < 0 Requires loaded operation to occur Often not discovered until field commissioning Cannot be balanced!!

43 Example Vibration Phenomena Rotordynamic Instability Cont. Typical Sources of Destabilizing Forces Annular Seals (labyrinth) Bearings (fixed pad types) Impeller excitation Secondary internal leakage paths Internal rotor friction Floating ring oil seals Methods to Improve Stability Tilt-pad bearings Damper seals (honeycomb, hole pattern) Squeeze film damper bearings Swirl Brakes/Shunt Injection Thicker shafts / Shorter bearing span

44 Example Vibration Phenomena Instability Example: High Pressure Centrifugal Compressor Instability Reference: Memmott, E.A., 1992, Stability of Centrifugal Compressors by Application of Tilt Pad Seals, Damper Bearings, and Shunt Holes, Proceedings of the Institute of Mechanical Engineers, IMechE , 7-10 September, 1992.

45 Example Vibration Phenomena Oil Whirl Frequency Tracks at 1/2X Running Speed Inner Loop Indicates Forward Subsynchronous Whirl

46 Example Vibration Phenomena Surge Lower frequency and near first natural frequency Surge control system Should prevent operation in surge at steady-state conditions May not keep compressor out of surge during upsets, especially ESD s Record surge control valve command and position along with vibration to troubleshoot

47 Example Vibration Phenomena Surge Detection Using Vibration and Process Variables During Rapid Shut-Down (ESD) Bearing Vibration (mils) Flow Orifice Delta-P (in H20) Flow Drops Rapidly Surge Surge Valve Position (%Closed) Closed Surge Valve Opening Delayed by 2 Seconds Speed (RPM) Open

48 Example Vibration Phenomena Rotating Stall Diffuser Stall 5-30% of running speed Occurs while operating near surge Tracks speed Point of inception exhibits hysteresis with flow Associated droop in headflow curve shape Head Blue = Decreasing Flow Red = Increasing Flow Hysteresis Flow Reference: Sorokes, J.M., Kuzdzal, M.J., Sandberg, M.R., Colby, G.M., 1994, Recent Experiences in Full Load Full Pressure Shop Testing of a High Pressure Gas Injection Centrifugal Compressor, Proceedings of the 23 rd Turbomachinery Symposium. Stall 1X

49 Example Vibration Phenomena Unsteady Aerodynamic Excitation Caused by turbulence in the flow field at high load

50 Example Vibration Phenomena Wiped Journal Bearing Example Spectrum Low frequency response

51 Example Vibration Phenomena Damaged Bearing Pads on Tilt-Pad Bearing Produces Asymmetry Causing Backward Whirl Rotation Whirl

52 Example Vibration Phenomena Loose Component on the Shaft Amplitude/Phase shows Hysteresis Does not track same path during run-up/shut-down Caused by dry-gas seal in this example Polar Plot Shut-Down Run-Up

53 Example Vibration Phenomena Mis-alignment Polar Plot Shows Phase Rolling the Wrong Way When Approaching the Critical Speed Decreasing Phase Angle

54 Example Vibration Phenomena Mis-alignment cont. Shaft Position on Drive-End does not Drop in Bearing Actually rises in bearing during shutdown Drive End Non-Drive End Shaft Rises In Bearing During Shutdown Shaft Drops In Bearing During Shutdown

55 Example Vibration Phenomena Mis-alignment cont. Orbit showing 2X vibration Reference: Simmons, H.R., Smalley, A.J., 1989, Effective Tools for Diagnosing Elusive Turbomachinery Dynamics Problems in the Field, Presented at the Gas Turbine and Aeroengine Congress and Exposition, June 4-8, 1989, Toronto, Ontario, Canada

56 Example Vibration Phenomena Torsional Vibration Steady-State Avoid resonance of 1X running speed Transient Start-up or Short Circuit of Motors Strain Gages or Torsiographs typically used for measurement Torsional Crack in Shaft Measured Stress in Coupling During Synchronous Motor Start

57 Example Vibration Phenomena Torsional Vibration Cont. Measured Coupling Stress of Gas Turbine Driven Compressor Package with Gear 1X Tracking Shows Location of Torsional Natural Frequencies Reference: Smalley, A.J., 1977, Torsional System Damping, Presented at the Vibration Institute Machinery Vibration Monitoring and Analysis Meeting, Houston, TX, April 19-21, 1983.

58 Summary Our Understanding of Rotordynamics has Greatly Improved over the Last 50 years Including Complex Rotor/Fluid Interaction Modern Analysis Tools Can Minimize the Risk of Encountering a Critical Speed or Stability Problem on New Equipment Tools validated against test rig and full-scale testing results Vibration Equipment in the Hands of the Right Expertise can Solve a Variety of Vibration Issues Key Steps: Choose the right type of instrumentation for the machine and vibration type Correct installation and wiring to prevent noise and false signals important Use the appropriate data acquisition equipment Correlate vibration with key process parameters Troubleshooting often requires controlled changes of process parameters (eg. Speed, load, pressure, temperature, etc.) Do Not be slow to ask for help Down time and loss production can far out weigh cost of consultants fees

59 Questions??? Dr. J. Jeffrey Moore Southwest Research Institute (210)