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© CADFEM 2014
Rotordynamics SimulationM. Moosrainer, CADFEM GmbH,ACUM 2014 in Nürnberg am 05.06.2014
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• Rotor of low pressure turbine burst in 30 pieces
• 1300 kg piece found in 1.3 km distance
• Power plant had to shut down
1987 Burst Low Pressure Turbine in Power Plant Irsching (Bavaria)https://www.allianz.com/de/presse/news/geschaeftsfelder/versicherung/news_2012-11-21.html
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shut down• Millions of property
damage • owing to favorable
circumstances no persons injured
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• Introduction
• Rotordynamic Effects
• Rotordynamics in ANSYS Mechanical & Applications
• Bearing Models in ANSYS Mechanical & Beyond
Workshop Agenda
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Rotating Machinery: Wind Power Plant
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~ 10 rpm
• turbojet
Rotating Machinery: Turbo Engines
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• turbocharger
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~ 10.000 rpm
~ 100.000 rpm
• hard disk
• centrifuge
Rotating Machinery: Hard Disks & Centrifuges
~ 5.000 rpm
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• centrifuge
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~ 1.000.000 rpm
Rotordynamic Effects
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Rotordynamic Effects
Resulting Bearing Force: Elastic Rotor vs. Rigid Rotor
• Observe the following video of a run-up of a simple elastic rotorhttp://www.youtube.com/watch?feature=player_detailpage&v=dO51IjGKrTM
• imbalance force amplitude F of an elastic rotor with increasing
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rotational speed• result presented as ratio of force F
referred to elastic restoring force = eccentricity ε times stiffness k
• note rigid rotor force increasing quadratically whereas elastic rotor force is approaching static elastic restoring force in the limit of high rotational speed after having passed the critical resonance case Ω/ω=1.
• Static balancing of a rigid rotor
• Dynamic balancing of a rigid rotor
What is Rotordynamics?
90% of all RD tasks
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• Dynamic response of an elastic rotor
• key task: avoid instable behavior in operation mode
• one disk:• sign shift for deformation ρs at
resonance Ω=ω from positive to negative
• asymptotic behavior: center of gravity G approaches axes of rotation (self-centering of the rotating mass)
Rotordynamic Effects: Self-Centering
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centering of the rotating mass)
• N disks:• more complex, but no new
phenomena J
For many rotors self-excited bending vibrations occur beyond a certain limit frequency Ωl. Reasons for instabilities:
• internal rotor friction & internal (= rotating) damping mechanisms (!)• journal bearing effects at high rotational speed• self-excitation due to sealing gap• insufficient parameters for magnetic bearing regulator
Rotordynamic Effects: Instable Behavior
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• Ω=0: symmetryà two stationaryorthogonal bending modes in y and z
• Ω<ω: sub-critical motion of shaft centerline point S rotational speed Ω
Rotordynamic Effects: Forward Whirl – Backward Whirl – Orbit
Ω
S
GO
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• ω: modes shows two counter-rotating circular motions with eigenfrequencyω (don’t mix up with rotational speed Ω!)
• forward whirl FW: ω same direction as Ω• backward whirl BW: ω oposite direction of Ω
• superposition of those rotating vectors yields an elliptical orbit
rε
Ω
G
z, Re
y, Im1hr
2hr
ω (FW)
ω (BW)Ω
• balance of moment of momentum
}F{{u}]K[}u]){gyr[C([C]}u[M]{ =+++ &&&
Rotordynamic Effects: Gyroscopic Matrix
úúú
û
ù
êêê
ë
é
WQ-WQ+
úúú
û
ù
êêê
ë
é
QQQ
=úúú
û
ù
êêê
ë
é
ysp
zsp
zsa
ysa
xsp
z
y
x
MMM
jj
jjj
&
&
&&
&&
&& 0 z’ x’
xz
Ω
ysj&
Mz
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• 1st line simply gives the torque moment balancing the angular acceleration of the shaft.
• gyroscopic moments: 2nd & 3rd line are the effects of the moments of inertia of the disc which work against any inclination of the disc à sort of “stiffening”
• gyroscopic moments: 2nd & 3rd line show coupling of two DOFs, e.g. φys andφzsà unsymmetric matrix à prone to instability
• gyroscopic moments are a function of angular velocityà gyroscopic matrix[Cgyr]= sort of unsymmetric „damping matrix“à special ANSYS solvers
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• ANSYS shaft eigenfrequencieswithout gyroscopic moments
• ANSYS shaft eigenfrequencieswith gyroscopic moments
Rotordynamic Effects: Gyroscopic Matrix – Campbell Plot
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Rotordynamics in ANSYS & Applications
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Rotordynamics in ANSYS & Applications
• Doing rotordynamics (modal, harmonic, transient) within a unique environment
• Established, persistent workflow: parametrized CAD geometry, automeshing, simulation, sensitivity studies, optimization
• Easy modelling with required accuracy: beam … solid models
Rotordynamics in ANSYS means …
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• Task: compute the stability of a rotor• stabilizing external stationary
damping à damping in bushing
• destabilizing (!) internal rotating damping à material damping in the rotor
Rotordynamics in ANSYS: GUI Workflow
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damping in the rotor• define Bushing for bearings
• GUI or ASCII file• apply rotational velocity &
Coriolis Effect
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Rotordynamics in ANSYS: Campbell Diagram Frequency
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exp(σt)
Rotordynamics in ANSYS: Campbell Diagram Stability
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exp(σt)§σ neg.: stable§σ pos.: unstable
Rotordynamics in ANSYS: Animate Stable/Instable Modes
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Rotor Stable Backward Mode1@1000rpm Rotor Unstable Forward Mode2@1000rpm
Rotor Undetermined Mode3@0rpm Rotor Unstable Forward Mode5@2000rpm
Rotordynamics in ANSYS: Modelling Options
Multi spool: beam models displayed in solid shape, N shafts @ N rpm
HDD: solid models
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Shaft: 2.5D axiharmonic models
• test rig for basic research on high-temperature (-250°C) superconductors• significant improvement of efficiency for power plant generators• rotordynamic simulation to investigate characteristics of eigenfrequencies and
modal damping of a 4t rotor taking into account gyroscopic effects within a range up to 3600 rpm
Rotordynamic Application: Siemens Generator Basic Research
© CADFEM 2014 24Courtesy of Siemens
• Apply point masses• Spring-damper
properties of bearings• Rotational velocity
Solid Model of the Rotor
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Courtesy of Siemens
Mode #2@3000rpm: Forward Whirl – Observe Damped Rotation in +X
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Mode Comparison: 3D Solid – 1D Beam – 2.5D Axiharmonic Model
Excellent
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Excellent agreement
• Mode #2: f=11.446 Hz
Campbell Plot of Eigenfrequencies for 3D Solid Model
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• Mode #2: ξ=3%
Campbell Plot of Modal Damping for 3D Solid Model
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Performance Comparison of Rotor Models on 8 Cores
100%
120%
Elapsed Time [s] for Complex Modal Analysis
A:3D-Modell B:1D-Modell C:2.5D-Modell
Anzahl Knoten 178319 265 28701
Anzahl Elemente 106355 132 2612
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• conclusion:• 2.5D axiharmonic
model is the optimal compromise between accuracy (3D) and performance (1D)
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0%
20%
40%
60%
80%
100%
3D Solid
1D Beam
2.5D Axiharmonic
0.4%
Structural Elements for Rotating PartsElement Type DetailStructural Mass MASS21
3D Beam BEAM188BEAM189
3D Pipe PIPE288
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3D Pipe PIPE288PIPE289
Structural Shell SHELL181SHELL281
3D Structural SolidSOLID185SOLID186SOLID187
General Axisymmetric Solid SOLID272SOLID273
In Brief: Rotordynamics Gives an Answer To …
• Unbalance Response
Centrifuge
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• Transient Analysis – Stability Verification @ different rpm
Courtesy of Beckman Coulter, Inc.
Stable Orbits @ rpm1 Unstable Orbits @ rpm2
run-up: rpm ↑
Bearing Models in ANSYS Mechanical
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Bearing Models in ANSYS Mechanical
Bearing Models in ANSYS Mechanical
Element Description Characteristics cross terms
Nonlinear characteristics
COMBIN14 Uniaxial spring/damper None NoneCOMBI214 2D spring/damper Unsymmetric Function of W and
eccentricityMATRIX27 General stiffness and
damping matricesUnsymmetric None
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damping matricesMPC184 Multipoint constraint Symmetric for both
linear and nonlinear Function of the displacement
e.g. COMBI214 stiffness and damping incl. cross coupling terms import from ASCII file
orMPC184 Bushing
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Flexible Support: Chiller – Full Model & CMS SuperelementFinite element model of rotor and impellersSolid Model of Compressor Shaft plus
Chiller Assembly in ANSYS Workbench
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Courtesy of Trane, a business of American Standard, Inc. Housing and entire chiller assembly represented by a CMS superelement: à accurate dynamic behavior of both full rotor & support structure
Advanced: Elastohydrodynamics (EHD) e.g. Radial Journal Bearings
• Bartel, D., Uni Magdeburg, IMK: Reibungsreduzierung von mischreibungsbeanspruchten Tribosystemen durch Simulation.8. CADFEM CAE Forum (2011)
• Reduction of Navier Stokes Equation: Reynold’s Approach for
Beginning of the pressure distribution
Flow
dire
ctio
n
Cavitation zone
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Equation: Reynold’s Approach for Thin Fluid Films in Gaps à Tribo-X
fluid EHD result:pressure distribution
structural EHD result:shaft displacement curvesafter different operating times(wear calculation)
Flow
dire
ctio
n
End of the pressure distribution
ANSYS Customization: FEM & EHD bidirectional coupled simulation
gap• Radial journal bearing
• challenge: tiny clearances (≈1‰ of Ø) and even smaller oil film thickness
• FSI coupled FEM/CFD still too expensive for every-day engineering design decisions
• CADFEM solution (in progress): bi-directional coupling of two solvers
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bearing
shaft
directional coupling of two solvers• ANSYS (FEM): flexible bearing and shaft
dynamics• Tribo-X (EHD): Reynolds solver for fluid oil
film dynamics • consistent, bi-directional coupling via
ANSYS interface programming: Euler-Lagrange-Mapping
FEM/EHD Validation Example: Radial Journal Bearing from DIN 31652
Quantity Value
Bearing Diameter D 120 mm
Bearing Width B 60 mm
Bearing Clearance y 1,558 ‰ (C = 186,96 µm)
Load F 38000 N
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Speed of rotation n 2000 rpm
Oil viscosity h 28,7 mPas (ISO VG 100 at 75°C)
Oil density r 900 kg/m³
Oil supply via circumference
Oil supply pressure pzu 0,5 MPa
Material parameter of the shaft E = 210000 N/mm² / n = 0,3
Material parameter of the bearing brass E = 150000 N/mm² / n = 0,3
FEM/EHD Rigid Shaft & Rigid Bearing: Motion & Pressure Distribution
• gradual increase of hydrodynamic pressure with increasing rpm and shaft displacement• correct values for gap, pressure maximum and bearing force for a given eccentricityà validation successful
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FEM/EHD Rigid Shaft & Elastic Bearing vs. Elastic Shaft & Elastic BearingP
ress
ure
Dis
tribu
ion
decreasingpressuremaximum
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pmax = 31,2 MPa
hmin = 11,7 µm
pmax = 35,1 MPa
hmin = 12,6 µm
Pre
ssur
eG
ap D
istri
butio
n
maximum
decreasinggap minimum
Rigid analysis not sufficientElasticity significant: FEM/EHD
FEM/EHD: Transient Simulation of Piston – Crankshaft Assembly
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ANSYS & 3D-TEHD-Simulationsprogramm Tribo-XSimulation auf Mikroebene(Wenn Makroebene glatt gerechnet wird.)
Flussfaktoren
Festkörper-kontaktdrücke
Ken
nfel
dlös
unge
nTEHD-Modul + MR + Verschleiß
Simulation auf Makroebene(Bei kleinen Kontaktflächen rau, bei großen Kontaktflächen glatt.)
lin/nichtlin. Dynamik
ANSYS Mechanical
Materialgesetze
Kontaktformulierungen
Hydrodynamischer Druck
Festkörperkontaktdruck
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Grenzreibungs-zahlen
Ken
nfel
dlös
unge
n
effiziente Solver
à v, gap ß t
Prozess: CAD, Param.
Ordnungsred.: CMS
KontaktformulierungenVerformung
Schmierspalthöhe
Spaltfüllungsgrad Kavitation
Reibung
Verschleiß
Temperatur
Doing rotordynamics via FEM using ANSYS means:• CAD import & automatic meshing• A wide range of elements supporting gyroscopic effects: 1D, 2D, 3D, 2.5D (!)• Accurate modeling of the mass and inertia • analysis types - including prestress: modal, harmonic, transient• proper solver technology: UNSYM, QRDAMP, DAMP accounting for damping,
Summary
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gyroscopic matrix and unsymmetric system of equation not just for simple beam models but also for huge solid models.
• multi-spool dynamics simulation• The ability of solid element meshes to account for the flexibility of the disk as well
as the possible coupling between disk and shaft vibrations.• account for flexibility of supporting structure and/or the disks (e.g. CMS approach)• library of bearing elements + option to extend it by customization, e.g. FEM/EHD• dedicated postprocessing for rotor dynamics: Campbell diagram, critical speed
table extraction, orbit plots, …
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