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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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