ch5 2-ansys v11 rotordynamics

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ANSYS Structural DynamicsANSYS Structural Dynamics

Aline BELEYPierre THIEFFRYANSYS, Inc.

Aline BELEYPierre THIEFFRYANSYS, Inc.


1 Why / what is rotordynamics2 Equations for rotating structures3 Rotating and stationary frame of reference4 Elementsthat support Coriolis and/or gyroscopicmatrices5 CORIOLIS command6 Campbell diagram - PLCAMP, PRCAMP, CAMP7 Backward / forward whirl & instability

Rotordynamics outlineRotordynamics outline

Outline


12 Examples- 3D beam- 3D thin disk (solid)- Nelson (beam)

- Multi-spool with unbalance (beam)- Transient orbits

- Industrial rotor models

Rotordynamics outline…Rotordynamics outline…

Outline …

8 Multi-spool rotors9 Whirl orbit plots – PLORB, PRORB10 Bearing element – COMBIN21411 Unbalanceresponse – SYNCHRO


• High speed machinery such as Turbine Engine Rotors, Computer Disk Drives, etc.

• Very small rotor-stator clearances• Flexible bearingsupports – rotor instability

Rotordynamics 1) why / what is rotordynamics ?Rotordynamics 1) why / what is rotordynamics ?

Why rotordynamics ?


• Finding critical speeds• Unbalance responsecalculation

• Response to Base Excitation• Rotor whirl and system stability

predictions

• Transient start-up and stop

What is rotordynamics ?



• Model gyroscopic momentsgenerated by rotating parts.

• Account for bearing flexibility (oil film bearings)

• Model rotor imbalance and other excitation forces (synchronousand asynchronousexcitation).


What analysis features are needed ?


Bearing support coefficients

=

+

y

x

y

x

yyyx

xyxx

y

x

yyyx

xyxx

F

F

u

u

KK

KK

u

u

CC

CC

&

&

Bearing coefficients may be function of rotational speed:

Typical Rotor – Bearing System

Rotordynamics 2) theoryRotordynamics 2) theory

)()( ωω KC


[ ] [ ] [ ] { }F}{K}]){gyrC[C(}{M =+++ uuu &&&

Rotordynamics2) theory

Dynamic equation in stationary reference frame


By extension, the Coriolis force in a static analysis:

}u]{corC[}c{fr&=

∫ ΦΦ= dvωρ T2]corC[

Coriolis matrix in dynamic analyses:

[ ] [ ] [ ] { }F}r

]){uspin[KK(}r

u]){cor[CC(}r

u{M =−+++ &&&

ωω−ω−ω

ωω−=ω

0

0

0

xy

xz

yz

Rotordynamics3) reference frames

Dynamic equation in rotating reference frame


Stationary Reference Frame Rotating Reference Frame

Not applicable in static analysis (ANTYPE , STATIC).

In static analysis, Coriolis force vector can be applied via the IC command

Can generate Campbell plots for computing rotor critical speeds.

Campbell plots are not applicable for computing rotor critical speeds.

Structure must be axi-symmetric about spin axis.

Structure need not be axi-symmetric about spin axis.

Rotating structure can be part of a stationary structure (ex: Gas Turbine Engine rotor-stator assembly).

Rotating structure must be the only part of an analysis model (ex: Gas Turbine Engine Rotor).

Supports more than one rotating structure spinning at different rotational speeds about different axes of rotation (ex: a multi-spool Gas Turbine Engine).

Supports only a single rotating structure (ex: a single-spool Gas Turbine Engine).

Ref:

Advanced Analysis Guide –

Section 8.4 -Choosing the Appropriate Reference Frame Option

Rotordynamics3) reference frames


Applicable ANSYS element types

Stationary Reference Frame

Rotating Reference Frame

Rel. 10.0 BEAM4, PIPE16, MASS21 BEAM188, BEAM189

SHELL181, PLANE182, PLANE183, SOLID185 SOLID186, SOLID187, BEAM188, BEAM189, SOLSH190, MASS21

Rel. 11.0 SOLID185, SOLID186,SOLID187, SOLID45, SOLID95

Rotordynamics4) ANSYS elements

Rel. 12.0(planned)

SHELL181, SHELL63, SHELL93, SOLSH190


CORIOLIS, Option, --, --, RefFrame

Specifies Coriolis effects flag for a rotating structure.SOLUTION: inertia

Option

1 (ON or YES) – Activate Coriolis effects (default).

0 (OFF or NO) -- Deactivate.

RefFrame

1 (ON or YES) – Activate stationary reference frame.

0 (OFF or NO) – Deactivate (default).

Rotordynamics5) commands

Coriolis / Gyroscopic effect


OMEGA, OMEGX, OMEGY, OMEGZ, KSPIN

Rotational velocity of the structure.SOLUTION: inertia

CMOMEGA, CM_NAME, OMEGAX, OMEGAY, OMEGAZ, X1, Y1, Z1, X2, Y2, Z2, KSPIN

Rotational velocity -element component about a user-defined rotational axis.

SOLUTION: inertia

Rotordynamics5) commands

activateKSPIN for gyroscopic effect in rotating reference frame(by default for dynamic analyses)

Specify rotational velocity:ω


Rotordynamics – 6) Campbell diagramRotordynamics – 6) Campbell diagram

• Variation of the rotor natural frequency with respect to rotor speed ω

• In modal analysis perform multiple load steps at different angular velocities ω

• In post processor (POST1), use Campbell commands

– PLCAMP: display Campbell diagram– PRCAMP: print frequencies and critical speeds– CAMPB: support Campbell for prestressed structures

Campbell diagram


Rotordynamics –6) Campbell diagramRotordynamics –6) Campbell diagram

Campbell diagram

PLCAMP , Option, SLOPE, UNIT, FREQB, Cname, STABVALOption

Flag to activate or deactivate sorting SLOPE

The slope of the line which represents the number of excitations per revolution of the rotor.

UNITSpecifies the unit of measurement for rotational angular velocities

FREQBThe beginning, or lower end, of the frequency range of interest.

CnameThe rotating component name

STABVAL

Plot the real part of the eigenvalue (Hz)


Rotordynamics –7) rotor whirl and instabilityRotordynamics –7) rotor whirl and instability

Rotor whirl motion

whirl motion

ω

Elliptical whirl orbit

x

y


Rotordynamics –7) rotor whirl and instabilityRotordynamics –7) rotor whirl and instability

Rotor whirl motion

As frequencies split with increasing spin velocity, ANSYS identifies:

• forward (FW) and backward (BW) whirl

• stable / unstable operation

• critical speeds (PRCAMP)


Rotordynamics –8) multi-spool rotorsRotordynamics –8) multi-spool rotors

More than 1 spool and / or non-rotating parts, use components (CM ) and component rotational velocities

(CMOMEGA).

PLCAMP, Option, SLOPE, UNIT, FREQB, Cname

component name SPOOL1

Multi-spool rotors


Rotordynamics– 8) multi-spool rotorRotordynamics– 8) multi-spool rotor

Whirl animation (ANHARM command) Multi-spool rotors


• In a plane perpendicular to the spin axis, the orbit of a node is an ellipse

• It is defined by 3 characteristics: semi axes A , B and phase ψψψψ in a local coordinate system (x, y, z) where x is the rotation axis

• Angle ϕϕϕϕ is the initial position of the node with respect to the major semi-axis A.

Rotordynamics –9) whirl orbit plot / printRotordynamics –9) whirl orbit plot / print

Whirl orbit plot


PRINT ORBITS FROM NODAL SOLUTION LOCAL y AXIS OF ORBITS IN GLOBAL COORDINATES 0.0000E+00 0.1000E+01 0.0000E+00 LOAD STEP= 1 SUBSTEP= 4 RFRQ= 0.0000 IFRQ= 2.5606 LOAD CASE= 0 ORBIT NODE A B PSI PHI ymax zmax 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3 0.38232 0.38232 0.0000 0.0000 0.38232 0.38232 4 0.70711 0.70711 0.0000 0.0000 0.70711 0.70711 5 0.92301 0.92301 0.0000 0.0000 0.92301 0.92301

Rotordynamics – 9) whirl orbit plot / printRotordynamics – 9) whirl orbit plot / print

Print orbit: PRORB

Plot orbit: PLORBWhirl orbit plot / print


Rotordynamics – 10) bearing elementRotordynamics – 10) bearing element

COMBI214

Bearing element

• 2D spring/damper with cross-couplingterms

• REAL constants are stiffness and damping coefficients

• REAL constants can be table parameters varying with spin velocity


Rotordynamics – 10) bearing elementRotordynamics – 10) bearing element

Bearing element

k = k (ω)c = c (ω)

! Example of table parameters inputomega1 = 0.KYY1 = 1.e+4KZZ1 = 1.e+7omega2 = 250.KYY2 = 1.e+5KZZ2 = 1.e+7omega3 = 500.KYY3 = 1.e+6KZZ3= 1.e+7

/com, Tabular data definition*DIM,KYY,table,3,1,1,omegsKYY(1,0) = omega1 , omega2 , omega3KYY(1,1) = KYY1 , KYY2 , KYY3*DIM,KZZ,table,3,1,1,omegsKZZ(1,0) = omega1 , omega2 , omega3KZZ(1,1) = KZZ1 , KZZ2 , KZZ3et, 3, 214keyopt, 3, 2, 1 ! YZ planer,1, %KYY%, %KZZ%

Tabular input for

REAL constant


Rotordynamics – 11) unbalance responseRotordynamics – 11) unbalance response

Possible excitations caused by rotation velocity ωωωω are:

– Unbalance (ω)

– Coupling misalignment (2* ω)

– Blade, vane, nozzle, diffusers (s* ω)

– Aerodynamic excitations as in centrifugal compressors (0.5* ω)

Unbalance response


SYNCHRO, ratio, cname– ratio

• The ratio between the frequency of excitation, f, and the frequency of the rotational velocity of the structure.

– Cname• The name of the rotating component on which to apply the harmonic excitation.

Note: The SYNCHRO command is valid only for full harmonic analysis (HROPT,Method = FULL)

Rotordynamics – 11) unbalance responseRotordynamics – 11) unbalance response

Unbalance response

ω= 2πf / ratio where, f = excitation frequency (defined in HARFRQ)

The rotational velocity, ω, is applied along the direction cosines of the rotation axis (specified via an OMEGA or CMOMEGA command)

Ansys command for synchronous and asynchronous forces


! Example of input file

/prep7…F0=m*rF, node, fy, F0

F, node, fz, , - F0

How to input unbalance forces?

Rotordynamics – 11) unbalance response

tjbz ejFF ω−==>

tjbby eFcosFF ωω == t

( )2/-tcosFsinFF bbz πωω == t

yF

zF

20

2b FmrF ω=ω=z

y

m

tωr

Unbalance response


ω ω ω ω = 30,000 rpm

CORIO, on, , , on

Modal analysis of a 3D beam (SOLID185 – SOLID45)

Rotordynamics –12) examples

Stationary reference frame

Ex: 1a

ωr


Frequenciesat 30,000 rpm usingQRDAMP eigensolver

Finite element solution(SOLID185)

1 -0.62751987E-08 0.27924146E-03j

-0.62751987E-08 -0.27924146E-03j

2 0.0000000 4.6316102 j

0.0000000 -4.6316102 j

3 0.0000000 8.2842343 j

0.0000000 -8.2842343 j

4 0.0000000 18.515548 j

0.0000000 -18.515548 j

5 0.0000000 33.062286 j

0.0000000 -33.062286 j

6 0.0000000 41.619417 j

0.0000000 -41.619417 j

7 0.0000000 73.890203 j

0.0000000 -73.890203 j

8 0.0000000 74.113637 j

0.0000000 -74.113637 j

Analytical solutionfrom beam theory

1 0 0.00000000 j0 - 0.00000000 j

2 0 4.64000956 j0 - 4.64000956 j

3 0 8.32109166 j0 - 8.32109166 j

4 0 18.56003830 - 18.5600383

5 0 33.2843666 j0 - 33.2843666 j

6 0 41.7600861 j0 41.7600861 j

7 0 74.889824 j0 - 74.889824 j

8 0 74.2401530 j0 -74.2401530 j

Ref: Gerhard Sauer & Michael Wolf, ‘FEA of Gyroscopic effects‘, Finite Elements in Analysis & Design, 5, (1989), 131-140


Ex: 1a

less than 0.5% error


Ex: 1a


Mode 1 - Backward whirlMode 2 - Forward whirl

Animation of the whirl using ANHARM command


/com, SOLID185coriolis, on omega, 2*62.832, 0, 0 ! (20 Hz)

Ex: 1b Clamped-free beam in rotating reference frame

SOLID185 BEAM188 196.42 195.61 First Bending 236.28 235.34 658.52 666.36 Second Bending 698.06 705.42

torsion 782.58 782.79 1340.9 1385.3 Third Bending 1380.0 1423.5

Comparison of frequencies SOLID185 / BEAM188



Ex: 2 Campbell diagram of spinning disk




Ex: 2

/com animation of the whirlset,1,5plnsol,u,sumanharm ! >>>>>>>> ��

Spinning disk modeled with solid elements (SOLID45)


1522.01516.21273.01272.0FWFW6

1066.51068.71273.01272.0BWBW5

842.6844.9806.4808.8FWFW4

760.0762.4806.4808.8BWBW3

330.6329.8271.1271.2FWFW2

213.6214.5271.1271.2BWBW1

[1]Ansys[1]Ansys[1]AnsysF (Hz)

70,000 rpm0 rpmWhirl

Damped Natural Frequencies (Hz)

1522.01516.21273.01272.0FWFW6

1066.51068.71273.01272.0BWBW5

842.6844.9806.4808.8FWFW4

760.0762.4806.4808.8BWBW3

330.6329.8271.1271.2FWFW2

213.6214.5271.1271.2BWBW1

[1]Ansys[1]Ansys[1]AnsysF (Hz)

70,000 rpm0 rpmWhirl

Damped Natural Frequencies (Hz)

96,45795,747

64,75264,924

49,98350,114

46,61246,729

17,15917,146

15,47015,494

[1]Ansys

Critical speeds (rpm)

96,45795,747

64,75264,924

49,98350,114

46,61246,729

17,15917,146

15,47015,494

[1]Ansys

Critical speeds (rpm)


Ex: 3 Nelson rotor modeled with BEAM188

Ref. [1]: ‘Dynamics of rotor-bearing systems using finite elements’, J. of Eng. for Ind., May 1976


/com, animation of the whirlset,1,5plnsol,u,sumanharm !>>>>>>>> ��

Ex: 3 Animation of the whirl (Nelson rotor using BEAM188)



Twin spool rotor model

- 2 spools (BEAM188)

- 4 bearings (COMBI214)

- 4 disks (MASS21)

Ex: 4 Unbalance response of a twin spool rotor


Disks are not visible (MASS21)


! Campbell plot of inner spoolplcamp, ,1.0, rpm, , innSpool

Ex: 4 Unbalance response of a twin spool rotor (Harmonic Analysis)

! Input unbalance forces

f0 = 70e-6

F, 7, FY, f0F, 7, FZ, , -f0

! Solve

/SOLU

antype, harmic

synchro, , innSpool



/POST1

set,1, 262

/view, , 1, 1, 1

plorb ! >>>>> ��


Ex: 4 Unbalance response of a twin spool rotor (Harmonic analysis)


unsymmetric bearings

Stableat 30,000 rpm(3141.6 rad/sec)


Ex: 5

Transient orbital motion – rotor instability

Unstableat 60,000 rpm(6283.2 rad/sec)



Ex: 5

L O A D S T E P O P T I O N S LOAD STEP NUMBER. . . . . . . . . . . . . . . . 2 INERTIA LOADS X Y Z OMEGA. . . . . . . . . . . . 3141.6 0.0000 0.0000 ***** DAMPED FREQUENCIES FROM REDUCED DAMPED EIGE NSOLVER ***** MODE COMPLEX FREQUENCY (HERTZ) MODAL DAMPING RATIO 1 -27.142724 203.90118 j 0.13195307 -27.142724 -203.90118 j 0.13195307 2 -0.18391233 272.56561 j 0.67474502E-03 -0.18391233 -272.56561 j 0.67474502E-03

All complex frequencies real parts are negative

L O A D S T E P O P T I O N S LOAD STEP NUMBER. . . . . . . . . . . . . . . . 3 INERTIA LOADS X Y Z OMEGA. . . . . . . . . . . . 6283.2 0.0000 0.0000 ***** DAMPED FREQUENCIES FROM REDUCED DAMPED EIGE NSOLVER ***** MODE COMPLEX FREQUENCY (HERTZ) MODAL DAMPING RATIO 1 -30.277781 186.52468 j 0.16022861 -30.277781 -186.52468 j 0.16022861 2 6.0020412 289.58296 j 0.20722049E-01 6.0020412 -289.58296 j 0.20722049E-01

One complex frequency has a positive real part

Damped frequencies from QRDAMP

eigensolver

Modal analysis – rotor instability

Stableat 30,000 rpm(3141.6 rad/sec)

Unstableat 60,000 rpm(6283.2 rad/sec)


1 Hard Disk Drive (I.Y. Shen and C.-P. Roger Ku “A non-Classical Vibration Analysis of Multiple Rotating Disks/Shaft Assembly” ASME 1997)

1 Model2 Campbell analysis3 Mode shapes analysis

2 Blower Shaft1 Model2 Modal analysis3 Unbalance synchronous response4 Transient start-up5 Campbell with thermal prestress

Rotordynamics –12) applications


Hard Disk Drive - modelHard Disk Drive - model

ANSYS 4 disks modelDisks thickness = 0.8mm

Total mass = 87.5gSpin = 755 rd/s7855 elements

3 disks HDD sketch


Hard Disk Drive - CampbellHard Disk Drive - Campbell

***** FREQUENCIES (Hz) FROM CAMPBELL (sorting on) * **** Spin(rd/s) 0.000 376.992 753.984 3 BW 577.879 521.296 470.631 4 FW 578.196 640.950 709.918 5 BW 654.745 654.745 654.744 6 BW 668.441 611.326 559.352 7 BW 668.441 611.326 559.352 8 BW 668.441 611.326 559.352 9 FW 668.759 731.224 799.040 10 FW 668.759 731.224 799.040 11 FW 668.759 731.224 799.040 12 BW 668.834 668.834 668.833

Balanced and Unbalanced modes in Stationary Reference Frame

(i,j) x wherei is the number of nodal circlesj is the number of nodal diametersx is b for balanced or u for unbalanced

(0,1)u(0,0)u

(0,1)b

(0,0)b


Hard Disk Drive – mode shapesHard Disk Drive – mode shapes

2 modes (0,1) unbalanced : FW and BW

Disks are vibrating in phase Hub is titlting



Animation of (0,1)u

Hub looks still because its displacements are small compared to the disks displacements



6 modes (0,1) balanced : 3 FW and 3 BW

1

2 3

Disks are not vibrating in phase



Animation of first (0,1)b

Hub is still while disks are vibrating



1 modes (0,0) unbalanced

Disks are vibrating in phase Hub is moving axially



Animation of (0,0)u

Hub looks still because its displacements are small compared to the disks displacements



3 modes (0,0) balanced

1

2 3

Disks are not vibrating in phase


Blower Shaft - modelBlower Shaft - model

Impeller to pump hot hydrogen rich mix of gas and liquid into Solid Oxyde Fluid Cell.

Spin 10,000 rpm

ANSYS Model of rotating part

99 beam elements 2 bearing elements


Blower Shaft - modal analysisBlower Shaft - modal analysis

Frequencies and corresponding mode shapes orbits ***** FREQUENCIES (Hz) FROM CAMPBELL (sorting on) ***** Spin(rpm) 0.000 5000.000 10000.000 1.00xSpin 0.000 83.333 166.667 1 BW 115.552 105.999 96.640 2 FW 115.552 124.949 133.875 3 BW 490.534 448.773 413.217 4 FW 490.534 537.184 586.075


Blower Shaft – modal analysisBlower Shaft – modal analysis

Campbell diagram

Frequency values

Stability values


Blower Shaft – critical speedBlower Shaft – critical speed

First FW critical speed

***** CRITICAL SPEEDS (rpm) FROM CAMPBELL (sor ting on) ***** Slope of line : 1.000 1 6222.614 2 7796.469 3 none 4 none

Bearings are symmetric so FW critical speeds will be the only excited ones


Blower Shaft – unbalance responseBlower Shaft – unbalance response

Harmonic response to disk unbalance- Disk eccentricity is .002”- Disk mass is .0276 lbf-s2/in. - Sweep frequencies 0-10000 rpm

Amplitude of displacement at disk Orbits at critical speed


Blower Shaft – unbalance responseBlower Shaft – unbalance response

Bearings reactions

Forward bearing is more loaded than rear one as first mode is a disk mode.


Blower Shaft – start upBlower Shaft – start up

Transient analysis

- Ramped rotational velocity over 4 seconds

- Unbalance transient forces FY and FZ at disk

0 0.5 1 1.5 2 2.5 3 3.5 40

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Time (s)

Rot

atio

nal v

eloc

ity (

rpm

)

Zoom of transient force



Displacement UY and UZ at diskzoom on critical speed passage Amplitude of

displacement at disk

22zy UUAmpl +=



Transient orbits0 to 4 seconds 3 to 4 seconds

As bearings are symmetric, orbits are circular


Blower Shaft – prestressBlower Shaft – prestress

Include prestress due to thermal loading:

Thermal body load up to 1500 deg F

Resulting static displacements


Blower Shaft - prestressBlower Shaft - prestress

Cambpell diagram comparison

No prestress With thermal prestress


Compressor: Free-Free Testing Apparatus used for

Initial Model Calibration

Compressor: Free-Free Testing Apparatus used for

Initial Model Calibration

+Z

Courtesy of Trane, a business of American Standard, Inc.


Compressor: Location of Lumped Representation of

Impellers and Bearings

Compressor: Location of Lumped Representation of

Impellers and Bearings



Compressor: SOLID185 Mesh of ShaftCompressor: SOLID185 Mesh of Shaft

Very stiff symmetric contact between axial segments


Compressor: Forward Whirl ModeCompressor: Forward Whirl Mode



Compressor: Backward Whirl ModeCompressor: Backward Whirl Mode



Compressor: Campbell Diagram with Variable BearingsCompressor: Campbell Diagram with Variable Bearings


Solid Model of Rotor with Chiller AssemblySolid Model of Rotor with Chiller Assembly



Meshed Rotor and Chiller AssemblyMeshed Rotor and Chiller Assembly



Analysis model – Supporting Structure

Represented by CMS Super Element

Analysis model – Supporting Structure

Represented by CMS Super Element

Housing and Entire Chiller Assembly Represented by a CMS Superelement

Finite Element Model of Rotor and Impellers



Analysis ModelAnalysis Model

Impellers

Bearing Locations

Outline of CMS Superelement



Typical Mode AnimationTypical Mode Animation



Additional v11 Web EventsAdditional v11 Web Events

• ANSYS v11 Update• v11 Enhancements to Elements, Materials and Solvers• ANSYS CFX v11 Update • Pressure Vessel Module• Rotordynamics with ANSYS v11• ANSYS CFX TurboSystem• Fluid Structure Interaction - ANSYS and CFX• CFD Analysis with ANSYS CFX• ANSYS AUTODYN in Workbench• Design Modifications without CAD• Up-Front CFD using ANSYS CFX• Random Vibration Solutions in Workbench

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ch5 2-ansys v11 rotordynamics

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