ansys v11 rotor dynamics web seminar
TRANSCRIPT
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Welcome!Welcome!
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ANSYS Structural DynamicsANSYS Structural Dynamics
Aline BELEYPierre THIEFFRYANSYS, Inc.
Aline BELEYPierre THIEFFRYANSYS, Inc.
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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
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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
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• 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 ?
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• Finding critical speeds• Unbalance responsecalculation
• Response to Base Excitation• Rotor whirl and system stability
predictions
• Transient start-up and stop
What is rotordynamics ?
Rotordynamics 1) why / what is rotordynamics ?Rotordynamics 1) why / what is rotordynamics ?
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• Model gyroscopic momentsgenerated by rotating parts.
• Account for bearing flexibility (oil film bearings)
• Model rotor imbalance and other excitation forces (synchronousand asynchronousexcitation).
Rotordynamics 1) why / what is rotordynamics ?Rotordynamics 1) why / what is rotordynamics ?
What analysis features are needed ?
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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
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[ ] [ ] [ ] { }F}{K}]){gyrC[C(}{M =+++ uuu &&&
Rotordynamics2) theory
Dynamic equation in stationary reference frame
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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
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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
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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
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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
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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
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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
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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)
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Rotordynamics –7) rotor whirl and instabilityRotordynamics –7) rotor whirl and instability
Rotor whirl motion
whirl motion
ω
Elliptical whirl orbit
x
y
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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)
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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
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Rotordynamics– 8) multi-spool rotorRotordynamics– 8) multi-spool rotor
Whirl animation (ANHARM command) Multi-spool rotors
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• 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
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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
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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
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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
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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
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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
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! 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
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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
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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
Rotordynamics –12) examples
Ex: 1a
less than 0.5% error
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Ex: 1a
Rotordynamics –12) examples
Mode 1 - Backward whirlMode 2 - Forward whirl
Animation of the whirl using ANHARM command
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/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
Rotordynamics –12) examples
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Ex: 2 Campbell diagram of spinning disk
Rotordynamics –12) examples
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Rotordynamics –12) examples
Ex: 2
/com animation of the whirlset,1,5plnsol,u,sumanharm ! >>>>>>>> ����
Spinning disk modeled with solid elements (SOLID45)
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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)
Rotordynamics –12) examples
Ex: 3 Nelson rotor modeled with BEAM188
Ref. [1]: ‘Dynamics of rotor-bearing systems using finite elements’, J. of Eng. for Ind., May 1976
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/com, animation of the whirlset,1,5plnsol,u,sumanharm !>>>>>>>> ����
Ex: 3 Animation of the whirl (Nelson rotor using BEAM188)
Rotordynamics –12) examples
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Twin spool rotor model
- 2 spools (BEAM188)
- 4 bearings (COMBI214)
- 4 disks (MASS21)
Ex: 4 Unbalance response of a twin spool rotor
Rotordynamics –12) examples
Disks are not visible (MASS21)
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! 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
Rotordynamics –12) examples
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/POST1
set,1, 262
/view, , 1, 1, 1
plorb ! >>>>> ����
Rotordynamics –12) examples
Ex: 4 Unbalance response of a twin spool rotor (Harmonic analysis)
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unsymmetric bearings
Stableat 30,000 rpm(3141.6 rad/sec)
Rotordynamics –12) examples
Ex: 5
Transient orbital motion – rotor instability
Unstableat 60,000 rpm(6283.2 rad/sec)
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Rotordynamics –12) examples
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)
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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
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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
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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
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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
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Hard Disk Drive – mode shapesHard Disk Drive – mode shapes
Animation of (0,1)u
Hub looks still because its displacements are small compared to the disks displacements
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Hard Disk Drive – mode shapesHard Disk Drive – mode shapes
6 modes (0,1) balanced : 3 FW and 3 BW
1
2 3
Disks are not vibrating in phase
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Hard Disk Drive – mode shapesHard Disk Drive – mode shapes
Animation of first (0,1)b
Hub is still while disks are vibrating
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Hard Disk Drive – mode shapesHard Disk Drive – mode shapes
1 modes (0,0) unbalanced
Disks are vibrating in phase Hub is moving axially
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Hard Disk Drive – mode shapesHard Disk Drive – mode shapes
Animation of (0,0)u
Hub looks still because its displacements are small compared to the disks displacements
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Hard Disk Drive – mode shapesHard Disk Drive – mode shapes
3 modes (0,0) balanced
1
2 3
Disks are not vibrating in phase
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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
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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
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Blower Shaft – modal analysisBlower Shaft – modal analysis
Campbell diagram
Frequency values
Stability values
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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
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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
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Blower Shaft – unbalance responseBlower Shaft – unbalance response
Bearings reactions
Forward bearing is more loaded than rear one as first mode is a disk mode.
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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
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Blower Shaft – start upBlower Shaft – start up
Displacement UY and UZ at diskzoom on critical speed passage Amplitude of
displacement at disk
22zy UUAmpl +=
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Blower Shaft – start upBlower Shaft – start up
Transient orbits0 to 4 seconds 3 to 4 seconds
As bearings are symmetric, orbits are circular
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Blower Shaft – prestressBlower Shaft – prestress
Include prestress due to thermal loading:
Thermal body load up to 1500 deg F
Resulting static displacements
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Blower Shaft - prestressBlower Shaft - prestress
Cambpell diagram comparison
No prestress With thermal prestress
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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.
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Compressor: Location of Lumped Representation of
Impellers and Bearings
Compressor: Location of Lumped Representation of
Impellers and Bearings
Courtesy of Trane, a business of American Standard, Inc.
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Compressor: SOLID185 Mesh of ShaftCompressor: SOLID185 Mesh of Shaft
Very stiff symmetric contact between axial segments
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Compressor: Forward Whirl ModeCompressor: Forward Whirl Mode
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Compressor: Backward Whirl ModeCompressor: Backward Whirl Mode
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Compressor: Campbell Diagram with Variable BearingsCompressor: Campbell Diagram with Variable Bearings
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Solid Model of Rotor with Chiller AssemblySolid Model of Rotor with Chiller Assembly
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Meshed Rotor and Chiller AssemblyMeshed Rotor and Chiller Assembly
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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
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Analysis ModelAnalysis Model
Impellers
Bearing Locations
Outline of CMS Superelement
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Typical Mode AnimationTypical Mode Animation
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