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ANSYS_V11_Rotordynamics.pdf
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© 2007 ANSYS, Inc. All rights reserved.
1
ANSYS, Inc. Proprietary
ANSYS Structural
Dynamics
Aline BELEY
Pierre THIEFFRY
ANSYS, Inc.
© 2006 ANSYS, Inc. All rights reserved.
2
ANSYS, Inc. Proprietary
Rotordynamics
outline
outline
Outline
1
2
3
4
5
6
7
Why / what is rotordynamics
Equations for rotating structures
Rotating and stationary frame of reference
Elements that support Coriolis and/or gyroscopic matrices
CORIOLIS command
Campbell diagram - PLCAMP, PRCAMP, CAMP
Backward / forward whirl & instability
© 2007 ANSYS, Inc. All rights reserved.
3
ANSYS, Inc. Proprietary
Rotordynamics
outline
outline…
Outline …
8
9
10
11
Multi-spool rotors
Whirl orbit plots – PLORB, PRORB
Bearing element – COMBIN214
Unbalance response – SYNCHRO
12 Examples
- 3D beam
- 3D thin disk (solid)
- Nelson (beam)
- Multi-spool with unbalance (beam)
- Transient orbits
- Industrial rotor models
© 2007 ANSYS, Inc. All rights reserved.
4
ANSYS, Inc. Proprietary
Rotordynamics
1)
1) why
why // what
what is
is rotordynamics
rotordynamics ??
Why rotordynamics ?
• High speed machinery such as Turbine
Engine Rotors, Computer Disk Drives, etc.
• Very small rotor-stator clearances
• Flexible bearing supports – rotor instability
© 2007 ANSYS, Inc. All rights reserved.
5
ANSYS, Inc. Proprietary
Rotordynamics
1)
1) why
why // what
what is
is rotordynamics
rotordynamics ??
What is rotordynamics ?
•
•
•
•
Finding critical speeds
Unbalance response calculation
Response to Base Excitation
Rotor whirl and system stability
predictions
• Transient start-up and stop
© 2007 ANSYS, Inc. All rights reserved.
6
ANSYS, Inc. Proprietary
Rotordynamics
1)
1) why
why // what
what is
is rotordynamics
rotordynamics ??
What analysis features are needed ?
• Model gyroscopic moments generated
by rotating parts.
• Account for bearing flexibility (oil film
bearings)
• Model rotor imbalance and other
excitation forces (synchronous and
asynchronous excitation).
© 2007 ANSYS, Inc. All rights reserved.
7
ANSYS, Inc. Proprietary
Rotordynamics
2)
2) theory
theory
Typical Rotor – Bearing System
Bearing support coefficients
C xx
C
 yx
C xy  u& x  K xx
&  + 

C yy  u y  K yx
K xy  u x  Fx 
 = 

K yy  u y  Fy 
Bearing coefficients may be function of rotational speed:
C (ω )
© 2007 ANSYS, Inc. All rights reserved.
K (ω )
8
ANSYS, Inc. Proprietary
Rotordynamics
2) theory
Dynamic equation in stationary reference frame
[M ]{u&&} + ([C] + [Cgyr ]){u&} + [K ]{u} = {F}
© 2007 ANSYS, Inc. All rights reserved.
9
ANSYS, Inc. Proprietary
Rotordynamics
3) reference frames
Dynamic equation in rotating reference frame
[M ]{&u& r } + ([C] + [Ccor ]){u& r } + ([K ] − [K spin ]){u r } = {F}
Coriolis matrix in dynamic analyses:
[Ccor ] = 2∫ ρ Φ T ω Φ dv
 0

ω =  ωz

− ωy
− ωz
0
ωx
ωy 

− ωx 

0 

By extension, the Coriolis force in a static analysis:
{f c } = [Ccor ]{u& r }
© 2007 ANSYS, Inc. All rights reserved.
10
ANSYS, Inc. Proprietary
Rotordynamics
3) reference frames
Stationary Reference Frame
Ref:
Advanced
Analysis
Guide –
Section 8.4 Choosing the
Appropriate
Reference
Frame Option
© 2007 ANSYS, Inc. All rights reserved.
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).
11
ANSYS, Inc. Proprietary
Rotordynamics
4) ANSYS elements
Applicable ANSYS element types
Stationary Reference
Frame
Rel. 10.0
BEAM4, PIPE16,
MASS21 BEAM188,
BEAM189
Rel. 11.0
SOLID185, SOLID186,
SOLID187, SOLID45,
SOLID95
Rel. 12.0
(planned)
© 2007 ANSYS, Inc. All rights reserved.
Rotating Reference
Frame
SHELL181, PLANE182,
PLANE183, SOLID185
SOLID186, SOLID187,
BEAM188, BEAM189,
SOLSH190, MASS21
SHELL181, SHELL63,
SHELL93, SOLSH190
12
ANSYS, Inc. Proprietary
Rotordynamics
5) commands
Coriolis / Gyroscopic effect
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).
© 2007 ANSYS, Inc. All rights reserved.
13
ANSYS, Inc. Proprietary
Rotordynamics
5) commands
Specify rotational velocity:
ω
OMEGA, OMEGX, OMEGY, OMEGZ, KSPIN
Rotational velocity of the structure.
SOLUTION: inertia
activate KSPIN for gyroscopic
effect in rotating reference frame
(by default for dynamic analyses)
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
© 2007 ANSYS, Inc. All rights reserved.
14
ANSYS, Inc. Proprietary
Rotordynamics – 6)
6) Campbell
Campbell diagram
diagram
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
© 2007 ANSYS, Inc. All rights reserved.
15
ANSYS, Inc. Proprietary
Rotordynamics – 6)
6) Campbell
Campbell diagram
diagram
Campbell diagram
PLCAMP, Option, SLOPE, UNIT, FREQB, Cname, STABVAL
Option
Flag to activate or deactivate sorting
SLOPE
The slope of the line which represents the number of
excitations per revolution of the rotor.
UNIT
Specifies the unit of measurement for rotational angular
velocities
FREQB
The beginning, or lower end, of the frequency range of
interest.
Cname
The rotating component name
STABVAL
Plot the real part of the eigenvalue (Hz)
© 2007 ANSYS, Inc. All rights reserved.
16
ANSYS, Inc. Proprietary
Rotordynamics – 7) rotor whirl and instability
Rotor whirl motion
y
ω
whirl motion
x
Elliptical whirl orbit
© 2007 ANSYS, Inc. All rights reserved.
17
ANSYS, Inc. Proprietary
Rotordynamics – 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)
© 2007 ANSYS, Inc. All rights reserved.
18
ANSYS, Inc. Proprietary
Rotordynamics – 8)
8) multi-spool
multi-spool rotors
rotors
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
© 2007 ANSYS, Inc. All rights reserved.
19
ANSYS, Inc. Proprietary
Rotordynamics – 8)
8) multi-spool
multi-spool rotor
rotor
Multi-spool rotors
© 2007 ANSYS, Inc. All rights reserved.
Whirl animation (ANHARM command)
20
ANSYS, Inc. Proprietary
Rotordynamics – 9)
9) whirl
whirl orbit
orbit plot
plot // print
print
Whirl orbit plot
•
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 ψ in a local
coordinate system (x, y, z) where x is
the rotation axis
•
Angle ϕ is the initial position of the
node with respect to the major semi-axis
A.
© 2007 ANSYS, Inc. All rights reserved.
21
ANSYS, Inc. Proprietary
Rotordynamics –– 9)
9) whirl
whirl orbit
orbit plot
plot // print
print
Whirl orbit plot / print
Plot orbit: PLORB
Print orbit: PRORB
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
RFRQ=
0.0000
ORBIT
NODE
1
2
3
4
5
A
0.0000
0.0000
0.38232
0.70711
0.92301
SUBSTEP=
IFRQ=
B
0.0000
0.0000
0.38232
0.70711
0.92301
© 2007 ANSYS, Inc. All rights reserved.
4
2.5606
PSI
0.0000
0.0000
0.0000
0.0000
0.0000
LOAD CASE=
PHI
0.0000
0.0000
0.0000
0.0000
0.0000
0
ymax
0.0000
0.0000
0.38232
0.70711
0.92301
22
zmax
0.0000
0.0000
0.38232
0.70711
0.92301
ANSYS, Inc. Proprietary
Rotordynamics – 10)
10) bearing
bearing element
element
Bearing element
COMBI214
• 2D spring/damper with cross-coupling
terms
• REAL constants are stiffness and
damping coefficients
• REAL constants can be table
parameters varying with spin velocity
© 2007 ANSYS, Inc. All rights reserved.
23
ANSYS, Inc. Proprietary
Rotordynamics – 10)
10) bearing
bearing element
element
Bearing element
! Example of table parameters input
omega1 = 0.
KYY1 = 1.e+4
KZZ1 = 1.e+7
omega2 = 250.
KYY2 = 1.e+5
KZZ2 = 1.e+7
omega3 = 500.
KYY3 = 1.e+6
KZZ3= 1.e+7
REAL constant
/com, Tabular data definition
*DIM,KYY,table,3,1,1,omegs
KYY(1,0) = omega1 , omega2 , omega3
KYY(1,1) = KYY1 , KYY2 , KYY3
*DIM,KZZ,table,3,1,1,omegs
KZZ(1,0) = omega1 , omega2 , omega3
KZZ(1,1) = KZZ1 , KZZ2 , KZZ3
et, 3, 214
keyopt, 3, 2, 1
! YZ plane
r,1, %KYY%, %KZZ%
k = k (ω)
c = c (ω)
© 2007 ANSYS, Inc. All rights reserved.
Tabular input for
24
ANSYS, Inc. Proprietary
Rotordynamics – 11)
11) unbalance
unbalance response
response
Unbalance response
Possible excitations caused by rotation velocity ω are:
– Unbalance (ω)
– Coupling misalignment (2* ω)
– Blade, vane, nozzle, diffusers (s* ω)
– Aerodynamic excitations as in centrifugal compressors (0.5* ω)
© 2007 ANSYS, Inc. All rights reserved.
25
ANSYS, Inc. Proprietary
Rotordynamics – 11)
11) unbalance
unbalance response
response
Unbalance response
Ansys command for
SYNCHRO, ratio,
– ratio
•
–
synchronous and asynchronous forces
cname
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)
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)
© 2007 ANSYS, Inc. All rights reserved.
26
ANSYS, Inc. Proprietary
Rotordynamics – 11) unbalance response
Unbalance response
How to input unbalance forces?
Fy = Fb cos ω t = Fb e j ω t
Fz = Fb sin ω t = Fb cos (ω t - π / 2 )
=> Fz = − jF b e j ω t
Fz
! Example of input file
z
/prep7
…
F0=m*r
F, node, fy, F0
F, node, fz, , - F0
© 2007 ANSYS, Inc. All rights reserved.
Fb = mrω 2 = F0 ω 2
m
r
ωt
y
27
Fy
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 1a
Modal analysis of a 3D beam (SOLID185 – SOLID45)
Stationary
reference frame
CORIO, on, , , on
r
ω
ω = 30,000 rpm
© 2007 ANSYS, Inc. All rights reserved.
28
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Analytical solution
from beam theory
Ex: 1a
Frequencies
at 30,000 rpm using
1
0
0
Finite element solution
(SOLID185)
0.00000000 j
- 0.00000000 j
QRDAMP eigensolver
1 -0.62751987E-08
0.27924146E-03j
-0.62751987E-08
-0.27924146E-03j
2
2
0
0
4.64000956 j
- 4.64000956 j
3
3
Ref: Gerhard Sauer &
Michael Wolf, ‘FEA of
Gyroscopic effects‘, Finite
Elements in Analysis &
Design, 5, (1989), 131-140
4
0
0
0
0
8.32109166 j
- 8.32109166 j
18.5600383
- 18.5600383
5
0
0
33.2843666 j
- 33.2843666 j
6
0
0
41.7600861 j
41.7600861 j
less than
0.5% error
4
5
6
7
7
0
0
74.889824 j
- 74.889824 j
8
8
© 2007 ANSYS, Inc. All rights reserved.
0
0
74.2401530 j
-74.2401530 j
29
0.0000000
4.6316102 j
0.0000000
-4.6316102 j
0.0000000
8.2842343 j
0.0000000
-8.2842343 j
0.0000000
18.515548 j
0.0000000
-18.515548 j
0.0000000
33.062286 j
0.0000000
-33.062286 j
0.0000000
41.619417 j
0.0000000
-41.619417 j
0.0000000
73.890203 j
0.0000000
-73.890203 j
0.0000000
74.113637 j
0.0000000
-74.113637 j
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 1a
Animation of the whirl using ANHARM command
Mode 1 - Backward whirl
Mode 2 - Forward whirl
© 2007 ANSYS, Inc. All rights reserved.
30
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 1b
Clamped-free beam in rotating reference frame
/com, SOLID185
coriolis, on
omega, 2*62.832, 0, 0
! (20 Hz)
Comparison of frequencies SOLID185 / BEAM188
SOLID185
196.42
236.28
658.52
698.06
782.58
1340.9
1380.0
First Bending
Second Bending
torsion
Third Bending
© 2007 ANSYS, Inc. All rights reserved.
31
BEAM188
195.61
235.34
666.36
705.42
782.79
1385.3
1423.5
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 2
Campbell diagram of spinning disk
© 2007 ANSYS, Inc. All rights reserved.
32
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 2
Spinning disk modeled with solid elements (SOLID45)
/com animation of the whirl
set,1,5
plnsol,u,sum
anharm ! >>>>>>>> © 2007 ANSYS, Inc. All rights reserved.
33
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 3
Nelson rotor modeled with BEAM188
Damped Natural Frequencies (Hz)
Whirl
0 rpm
70,000 rpm
[1]
Ansys
F (Hz)
Ansys
[1]
Ansys
[1]
1
BW
BW
271.2
271.1
214.5
213.6
2
FW
FW
271.2
271.1
329.8
330.6
3
BW
BW
808.8
806.4
762.4
760.0
4
FW
FW
808.8
806.4
844.9
842.6
5
BW
BW
1272.0
1273.0
1068.7
1066.5
6
FW
FW
1272.0
1273.0
1516.2
1522.0
Critical speeds (rpm)
Ansys
[1]
15,494
15,470
17,146
17,159
46,729
46,612
50,114
49,983
64,924
64,752
95,747
96,457
© 2007 ANSYS, Inc. All rights reserved.
Ref. [1]: ‘Dynamics of rotorbearing systems using finite
elements’, J. of Eng. for Ind.,
May 1976
34
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 3
Animation of the whirl (Nelson rotor using BEAM188)
/com, animation of the whirl
set,1,5
plnsol,u,sum
anharm
!>>>>>>>> © 2007 ANSYS, Inc. All rights reserved.
35
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 4
Unbalance response of a twin spool rotor
Twin spool rotor model
- 2 spools (BEAM188)
- 4 bearings (COMBI214)
- 4 disks (MASS21)
Disks are not visible (MASS21)
© 2007 ANSYS, Inc. All rights reserved.
36
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 4
Unbalance response of a twin spool rotor (Harmonic Analysis)
! Campbell plot of inner spool
plcamp, ,1.0, rpm, , innSpool
© 2007 ANSYS, Inc. All rights reserved.
! Input unbalance forces
f0 = 70e-6
F, 7, FY, f0
F, 7, FZ, , -f0
37
! Solve
/SOLU
antype, harmic
synchro, , innSpool
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 4
Unbalance response of a twin spool rotor (Harmonic analysis)
/POST1
set,1, 262
/view, , 1, 1, 1
plorb
! >>>>> © 2007 ANSYS, Inc. All rights reserved.
38
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 5
Transient orbital
motion – rotor
instability
unsymmetric bearings
Stable at 30,000 rpm
Unstable at 60,000 rpm
(3141.6 rad/sec)
© 2007 ANSYS, Inc. All rights reserved.
(6283.2 rad/sec)
39
ANSYS, Inc. Proprietary
Rotordynamics – 12) examples
Ex: 5
Modal analysis – rotor instability
Damped frequencies
from QRDAMP
eigensolver
Stable at 30,000 rpm
Unstable at 60,000 rpm
(3141.6 rad/sec)
(6283.2 rad/sec)
LOAD STEP OPTIONS
LOAD STEP OPTIONS
LOAD STEP NUMBER. . . . . . . . . . . . . . . . 2
INERTIA LOADS
X
Y
OMEGA. . . . . . . . . . . .
3141.6
0.0000
LOAD STEP NUMBER. . . . . . . . . . . . . . . . 3
INERTIA LOADS
X
Y
OMEGA. . . . . . . . . . . .
6283.2
0.0000
Z
0.0000
Z
0.0000
***** DAMPED FREQUENCIES FROM REDUCED DAMPED EIGENSOLVER *****
***** DAMPED FREQUENCIES FROM REDUCED DAMPED EIGENSOLVER *****
MODE
MODE
1
2
COMPLEX FREQUENCY (HERTZ)
-27.142724
-27.142724
-0.18391233
-0.18391233
203.90118 j
-203.90118 j
272.56561 j
-272.56561 j
MODAL DAMPING RATIO
1
0.13195307
0.13195307
0.67474502E-03
0.67474502E-03
2
All complex frequencies real
parts are negative
© 2007 ANSYS, Inc. All rights reserved.
COMPLEX FREQUENCY (HERTZ)
-30.277781
-30.277781
6.0020412
6.0020412
186.52468 j
-186.52468 j
289.58296 j
-289.58296 j
MODAL DAMPING RATIO
0.16022861
0.16022861
0.20722049E-01
0.20722049E-01
One complex frequency
has a positive real part
40
ANSYS, Inc. Proprietary
Rotordynamics – 12) applications
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)
2
1 Model
2 Campbell analysis
3 Mode shapes analysis
Blower Shaft
1 Model
2 Modal analysis
3 Unbalance synchronous response
4 Transient start-up
5 Campbell with thermal prestress
© 2007 ANSYS, Inc. All rights reserved.
41
ANSYS, Inc. Proprietary
Hard Disk Drive - model
3 disks HDD sketch
ANSYS 4 disks model
Disks thickness = 0.8mm
Total mass = 87.5g
Spin = 755 rd/s
7855 elements
© 2007 ANSYS, Inc. All rights reserved.
42
ANSYS, Inc. Proprietary
Hard Disk Drive - Campbell
Balanced and Unbalanced modes in
Stationary Reference Frame
***** FREQUENCIES (Hz) FROM CAMPBELL (sorting on) *****
Spin(rd/s)
3
4
5
6
7
8
9
10
11
12
BW
FW
BW
BW
BW
BW
FW
FW
FW
BW
0.000
577.879
578.196
654.745
668.441
668.441
668.441
668.759
668.759
668.759
668.834
376.992
521.296
640.950
654.745
611.326
611.326
611.326
731.224
731.224
731.224
668.834
753.984
470.631
709.918
654.744
559.352
559.352
559.352
799.040
799.040
799.040
668.833
(0,1)u
(0,0)u
(0,1)b
(0,0)b
(i,j)x where
i is the number of nodal circles
j is the number of nodal diameters
x is b for balanced or u for unbalanced
© 2007 ANSYS, Inc. All rights reserved.
43
ANSYS, Inc. Proprietary
Hard Disk Drive – mode shapes
2 modes (0,1) unbalanced : FW and BW
Disks are vibrating in phase
© 2007 ANSYS, Inc. All rights reserved.
Hub is titlting
44
ANSYS, Inc. Proprietary
Hard Disk Drive – mode shapes
Animation of (0,1)u
Hub looks still
because its
displacements are
small compared to the
disks displacements
© 2007 ANSYS, Inc. All rights reserved.
45
ANSYS, Inc. Proprietary
Hard Disk Drive – mode shapes
6 modes (0,1) balanced : 3 FW and 3 BW
1
2
© 2007 ANSYS, Inc. All rights reserved.
Disks are
not
vibrating
in phase
3
46
ANSYS, Inc. Proprietary
Hard Disk Drive – mode shapes
Animation of first (0,1)b
Hub is still
while disks
are
vibrating
© 2007 ANSYS, Inc. All rights reserved.
47
ANSYS, Inc. Proprietary
Hard Disk Drive – mode shapes
1 modes (0,0) unbalanced
Disks are vibrating in phase
© 2007 ANSYS, Inc. All rights reserved.
Hub is moving axially
48
ANSYS, Inc. Proprietary
Hard Disk Drive – mode shapes
Animation of (0,0)u
Hub looks still
because its
displacements are
small compared to the
disks displacements
© 2007 ANSYS, Inc. All rights reserved.
49
ANSYS, Inc. Proprietary
Hard Disk Drive – mode shapes
3 modes (0,0) balanced
1
2
© 2007 ANSYS, Inc. All rights reserved.
Disks are
not
vibrating
in phase
3
50
ANSYS, Inc. Proprietary
Blower 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
© 2007 ANSYS, Inc. All rights reserved.
51
ANSYS, Inc. Proprietary
Blower Shaft - modal analysis
Frequencies and corresponding mode shapes orbits
***** FREQUENCIES (Hz) FROM CAMPBELL (sorting on) *****
Spin(rpm)
0.000
1.00xSpin
1 BW
2 FW
3 BW
4 FW
0.000
115.552
115.552
490.534
490.534
© 2007 ANSYS, Inc. All rights reserved.
5000.000
10000.000
83.333
105.999
124.949
448.773
537.184
166.667
96.640
133.875
413.217
586.075
52
ANSYS, Inc. Proprietary
Blower Shaft – modal analysis
Campbell diagram
Stability values
Frequency values
© 2007 ANSYS, Inc. All rights reserved.
53
ANSYS, Inc. Proprietary
Blower Shaft – critical speed
First FW critical speed
***** CRITICAL SPEEDS (rpm) FROM CAMPBELL (sorting on) *****
Slope of line :
1
2
3
4
1.000
6222.614
7796.469
none
none
Bearings are symmetric so
FW critical speeds will be
the only excited ones
© 2007 ANSYS, Inc. All rights reserved.
54
ANSYS, Inc. Proprietary
Blower 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
© 2007 ANSYS, Inc. All rights reserved.
Orbits at critical speed
55
ANSYS, Inc. Proprietary
Blower Shaft – unbalance response
Bearings reactions
Forward bearing is
more loaded than
rear one as first
mode is a disk mode.
© 2007 ANSYS, Inc. All rights reserved.
56
ANSYS, Inc. Proprietary
Blower Shaft – start up
Transient analysis
10000
- Ramped rotational velocity over 4 seconds
8000
7000
Rotational velocity (rpm)
- Unbalance transient forces FY and FZ at disk
9000
6000
5000
4000
3000
2000
1000
0
0
0.5
1
1.5
2
Time (s)
2.5
3
3.5
4
Zoom of
transient
force
© 2007 ANSYS, Inc. All rights reserved.
57
ANSYS, Inc. Proprietary
Blower Shaft – start up
Displacement UY and UZ at disk
zoom on critical speed passage
Amplitude of
displacement at disk
Ampl = U y2 + U z2
© 2007 ANSYS, Inc. All rights reserved.
58
ANSYS, Inc. Proprietary
Blower Shaft – start up
Transient orbits
0 to 4 seconds
3 to 4 seconds
As bearings are symmetric, orbits are circular
© 2007 ANSYS, Inc. All rights reserved.
59
ANSYS, Inc. Proprietary
Blower Shaft – prestress
Include prestress due to thermal loading:
Thermal body load up to 1500 deg F
Resulting static displacements
© 2007 ANSYS, Inc. All rights reserved.
60
ANSYS, Inc. Proprietary
Blower Shaft - prestress
Cambpell diagram comparison
No prestress
© 2007 ANSYS, Inc. All rights reserved.
With thermal prestress
61
ANSYS, Inc. Proprietary
Compressor:
Compressor: Free-Free
Free-Free Testing
Testing Apparatus
Apparatus used
used for
for
Initial
Initial Model
Model Calibration
Calibration
+Z
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
62
ANSYS, Inc. Proprietary
Compressor:
Compressor: Location
Location of
of Lumped
Lumped Representation
Representation of
of
Impellers
Impellers and
and Bearings
Bearings
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
63
ANSYS, Inc. Proprietary
Compressor:
Compressor: SOLID185
SOLID185 Mesh
Mesh of
of Shaft
Shaft
Very stiff symmetric contact
between axial segments
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64
ANSYS, Inc. Proprietary
Compressor:
Compressor: Forward
Forward Whirl
Whirl Mode
Mode
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
65
ANSYS, Inc. Proprietary
Compressor:
Compressor: Backward
Backward Whirl
Whirl Mode
Mode
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
66
ANSYS, Inc. Proprietary
Compressor:
Compressor: Campbell
Campbell Diagram
Diagram with
with Variable
Variable Bearings
Bearings
© 2007 ANSYS, Inc. All rights reserved.
67
ANSYS, Inc. Proprietary
Solid
Solid Model
Model of
of Rotor
Rotor with
with Chiller
Chiller Assembly
Assembly
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
68
ANSYS, Inc. Proprietary
Meshed
Meshed Rotor
Rotor and
and Chiller
Chiller Assembly
Assembly
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
69
ANSYS, Inc. Proprietary
Analysis
Analysis model
model –– Supporting
Supporting Structure
Structure
Represented
Represented by
by CMS
CMS Super
Super Element
Element
Finite Element Model
of Rotor and Impellers
Housing and Entire
Chiller Assembly
Represented by a CMS
Superelement
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
70
ANSYS, Inc. Proprietary
Analysis
Analysis Model
Model
Bearing
Locations
Impellers
Outline of CMS
Superelement
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
71
ANSYS, Inc. Proprietary
Typical
Typical Mode
Mode Animation
Animation
Courtesy of Trane, a business of American Standard, Inc.
© 2007 ANSYS, Inc. All rights reserved.
72
ANSYS, Inc. Proprietary
Additional v11 Web Events
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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
http://www.ansys.com/special/ansys11/email1.htm
© 2007 ANSYS, Inc. All rights reserved.
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ANSYS, Inc. Proprietary
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