2008 international ansys conference · © 2008 ansys, inc. all rights reserved. 2 ansys, inc....
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© 2008 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary
2008 International
ANSYS Conference
Piezoelectric Fan Modeling
FSI Analysis using ANSYS and CFXCourtesy of PIEZO Systems Inc.
Rich Lange, Stephen Scampoli, Naseem Ansari,
and Dan Shaw
ANSYS Inc.
© 2008 ANSYS, Inc. All rights reserved. 2 ANSYS, Inc. Proprietary
Scope of Presentation
• Outline the workings of the Piezoelectric fan
• Discuss the processing of the Piezoelectric data
• Show analysis settings
• Discuss the Coupling with CFX
• Show results
© 2008 ANSYS, Inc. All rights reserved. 3 ANSYS, Inc. Proprietary
The Piezoelectric Fan
• Piezoelectric Fan– Spot Cooling for Electronic Components
– Low Magnetic Permeability
– Blade driven by Piezoelectric Bimorph
Blade
Bimorph
FR4 Board
Courtesy: PIEZO Systems Inc
© 2008 ANSYS, Inc. All rights reserved. 4 ANSYS, Inc. Proprietary
Piezoelectricity
• Piezoelectricity is a property of some materials (notably
crystals and certain ceramics) to generate an electric
potential in response to applied mechanical stress
– Piezoelectric effect is reversible
• Materials exhibiting the direct piezoelectric effect (stress
electricity) also exhibit the converse piezoelectric effect
(electricity stress)
• For example, lead zirconate titanate crystals exhibit a
maximum strain rate of ~0.1%
• For stress induced electricity in piezo-materials, voltage
often varies in time
© 2008 ANSYS, Inc. All rights reserved. 5 ANSYS, Inc. Proprietary
Finite Element Model with Boundary
Conditions
Two piezoelectric layers
Courtesy: PIEZO Systems Inc
Bottom piezoelectric Layer: 0 Volt
Top Piezoelectric Layer: 115 [V] sin((2π/0.4[s])t)
The voltage variance produces the fan motion.
Fix Support at holes
© 2008 ANSYS, Inc. All rights reserved. 6 ANSYS, Inc. Proprietary
Piezoelectrics - Equations
L
F
V
u
K K
K K
V
u
C 0
0 C
V
u
0
0M
VZ
Zu
v
u
T
0
Structural Terms
nodal forces
nodal displacements
mass damping stiffness
Dielectric Terms
damping permittivity
electric potential
electric charge
coupling terms
© 2008 ANSYS, Inc. All rights reserved. 7 ANSYS, Inc. Proprietary
Model Input
• The equation describing the voltage variation is created in ANSYS Classic equation editor– Create the function and save it
– Once the constants in the equation are defined, a table is created in ANSYS that describes the specific equation
– The log file of the resulting table can easily become a Command object in Simulation
– The boundary condition then simply gets applied as a tabular load
© 2008 ANSYS, Inc. All rights reserved. 8 ANSYS, Inc. Proprietary
Function and Table
• Ansys Utility Menu – Parameters> Functions> Define/Edit
• Enter the function, defining the voltage as a constant Volume– File>Save (give a name)
• Ansys Utility Menu – Parameters>Functions>Read From File
© 2008 ANSYS, Inc. All rights reserved. 9 ANSYS, Inc. Proprietary
Resulting Log File
• This is representative of what will go in the
command snippet to represent the table
© 2008 ANSYS, Inc. All rights reserved. 10 ANSYS, Inc. Proprietary
Voltage Boundary Conditions -
Command Snippets
Bottom Layer: Voltage = 0 Volt
Top Layer:
Voltage = 115 [V] sin((2π/0.4[s])t)
Snippet for entering a formula
in SIMULATION
© 2008 ANSYS, Inc. All rights reserved. 11 ANSYS, Inc. Proprietary
Piezoelectric Material Data Input
• Piezoelectric material data is supplied in different formats
– Discussed in ANSI/IEEE Std 176-1987, “Standard on Piezoelectricity”
• All industry standard material property data formats are not compatible with ANSYS– Data must be converted into ANSYS compatible form
• Also, material data is typically supplied with the polarization direction as Z (or 3), the longitudinal direction as X (or 1), and the transverse direction as Y (or 2)
– In our example, the polarization direction is Y, the longitudinal direction X, and the transverse direction Z. Thus, the supplied material data must be transformed appropriately
© 2008 ANSYS, Inc. All rights reserved. 12 ANSYS, Inc. Proprietary
Introduction (cont)
• For static or low frequency devices (e.g., sensors), material
property data are typically provided as
– Compliance measured under constant electric field [sE],
– Piezoelectric strain matrix [d], and
– Relative permittivity measured under constant stress [εT]
• For higher frequencies devices (e.g., resonators), material
property data are typically provided as
– Stiffness measured under constant electric field [cE],
– Piezoelectric stress matrix [e], and
– Relative permittivity measured under constant strain [εS]
© 2008 ANSYS, Inc. All rights reserved. 13 ANSYS, Inc. Proprietary
Required Material Properties
• For static analyses, piezoelectric materials are characterized by
– Structural elasticity
– Piezoelectric coupling
– Dielectric permittivity
• For dynamic analyses, additional data are required
– Density
– Structural damping
– Dielectric damping
• Piezoelectric behavior can
be defined using different
material properties
– Structural elasticity
• Moduli of elasticity
• Stiffness matrix
• Compliance matrix
– Piezoelectric coupling
• Piezoelectric matrix
– Dielectric permittivity
• Relative permittivity
• Relative permittivity matrix
© 2008 ANSYS, Inc. All rights reserved. 14 ANSYS, Inc. Proprietary
ANSYS Commands – MP Command
• Material properties are entered into ANSYS using either the MP (for isotropic or orthotropic properties) or TB commands (when tabular input is required)
• TB, LAB, MAT, NTEMP, NPTS, TBOPT, EOSOPT– LAB: material model
• PIEZ = piezoelectric matrix
• ANEL = anisotropic elastic matrix
– TBOPT: options within material model (stress or strain based)
– EOSOPT: equation of state
• TBDATA command enters the values into the table– Defines data for the table specified on the last issued TB
command at the temperature specified on the last issued TBTEMP command
• TBDATA, STLOC, C1, C2, C3, C4, C5, C6
– STLOC: starting location
– C1, C2, C3, C4, C5, C6: data to be input
© 2008 ANSYS, Inc. All rights reserved. 15 ANSYS, Inc. Proprietary
Elastic Coefficients
• IEEE Standard 176 specifies standard 6x6 format for elasticity matrix– Row order is {x, y, z, yz, xz, xy}
• ANSYS uses the standard structural mechanics format– Row order is {x, y, z, xy, yz, xz}
• Order of the shear terms is different– IEEE Standard 176 row 4 is equivalent to ANSYS row 5
– IEEE Standard 176 row 5 is equivalent to ANSYS row 6
– IEEE Standard 176 row 6 is equivalent to ANSYS row 4
© 2008 ANSYS, Inc. All rights reserved. 16 ANSYS, Inc. Proprietary
Elastic Coefficients (cont)
• For ANSYS piezoelectric elements to be compatible with
other ANSYS elements, elasticity matrices must use
consistent formats
– Shear rows must be reordered
666564636261
565554535251
464544434241
363534333231
262524232221
615141312111
cccccc
cccccc
cccccc
cccccc
cccccc
cccccc
666564636261
565554535251
464544434241
363534333231
262524232221
615141312111
cccccc
cccccc
cccccc
cccccc
cccccc
cccccc
IEEE Standard 176 Format ANSYS Format
© 2008 ANSYS, Inc. All rights reserved. 17 ANSYS, Inc. Proprietary
• Elasticity matrix is input in Stiffness form using TB,ANEL
with TBOPT = 0
– Input order is based on position in the matrix
Anisotropic Elastic Coefficients (cont)
TB,ANEL,matid#,0
TBDATA,1,13.2,7.1,7.3
TBDATA,7,13.2,7.3
TBDATA,12,11.5
TBDATA,16,3
TBDATA,19,2.6
TBDATA,21,2.6
2ANSYSm
N
21
2019
181716
15141312
1110987
654321
6.2
06.2
000.3
0005.11
00030.72.13
00030.710.72.13
10C 10E
© 2008 ANSYS, Inc. All rights reserved. 18 ANSYS, Inc. Proprietary
Input Elastic Coefficients
• As with stiffness matrix, if elasticity matrix is provided as a
compliance matrix at constant electric field (sE) in IEEE
Standard 176 form, it must be converted to ANSYS format
– IEEE Standard 176 format
– convert to ANSYS format
by rearranging rows
4 5
5 6
6 4
2IEEEm
N
6.2
06.2
000.3
0005.11
00030.72.13
00030.710.72.13
10s 10E
2ANSYSm
N
6.2
00.3
006.2
0005.11
00030.72.13
00030.710.72.13
10s 10E
© 2008 ANSYS, Inc. All rights reserved. 19 ANSYS, Inc. Proprietary
Input Elastic Coefficients
• For this example, in addition to converting the elasticity data from the IEEE format to the ANSYS format, it must be also rotated so that the polarization direction is Y rather than Z– Z data becomes Y data
– Y data becomes Z data
– X data remains the same
2ANSYSm
N
6.2
00.3
006.2
0005.11
00030.72.13
00030.710.72.13
10s 10E
2
10
ANSYSm
N
0.3
06.2
006.2
0030.72.13
00005.11
00030.710.72.13
10
Es
Order for the TBDATA commands
follows the schematic on the right
hand side
See Command Snippet for the
TBDATA commands
© 2008 ANSYS, Inc. All rights reserved. 20 ANSYS, Inc. Proprietary
Piezoelectric Coefficients
• IEEE Standard 176 uses a standard textbook 3x6 format for the piezoelectric coupling matrix– Order is {x, y, z, yz, xz, xy}
• ANSYS uses a 6x3 format for the piezoelectric matrix– Order is {x, y, z, xy, yz, xz}
• As with elasticity matrix, order of shear terms is incompatible between IEEE Standard 176 and ANSYS and must be reordered– In addition, rows and columns are transposed
• To convert piezoelectric coefficient data provided in the IEEE Standard 176 format into the ANSYS format– Matrix must be transposed
– Rows 4, 5, and 6 must be appropriately interchanged
© 2008 ANSYS, Inc. All rights reserved. 21 ANSYS, Inc. Proprietary
Piezoelectric Coefficients (cont)
363534333231
262524232221
615141312111
dddddd
dddddd
dddddd
636261
535251
4341
333231
232221
312111
ddd
ddd
ddd
ddd
ddd
ddd
42
636261
535251
4341
333231
232221
312111
ddd
ddd
ddd
ddd
ddd
ddd
42
Typical Piezoelectric Matrix
535251
434241
6361
333231
232221
312111
ddd
ddd
ddd
ddd
ddd
ddd
62
Transposed Piezoelectric Matrix ANSYS Piezoelectric Matrix
Transposed Piezoelectric Matrix
© 2008 ANSYS, Inc. All rights reserved. 22 ANSYS, Inc. Proprietary
Piezoelectric Coefficients
• Piezoelectric coefficients are provided in stress form in IEEE Standard 176 format
– To convert to ANSYS format, first transpose the matrix
– Then rearrange rows 4, 5, & 6
C
NIEEE
000
005.10
05.100
1.1400
1.400
1.400
d T
005.10
05.100
000
1.1400
1.400
1.400
d ZANSYS,
© 2008 ANSYS, Inc. All rights reserved. 23 ANSYS, Inc. Proprietary
Piezoelectric Coefficients
• Finally, Y being the direction of
polarization instead of Z must be
accounted for
• Piezoelectric coefficients in the
stress form are input using
TB,PIEZ with TBOPT = 0
– Input order is based on position
in matrix
005.10
05.100
000
1.1400
1.400
1.400
d ZANSYS,
181716
151413
121110
987
654
321
000
5.1000
005.10
01.40
01.140
01.40
Y,d ANSYS
See Command Snippet for TBDATA commands
636261
535251
434241
333231
232221
312111
dddzx
dddyz
dddxy
dddz
dddy
dddx
zyx
424341
525351
626361
222321
323331
213111
dddyx
dddzy
dddxz
dddy
dddz
dddx
yzx
© 2008 ANSYS, Inc. All rights reserved. 24 ANSYS, Inc. Proprietary
Piezoelectric Material Defined -
Command Snippets
Anisotropic Elastic matrix
Piezoelectric matrix
Coupled Element 226
© 2008 ANSYS, Inc. All rights reserved. 25 ANSYS, Inc. Proprietary
Piezoelectric Solution
• Static
– SPARSE is the recommended solver
• Transient
– SPARSE is the recommended solver
– recommended TINTP (transient algorithm) settings• ALPHA = 0.25
• DELTA = 0.5
• THETA = 0.5
• Modal
– Block Lanczos is the recommended solver
• Harmonic
– SPARSE is the recommended solver
– harmonically varying displacement produces a current
– applied current produces a vibration
© 2008 ANSYS, Inc. All rights reserved. 26 ANSYS, Inc. Proprietary
Electric Potential
© 2008 ANSYS, Inc. All rights reserved. 27 ANSYS, Inc. Proprietary
Blade Movements
Displacement
Exaggerated and Not to Scale
t=0.1 Sec
Equivalent
stresses
t=0.3 Sec
© 2008 ANSYS, Inc. All rights reserved. 28 ANSYS, Inc. Proprietary
CFX Model
• Flow domain internal boundary is the device.
• Blue arrows represent “Opening Condition”
– Fluid may move in and out such boundaries
© 2008 ANSYS, Inc. All rights reserved. 29 ANSYS, Inc. Proprietary
CFX Setup
• Flow domain Default is the FSI boundary
Force – Displacement transfers
© 2008 ANSYS, Inc. All rights reserved. 30 ANSYS, Inc. Proprietary
CFX Setup
• In some cases, the MFX two
way procedure is made more
robust with the use of an
Implicit form of Artificial
Compressibility
• This is implemented by
setting up a zero fluid mass
source on the FSI boundary
and using a Total Mass
Source Pressure Coefficient
as shown
© 2008 ANSYS, Inc. All rights reserved. 31 ANSYS, Inc. Proprietary
Blade Displacement at 0.1 sec
ANSYS
CFX
© 2008 ANSYS, Inc. All rights reserved. 32 ANSYS, Inc. Proprietary
Blade Displacements at 0.3 sec
CFX
ANSYS
© 2008 ANSYS, Inc. All rights reserved. 33 ANSYS, Inc. Proprietary
Velocity Contours in CFX
Time = 0.1 sec. 0.2 sec. 0.3 sec. 0.4 sec.
© 2008 ANSYS, Inc. All rights reserved. 34 ANSYS, Inc. Proprietary
Summary
• Demonstrated the Multiphysics analysis of a
piezo-electric fan with ANSYS and CFX in the
MFX Solver
• The Workbench platform is shown to be flexible
enough to handle non-native applications
• Procedures exist to easily convert the
piezoelectric property data to the ANSYS format
• The robustness of Two-Way FSI coupling is
enhanced with artificial compressibility