2008 ANSYS, Inc.All rights reserved. 1 ANSYS, Inc.
Proprietary2008 International ANSYS ConferencePiezoelectric Fan
ModelingFSI Analysis using ANSYS and CFXCourtesy of PIEZO Systems
Inc.Rich Lange, Stephen Scampoli, Naseem Ansari, and Dan ShawANSYS
Inc. 2008 ANSYS, Inc.All rights reserved. 2 ANSYS, Inc.
ProprietaryScope 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. ProprietaryThe
Piezoelectric Fan Piezoelectric Fan Spot Cooling for Electronic
Components Low Magnetic Permeability Blade driven by Piezoelectric
BimorphBlade Bimorph FR4 BoardCourtesy: PIEZO Systems Inc 2008
ANSYS, Inc.All rights reserved. 4 ANSYS, Inc.
ProprietaryPiezoelectricity 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.
ProprietaryFinite Element Model with Boundary ConditionsTwo
piezoelectric layersCourtesy: PIEZO Systems IncBottom piezoelectric
Layer: 0 VoltTop Piezoelectric Layer: 115 [V] sin((2/0.4[s])t)The
voltage variance produces the fan motion.Fix Support at holes 2008
ANSYS, Inc.All rights reserved. 6 ANSYS, Inc.
ProprietaryPiezoelectrics - Equations )`=)`(((
+)`((
+)`((
LFVuK KK KVuC 00 CVu 00 MV ZZ uvuT 0
Structural Termsnodal forcesnodal displacementsmass damping
stiffnessDielectric Termsdamping permittivityelectric
potentialelectric chargecoupling terms 2008 ANSYS, Inc.All rights
reserved. 7 ANSYS, Inc. ProprietaryModel 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. ProprietaryFunction 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. ProprietaryResulting 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. ProprietaryVoltage Boundary Conditions -Command SnippetsBottom
Layer: Voltage = 0 VoltTop Layer: Voltage = 115 [V]
sin((2/0.4[s])t)Snippet for entering a formula in SIMULATION 2008
ANSYS, Inc.All rights reserved. 11 ANSYS, Inc.
ProprietaryPiezoelectric 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.
ProprietaryIntroduction (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 [T] 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 [S] 2008 ANSYS, Inc.All rights reserved. 13
ANSYS, Inc. ProprietaryRequired 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. ProprietaryANSYS 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. ProprietaryElastic
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.
ProprietaryElastic Coefficients (cont) For ANSYS piezoelectric
elements to be compatible with other ANSYS elements, elasticity
matrices must use consistent formats Shear rows must be
reordered(((((((((
66 65 64 63 62 6156 55 54 53 52 5146 45 44 43 42 4136 35 34 33
32 3126 25 24 23 22 2161 51 41 31 21 11c c c c c cc c c c c cc c c
c c cc c c c c cc c c c c cc c c c c c(((((((((
66 65 64 63 62 6156 55 54 53 52 5146 45 44 43 42 4136 35 34 33
32 3126 25 24 23 22 2161 51 41 31 21 11c c c c c cc c c c c cc c c
c c cc c c c c cc c c c c cc c c c c cIEEE Standard 176 Format
ANSYS Format 2008 ANSYS, Inc.All rights reserved. 17 ANSYS, Inc.
Proprietary Elasticity matrix is input in Stiffness form using
TB,ANELwith TBOPT = 0 Input order is based on position in the
matrixAnisotropic Elastic Coefficients
(cont)TB,ANEL,matid#,0TBDATA,1,13.2,7.1,7.3TBDATA,7,13.2,7.3TBDATA,12,11.5TBDATA,16,3TBDATA,19,2.6TBDATA,21,2.62ANSYSmN(((((((((
(((((((((
=2120 1918 17 1615 14 13 1211 10 9 8 76 5 4 3 2 16 . 20 6 . 20 0
0 . 30 0 0 5 . 110 0 0 30 . 7 2 . 130 0 0 30 . 7 10 . 7 2 . 1310
C10 E 2008 ANSYS, Inc.All rights reserved. 18 ANSYS, Inc.
ProprietaryInput 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 rows4 55 66 42IEEEmN(((((((((
=6 . 20 6 . 20 0 0 . 30 0 0 5 . 110 0 0 30 . 7 2 . 130 0 0 30 .
7 10 . 7 2 . 1310 s10 E2ANSYSmN(((((((((
=6 . 20 0 . 30 0 6 . 20 0 0 5 . 110 0 0 30 . 7 2 . 130 0 0 30 .
7 10 . 7 2 . 1310 s10 E 2008 ANSYS, Inc.All rights reserved. 19
ANSYS, Inc. ProprietaryInput 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 same2ANSYSmN(((((((((
=6 . 20 0 . 30 0 6 . 20 0 0 5 . 110 0 0 30 . 7 2 . 130 0 0 30 .
7 10 . 7 2 . 1310 s10 E210ANSYSmN0 . 30 6 . 20 0 6 . 20 0 30 . 7 2
. 130 0 0 0 5 . 110 0 0 30 . 7 10 . 7 2 . 1310(((((((((
=EsOrder for the TBDATA commands follows the schematic on the
right hand sideSee Command Snippet forthe TBDATA commands 2008
ANSYS, Inc.All rights reserved. 20 ANSYS, Inc.
ProprietaryPiezoelectric 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.
ProprietaryPiezoelectric Coefficients (cont)((((
36 35 34 33 32 3126 25 24 23 22 2161 51 41 31 21 11d d d d d dd
d d d d dd d d d d d(((((((((
63 62 6153 52 5143 4133 32 3123 22 2131 21 11d d dd d dd d dd d
dd d dd d d42(((((((((
63 62 6153 52 5143 4133 32 3123 22 2131 21 11d d dd d dd d dd d
dd d dd d d42Typical Piezoelectric Matrix (((((((((
53 52 5143 42 4163 6133 32 3123 22 2131 21 11d d dd d dd d dd d
dd d dd d d62Transposed Piezoelectric MatrixANSYS Piezoelectric
Matrix Transposed Piezoelectric Matrix 2008 ANSYS, Inc.All rights
reserved. 22 ANSYS, Inc. ProprietaryPiezoelectric 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, & 6CNIEEE(((((((((
=0 0 00 0 5 . 100 5 . 10 01 . 14 0 01 . 4 0 01 . 4 0
0dT(((((((((
=0 0 5 . 100 5 . 10 00 0 01 . 14 0 01 . 4 0 01 . 4 0 0dZ ANSYS,
2008 ANSYS, Inc.All rights reserved. 23 ANSYS, Inc.
ProprietaryPiezoelectric 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(((((((((
=0 0 5 . 100 5 . 10 00 0 01 . 14 0 01 . 4 0 01 . 4 0 0dZ
ANSYS,(((((((((
(((((((((
=18 17 1615 14 1312 11 109 8 76 5 43 2 10 0 05 . 10 0 00 0 5 .
100 1 . 4 00 1 . 14 00 1 . 4 0Y , dANSYSSee Command Snippet for
TBDATA commands63 62 6153 52 5143 42 4133 32 3123 22 2131 21 11d d
d zxd d d yzd d d xyd d d zd d d yd d d xz y x 42 43 4152 53 5162
63 6122 23 2132 33 3121 31 11d d d yxd d d zyd d d xzd d d yd d d
zd d d xy z x 2008 ANSYS, Inc.All rights reserved. 24 ANSYS, Inc.
ProprietaryPiezoelectric Material Defined -Command
SnippetsAnisotropic Elastic matrixPiezoelectric matrixCoupled
Element 226 2008 ANSYS, Inc.All rights reserved. 25 ANSYS, Inc.
ProprietaryPiezoelectric 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. ProprietaryElectric Potential 2008
ANSYS, Inc.All rights reserved. 27 ANSYS, Inc. ProprietaryBlade
MovementsDisplacement Exaggerated andNot to Scalet=0.1
SecEquivalent stressest=0.3 Sec 2008 ANSYS, Inc.All rights
reserved. 28 ANSYS, Inc. ProprietaryCFX 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. ProprietaryCFX Setup Flow domain
Default isthe FSI boundaryForce Displacement transfers 2008 ANSYS,
Inc.All rights reserved. 30 ANSYS, Inc. ProprietaryCFX 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.
ProprietaryBlade Displacement at 0.1 secANSYSCFX 2008 ANSYS,
Inc.All rights reserved. 32 ANSYS, Inc. ProprietaryBlade
Displacements at 0.3 secCFXANSYS 2008 ANSYS, Inc.All rights
reserved. 33 ANSYS, Inc. ProprietaryVelocity Contours in CFXTime
=0.1 sec. 0.2 sec. 0.3 sec. 0.4 sec. 2008 ANSYS, Inc.All rights
reserved. 34 ANSYS, Inc. ProprietarySummary 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
