2008 international ansys conference · © 2008 ansys, inc. all rights reserved. 2 ansys, inc....

© 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.


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


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


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


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


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


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


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


Resulting Log File

• This is representative of what will go in the

command snippet to represent the table


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


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


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]


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


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


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


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


• 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


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


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


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


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



• 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,



• 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


Piezoelectric Material Defined -

Command Snippets

Anisotropic Elastic matrix

Piezoelectric matrix

Coupled Element 226


Piezoelectric Solution

• Static

– SPARSE is the recommended solver

• Transient


– recommended TINTP (transient algorithm) settings• ALPHA = 0.25

• DELTA = 0.5

• THETA = 0.5

• Modal

– Block Lanczos is the recommended solver

• Harmonic


– harmonically varying displacement produces a current

– applied current produces a vibration


Electric Potential


Blade Movements

Displacement

Exaggerated and Not to Scale

t=0.1 Sec

Equivalent

stresses

t=0.3 Sec


CFX Model

• Flow domain internal boundary is the device.

• Blue arrows represent “Opening Condition”

– Fluid may move in and out such boundaries


CFX Setup

• Flow domain Default is the FSI boundary

Force – Displacement transfers


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


Blade Displacement at 0.1 sec

ANSYS

CFX


Blade Displacements at 0.3 sec

CFX

ANSYS


Velocity Contours in CFX

Time = 0.1 sec. 0.2 sec. 0.3 sec. 0.4 sec.


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

2008 international ansys conference · © 2008 ansys, inc. all rights reserved. 2 ansys, inc....

Documents