Page 1

A Directional Dogbone Flextensional Sonar

Transducer

Stephen C. ButlerNaval Undersea Warfare Center

Newport, RI 02841 USA

7-9 Oct 2010

COMSOL Conference 2010Boston, MA

COMSOL Conference 2010 Boston Presented at the

Page 2

Introduction

Sonar transducers are electro-acoustic devices used for transmitting and receiving acoustic energy for the purpose of detection and location of underwater objects.

In order to transmit energy in one direction, sonar Class IV flextensional transducers are combined into arrays of elements that are spaced a 1/4 wavelength apart. The directionality (front-to-back pressure ratio) in practice is a modest 6 dB due to diffraction.

A new class of transducer the Directional “dogbone” flextensional transducers which generates cardioid beams could replace these dual line array. This will reduce weight, cost and increase front-to-back ratio greater than 20 dB.

COMSOL with Acoustics Module is used to predict in-water electro-acoustic performance and is compared with experimental data. COMSOL is then used to calculate the complex drive coefficients used to drive the transducer into the directional mode.

Page 3

Sonar uses Transmitted and Reflected Sound Waves to Locate Underwater Objects

OBJECT

REFLECTEDWAVE

TRANSMITTEDWAVE

PROJECTORSHYDROPHONES

Page 4

Two Line Arrays and Planar Arrays of Projector Elements that are Several Wavelengths Long and Spaced a 1/4

Wavelength Apart.

/4 /4

a) Two Line Arrays b) Two Planar Arrays

Directionof Beam

Directionof Beam

Page 5

Modeled Beam Patterns for Two sources spaced a 1/4 wavelength apart with one of the sources driven 90 degrees

out of phase with the other sources, a) for Point Source Element and b) Real Case Flextensional Elements.

0°

270°

180°

90°

Beam Pattern0dB ref = 0 dB re. uPa @ 1m-3dB BeamWidth = 179.82 Deg.DI = 3 dB

Range

30 dB

40 dB

50 dB

0

-5

-10

-15

0°

270°

180°

90°

Beam Pattern0dB ref = 158 dB re. uPa @ 1m-3dB BeamWidth = 130.02 Deg.DI = 4.9 dB

Range

30 dB

40 dB

50 dB

0

-5

-10

-15

/4/4

a) Ideal Case b) Real Casecaused by diffraction

Front/Back = 6 dBBack is an ideal Null

Page 6

Synthesis of a Directional Flextensional

1 cos(θ)

0

30

6090

120

150

180

210

240270

300

330

1

0.5

0

1.2

0o( )0

30

6090

120

150

180

210

240270

300

330

1

0.5

0

1.2

0d( )+ =+ +_

Omni Dipole

0

30

6090

120

150

180

210

240270

300

330

1

0.5

0

1.2

0F( )+

[1+cos(θ)]1/2

True Cardioid

a) Omni b) Dipole c) Cardioid

An other way to generate a directional cardioid Beam

Page 7

Two Line Arrays of Projector Elements that are Several Wavelengths Long and Spaced a 1/4 Wavelength Apart

Replaced by One Line Array of Directional Dogbone Transducers

/4

a) Conventionaltwo lines

F/B < 15 dB

b) Directionalone line

(Replacement)F/B > 20 dB

Page 8

Class IV Flextensional Transducer and Class VII “Dogbone” Flextensional Transducer

a) Class IV Flextensional b) Class VII Flextensional

Page 9

Model Verification Procedure

• Validate COMSOL Model with Measured Results of a standard Omni Mode Dogbone Flextensional Sonar Transducer

• Then predict the directional operation mode

Page 10

Class VII “Dogbone” Flextensional Sonar Transducer, a) Shell and Ceramic Stack and b) Encapsulated

a) Shell and Ceramic Stack b) Encapsulated

Page 11

COMSOL Stack a) Subdomain Settings and b) Boundary Settings for Piezo Plane Strain (smppn) application and c)

Electric Potential and Field Arrows results

b) Boundary Settingsa) Subdomain Settings c) Electric Potential and Field Arrows

y

x

Page 12

Electrical Input Impedance

IU =-(up(Jdy_smppn))*z

ID =-(down(Jdy_smppn))*z

Integrate Displacement Current Density for Input Current

Admittance is:

Y =I/V=abs(ID)+abs(IU)

G= real(ID)-real(IU)

B= imag(ID)-imag(IU)

C= (imag(ID)-imag(IU))/(2*pi*freq)

Capacitance is:

Current into upper plate

Current into down plate

Y=1/Z

Magnitude

Real Part

Imaginary Part

B/ω

For V = 1

Z = Impedance

Page 13

Piezoelectric Stack In-air Admittance Magnitude Response

Measured (____) and COMSOL Modeled (oooo)Y

0.00001

0.0001

0.001

0.01

0.1

1

10

0 2 4 6 8 10 12 14 16 18 20 22Frequency (kHz)

Y (S

)

Page 14

COMSOL Fluid, Shell and StackSubdomain Settings and Boundary Settings for

Pressure Acoustics (acpr) application

b) Boundary Settingsa) Subdomain SettingsBlue - Water fluid two wavelength at 3 kHzYellow - PML one wavelength Mesh 16312 Triangular Element

Page 15

Sound Pressure Level

2 in denominator indicates pressure is a peak value, Therefore Voltage Potential on transducer should be a peak value V = 1.414

COMSOL SPL is given by,

The more common form of SPL in terms of rms pressure is given by,

TVR = SPL-10log10(1/h)-10log10(1/r)

Transmit voltage response for 2-D model is given by,

h is the transducer height in the z-directionr is the radial distance pressure point

dB ref 1µPa/Vrms at 1m

pref = 1 µPa for Water )2(log102*

10 refpppSPL

)(log20 10 refrms ppSPL

Page 16

Transmit Voltage Response Measured (____) and COMSOL Modeled (oooo)

Transmit Voltage Response Stave Side

110

120

130

140

150

160

0 2000 4000 6000 8000 10000 12000 14000 16000

Frequency (Hz)

TVR

(dB

re. 1

uPa/

V@

1m)

28-Aug-96 11:53:04

Page 17

In-water Conductance ResponseMeasured (____) and COMSOL Modeled (oooo)

CONDUCTANCE

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

0 2000 4000 6000 8000 10000 12000 14000 16000

Frequency (Hz)

G (u

S)28-Aug-96 11:53:04

Page 18

In-water Susceptance Response Measured (____) and COMSOL Modeled (oooo)

SUSCEPTANCE

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0 2000 4000 6000 8000 10000 12000 14000 16000

Frequency (Hz)

B (u

S)28-Aug-96 11:53:04

Page 19

Beam Patterns in Omni Mode Measured and COMSOL Modeled

at 3 kHz, 5 kHz and 9.6 kHz

0°

270°

180°

90°

Beam Pattern0dB ref = 110.3 dB re. uPa @ 1m-3dB BeamWidth = 38.63 Deg.DI = 3.2 dB

Range

30 dB

40 dB

50 dB

0

-5

-10

-15

0°

270°

180°

90°

Beam Pattern0dB ref = 100.2 dB re. uPa @ 1mNo -3dB BeamWidthDI = -0.7 dB

Range

30 dB

40 dB

50 dB

0

-5

-10

-15

0°

270°

180°

90°

Beam Pattern0dB ref = 97.6 dB re. uPa @ 1m-3dB BeamWidth = 93.42 Deg.DI = -1.1 dB

Range

30 dB

40 dB

50 dB

0

-5

-10

-15

0°

270°

180°

90°

Beam Pattern0dB ref = 193 dB re. uPa @ 1m-3dB BeamWidth = 35.36 Deg.DI = 3.11 dB

Range

30 dB

40 dB

50 dB

SENECA LAKE

CML 288 TAP 58FT 100VRMS F-37 #280 SS-206.6 S/N 001(PATTERN)

28-Aug-96 12:03:319600 Hz File: NUWCDOG.16

0

-5

-10

-15

0°

270°

180°

90°

Beam Pattern0dB ref = 175.2 dB re. uPa @ 1m-3dB BeamWidth = 75.87 Deg.DI = 3.67 dB

Range

30 dB

40 dB

50 dB

SENECA LAKE

S11-48 1250TAP 58FT 100VRMS F-37 #280 SS-206.6 S/N 1

27-Aug-96 15:14:575000 Hz File: NUWCDOG.2

0

-5

-10

-15

0°

270°

180°

90°

Beam Pattern0dB ref = 182.6 dB re. uPa @ 1mNo -3dB BeamWidthDI = 1.02 dB

Range

30 dB

40 dB

50 dB

SENECA LAKE

S11-48 1250TAP 58FT 100VRMS F-37 #280 SS-206.6 S/N 1

27-Aug-96 15:07:443000 Hz File: NUWCDOG.1

0

-5

-10

-15

3 kHz 5 kHz 9.6 kHz

a) Measured

b) COMSOL Modeled

3 kHz 5 kHz 9.6 kHz

Page 20

Directional Dogbone Flextensional Sonar Transducer

PZT Stack b PZT Stack a

Inactive PZT

Shell Staveor Beam

Shell End

Insulator

Page 21

FEA Shell and Stack Modes

Displacements and PZT Stack Electric Fields

Omni Mode Dipole Mode Directional Mode

Ea=1VEb=1V

Ea=1VEb=-1V Ea/Eb = Complex Drive

minimizedmotion

+ =side Aside B enhanced

motion

Page 22

Po Pd

RPPPE

RPPPE

dodb

doda

1/)(

1/)(

Voltage Drive Configuration

ComplexDrive VoltageCoeff

All Pressures Normalized to Dipole Pressure Field Pd

Complex Far Field Pressure

+ =1 1 -1 1 PdirctEb Ea

do PPR /where

RREE ba 1/1/

Page 23

COMSOL Modeleda) Pressure and b) SPL Surface Plots in the

Omnidirectional, Dipole and Directional Modes at 3 kHz

Omni Mode Dipole Mode Directional Mode

a) Pressure Surface Plots

b) SPL Surface Plots

Page 24

FEA Molded Beam Patternat 3 kHz

Omni Mode Dipole Mode Directional Mode

EA=1VEB=1V

EA=1VEB=-1V

EA= -0.721-j0.244= 0.761@-161.3 degEB=1VFront/Back ratio = 67.6 dB

0°

270°

180°

90°

Beam Pattern0dB ref = 141.2 dB re. uPa @ 1m-3dB BeamWidth = 142.53 Deg.DI = -59.8 dB

Range

30 dB

40 dB

50 dB

0

-5

-10

-15

0°

270°

180°

90°

Beam Pattern0dB ref = 134 dB re. uPa @ 1m-3dB BeamWidth = 89.61 Deg.DI = 4.8 dB

Range

30 dB

40 dB

50 dB

0

-5

-10

-15

0°

270°

180°

90°

Beam Pattern0dB ref = 100.2 dB re. uPa @ 1mNo -3dB BeamWidthDI = -0.7 dB

Range

30 dB

40 dB

50 dB

0

-5

-10

-15

Same results obtained from 1kHz – 6 kHz, with Front/Back > 50 dB over Band

Page 25

Summary

The Directional Dogbone Flextensional Transducer Generates Cardioid Directional Beam Patterns

» Front to Back ratio > 50 dB

» That can be steered Left or Right

– Reduces Ambiguity

– Reduced reverberation

– Improve detection rates

Broadband > Octave

Reduced Size, Weight and Cost