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This is to certify that the

thesis entitled

THE DEVELOPMENT OF AN ACOUSTIC ENERGY
ABSORBER FOR NOISE CONTROL APPLICATIONS

presented by

GREGORY DAVID HALL

has been accepted towards fulfillment
of the requirements for

MASTERS MECHANICAL ENGINEERING

degree in

 

 

 

9/2 9‘5/95

0.7539 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

LIBRARY
Michigan State
UnIversIty

 

 

 

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{—7

MSU Is An Affirmative Action/Equal Opportunity Institution
cWMprnMI

 

 

 

 

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THE DEVELOPMENT OF AN ACOUSTIC ENERGY ABSORBER FOR NOISE
CONTROL APPLICATIONS

By

Gregory David Hall

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1993

ABSTRACT

THE DEVELOPMENT OF AN ACOUSTIC ENERGY ABSORBER FOR NOISE
CONTROL APPLICATIONS

By

Gregory David Hall

Consumer perception of noise plays in important role in the automotive industry.
High levels of interior noise have a tiring effect on the driver and are perceived to be an
indicator of inferior quality. An Active Acoustic Sink (AAS) serves as a sink for acoustic
energy to reduce the level of noise at all points in an enclosed space by absorbing the
acoustic energy of incident sound waves. The first part of the research effort was to
compensate an audio speaker, using speaker velocity feedback, to improve its bandwidth
and reduce its phase shift. The compensated speaker was then used as the control
actuator of the AAS to dissipate acoustic energy. Experimental results indicated that the
AAS had increased acoustic energy absorption up to 182% over the absorption of an

uncontrolled speaker from 65-120 Hz.

ACKNOWLEDGMENTS

I would like to thank Professor Clark Radcliffe of the Department of Mechanical
Engineering at Michigan State University for his support and guidance as well as the idea
for the acoustic energy absorber. I would also like to thank my wife, Tonya, and my

parents for their moral and financial support during my graduate studies.

iii

TABLE OF CONTENTS

List of Tables ................................................................................................................. v
List of Figures ................................................................................................................ vi
Nomenclature ................................................................................................................. vii
Introduction .................................................................................................................... 1
An Acoustic Energy Absorber ....................................................................................... 2
Speaker Compensation ................................................................................................... 4
Active Acoustic Absorber Implementation .................................................................... 7
Experimental Results ...................................................................................................... 11
Conclusions .................................................................................................................... 16
List Of References .......................................................................................................... 17

Appendix A - Materials Required and Wiring Schematic ............................................. l8

LIST OF TABLES

 

Number Title P822
Table 1 Results of Speaker Compensation (20- 100 Hz) 7
Table 2 Acoustic Energy Absorbed By AAS Compared To Uncontrolled 13

State

LIST OF FIGURES

 

Number Title Page
Figure 1 Effect of Controller on Acoustic Intensity 3
Figure 2 Block Diagram of the Active Acoustic Sink 4
Figure 3 Typical Speaker Velocity/Voltage and Pressure/Voltage 5
Frequency Responses
Figure 4 Speaker Velocity Feedback 5
Figure 5 Open Loop Frequency Response of Speaker Velocity Feedback 6
System
Figure 6 Closed L00p Frequency Response of Speaker Velocity Feedback 7
System
Figure 7 Open Loop System 8
Figure 8 Open Loop Response (Ka=2.0) 8
Figure 9 Frequency Response with Velocity Measured from Speaker 10
Back EMF
Figure 10 Frequency Response as Measured by Laser Velocity Transducer 10
Figure 11 Frequency Response of Laser Velocity Transducer/Speaker 10
Back EMF
Figure 12 Experimental Set Up 11
Figure 13 Acoustic Energy Absorbed By AAS 12
Figure 14 Uncontrolled System Pressure / Velocity Frequency Response 14
Figure 15 Controlled System Pressure / Velocity Frequency Response 14
Figure 16 Speaker Frequency Response 14
Figure 17 SPL / I for Uncontrolled System 15
Figure 18 SPL / I for Controlled System 16
Figure A1 Wiring Schematic of Active Acoustic Sink 19

vi

b1

e(t)

Vd

Vspkr

P0
(P00)

NOMENCLATURE

elecuomagnetic coupling factor
speed of sound

voltage

back emf

transfer function of the speaker
acoustic intensity vector
acoustic intensity

absorber gain

proportional gain

speaker coil inductance

desired pressure

reference pressure

input

velocity vector

desired velocity

speaker velocity

speaker impedance

density of air

characteristic impedance

vii

INTRODUCTION

Consumer perception of noise has become increasingly important in the
automotive industry. A high level of vehicle noise is undesirable due to its tiring effect
on the driver and passengers. A high level of interior noise is also perceived to be an

indicator of an inferior product.

Noise treatment is obtained by either passive or active solutions. Passive
solutions such as sound absorbent materials are ineffective at low frequencies (< 200 Hz)
due to the large thickness of material required to absorb the sound waves (Everest, 1989).
Active noise cancellation has been applied commercially, but it is limited in that it can
only eliminate the offending noise at measurement microphone locations. An Active
Acoustic Sink (AAS) serves as a sink for acoustic energy in order to reduce the level of
noise at all points in an enclosed space by absorbing the acoustic energy of incident

sound waves.

The research problem is to determine whether an electronics driven speaker can
be designed to absorb acoustic energy out of an acoustic volume. Acoustic intensity is
the quantity used for both the basis of the design and for the subsequent evaluation of the
design. Acoustic intensity is easily measured using commercial instrumentation such as
the Brijel & szer Sound Intensity Probe (Type 3519). The first part of the research effort
produced an audio speaker compensated to provide accurate tracking of velocity signals
generated by a controller. The second research effort produced a controller using the

compensated speaker to dissipate sound.

Page 1

AN ACOUSTIC ENERGY ABSORBER

The two approaches to reducing the sound pressure level at a point are
cancellation and acoustic energy dissipation. Noise cancellation involves measuring an
input pressure and then creating an equivalent pressure in the opposing direction. The
addition of out of phase "anti-noise" to the disturbance results in a zero response at the
disturbance point. An alternate approach to decreasing sound pressure level involves
reducing acoustic energy using active control. Techniques using acoustic energy
dissipation cannot achieve a zero noise level response but reduce the sound pressure level

at all points in an acoustic volume.

The history of acoustic energy absorption dates back to the early 1950's when
Olson and May built an "Electronic Sound Absorber" (Olson and May, 1953). In contrast
to its name, this device did not actually absorb acoustic energy. It used electronics to
maintain a zero pressure level at a microphone measurement location and hence was the
first sound cancellation system. Today, "anti-noise" sound cancellation remains the

dominant approach to active noise control.

There are two problems with noise cancellation that have stimulated interest in
alternate methods of noise control. First, cancellation is limited to applications in which
the control actuator is co-located with the disturbance. Second, phase distortion of the
anti-phase signal could result in the noise being increased rather than eliminated.
Techniques using acoustic energy dissipation are not restricted by the need to know the

spatial location of the disturbance.

Page 2

Page 3
Acoustic intensity is the quantity used for both the basis of the design and for the
subsequent evaluation of the design. It is defined as the average rate at which sound

energy is transmitted through a unit area (Beranek, 1986).

I=P-v (1)

The objective of the active acoustic sink is to maximize the component of acoustic
intensity vector that is directed into the speaker. An uncontrolled speaker will have some
acoustic intensity directed into the speaker because of its mechanical dissipation. A
controlled speaker will be designed to have a greater magnitude of acoustic intensity

directed into the speaker (Figure 1).

 

 

Acoustic Acoustic

Intensity Intensity
<— ‘—
‘— ‘—
‘— ‘———
‘— ‘—
‘— ‘—
‘— <—

Uncontrolled State Controlled State

Figure 1. Effect of Controller on Acoustic Intensity

Speaker velocity must be accurately tracked to guarantee acoustic energy flow
into the speaker. Pressure cannot be controlled because it is a response, but it can be
easily measured using a microphone. The measured pressure can be multiplied by an

absorber gain, K a, to obtain the velocity, which may be controlled using a prototype AAS

(Figure 2).

v = v(P) = —K,P (2)

Page4
Acoustic intensity (1) may be expressed as the product of the negative of the absorber

gain, Ka, and the pressure, P, squared.

1 = —KaP2 (3)

If the speaker velocity can accurately track the measured pressure (2), the resulting
acoustic intensity (3) will always have a negative sign and thus be directed into the

speaker.

Acoustic Volume

Absorber 8(1) Speaker 7 ,
. Gain compensation 5.
‘ {

Figure 2. Block Diagram of the Active Acoustic Sink

 

 

 

 

 

 

 

 

 

 

SPEAKER COMPENSATION

Speaker compensation is needed to allow the use of a limited bandwidth audio
speaker as a control actuator for low frequency noise control (Radcliffe and Gogate,
1992). The typical audio speaker is designed to provide a flat pressure frequency
response (Figure 3), however, the pressure response is proportional to speaker cone
acceleration which provides a non-constant velocity frequency response (Figure 3). The
use of an audio speaker in control applications requires a flat velocity frequency response
with phase as close to zero as possible. The zero phase condition is what ensures that the
sign of the acoustic intensity is negative and thus acoustic energy is directed into the

speaker

 

 

Pressure by Voltage

”\ .............

0 50 100 150
Frequency (Hz) Frequency (Hz)

Gain (dB)

 

 

 

 

 

 

 

Figure 3. Typical Speaker VelocityNoltage and Pressure/Voltage Frequency Responses

 

 

 

v + Proportional 8(1) Speaker v
d Controller ——~ Dynamics Sp,” 7*

 

 

 

 

 

 

 

 

Figure 4. Speaker Velocity Feedback

Velocity feedback compensation (Figure 4) increases the speaker bandwidth and
reduces the phase shift. Speaker velocity may be obtained with a dual-coil speaker in
which the second set of speaker leads is used to acquire the speaker back emf, eb, which

is proportional to the speaker velocity, vsph, at low frequencies.

6b = (bI)V‘Pb (4)

The constant of proportionality, bl, is the speaker electromagnetic coupling factor.

The closed loop transfer function of the speaker velocity feedback loop is
obtained from the speaker velocity feedback block diagram (Figure 4) where G Spkr

represents the transfer function relating the speaker velocity to the drive voltage, e(t).

 

vrpkr = Kstpb (5)
vd 1 + K POW,

Page6
The speaker velocity transfer function (5) indicates that we would optimally like to drive
the proportional gain, K p, as high as possible to achieve unity. A unity gain would
represent a perfect tracking of the desired velocity, vd, by the speaker. The gain and
phase margins of the open loop response must be determined to find the maximum value

of the proportional gain, KP, that yields a stable response.

The open loop frequency response of the speaker velocity feedback system
(Figure 5) exhibits magnitude varying over 20 dB and a phase shift varying almost 180
degrees. Closed loop speaker velocity feedback response (Figure 6) with a proportional
gain, K p, equal to 10.0 provides a magnitude response that varies less than 4 dB and
phase distortion less than 30 degrees for a bandwidth of 10-810 Hz. This proportional

gain setting was close to the threshold of instability and was chosen to be the largest

 

 

 

 

 

possible stable gain.
10 7 r T f T f T T t t T 7 T
E
3
c:
'8
O
_20 : ::::::;; : :::::::
101 102 103
Frequency (Hz)
200

 

 

 

 

Phase (degrees)

 

 

101 102 103

Frequency (Hz)

Figure 5. Open Loop Frequency Response of Speaker Velocity Feedback System

 

 

 

 

Gain (dB)

 

 

 

 

101 102 103

 

 

 

 

Phase (degrees)

 

 

10 1 10 2 10 3
Frequency (Hz)

Figure 6. Closed Loop Frequency Response of Speaker Velocity Feedback System

Table 1. Results of Speaker Compensation (20100 Hz)

 

 

 

 

Com ensation Gain Variation dB Phase Variation (1 ees
Uncompensated Speaker 10 95
Compensated Kp=1 7 9O
Compensated Kp=5 3 60
Compensated Kp=10 1 30

 

 

 

 

 

ACTIVE ACOUSTIC ABSORBER IMPLEMENTATION

The active acoustic sink drives speaker surface velocity, vsph, so that it tracks
measured pressure, PM], resulting in local acoustic intensity always being directed into

the speaker. This process would appear to be open loop, however, the acoustics of the

Page8
space provide a transfer function between speaker velocity and local measured pressure.
A typical feedback control design using an open loop Bode diagram was performed

because the system could be represented as closed loop.

The Open loop transfer function was obtained by breaking the measured pressure,
P,,,-, feedback path and inserting the reference voltage, r (Figure 7). In this configuration,
an absorber gain, K a, of 2.0 yielded a gain margin of 7 dB with infinite phase margin
(Figure 8). This was the maximum value of absorber gain, K a, that met the usual

minimum requirement of 6-8 dB gain margin (Ogata, 1986).

Acoustic Volume

 

 

‘ “Either Speaker
arn ompensation

x
r input

Figure 7. Open Loop System

 

 

 

 

 

 

 

 

Gain (dB)

 

 

 

 

 

 

 

 

101 102 103 101 102 103
Frequency (Hz) Frequency (Hz)

Figure 8. Open Loop Response (Ka=2.0)

Open loop frequency responses of pressure, Pnf, by speaker velocity, vsph, were

generated for both the case where speaker velocity was measured from speaker back emf,

Page 9
ch, (Figure 9) and the case where the speaker velocity was measured using a Briiel &
Kjar (Type 3544) Laser Velocity Transducer (Figure 10). Both responses provide
similar responses up to approximately 120 Hz. At this frequency, the speaker back emf,
eb, measured from the speaker coil leads does not accurately represent the speaker cone
velocity, vspb. This error is due to the assumption that the inductance of the speaker coil,
Lem-1, is negligible for low frequencies (Colloms, 1985). For low frequencies, the electric
time constant determined by speaker inductance is much smaller than the mechanical
time constant. This allows speaker inductance to be neglected and thus enables the
speaker velocity to be obtained at low frequencies using the speaker coils (Radcliffe and
Gogate, 1992). At higher frequencies, the inductance causes the speaker coils to be an
inaccurate velocity sensor. At frequencies above 150 Hz, large fluctuations in the
frequency response (Figure 10) indicate that the Laser Velocity Transducer may also be

providing inaccurate velocity measurements.

A frequency response (Figure 11) representing the transfer function relating the
velocities measured by the Laser Velocity Transducer and speaker back emf, 85, clearly
illustrates the influence of the inductance of the speaker coil, Lem-1, on the velocity
measurement. The open loop speaker response (Figure 5) indicates that there is a zero
appearing in the open loop speaker transfer function at 120 Hz. This zero is attributed to
the resonance due to the speaker coil inductance. The large phase change in the velocity
measurement technique frequency response (Figure 11) at 120 Hz restricts controller
operation to below that frequency. An improved velocity sensor would improve the

tracking of the control signal velocity and thus improve performance.

Page 10

 

 

Gain (dB)

 

 

 

 

 

 

 

 

10l 102 103 to1 102' 103
Frequency (Hz) Frequency (Hz)

Figure 9. Frequency Response with Velocity Measured from Speaker Back EMF

 

 

 

 

 

 

 

 

 

 

0 .
-10 ...................... .. .
at?
V -20 s .- ttt ............
iii
-30 ................................
.40 222222222 2...... ......... .. . .
10‘ 102 103 101 102 10’
Frequency (Hz) Frequency (Hz)

Figure 10. Frequency Response as Measured by Laser Velocity Transducer

 

 

Gain (dB)

 

 

 

 

 

 

 

 

101 102 '10’ 10' 102 103
Frequency (Hz) Frequency (Hz)

Figure 11. Frequency Response of Laser Velocity Transducer/Speaker Back EMF

Page 11
EXPERIMENTAL RESULTS

Acoustic energy absorption was measured to determine the effectiveness of the
active acoustic sink. A random noise signal was generated and amplified to a sound
pressure level (SPL) of 120 dB. Acoustic intensity was measured at the front of the

speaker for both the controlled and uncontrolled states (Figure 12).

 

 

 

 

 

 

 

mimphon I Electronics
. . . ‘19 2') Frent mic
acoustic intensity
measured in z-direcrion
adjacent to microphone Velocity from speaker

 

 

 

 

 

Figure 12. Experimental Set Up

Acoustic intensity measurements (Figure 13) taken with a Briiel & Kjaer Sound
Intensity Probe (Type 3519) clearly indicate that there is an increase in the absorption of
acoustic energy over the range of measurement. The uncontrolled speaker had no
connections applied, hence, there was no coil current and only mechanical dissipation.
The increase in acoustic energy absorbed ranged from 9% over 70-80 Hz and 182% over
110-120 Hz (Table 2). The performance of the controller began to decrease above the
bandwidth limitation (120 Hz) imposed by using speaker back emf as the speaker

velocity sensor.

Acoustic intensity measurement problems were encountered below 65 Hz. The
acoustic intensity measurements obtained below this frequency appeared to be unreliable.

This was confirmed by measuring the acoustic intensity from a speaker emitting random

Page 12
noise below 65 Hz. The results showed only small amounts of acoustic intensity
fluctuating in direction instead of large values of acoustic intensity directed out of the
speaker. Subsequent measurements produced expected results at frequencies greater than
65 Hz. This behavior occurred both in the laboratory and when the tests were conducted
outside the building in an unenclosed space. The measurement problem raises questions
about the accuracy of the measurements made slightly above 65 Hz. If the acoustic
intensity cannot be measured with any accuracy below 65 Hz, it is likely that the

measurements over the 70-80 or 80-90 Hz bands may also contain some error.

Acoustic Energy Absorbed

 

 

 

 

 

 

Acoustic Intensity (dB)

    

Controlled

95 105 115 1 "3'35. Uncontrolled

Center Band Frequency (Hz)

Figure 13. Acoustic Energy Absorbed By AAS

Page 13

Table 2. Acoustic Energy Absorbed By AAS Compared To Uncontrolled State

 

 

 

 

 

 

 

 

 

 

 

Frsfluemy Band Change
70-80 +9%
80-90 +78%
90-100 +124%

100-1 10 +124%
1 10- 120 +182%
120- 130 +124%
130-140 +41%
140-150 -20%

 

Pressure by velocity transfer functions were obtained to provide an additional
means to validate the effectiveness of the AAS. Pressure by velocity equals the

impedance of the speaker, Z.

 

= Z (6)

A successful controller would indicate a change in impedance between the controlled and
uncontrolled state. For the velocity to accurately track the pressure, the impedance of the
controlled speaker would have to equal one. This corresponds to a pressure by velocity
transfer function with 0 dB gain and 0 degree phase over the bandwidth of the controller.
A comparison of the pressure by speaker velocity transfer function for the uncontrolled
(Figure 14) and the controlled speaker (Figure 15) validates the prediction that the AAS
controls the impedance of the speaker. The pressure by velocity transfer function for the
controlled speaker (Figure 15) has gain between 1 and -3 dB and phase between 0 and 45
degrees over a 65-120 Hz bandwidth. The pressure by speaker velocity transfer function
(Figure 14) for the uncontrolled speaker closely resembles the drive velocity by speaker

velocity transfer function (Figure 16) obtained for the uncompensated audio speaker.

Page 14

 

 

 

 

 

 

 

 

100 150 100 150
Frequency (Hz) Frequency (Hz)

Figure 14. Uncontrolled System Pressure / Velocity Frequency Response

 

 

20 T I f

10 .....

 

Gain (dB)

Phase (degrees)

-100 .............. .....

 

 

 

 

 

 

100 150
Frequency (Hz) Frequency (Hz)

 

Figure 15. Controlled System Pressure / Velocity Frequency Response

 

 

Gain (dB)

 

 

 

 

 

 

 

100 150 100 150
Frequency (Hz) Frequency (Hz)

Figure 16. Speaker Frequency Response

Page 15
Sound pressure level divided by acoustic intensity is a final method to confirm the
effectiveness of the AAS. Simplification of the ratio shows that this expression

represents the impedance of the speaker.

.__=_=_=z (7)

The ratio of sound pressure level to acoustic intensity was calculated over a 65-100 Hz
bandwidth. A polynomial was fit to the measured data for both the uncontrolled and
controlled states. The best fit polynomial for the uncontrolled system (Figure 17) shows
in increasing value of SPL divided by acoustic intensity which tracks an increase of the
uncontrolled pressure by velocity frequency response (Figure 14). Similarly, the best fit
polynomial for the controlled system (Figure 18) shows a decreasing value of SPL
divided by acoustic intensity which tracks a decrease of the controlled pressure by

velocity frequency response (Figure 15).

 

30 I I

Best Fit Line -——-— I

201 Experimental Data W J

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a l
3
- 10
\
d l
U)

o +

-10 . . .
65 75 85 ' 95
Frequency (Hz)

Figure 17. SPL / I for Uncontrolled System

Page 16

 

 

 

 

 

 

 

 

 

 

 

 

 

30 j I
, Best Fit Line -—-— 1
20 Experimental Data W I
a 4
B
2 IO
53 .
U)
0 - _
-10 I I t I 1
65 75 85 95
Frequency (Hz)

Figure 18. SPL / I for Controlled System

CONCLUSIONS

A prototype Active Acoustic Sink was constructed to determine if an
electronically driven speaker can be built to absorb acoustic energy. A speaker was
successfully compensated using speaker velocity feedback. The compensated speaker
had 1 dB of gain variance and only 30 degrees of phase shift over a 20-120 Hz
bandwidth. Through a comparison of speaker velocity and speaker back emf, it was
determined that the speaker back emf, eb, does not provide an accurate representation of
the speaker cone velocity above 120 Hz. The compensated speaker was used as a control
actuator for the AAS, and the effectiveness of the AAS was determined by measuring the
acoustic intensity at the face of the speaker. The impedance of the controlled speaker was
measured and found to be close to the desired value of one. This value of the impedance
ensured that the velocity was accurately tracking the measured pressure. The results
indicate that there is an increase (up to 182%) of acoustic energy absorption using the

AAS over a 65-120 Hz bandwidth.

LIST OF REFERENCES

LIST OF REFERENCES

Colloms, M. High Performance Loudspeakers. New York: John Wiley & Sons, 1985.

Everest, RA. The Master Handbook of Acoustics. Blue Ridge Summit, PA: Tab Books,
1989.

Olson, HF. and E.G. May. "Electronic Sound Absorber". The Journal of the Acoustical
Society of America, Volume 25, Number 6, November 1953.

Ogata, Katsuhiko. Modern Control Engineering. New Delhi: Prentice Hall of India,
1986.

Radcliffe, C.J., and SD. Gogate. "Identification and Modeling of Speaker Dynamics for

Acoustic Control Applications". ASME WAM Symposium on Active Control of
Noise and Vibration, 1992.

Page 17

APPENDIX A

Page 18

APPENDIX A - MATERIALS REQUIRED AND WIRING SCHEMATIC

The following materials were required for the construction of the AAS:

(1) 400 W Resistor

(1) 10 kW Resistor

(6) 1 kW Resistors

(4) 22 rtF Capacitors

(4) 741 Operational Amplifiers

(1) Realistic 40W Stereo Power Booster
(1) 12" Realistic Subwoofer w/ enclosure

Eeedlzaclssonmllet

(3) 1 k9 Resistors

(1) 2 k9 Resistors

(2) 22 11F Capacitors

(2) 741 Operational Amplifiers
(1) Electret Tie Pin Microphone

Miscellaneous

Breadboard

Micronta Regulated 12 V Power Supply
Misc. BNC Connectors

Misc. Wires

Page 19

 

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