measurement of muffler insertion and transmission...

D. W. Herrin, Ph.D., P.E. University of Kentucky

Department of Mechanical Engineering

Measurement of Muffler Insertion and Transmission Loss

Muffler Simulation

Noise and Vibration Short Course

Dept. of Mech. Engineering University of Kentucky

2

Overview

  Transmission Loss

  Insertion Loss

  Source Impedance

Muffler Simulation



3

Sound Wave Reflections in Engines

Muffler

Engine

Waves leaving engine

Reflected from muffler

Reflected from engine

Waves leaving muffler

Reflected from open end


Resonances can form in the exhaust and tail pipes as well as within the muffler.

Muffler Simulation



4

Source Wi

Muffler

Anechoic termination

t

i

WWTL 10log10=

Wt

Transmission Loss

Muffler Simulation



5

Loudspeaker

Microphones

pi

pr

1 2 3

pt=p3

Muffler Anechoic

termination Decomposition

x12

Measurement Three Point Method

Not Recommended

Muffler Simulation



6

Measuring Transmission Loss

Muffler Anechoic termination

Muffler Simulation



7

0

10

20

30

40

50

0 500 1000 1500 2000 2500 3000

Frequency (Hz)

TL (d

B)

Three-point methodBEM Ø6.035

8

Ø1.375 Ø1.375

TL of an Expansion Chamber

Muffler Simulation



8

Loudspeaker

Impedance tube Muffler

1 3 4 2

Loudspeaker 1 3 4 2

Configuration b

Configuration a

Zr

Zr’

arbitrary

Measurement Two-Source Method Munjal and Doige, 1990

Muffler Simulation



9

Measure 6 transfer functions

Calculate four-pole parameters Calculate TL

Loudspeaker Muffler

1 3 4 2

Load 1

1 3 4 2

Absorbing material

Open

Load 2

To and Doige, 1979

Measurement Two Load Method

Muffler Simulation



10

0

20

40

60

80

100

0 500 1000 1500 2000 2500 3000Frequency (Hz)

TL (d

B)

Two-source methodTwo-load method

Ø1.375

2.24

12

Ø6.035Ø1.375

4.125

2.24

Ø1.375

Measurement Expansion Chamber

Muffler Simulation



11

0

20

40

60

80

100

0 500 1000 1500 2000 2500 3000Frequency (Hz)

TL (d

B)

Two-source methodBEM

Ø1.375

2.24

8

Ø6.035Ø1.375

4.125

2.24

Ø1.375

Simulation vs. Measurement

Muffler Simulation



12

Overview


  Insertion Loss


Muffler Simulation



13

Insertion Loss Example

Muffler Simulation



14

Design 1 Helmholtz Resonator Only

Helmholtz Resonator

5

6 x 3.75

φ 1.875

10

Units: Inches

φ 1.875

2) Tuned to 96 Hz

1) Increase volume

Muffler Simulation



15

Design 2 Helmholtz Resonator + Side Branch

Helmholtz Resonator

5.5

6 x 3.75

φ 1.875

10

Units: Inches

φ 1.875

Side Branch

34

φ 1.875

7

Tuned to 92 Hz

Tuned to 98 Hz

Muffler Simulation



16

Design 3 Helmholtz Resonator + Side Branch

Helmholtz Resonator

5

6 x 3.75

φ 1.875

10

Units: Inches

φ 1.875

Side Branch

22.8

φ 1.875

7

Tuned to 144 Hz

Tuned to 96 Hz

Muffler Simulation



17

Insertion Loss Measurement

Source

SPL1

(dB) 12 SPLSPLIL −=

Muffler

SPL2

Source

), ZC, D, Zf ( A, B, IL rs=

Zs

Zr

Muffler Simulation



18

Insertion Loss Measurement

SPL2

SPL1

(dB) 12 SPLSPLIL −=

Loudspeaker

Helmholtz Resonator Side Branch

Microphone

Muffler Simulation



19

Measured Insertion Loss Comparison

-30

-20

-10

0

10

20

30

40

50

0 50 100 150 200

Frequency (Hz)

Inse

rtion

Los

s (d

B)

Design 1: Helmholtz Resonator Only

Design 2: Helmholtz Resonator + Side Branch - 98 Hz

Design 3: Helmholtz Resonator + Side Branch -144 Hz

Muffler Simulation



20

Effect of Source and Termination

Helmholtz Resonator

Source

Length?

Termination?

Muffler Simulation



21

-30

-20

-10

0

10

20

30

40

50

0 50 100 150 200 250 300 350 400

Frequency (Hz)

Inse

rtion

Los

s (d

B)

41 Inch Inlet61 Inch InletFiring Frequencies

Effect of Inlet Length

Muffler Simulation



22

Effect of Air Filter

-30

-20

-10

0

10

20

30

40

50

0 100 200 300 400

Frequency (Hz)

Inse

rtion

Los

s (d

B)

Helmholtz Resonator

Helmholtz Resonator + Air Filter

Firing Frequencies

Muffler Simulation



23

Overview


  Insertion Loss


Muffler Simulation



24

Sound Wave Reflections in Engines

Muffler

Engine

Waves leaving engine


Reflected from engine

Waves leaving muffler

Reflected from open end


Resonances can form in the exhaust and tail pipes as well as within the muffler.

Muffler Simulation



25

Sound Wave Reflections in Duct

Acoustic Source

Waves Leaving Source

Reflected from Attenuating Element

Reflected from Source

Attenuating Element (i.e. Load)

Acoustic Source

Waves Leaving Source

Reflected from Attenuating Element

Reflected from Source

Attenuating Element (i.e. Load)

Muffler Simulation



26

Physical Meaning of Circuit Analogy

Source Load

A B

x=0

k

c m

pL

ps

uppz

Smkmjc

Szz

Lss

ms

−=

⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛ −+

==

ω

Muffler Simulation



27

Equivalent Circuit Analogy

Source Zs , ps

ps pL

Load ZL, pL

zs

zL L

L

Ls

szp

zzp

=+

Muffler Simulation



28

Direct Method

Indirect Method

{{ Standing Wave Method

Two-microphone Method

Two-load Method

Three-load Method

Four-load Method

….. Etc.

Least Squares (multi-load) Method

{

Measurement Source Impedance

Muffler Simulation



29

Microphones

Primary Source

External Source

Intake Pipe

Microphones

Primary Source

External Source

Intake Pipe

  Standing Wave Method

  Two-microphone Method

Measurement Direct Method

Muffler Simulation



30

Source p’s, Z’s

pZpZ

)pp(ZZZ

LLLL

LLLLs

1221

2121

−

−=

pZpZ)ZZ(pp

pLLLL

LLLLs

1221

2121

−

−=

where: ZL1, ZL2 — load Impedance for tube lengths L1, L2

pL1, pL2 — complex sound pressure for tube lengths L1, L2

Li (i = 1,2)

Source ps, Zs Load pLi, ZLi

Engine

Measurement Two-Load Method

Muffler Simulation



31

Li (i = 1,2,…,n)

Source ps, Zs Load pLi, ZLi

Engine

2

2

∑

∑

<

<

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

−⋅−−

=

jiLL

ji LL

LLLL

s

ji

ji

ji

ji

VV

VV

ppVV

Z

where: ZLi — load impedance for tube length Li

pLi — complex sound pressure for tube length Li

VLi — volume velocity for tube length Li : VLi = pi / ZLi

)(1

1∑=

+=

n

i L

LSLs

i

ii

ZZZp

np

Measurement Least Squares Method

Muffler Simulation



32

Prediction of IL

), ZC, D, Zf ( A, B, IL rs=

⎥⎦

⎤⎢⎣

⎡

DCBA

12”

Source Zs , ps

5”

Zr

Load ZL, pL

Expansion Chamber

φ1.5”

6”

φ 6”

Muffler Simulation



33

Insertion Loss Prediction

-30

-20

-10

0

10

20

30

40

50

60

0 200 400 600 800 1000Frequency (Hz)

IL (d

B)

Actual source impedancePressure source (Zs=0)Velocity source (Zs=infinite)Anechoic source (Zs=rho*c)

Muffler Simulation



34

Four tube lengths:

6”, 13”, 18” and 25”

Test Case Engine Intake

Muffler Simulation



35

Measured Source Impedance

-5-4-3-2-1012345

0 200 400 600 800 1000Frequency (Hz)

Z s /

Z 0

RealImaginary

Muffler Simulation



36

Engine Intake Source Absorption

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000

Frequency (Hz)

Sou

rce

Abs

orpt

ion

Coe

ffici

ent

Muffler Simulation



37

Engine Exhaust

Layout 6 cylinder, 4 stroke Fuel Diesel Exhaust Diameter 4 inches Exhaust Temperature Around 420°C Exhaust Flow Rate 0.12 Mach Test RPM 2400 Test Output Torque Around 500 N·m

Pressure Sensors

Reference Accelerometer

Muffler Simulation



38

Source Impedance Real Part

-5

0

5

10

15

0 300 600 900 1200 1500

Sou

rce

Impe

danc

e (R

e)

Frequency (Hz)

2-Load

Wave Decomposition

Muffler Simulation



39

Tested Results Imaginary Part

-10

-5

0

5

10

0 300 600 900 1200 1500

Sou

rce

Impe

danc

e (Im

)

Frequency (Hz)

2-Load

Wave Decomposition

Muffler Simulation



40

IL Prediction Muffler Design

Two cross-flow chambers

Helmholtz resonator tuned to the firing frequency

0

20

40

60

80

100

0 500 1000 1500

Tran

smis

sion

Los

s (d

B)

Frequency (Hz)

Tuned to 120 Hz

Muffler Simulation



41

IL Prediction Comparison

0

20

40

60

80

100

0 300 600 900 1200 1500

Inse

rtion

Los

s (d

B)

Frequency (Hz)

Anechoic source

Measured source impedance

Muffler Simulation



42

Summary

  Transmission loss is a function of the silencer alone.

  Transmission loss can be measured using the two-load or two-source method.

  Insertion loss includes source and termination effects.

  Source impedance should be measured.

measurement of muffler insertion and transmission...

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