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Page 1: Current techniques for measuring Muffler Transmission Loss.

Current techniques for measuring

Muffler Transmission Loss

Page 2: Current techniques for measuring Muffler Transmission Loss.

Why Transmission Loss?

To understand how effectively an acoustical treatment can block the incident sound when designing a mechanical system

Transmission Loss quantifies the acoustical treatment for engineering application

Page 3: Current techniques for measuring Muffler Transmission Loss.

Parameters for acoustic performance of a Muffler

Noise reduction (NR):SPL difference across the muffler

Insertion loss (IL):SPL difference outside the system with and without the muffler present

Transmission Loss (TL):Sound power level difference between the incident and the transmitted wave assuming anechoic termination given by

=

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Methods for measuring TL:

Decomposition method Two Source method using 4 microphones Two Load method

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Decomposition Method:

AAS = Incident Auto Power Spectrum

BBS = Reflected Auto power spectrum

S33 = Transmitted Auto Power Spectrum

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Contd..

Decomposition Method: Muffler Transmission Loss is

given by:

Where Wi = Incident sound power Wt = Transmitted sound power

Inlet Sound Pressure can be decomposed into incident and reflected wave and respectively

Using Decomposition theory:

AAS BBS

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Contd.. Decomposition Method:

22S 11S

where and are the Auto spectra of the total acoustic pressure at 1 & 2 resp.

& are the real and imag part of cross spectrum between points 1 & 2

K = wave number

is the distance between the two microphones

The rms amplitude of incident sound wave and transmitted wave is given by:

pt = where incident & transmitted are the rms pressure amplitudesand S33 is the auto power spectrum

33S

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Contd.. Decomposition Method: Now the sound power of incident and reflected wave is given

by: and

where are the muffler inlet and outlet tube areas

Therefore ,Transmission Loss is given by:

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Contd..

Implementation of Decomposition Method

Find auto power & cross power spectrum at the two microphones 1 & 2

Utilize decomposition theory to find incident auto power spectra Find rms amplitude by taking the square root of the incident auto

power spectra and transmitted auto power spectra (measured directly from the microphone 3)

Plug in the calculated rms values in the TL equation

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Two Source Method:

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Contd..

Two Source Method:

Based on Transfer matrix approach-relation between input pressure & velocity to the output pressure and velocity Any acoustical element can be modeled by its four pole parameters which is given by:

where are the sound pressure amplitudes at the inlet & outlet are the particle velocity amplitudes at the inlet and the outlet

are the 4 pole parameters of the system

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Contd..

Two Source Method:

For Configuration ‘a’: The 4 pole equation for the element 2-3 is given by

where subscript ‘a’ refers to configuration a Also, 4 pole equations for elements 1-2 & 3-4 is given by

where are the microphone spacings for elements 1-2 & 3-4

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Contd..

Two Source Method:

Combining all the equations for 1-2,3-4 & 2-3 gives

For Configuration ‘b’: Moving sound source to the other side

For this configuration, the equation for element 3-2 is given by:

where

Page 14: Current techniques for measuring Muffler Transmission Loss.

Contd..

Two Source Method:

Now the combined equation for configuration ‘b’ is given by:

Now using these equations one can obtain 4 –pole parameters given by:

Page 15: Current techniques for measuring Muffler Transmission Loss.

Contd..

Two Source Method:

Therefore, Transmission Loss can be expressed by:

Also, transfer function ( ) is the ratio of cross and auto spectrums

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Contd..

Implementation of Two Source Method:

Use Two microphones with random excitation (or white noise) Obtain all transfer functions by moving one microphone and using the other as a reference Put the obtained transfer functions in the equations shown above to find the 4 pole parameters of the transformation matrix Find the TL by plugging the 4 pole parameters and the measured cross sectional areas of the tube in the equation given above

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Two Load Method Setup:

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Contd..

Two Load method:

Similar to the Two Source method with little changes as follows:

Instead of moving the sound source, two end conditions are applied to find 2 additional equations in order to solve the complete transfer matrix

Changing end conditions changes the impedance at the termination from to

Two loads can be 2 different length tubes, a single tube with & without absorbing material or even 2 different mufflers

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Contd..

Measurement setup for Two Load method

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Contd..

Calculations using Cross Spectrums for Two Load method :

Involves two basic measurements with two different terminations

Terminations must be very different

Generally open ended or anechoic (o) & closed ended or reverberant (c) terminations are used The equations utilized are as follows:

and

where A & B and C & D are the forward and backward complex pressure amplitudes wave in the source tube and receiving tube respectively with ‘a’ & ‘b’ denoting two different end conditions

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Contd..

Two Load Method: The 4 coefficients A,B,C,D can be calculated by the following relations:

where P1,P2,P3,P4 are the measured Sound Pressures

Now, using Cross spectrum and FRF’s to minimize noise in the signal, we can obtain the following equations:

where are the cross power spectrums using ‘o’ as a reference

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Contd.. Two Load Method:

The Transmission Loss coefficient is given by the ratio of amplitude A of incident wave and amplitude C of the transmitted wave assuming no reflection i.e D = 0

Therefore, from the above relations

where is the first element of the transfer matrix

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Contd..

Limitations of Cross Spectrums calculations and two load method:

Must require two different terminations Difficult to obtain ideal anechoic termination

There seems to be a flaw in the calculations of TL since they assume that the reflection to be zero i.e D =0 but we are also using the same equation with reverberant termination.

Prior to taking actual measurements, it requires complete measurements without inserting the acoustical material to assure that residual TL is much less than the measured TL If the numerical value of the difference in denominator becomes smaller than the absolute value of the absolute nos., then the solution becomes unstable

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Comparison of all 3 Methods

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Advantages of Two source method over other methods The above results indicate the limitation of

decomposition method in the absence of anechoic termination

Decomposition method does not lead to 4 pole parameters of muffler

Unlike two load method, two source method does not require any termination material at the end

Although Two load method is easier to employ but better results require two different loads

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General Procedure:

Impedance tube with small diameter (29mm) can be utilized for measuring TL of Briggs & Stratton Muffler The apparatus is designed to measure TL and other acoustics properties using the following ASTM E-1050 standard: Working frequency range: where size and spacing of microphones: Location of microphones: minimum of 3 tube diameter from source to first microphone Sound source- type & signal: random noise having uniform spectral density Length of tube: should be large for plane wave propagation Determining the individual microphone sensitivity (mV/Pa) Calibrate the microphones correctly Means of correcting the measured transfer function data for mismatch in both amplitude and phase responses of measurement channels

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Calibration of microphones setup

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contd..

Calculations for Calibration of microphones

Place a highly absorptive material to prevent strong acoustics reflections and to obtain most accurate correction factor possible Measure Transfer functions in 2 configuration 1 and 2 as shown

Compute the calibration factor representing the amplitude and phase mismatches

where

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Schematic diagram for STL measurement

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Impedance Tube setup

Small Impedance Tube Setup with 4 microphones

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References: Z. Tao and Seybert, A.F., “A review of current techniques for

measuring muffler TL” Seybert, A.F. and Ross, D.F., “Experimental Determination of

Acoustic Properties Using a Two microphone Random Excitation Technique,” J. Acoust. Soc. Am., 61, 1362-1370 (1977)

Munjal, M.L. and Doige A.G., “Theory of a Two Source-location Method for Direct Experimental Evaluation of the Four-pole Parameters of an Aeroacoustic Element,” Journal of Sound and Vibration, 141(2), 323-333 (1990)

ASTM standard, E1050-98, “Standard Test Method for Impedance and Absorption of Acoustical Material Using a Tube, Two Microphones and a Digital Frequency Analysis System,” (1998)

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