Current techniques for measuring

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Current techniques for measuring
Muffler Transmission Loss
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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

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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
Incident Auto Power Spectrum
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

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Contd..
Decomposition Method

• 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 amplitudes
• and S33 is the auto power spectrum
  

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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

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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
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Contd.. Two Source
Method
Also, transfer function ( ) is the ratio
of cross and auto spectrums
Therefore, Transmission Loss can be expressed by
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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 FRFs 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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