Current techniques for measuring

1. Current techniques for measuring Muffler Transmission Loss

2. 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

3. 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 =

4. Methods for measuring TL: • Decomposition method • Two Source method using 4 microphones • Two Load method

5. Decomposition Method: = Incident Auto Power Spectrum = Reflected Auto power spectrum S33 = Transmitted Auto Power Spectrum

6. 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:

7. 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

8. 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:

9. 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

10. Two Source Method:

11. 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

12. 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

13. 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

14. 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:

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

16. 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

17. Two Load Method Setup:

18. 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

19. Contd..Measurement setup for Two Load method

20. 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

21. 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

22. 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

23. 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

24. Comparison of all 3 Methods

25. 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

26. 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

27. Calibration of microphones setup

28. 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

29. Schematic diagramfor STL measurement

30. Impedance Tube setup Small Impedance Tube Setup with 4 microphones

31. 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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