Sound Quality Workshop- MarkMoeller

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NVCWK3
Linear Time Invariant System (lti)
Input x(t)
System h(t)
Output y(t)
Convolution Integral Fourier Transform
y(t )
t
x( )h(t
)d
x(t )e
i t
x(t ) * h(t )dtFra bibliotekX( )
Y( )
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H( )X ( )
NVCWK3
Simple Mechanical Oscillator Example
m
k c m = 0.5 kg k = 1000 Nt/m c = 0.5 kg/s fn = 7.12 Hz
Oscillator
cx k ( x) 0 m x
h(t ) 1 1
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Temperature (deg F)
The tiles used were designed for low temperatures. Results suggest that they performed better around 0 deg F near the SIL frequency range. No damping applied 50% damping tile coverage
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Schroeder Backwards Integration
EnvS(t )
t
h(t ) 2 dt
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Analog Reverberation Decay Method
Test Object
Shaker Switch Power Amplifier
Signal Conditioning Filter Averaging Amplifier Digital Event Recorder
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Power Injection Method
Power Input - measured
System
Power Transferred
Power Out =
tot
totEtot
=
in /
2 f Etot
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Power Injection Damping – Structural
log e d1 loge d 2 1 1 t1 log e c1 t2 c2
y ˆ b R
2
ˆ Xb
1
XX
Xy
2 2
ˆ Xy-N E y b y y-N E y
A coefficient of correlation approaching 1 suggests a good fit.
Temperature of the test part was monitored with an array of 4 thermocouples.
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Aluminum Fuselage, 50% Damping Tile Coverage
The temperature dependence of the damping tiles had a strong effect on the modal characteristic.
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Random Decrement Technique
Random Decrement:
DX 0
E x(t 2 ) x(t1 )
X0
DX 0
Where
X 0 Rx ( ) / Rx (0)
Rx ( ) E x(t ) x(t )
This is also called Output Only System Identification.
Power Injection Method
in
F G
G
2 d
M v
v M Fd
2
2
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Half Power Bandwidth Method
3 dB f fr
f / fr
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Aircraft Panel Example
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The test panel was then tested in an environmental chamber to evaluate damping tile effectiveness at low temperature.
Aluminum Fuselage Section
Shaker w/ Insulation Box
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Test Set Up
Response was measured with 6 accelerometers arrayed on the panel.
Shaker input was measured with a force transducer in-line with a stinger.
Accelerometer Graphic Level Recorder
Filter Strip Chart
Signal Generator
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Filter
Purpose – Eliminate out of band information so that the measurement is not contaminated. Considerations: • Center Frequency – frequency of interest •Bandwidth - what frequencies to pass • Roll Off – how rapidly the out of band frequencies are attenuated • Group Delay – response time of the filter • ‘Ringing’ – decay rate of filter
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Filter – Impulse Response Schroeder Envelope
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Impulse Response Decay Method
Measured FRF 1 kHz 1/3 Octave Bandpass Filtered
FRFs were band-limited at every 1/3 Octave of interest for frequency dependant results.
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Hilbert Transform
The Hilbert Transform creates the analytical complement to the signal.
Adding the squares of the signal and Hilbert Transform defines the envelope of the signal.
Signal Processing Considerations
Reverberation decay technique – Analog • Band Limited White Noise • Filter • Averaging Amplifier • Graphic Level Recorder • Strip Chart Digital Processing • Digital Filter • Digital Signal Processing
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Structural Damping
• In general, a single number representation of the structural loss factors is inadequate. • Damping can depend on multiple factors. • Frequency • Temperature • Pressurization • Frequency Dependence: Standard one third octave bands are: 100, 125, 160, 200, 250, 300, 400, 500, 630, 800, 1000 ………..
Measuring Structural Damping to Support SEA Model Development
Mark Moeller, Spirit AeroSystems
SEA Models
Source Path Receiver
• SEA models track the diffusion of energy in a system. • SEA models balance damping versus diffusion. • Damping is usually measured. • A robust damping measurement is required for SEA model building.
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Filter – IIR Bandpass
4th Order Butterworth 5000 Hz Center Frequency One Third Octave Bandwidth
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Filter – Impulse Response
• Rise Time • Ringing Requirement – Filters Impulse Response must decay much faster than the physical system of interest.