Chapter 3.1 Flashcards
Motion transducers(accelerometers)
Designed to provide an electric output signal (voltage) directly proportional to the acceleration in the measurement point.
u = Ca (C - proportionality constant(sensitivity))
for piezoelectric acc:
(base plate, PE crystal, seismic mass)
seismic mass important b/c gives sensitivity and upper freq limit for linear behavior(increased mass…increased increased force…increased sensitivity(but at the price of limiting the useful freq range)(also increased mass loading at response point may give measurement errors of course………..light structures should use optical methods!))
important to be able to use many accs simultaneously…for modal analysis they are cheap and with low upper freq
Acceleration signal conditioning
Before fed to the analyser input..need conditioning just like the force signal
preamplifiers amplify the signal to a level that assures a good use of the dynamic range
FILTERS remove parts of the signal not needed
make sure to sample w/ as high a rate as possible w/o getting data storage probs. Can always downsample, a high sampling rate increases dynamic range.
Response measurement in practice
threaded studs preferred for fixation, but at lower temps beeswax sufficient
usually 10-100 measurement points
If only a dual channel analyser available…acc or excit must be moved to get all data needed. If acc moved the test structure mass distribution changes b/w the measurements …violation of the fundamental requirement that the structure remain time invariant(may ruin modal analysis results) small mass variation can cause divergent results….instead better to use simultaneous accs to get consistent measurements and save measurement time!
FRF estimation - multichannel FFT analyzer (basic)
FRFs(such as receptances, are determined w/ multichannel FFT analyzers: they estimate the Fourier transforms of the input signals and FRF b/w it’s input signals. …all channels must have a common time base
ANTI-ALIASING FILTER: prevent signal distortion caused by the sampling procedure
A/D CONVERTER: signal is digitized it sampled from analog to digital
WEIGHTING WINDOW: since actual measurement is finite, in contrast to what is required by definition… WW needed to reduce the signal distorsión caused by the FFT-algorithm
AUTO spectra and CROSS spectrum then calculated and averaged to reduce influence of random noise
Finally FRF estimated from AUTO and CROSS
Digitalization of a signal - A/D conversion
(Analog to digital)
Output from a transducer usually analog
First signal filtered in low pass(anti-aliasing) filter w/ cutoff at freq = samp freq /2.56……prevents aliasing errors caused by sampling process
A/D also discretises the signal amplitude b/c the converter only has a limited amount of storage (introduces an amplitude RESOLUTION ERROR)
…resolve this with a HIGH PASS filter: improves the signal resolution when the contribution at low freqs from rigid body motion is large
Discrete Fourier transform
1) freq resolution increases with increased measurement time, ie the time record length
2) only signals exactly periodic in the time window, will be correctly transformed to the freq domain
3) leakage will occur if there is a mismatch b/w the beginning and end of the signal at 0 and time Ts
4) as a result of the sampling(A/D conversion), the spectrum is folded around multiple of half the sampling freq. Thus a freq component originally located at fs/2 + f is folded down to fs/2-f. This is called aliasing
Sampling - aliasing
Sampling inherently leads to aliasing problem. Sampling procedure has the effect to superpose the spectrum of the original signal with identical frequency shifted copies
Solutions:
1) samp freq chosen at least 2x the highest freq component in the signal
2) (feasible) before sampling, the signal is low pass filtered with a cutoff freq at freq samp/2 (anti aliasing filter)…….in practice freq samp > 2.56*freq upper
(All digital instruments performing any kind of A/D conversion should be equipped w/ anti aliasing filters)
Finite measurement time - windowing
If signal and it’s derivatives at the beginning and end are not equal, there will be error (in general all finite time records introduce errors in the transform of the windowed signal)
The FFT of a signal is identical to the transform of the original signal only if the signal is truly PERIODIC in the MEASUREMENT WINDOW……if periodic, weighting windows not needed……if not periodic, it’s transform will contain leakage errors.
Weighting window purpose: modify the signal within the time window so that it’s abrupt changes at the extension points are reduced. (However for a periodic curve, it would introduce leakage!)
Zero padding
Frequency resolution can be increased synthetically by appending time record with a sequence of 0’s. Increasing the apparent time record
(good for transient signals)
Averaging
Averaging helps reduce the influence of noise
Averaged cross spectrum G_ab - the process eliminates all signal components in B I correlated to A (so if G_ab = 0, A and B totally uncorrelated)
Frequency domain averaging - useful for reducing the influence of uncorrelated disturbances…….
Time domain averaging - introduces before the signal is Fourier transformed
FRF estimators
FRF is the linear relation b/w an input to a system and it’s response.
When signals include noise(either input, output or both are contaminated)…need to estimate…use an averages cross spectrum b/w the input and output signal, it will only contain contributions correlated b/w the input and output signals(so correlated noise eliminated)
Most often the force is more free from noise than the response…note either way a total noise cancellation requires an infinite number of averages
Source correlation technique - use whenever an approximately noise free source’s signal is available
The coherence function
Coherence used as an indicator for unreliable measurements
It is a function of the frequency and is always =< 1
….=1 perfect lin relationship
….=0 no lin relation at all
Thus less than 1 indicates that the estimated lin FRF may be unreliable. 1 does not necessarily mean reliable FRF estimates. Can receive less than 1 for:
1) uncorrelated noise present in either the measured input or output or both (Most common, significant when the motion signal is very small ie the structure is difficult to excite)
2) relationship b/w the input and output is non linear (problem if large excitations are needed, so large structures. Or where there there are small losses ie may be insufficient freq resolution(narrow resonance peaks))
3) time delay of the response signal so large that part of the time history response can not be recorded in that time period(physical distance b/w input and output transducers is large)
Physically interpreted as the linear relationship b/w the input and output signal.
Calibration
Complete calibration implies calibration of all parts of the measurement system …provides absolute values of force and motion
Use a reference object(known mass), m should be equal to F/a
Important that the force is applied in the measured DOF only(Other directions would contribute to the measured excitation but not the response)…straight rod often chosen since its 1D character makes it difficult to excite rotation
for freqs lower than 30% of the first quasi-longitudinal eigen freq the mass behaves as a rigid mass, oscillating back and forth on its suspension
Perform at beginning and end to assure reliable results
Multiple input FRF measurement
(More than one excitation supplied)
Same as single unit measurements, but 2 excitations measured simultaneously
Measurement problems (5 total)
1) Driving point receptances
2) Transducer mass loading
3) moment excitation
4) rotational motion
5) measurements on components
