Can damping ratio calculation be done in DDP? how

[Josephus]

This is the same request as posted in "audio & acoustic test & measurement". This is may be a better place to post it.

Using DDP functions I would like to know if it is possible to have a set of derived data point to determine the damping ratio of a tap test on tone wood that has a fast decay and/or the logarithmic decrements of the diminishing amplitude of the pulse. The Y unit should be in audio dB. Usually the frequency is pretty low from 50 Hz to 500 Hz.

Another derived function I would be interested would be the Q factor defined as = center frequency divided by the (frequency after minus frequency before) when the amplitude is 3 dB below the center frequency in the spectrum analyzer.

I just got the full package software and there is a lot to learn to navigate all that can be done.

Any assistance will be welcome. Thank you

[VirtinsTech]

Thank you for your questions.

The Q factor can be measured and displayed directly in Multi-Instrument under Bandwidth measurement mode, which can be activated by right clicking anywhere within the Spectrum Analyzer window and select [Spectrum Analyzer Processing]>"Parameter Measurement">"Bandwidth (-3dB)". Under this mode, the following three Derived Data Points are available for the Q factor derivation: f1Freq_A(Hz), BandWidthLowLimit_A(Hz), BandWidthHighLimit_A(Hz). The names of these DDP should be self-explanatory. The Q factor can be define as a User Defined Data Point using this formula: [f1Freq_A(Hz)]/([BandWidthHighLimit_A(Hz)]-[BandWidthLowLimit_A(Hz)]). Please refer to Section 10.2.2 of the software manual on how to define a UDDP. The following screenshot shows the result using the waveform data you sent to support@virtins.com.

Q-Factor.png (101.65 KiB) Viewed 167943 times

By the way, as shown above, the input is a little saturated as indicated by the Input Peak Level Indicator (100% and RED) displayed in the top right of the screen. Also, as the window function for spectrum analysis is centered at the middle of the sampled data, for impact test, setting the Trigger Delay to -50% will put the most important portion of the data in the middle of the screen.

[VirtinsTech]

If you want to get the overall decay curve, you can use AM demodulation to get the envelop of the impact curve. Right click anywhere within the oscilloscope and select [Oscilloscope Processing]>"Demodulation">"AM". Your wave file contains the same data in both channels. To display the original signal in Ch. A and the AM demodulated signal in Ch. B, select "Apply To" to Ch. "B" only. The result is shown below.

ImpactEnvelop.png (136.46 KiB) Viewed 167938 times

You can further apply a low pass filter to Ch. B to get a smoother decay curve, as shown below.

ImpactEnvelopLowPassFiltered.png (134.36 KiB) Viewed 167938 times

[VirtinsTech]

A sound level (in dB) is not an instantaneous value but a RMS value. A RMS value has a time duration in which the RMS is calculated. The impact process lasts very short. The waveform data provided is only 500 ms long. To display the sound level decay with the time, the time duration in which each sound level is calculated needs to be much shorter than 500ms. But it cannot be too short here as it is constrained by the peak frequency 193 Hz (about 5 ms).

Here, a time duration of 20 ms for sound level calculation is used. To obtain the sound level decay with time, the 20ms-long time window is moved along the time axis with an overlap ratio of 75%. The Data Logger function of MI is used to log the sound level variation with time.

The waveform data is saved in a wave file. Click the oscilloscope window, and select “20ms” in the T range selection box at the lower left corner of the screen. Go to [File]>[Open Frame by Frame] and select the wave file. Set the multimeter to dB mode so that the sound level DDP RMSDB_A(dB) will be available. Open the Data logger and select “RMSDB_A(dB)” to log. Finally, click the “Frame Auto Scroll” at the upper left corner of the screen to create the sound level decay curve automatically. (as shown below)

SoundLevelDecay.png (82.5 KiB) Viewed 167935 times

[Josephus]

Thank you very much for your patience, guidance and the extended demonstrations of the software capabilities in regards to my questions. This, by itself is a great tutorial (for me and maybe for others ). I really appreciate the time you took to post the screen shots with the explicit explanation. That is great support for a great software. So once again. THANK YOU.

[VirtinsTech]

Damping Ratio can be derived from the Q factor.

[Q Factor] = [Frequency Response Peak]/([-3dB Bandwidth High Limit]-[-3dB Bandwidth Low Limit])
[Damping Ratio] = 1/(2*[Q Factor])

Now, we can define two UDDPs in Multi-Instrument,
[Q Factor] = [f1Freq_A(Hz)]/([BandWidthHighLimit_A(Hz)]-[BandWidthLowLimit_A(Hz)])
[Damping Ratio] = ([BandWidthHighLimit_A(Hz)]-[BandWidthLowLimit_A(Hz)])/[f1Freq_A(Hz)]/2

QFactorAndDampingRatio.png (61.64 KiB) Viewed 136733 times

Note:
1. The impulse response waveform is not centered in the Oscilloscope. Hence Rectangle Window is used otherwise the useful part of the waveform may be greatly attenuated.
2. No frequency weighting should be used in the Spectrum Analyzer. The frequency response in the Spectrum Analyzer must be an unchanged one.
3. The Spectrum Analyzer is set to Bandwidth Measurement mode.
4. Large FFT size is used for better accuracy in -3dB bandwidth measurement. It must be equal to or greater than the Record Length.

[VirtinsTech]

Just an update, from MI 3.9.6, damping ratio measurement based on free vibration decay curve in time domain has been provided. This is in addition to the existing half-power method in frequency domain described above. The following example shows that the two methods match very well in the example. The Q factor, undamped and damped natural frequencies can also be measured simultaneously.

DampingRatio.png (104.51 KiB) Viewed 102457 times