2019-05-13 13:22:11 +02:00
<?xml version="1.0" encoding="utf-8"?>
< !DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
< html xmlns = "http://www.w3.org/1999/xhtml" lang = "en" xml:lang = "en" >
< head >
2020-11-12 10:30:56 +01:00
<!-- 2020 - 11 - 12 jeu. 10:27 -->
2019-05-13 13:22:11 +02:00
< meta http-equiv = "Content-Type" content = "text/html;charset=utf-8" / >
< title > Vibrations induced by the Slip-Ring and the Spindle< / title >
< meta name = "generator" content = "Org mode" / >
< meta name = "author" content = "Dehaeze Thomas" / >
2020-11-12 10:30:56 +01:00
< link rel = "stylesheet" type = "text/css" href = "https://research.tdehaeze.xyz/css/style.css" / >
< script type = "text/javascript" src = "https://research.tdehaeze.xyz/js/script.js" > < / script >
2019-05-13 13:22:11 +02:00
< / head >
< body >
< div id = "org-div-home-and-up" >
< a accesskey = "h" href = "../index.html" > UP < / a >
|
< a accesskey = "H" href = "../index.html" > HOME < / a >
< / div > < div id = "content" >
< h1 class = "title" > Vibrations induced by the Slip-Ring and the Spindle< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
2020-11-12 10:30:56 +01:00
< li > < a href = "#org2422081" > 1. Experimental Setup< / a > < / li >
< li > < a href = "#org6220fc6" > 2. Data Analysis< / a >
2019-05-13 13:22:11 +02:00
< ul >
2020-11-12 10:30:56 +01:00
< li > < a href = "#org122f0e9" > 2.1. Load data< / a > < / li >
< li > < a href = "#orgaea71b5" > 2.2. Voltage to Velocity< / a > < / li >
< li > < a href = "#org485d23f" > 2.3. Time domain plots< / a > < / li >
< li > < a href = "#org38cf97f" > 2.4. Frequency Domain< / a > < / li >
< li > < a href = "#orgbaa08aa" > 2.5. Relative Motion< / a > < / li >
< li > < a href = "#orgad3b42a" > 2.6. Save< / a > < / li >
< li > < a href = "#org0a44924" > 2.7. Conclusion< / a > < / li >
2019-05-13 13:22:11 +02:00
< / ul >
< / li >
< / ul >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org2422081" class = "outline-2" >
< h2 id = "org2422081" > < span class = "section-number-2" > 1< / span > Experimental Setup< / h2 >
2019-05-13 13:22:11 +02:00
< div class = "outline-text-2" id = "text-1" >
< p >
2020-04-27 11:35:57 +02:00
< b > Setup< / b > :
2019-05-13 13:22:11 +02:00
All the stages are OFF.
< / p >
< p >
Two geophone are use:
< / p >
< ul class = "org-ul" >
< li > One on the marble (corresponding to the first column in the data)< / li >
< li > One at the sample location (corresponding to the second column in the data)< / li >
< / ul >
< p >
Two voltage amplifiers are used, their setup is:
< / p >
< ul class = "org-ul" >
< li > gain of 60dB< / li >
< li > AC/DC switch on AC< / li >
< li > Low pass filter at 1kHz< / li >
< / ul >
< p >
A first order low pass filter is also added at the input of the voltage amplifiers.
< / p >
2020-04-27 11:35:57 +02:00
2019-05-13 13:22:11 +02:00
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Identify the vibrations induced by the rotation of the Slip-Ring and Spindle< / li >
< / ul >
2019-05-14 14:11:31 +02:00
2019-05-13 13:22:11 +02:00
< p >
2019-05-14 14:11:31 +02:00
< b > Measurements< / b > :
2019-05-13 13:22:11 +02:00
Three measurements are done:
< / p >
2019-05-13 22:36:14 +02:00
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Measurement File< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > < code > mat/data_024.mat< / code > < / td >
< td class = "org-left" > All the stages are OFF< / td >
< / tr >
< tr >
< td class = "org-left" > < code > mat/data_025.mat< / code > < / td >
< td class = "org-left" > The slip-ring is ON and rotates at 6rpm. The spindle is OFF< / td >
< / tr >
< tr >
< td class = "org-left" > < code > mat/data_026.mat< / code > < / td >
< td class = "org-left" > The slip-ring and spindle are both ON. They are both turning at 6rpm< / td >
< / tr >
< / tbody >
< / table >
< p >
Each of the measurement < code > mat< / code > file contains one < code > data< / code > array with 3 columns:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column number< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Geophone - Marble< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Geophone - Sample< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
2019-05-13 13:22:11 +02:00
< p >
2020-11-12 10:30:56 +01:00
A movie showing the experiment is shown on figure < a href = "#orgc1e7286" > 1< / a > .
2019-05-13 13:22:11 +02:00
< / p >
2020-11-12 10:30:56 +01:00
< div id = "orgc1e7286" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "./img/VID_20190510_155655.gif" alt = "VID_20190510_155655.gif" width = "300px" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Movie of the experiment, rotation speed is 6rpm< / p >
< / div >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org6220fc6" class = "outline-2" >
< h2 id = "org6220fc6" > < span class = "section-number-2" > 2< / span > Data Analysis< / h2 >
2019-05-13 13:22:11 +02:00
< div class = "outline-text-2" id = "text-2" >
< p >
2020-11-12 10:30:56 +01:00
< a id = "org8446070" > < / a >
2019-05-13 13:22:11 +02:00
< / p >
2020-11-12 10:30:56 +01:00
< div class = "note" id = "orga7b7a45" >
2019-05-13 13:22:11 +02:00
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/spindle_slip_ring_vibrations.zip" > here< / a > .
< / p >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org122f0e9" class = "outline-3" >
< h3 id = "org122f0e9" > < span class = "section-number-3" > 2.1< / span > Load data< / h3 >
2019-05-13 13:22:11 +02:00
< div class = "outline-text-3" id = "text-2-1" >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > of = load(< span class = "org-string" > 'mat/data_024.mat'< / span > , < span class = "org-string" > 'data'< / span > ); of = of.data; < span class = "org-comment" > % OFF< / span >
sr = load(< span class = "org-string" > 'mat/data_025.mat'< / span > , < span class = "org-string" > 'data'< / span > ); sr = sr.data; < span class = "org-comment" > % Slip Ring< / span >
sp = load(< span class = "org-string" > 'mat/data_026.mat'< / span > , < span class = "org-string" > 'data'< / span > ); sp = sp.data; < span class = "org-comment" > % Spindle< / span >
2020-04-27 11:35:57 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div class = "warning" id = "orgb2b819c" >
2020-04-27 11:35:57 +02:00
< p >
There is a sign error for the Geophone located on top of the Hexapod.
The problem probably comes from the wiring in the Slip-Ring.
< / p >
< / div >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > of(< span class = "org-type" > :< / span > , 2) = < span class = "org-type" > -< / span > of(< span class = "org-type" > :< / span > , 2);
sr(< span class = "org-type" > :< / span > , 2) = < span class = "org-type" > -< / span > sr(< span class = "org-type" > :< / span > , 2);
sp(< span class = "org-type" > :< / span > , 2) = < span class = "org-type" > -< / span > sp(< span class = "org-type" > :< / span > , 2);
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-orgaea71b5" class = "outline-3" >
< h3 id = "orgaea71b5" > < span class = "section-number-3" > 2.2< / span > Voltage to Velocity< / h3 >
2019-05-13 13:22:11 +02:00
< div class = "outline-text-3" id = "text-2-2" >
2020-04-27 11:35:57 +02:00
< p >
We convert the measured voltage to velocity using the function < code > voltageToVelocityL22< / code > (accessible < a href = "../src/index.html" > here< / a > ).
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > gain = 60; < span class = "org-comment" > % [dB]< / span >
2020-04-27 11:35:57 +02:00
2020-11-12 10:30:56 +01:00
of(< span class = "org-type" > :< / span > , 1) = voltageToVelocityL22(of(< span class = "org-type" > :< / span > , 1), of(< span class = "org-type" > :< / span > , 3), gain);
sr(< span class = "org-type" > :< / span > , 1) = voltageToVelocityL22(sr(< span class = "org-type" > :< / span > , 1), sr(< span class = "org-type" > :< / span > , 3), gain);
sp(< span class = "org-type" > :< / span > , 1) = voltageToVelocityL22(sp(< span class = "org-type" > :< / span > , 1), sp(< span class = "org-type" > :< / span > , 3), gain);
2020-04-27 11:35:57 +02:00
2020-11-12 10:30:56 +01:00
of(< span class = "org-type" > :< / span > , 2) = voltageToVelocityL22(of(< span class = "org-type" > :< / span > , 2), of(< span class = "org-type" > :< / span > , 3), gain);
sr(< span class = "org-type" > :< / span > , 2) = voltageToVelocityL22(sr(< span class = "org-type" > :< / span > , 2), sr(< span class = "org-type" > :< / span > , 3), gain);
sp(< span class = "org-type" > :< / span > , 2) = voltageToVelocityL22(sp(< span class = "org-type" > :< / span > , 2), sp(< span class = "org-type" > :< / span > , 3), gain);
2020-04-27 11:35:57 +02:00
< / pre >
< / div >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org485d23f" class = "outline-3" >
< h3 id = "org485d23f" > < span class = "section-number-3" > 2.3< / span > Time domain plots< / h3 >
2020-04-27 11:35:57 +02:00
< div class = "outline-text-3" id = "text-2-3" >
2019-05-13 13:22:11 +02:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-11-12 10:30:56 +01:00
plot(sp(< span class = "org-type" > :< / span > , 3), sp(< span class = "org-type" > :< / span > , 1), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Spindle - 6rpm'< / span > );
plot(sr(< span class = "org-type" > :< / span > , 3), sr(< span class = "org-type" > :< / span > , 1), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Slip-Ring - 6rpm'< / span > );
plot(of(< span class = "org-type" > :< / span > , 3), of(< span class = "org-type" > :< / span > , 1), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > );
2019-05-13 13:22:11 +02:00
hold off;
2020-11-12 10:30:56 +01:00
xlabel(< span class = "org-string" > 'Time [s]'< / span > ); ylabel(< span class = "org-string" > 'Velocity [m/s]'< / span > );
xlim([0, 100]);
legend(< span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'northeast'< / span > );
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "org4a00ffe" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "figs/slip_ring_spindle_marble_time.png" alt = "slip_ring_spindle_marble_time.png" / >
< / p >
2020-04-27 11:35:57 +02:00
< p > < span class = "figure-number" > Figure 2: < / span > Velocity as measured by the geophone located on the marble - Time domain< / p >
2019-05-13 13:22:11 +02:00
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-11-12 10:30:56 +01:00
plot(sp(< span class = "org-type" > :< / span > , 3), sp(< span class = "org-type" > :< / span > , 2), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Spindle and Slip-Ring'< / span > );
plot(sr(< span class = "org-type" > :< / span > , 3), sr(< span class = "org-type" > :< / span > , 2), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Only Slip-Ring'< / span > );
plot(of(< span class = "org-type" > :< / span > , 3), of(< span class = "org-type" > :< / span > , 2), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > );
2019-05-13 13:22:11 +02:00
hold off;
2020-11-12 10:30:56 +01:00
xlabel(< span class = "org-string" > 'Time [s]'< / span > ); ylabel(< span class = "org-string" > 'Velocity [m/s]'< / span > );
xlim([0, 100]);
legend(< span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'northeast'< / span > );
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "orgcea5a30" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "figs/slip_ring_spindle_sample_time.png" alt = "slip_ring_spindle_sample_time.png" / >
< / p >
2020-04-27 11:35:57 +02:00
< p > < span class = "figure-number" > Figure 3: < / span > Velocity as measured by the geophone at the sample location - Time domain< / p >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "org3c59dd5" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/slip_ring_spindle_sample_zoom.png" alt = "slip_ring_spindle_sample_zoom.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Velocity as measured by the geophone at the sample location - Time domain< / p >
2019-05-13 13:22:11 +02:00
< / div >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org38cf97f" class = "outline-3" >
< h3 id = "org38cf97f" > < span class = "section-number-3" > 2.4< / span > Frequency Domain< / h3 >
2020-04-27 11:35:57 +02:00
< div class = "outline-text-3" id = "text-2-4" >
2019-05-13 13:22:11 +02:00
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > dt = of(2, 3)< span class = "org-type" > -< / span > of(1, 3); < span class = "org-comment" > % [s]< / span >
2019-05-13 13:22:11 +02:00
2020-11-12 10:30:56 +01:00
Fs = 1< span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
2019-05-13 13:22:11 +02:00
2020-11-12 10:30:56 +01:00
win = hanning(ceil(10< span class = "org-type" > *< / span > Fs)); < span class = "org-comment" > % Window used< / span >
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< p >
First for the geophone located on the marble
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > [pxof_m, f] = pwelch(of(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
[pxsr_m, < span class = "org-type" > ~< / span > ] = pwelch(sr(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
[pxsp_m, < span class = "org-type" > ~< / span > ] = pwelch(sp(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
< p >
And for the geophone located at the sample position.
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > [pxof_s, < span class = "org-type" > ~< / span > ] = pwelch(of(< span class = "org-type" > :< / span > , 2), win, [], [], Fs);
[pxsr_s, < span class = "org-type" > ~< / span > ] = pwelch(sr(< span class = "org-type" > :< / span > , 2), win, [], [], Fs);
[pxsp_s, < span class = "org-type" > ~< / span > ] = pwelch(sp(< span class = "org-type" > :< / span > , 2), win, [], [], Fs);
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
< p >
2020-04-27 11:35:57 +02:00
And we plot the ASD of the measured velocities:
2019-05-13 13:22:11 +02:00
< / p >
< ul class = "org-ul" >
2020-11-12 10:30:56 +01:00
< li > figure < a href = "#orgf38cb1d" > 5< / a > for the geophone located on the marble< / li >
< li > figure < a href = "#orgbe7eafc" > 6< / a > for the geophone at the sample position< / li >
2019-05-13 13:22:11 +02:00
< / ul >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-11-12 10:30:56 +01:00
plot(f, sqrt(pxsp_m), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Spindle - 6rpm'< / span > );
plot(f, sqrt(pxsr_m), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Slip-Ring - 6rpm'< / span > );
plot(f, sqrt(pxof_m), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > );
2019-05-13 13:22:11 +02:00
hold off;
2020-11-12 10:30:56 +01:00
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'< / span > )
legend(< span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > );
xlim([2, 500]);
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "orgf38cb1d" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "figs/sr_sp_psd_marble_compare.png" alt = "sr_sp_psd_marble_compare.png" / >
< / p >
2020-04-27 11:35:57 +02:00
< p > < span class = "figure-number" > Figure 5: < / span > Comparison of the ASD of the measured velocities from the Geophone on the marble< / p >
2019-05-13 13:22:11 +02:00
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-11-12 10:30:56 +01:00
plot(f, sqrt(pxsp_s), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Spindle - 6rpm'< / span > );
plot(f, sqrt(pxsr_s), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Slip-Ring - 6rpm'< / span > );
plot(f, sqrt(pxof_s), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > );
2019-05-13 13:22:11 +02:00
hold off;
2020-11-12 10:30:56 +01:00
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'< / span > )
legend(< span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > );
xlim([2, 500]);
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "orgbe7eafc" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "figs/sr_sp_psd_sample_compare.png" alt = "sr_sp_psd_sample_compare.png" / >
< / p >
2020-04-27 11:35:57 +02:00
< p > < span class = "figure-number" > Figure 6: < / span > Comparison of the ASD of the measured velocities from the Geophone at the sample location< / p >
< / div >
< p >
2020-11-12 10:30:56 +01:00
We load the ground motion to compare with the measurements (Fig. < a href = "#org71b3fba" > 7< / a > ).
2020-04-27 11:35:57 +02:00
We see that the motion is dominated by the ground motion below 20Hz.
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > gm = load(< span class = "org-string" > '../ground-motion/mat/psd_gm.mat'< / span > , < span class = "org-string" > 'f'< / span > , < span class = "org-string" > 'psd_gv'< / span > );
2020-04-27 11:35:57 +02:00
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-11-12 10:30:56 +01:00
plot(f, sqrt(pxsp_m), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Spindle - 6rpm'< / span > );
plot(f, sqrt(pxsr_m), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Slip-Ring - 6rpm'< / span > );
plot(f, sqrt(pxof_m), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > );
plot(gm.f, sqrt(gm.psd_gv), < span class = "org-string" > 'k-'< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Ground Motion'< / span > );
2020-04-27 11:35:57 +02:00
hold off;
2020-11-12 10:30:56 +01:00
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'< / span > )
legend(< span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > );
xlim([2, 500]);
2020-04-27 11:35:57 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "org71b3fba" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/ty_comp_gm.png" alt = "ty_comp_gm.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Comparison of the ground velocity with the measured velocity (< a href = "./figs/ty_comp_gm.png" > png< / a > , < a href = "./figs/ty_comp_gm.pdf" > pdf< / a > )< / p >
2019-05-13 13:22:11 +02:00
< / div >
< / div >
< / div >
2020-04-27 11:35:57 +02:00
2020-11-12 10:30:56 +01:00
< div id = "outline-container-orgbaa08aa" class = "outline-3" >
< h3 id = "orgbaa08aa" > < span class = "section-number-3" > 2.5< / span > Relative Motion< / h3 >
2020-04-27 11:35:57 +02:00
< div class = "outline-text-3" id = "text-2-5" >
< p >
2020-11-12 10:30:56 +01:00
The relative velocity between the sample and the marble is shown in Fig. < a href = "#orgb098e37" > 8< / a > .
The velocity is integrated to have the relative displacement in Fig. < a href = "#org3dac066" > 9< / a > .
2020-04-27 11:35:57 +02:00
< / p >
2020-11-12 10:30:56 +01:00
< div id = "orgb098e37" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/rz_relative_velocity.png" alt = "rz_relative_velocity.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > Relative velocity between the hexapod and the marble (< a href = "./figs/rz_relative_velocity.png" > png< / a > , < a href = "./figs/rz_relative_velocity.pdf" > pdf< / a > )< / p >
< / div >
< p >
Time domain: Integration to have the displacement
< / p >
2020-11-12 10:30:56 +01:00
< div id = "org3dac066" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/rz_relative_motion.png" alt = "rz_relative_motion.png" / >
< / p >
< p > < span class = "figure-number" > Figure 9: < / span > Relative displacement between the Hexapod and the marble (< a href = "./figs/rz_relative_motion.png" > png< / a > , < a href = "./figs/rz_relative_motion.pdf" > pdf< / a > )< / p >
< / div >
< p >
We compute the PSD of the relative velocity between the sample and the marble.
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > [pxof_r, f] = pwelch(of(< span class = "org-type" > :< / span > , 2)< span class = "org-type" > -< / span > of(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
[pxsr_r, < span class = "org-type" > ~< / span > ] = pwelch(sr(< span class = "org-type" > :< / span > , 2)< span class = "org-type" > -< / span > sr(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
[pxsp_r, < span class = "org-type" > ~< / span > ] = pwelch(sp(< span class = "org-type" > :< / span > , 2)< span class = "org-type" > -< / span > sp(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
2020-04-27 11:35:57 +02:00
< / pre >
< / div >
< p >
2020-11-12 10:30:56 +01:00
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. < a href = "#orga42fb07" > 10< / a > .
2020-04-27 11:35:57 +02:00
< / p >
2020-11-12 10:30:56 +01:00
< div id = "orga42fb07" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/rz_psd_sample_granite_relative_comp.png" alt = "rz_psd_sample_granite_relative_comp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 10: < / span > Comparison of the PSD of the velocity of the Sample, Granite and relative velocity (< a href = "./figs/rz_psd_sample_granite_relative_comp.png" > png< / a > , < a href = "./figs/rz_psd_sample_granite_relative_comp.pdf" > pdf< / a > )< / p >
< / div >
< p >
2020-11-12 10:30:56 +01:00
Then, we display the PSD of the relative velocity for all three cases in Fig. < a href = "#org1f1dfc7" > 11< / a > .
2020-04-27 11:35:57 +02:00
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-11-12 10:30:56 +01:00
plot(f, sqrt(pxsp_r), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Spindle - 6rpm'< / span > );
plot(f, sqrt(pxsr_r), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Slip-Ring - 6rpm'< / span > );
plot(f, sqrt(pxof_r), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > );
2020-04-27 11:35:57 +02:00
hold off;
2020-11-12 10:30:56 +01:00
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'ASD of the relative velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'< / span > )
legend(< span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > );
xlim([2, 500]);
2020-04-27 11:35:57 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "org1f1dfc7" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/sr_sp_psd_relative_compare.png" alt = "sr_sp_psd_relative_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 11: < / span > Comparison of the ASD of the relative velocity< / p >
< / div >
< p >
2020-11-12 10:30:56 +01:00
The Cumulative Power Spectrum of the relative velocity is shown in Fig. < a href = "#org11a9cb7" > 12< / a > and in Fig. < a href = "#orga256753" > 13< / a > (integrated in reverse direction).
2020-04-27 11:35:57 +02:00
< / p >
2020-11-12 10:30:56 +01:00
< div id = "org11a9cb7" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/dist_rz_cps.png" alt = "dist_rz_cps.png" / >
< / p >
< p > < span class = "figure-number" > Figure 12: < / span > Cumulative Power Spectrum of the relative velocity (< a href = "./figs/dist_rz_cps.png" > png< / a > , < a href = "./figs/dist_rz_cps.pdf" > pdf< / a > )< / p >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "orga256753" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/dist_rz_cps_reverse.png" alt = "dist_rz_cps_reverse.png" / >
< / p >
< p > < span class = "figure-number" > Figure 13: < / span > Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) (< a href = "./figs/dist_rz_cps_reverse.png" > png< / a > , < a href = "./figs/dist_rz_cps_reverse.pdf" > pdf< / a > )< / p >
< / div >
< p >
2020-11-12 10:30:56 +01:00
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. < a href = "#orgb16a9f7" > 14< / a > .
2020-04-27 11:35:57 +02:00
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-11-12 10:30:56 +01:00
plot(f, sqrt(flip(< span class = "org-type" > -< / span > cumtrapz(flip(f), flip(pxsp_r< span class = "org-type" > ./< / span > (2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f)< span class = "org-type" > .^< / span > 2)))), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Spindle - 6rpm'< / span > );
plot(f, sqrt(flip(< span class = "org-type" > -< / span > cumtrapz(flip(f), flip(pxsr_r< span class = "org-type" > ./< / span > (2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f)< span class = "org-type" > .^< / span > 2)))), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Slip-Ring - 6rpm'< / span > );
plot(f, sqrt(flip(< span class = "org-type" > -< / span > cumtrapz(flip(f), flip(pxof_r< span class = "org-type" > ./< / span > (2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f)< span class = "org-type" > .^< / span > 2)))), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > );
2020-04-27 11:35:57 +02:00
hold off;
2020-11-12 10:30:56 +01:00
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'CAS of the relative displacement $\left[\frac{m}{\sqrt{Hz}}\right]$'< / span > )
legend(< span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > );
xlim([2, 500]);
2020-04-27 11:35:57 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "orgb16a9f7" class = "figure" >
2020-04-27 11:35:57 +02:00
< p > < img src = "figs/dist_rz_cas.png" alt = "dist_rz_cas.png" / >
< / p >
< p > < span class = "figure-number" > Figure 14: < / span > Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite (< a href = "./figs/dist_rz_cas.png" > png< / a > , < a href = "./figs/dist_rz_cas.pdf" > pdf< / a > )< / p >
< / div >
2020-11-12 10:30:56 +01:00
< / div >
< / div >
2020-04-27 11:35:57 +02:00
2020-11-12 10:30:56 +01:00
< div id = "outline-container-orgad3b42a" class = "outline-3" >
< h3 id = "orgad3b42a" > < span class = "section-number-3" > 2.6< / span > Save< / h3 >
< div class = "outline-text-3" id = "text-2-6" >
2020-04-27 11:35:57 +02:00
< p >
2020-11-12 10:30:56 +01:00
The Power Spectral Density of the relative velocity and of the hexapod velocity is saved for further analysis.
2020-04-27 11:35:57 +02:00
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > save(< span class = "org-string" > 'mat/pxsp_r.mat'< / span > , < span class = "org-string" > 'f'< / span > , < span class = "org-string" > 'pxsp_r'< / span > , < span class = "org-string" > 'pxsp_s'< / span > );
2020-04-27 11:35:57 +02:00
< / pre >
< / div >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org0a44924" class = "outline-3" >
< h3 id = "org0a44924" > < span class = "section-number-3" > 2.7< / span > Conclusion< / h3 >
< div class = "outline-text-3" id = "text-2-7" >
< div class = "important" id = "orga7d722f" >
2019-05-13 13:22:11 +02:00
< p >
2020-04-27 11:35:57 +02:00
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
< / p >
< p >
The Slip-Ring rotation induce almost no relative motion of the hexapod with respect to the granite (only a little above 400Hz).
2019-05-13 13:22:11 +02:00
< / p >
< p >
2020-04-27 11:35:57 +02:00
The Spindle rotation induces relative motion of the hexapod with respect to the granite above 20Hz.
2019-05-13 13:22:11 +02:00
< / p >
2020-04-27 11:35:57 +02:00
< / div >
2020-11-12 10:30:56 +01:00
< div class = "important" id = "orga4c2e01" >
2020-04-27 11:35:57 +02:00
< p >
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
< / p >
< ul class = "org-ul" >
< li > The peak is really sharp, could this be due to magnetic effect?< / li >
< li > Should redo the measurement with piezo accelerometers.< / li >
< / ul >
2019-05-13 13:22:11 +02:00
< / div >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2020-11-12 10:30:56 +01:00
< p class = "date" > Created: 2020-11-12 jeu. 10:27< / p >
2019-05-13 13:22:11 +02:00
< / div >
< / body >
< / html >
