243 lines
8.7 KiB
Org Mode
243 lines
8.7 KiB
Org Mode
#+TITLE: Vibrations induced by the Slip-Ring and the Spindle
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:DRAWER:
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#+STARTUP: overview
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#+LANGUAGE: en
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#+EMAIL: dehaeze.thomas@gmail.com
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#+AUTHOR: Dehaeze Thomas
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#+HTML_LINK_HOME: ../index.html
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#+HTML_LINK_UP: ../index.html
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
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#+HTML_MATHJAX: align: center tagside: right font: TeX
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :output-dir figs
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#+PROPERTY: header-args:shell :eval no-export
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:END:
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* Experimental Setup
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All the stages are OFF.
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Two geophone are use:
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- One on the marble (corresponding to the first column in the data)
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- One at the sample location (corresponding to the second column in the data)
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Two voltage amplifiers are used, their setup is:
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- gain of 60dB
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- AC/DC switch on AC
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- Low pass filter at 1kHz
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A first order low pass filter is also added at the input of the voltage amplifiers.
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*Goal*:
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- Identify the vibrations induced by the rotation of the Slip-Ring and Spindle
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Three measurements are done:
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| Measurement File | Description |
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|--------------------+----------------------------------------------------------------------|
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| =mat/data_024.mat= | All the stages are OFF |
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| =mat/data_025.mat= | The slip-ring is ON and rotates at 6rpm. The spindle is OFF |
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| =mat/data_026.mat= | The slip-ring and spindle are both ON. They are both turning at 6rpm |
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Each of the measurement =mat= file contains one =data= array with 3 columns:
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| Column number | Description |
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|---------------+-------------------|
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| 1 | Geophone - Marble |
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| 2 | Geophone - Sample |
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| 3 | Time |
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A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
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#+name: fig:exp_sl_sp_gif
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#+attr_html: :width 300px
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#+caption: Movie of the experiment, rotation speed is 6rpm
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[[file:./img/VID_20190510_155655.gif]]
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* Data Analysis
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/spindle_slip_ring_vibrations.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:spindle_slip_ring_vibrations>>
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#+begin_src bash :exports none :results none
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if [ matlab/spindle_slip_ring_vibrations.m -nt data/spindle_slip_ring_vibrations.zip ]; then
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cp matlab/spindle_slip_ring_vibrations.m spindle_slip_ring_vibrations.m;
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zip data/spindle_slip_ring_vibrations \
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mat/data_024.mat \
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mat/data_025.mat \
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mat/data_026.mat \
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spindle_slip_ring_vibrations.m
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rm spindle_slip_ring_vibrations.m;
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fi
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#+end_src
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#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/spindle_slip_ring_vibrations.zip][here]].
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#+end_note
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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** Load data
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#+begin_src matlab
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of = load('mat/data_024.mat', 'data'); of = of.data;
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sr = load('mat/data_025.mat', 'data'); sr = sr.data;
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sp = load('mat/data_026.mat', 'data'); sp = sp.data;
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#+end_src
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** Time domain plots
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#+begin_src matlab
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figure;
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hold on;
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plot(sp(:, 3), sp(:, 1), 'DisplayName', 'Spindle - 6rpm');
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plot(sr(:, 3), sr(:, 1), 'DisplayName', 'Slip-Ring - 6rpm');
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plot(of(:, 3), of(:, 1), 'DisplayName', 'OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 100]); ylim([-10 10]);
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legend('Location', 'northeast');
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#+end_src
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#+NAME: fig:slip_ring_spindle_marble_time
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/slip_ring_spindle_marble_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:slip_ring_spindle_marble_time
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#+CAPTION: Measurement of the geophone located on the marble - Time domain
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#+RESULTS: fig:slip_ring_spindle_marble_time
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[[file:figs/slip_ring_spindle_marble_time.png]]
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#+begin_src matlab
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figure;
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hold on;
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plot(sp(:, 3), sp(:, 2), 'DisplayName', 'Spindle and Slip-Ring');
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plot(sr(:, 3), sr(:, 2), 'DisplayName', 'Only Slip-Ring');
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plot(of(:, 3), of(:, 2), 'DisplayName', 'OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 100]); ylim([-10 10]);
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legend('Location', 'northeast');
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#+end_src
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#+NAME: fig:slip_ring_spindle_sample_time
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/slip_ring_spindle_sample_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:slip_ring_spindle_sample_time
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#+CAPTION: Measurement of the geophone at the sample location - Time domain
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#+RESULTS: fig:slip_ring_spindle_sample_time
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[[file:figs/slip_ring_spindle_sample_time.png]]
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** Frequency Domain
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We first compute some parameters that will be used for the PSD computation.
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#+begin_src matlab :results none
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dt = of(2, 3)-of(1, 3);
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Fs = 1/dt; % [Hz]
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win = hanning(ceil(10*Fs));
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#+end_src
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Then we compute the Power Spectral Density using =pwelch= function.
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First for the geophone located on the marble
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#+begin_src matlab
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[pxof_m, f] = pwelch(of(:, 1), win, [], [], Fs);
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[pxsr_m, ~] = pwelch(sr(:, 1), win, [], [], Fs);
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[pxsp_m, ~] = pwelch(sp(:, 1), win, [], [], Fs);
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#+end_src
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And for the geophone located at the sample position.
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#+begin_src matlab
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[pxof_s, f] = pwelch(of(:, 2), win, [], [], Fs);
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[pxsr_s, ~] = pwelch(sr(:, 2), win, [], [], Fs);
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[pxsp_s, ~] = pwelch(sp(:, 2), win, [], [], Fs);
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#+end_src
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And we plot the ASD of the measured signals:
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- figure [[fig:sr_sp_psd_marble_compare]] for the geophone located on the marble
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- figure [[fig:sr_sp_psd_sample_compare]] for the geophone at the sample position
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(pxsp_m), 'DisplayName', 'Spindle - 6rpm');
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plot(f, sqrt(pxsr_m), 'DisplayName', 'Slip-Ring - 6rpm');
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plot(f, sqrt(pxof_m), 'DisplayName', 'OFF');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:sr_sp_psd_marble_compare
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/sr_sp_psd_marble_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:sr_sp_psd_marble_compare
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#+CAPTION: Comparison of the ASD of the measured voltage from the Geophone on the marble
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#+RESULTS: fig:sr_sp_psd_marble_compare
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[[file:figs/sr_sp_psd_marble_compare.png]]
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(pxsp_s), 'DisplayName', 'Spindle - 6rpm');
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plot(f, sqrt(pxsr_s), 'DisplayName', 'Slip-Ring - 6rpm');
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plot(f, sqrt(pxof_s), 'DisplayName', 'OFF');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:sr_sp_psd_sample_compare
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/sr_sp_psd_sample_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:sr_sp_psd_sample_compare
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#+CAPTION: Comparison of the ASD of the measured voltage from the Geophone at the sample location
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#+RESULTS: fig:sr_sp_psd_sample_compare
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[[file:figs/sr_sp_psd_sample_compare.png]]
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** Conclusion
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#+begin_important
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The slip-ring rotation induces almost no vibrations on the marble, and only a little vibrations on the sample above 100Hz.
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The spindle rotation induces a lot of vibrations of the sample as well as on the granite.
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There is a huge peak at 24Hz on the sample vibration but not on the granite vibration.
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#+end_important
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