#+TITLE: Vibrations induced by the Slip-Ring and the Spindle
:DRAWER:
#+STARTUP: overview

#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

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#+HTML_LINK_UP: ../index.html

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#+HTML_MATHJAX: align: center tagside: right font: TeX

#+PROPERTY: header-args:matlab  :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs

#+PROPERTY: header-args:shell  :eval no-export
:END:

* Experimental Setup
*Setup*:
All the stages are OFF.

Two geophone are use:
- One on the marble (corresponding to the first column in the data)
- One at the sample location (corresponding to the second column in the data)

Two voltage amplifiers are used, their setup is:
- gain of 60dB
- AC/DC switch on AC
- Low pass filter at 1kHz

A first order low pass filter is also added at the input of the voltage amplifiers.


*Goal*:
- Identify the vibrations induced by the rotation of the Slip-Ring and Spindle


*Measurements*:
Three measurements are done:
| Measurement File   | Description                                                          |
|--------------------+----------------------------------------------------------------------|
| =mat/data_024.mat= | All the stages are OFF                                               |
| =mat/data_025.mat= | The slip-ring is ON and rotates at 6rpm. The spindle is OFF          |
| =mat/data_026.mat= | The slip-ring and spindle are both ON. They are both turning at 6rpm |

Each of the measurement =mat= file contains one =data= array with 3 columns:
| Column number | Description       |
|---------------+-------------------|
|             1 | Geophone - Marble |
|             2 | Geophone - Sample |
|             3 | Time              |

A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].

#+name: fig:exp_sl_sp_gif
#+attr_html: :width 300px
#+caption: Movie of the experiment, rotation speed is 6rpm
[[file:./img/VID_20190510_155655.gif]]

* Data Analysis
  :PROPERTIES:
  :header-args:matlab+: :tangle matlab/spindle_slip_ring_vibrations.m
  :header-args:matlab+: :comments org :mkdirp yes
  :END:
  <<sec:spindle_slip_ring_vibrations>>

** ZIP file containing the data and matlab files                     :ignore:
#+begin_src bash :exports none :results none
  if [ matlab/spindle_slip_ring_vibrations.m -nt data/spindle_slip_ring_vibrations.zip ]; then
    cp matlab/spindle_slip_ring_vibrations.m spindle_slip_ring_vibrations.m;
    zip data/spindle_slip_ring_vibrations \
        mat/data_024.mat \
        mat/data_025.mat \
        mat/data_026.mat \
        spindle_slip_ring_vibrations.m
    rm spindle_slip_ring_vibrations.m;
  fi
#+end_src

#+begin_note
  All the files (data and Matlab scripts) are accessible [[file:data/spindle_slip_ring_vibrations.zip][here]].
#+end_note

** Matlab Init                                              :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
  <<matlab-dir>>
  addpath('../src');
#+end_src

#+begin_src matlab :exports none :results silent :noweb yes
  <<matlab-init>>
#+end_src

** Load data
#+begin_src matlab
  of = load('mat/data_024.mat', 'data'); of = of.data;
  sr = load('mat/data_025.mat', 'data'); sr = sr.data;
  sp = load('mat/data_026.mat', 'data'); sp = sp.data;
#+end_src

** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/Cloud/These/meas/src/index.org][here]]).

#+begin_src matlab
  gain = 60; % [dB]

  of(:, 1) = voltageToVelocityL22(of(:, 1), of(:, 3), gain);
  sr(:, 1) = voltageToVelocityL22(sr(:, 1), sr(:, 3), gain);
  sp(:, 1) = voltageToVelocityL22(sp(:, 1), sp(:, 3), gain);

  of(:, 2) = voltageToVelocityL22(of(:, 2), of(:, 3), gain);
  sr(:, 2) = voltageToVelocityL22(sr(:, 2), sr(:, 3), gain);
  sp(:, 2) = voltageToVelocityL22(sp(:, 2), sp(:, 3), gain);
#+end_src

** Time domain plots
#+begin_src matlab
  figure;
  hold on;
  plot(sp(:, 3), sp(:, 1), 'DisplayName', 'Spindle - 6rpm');
  plot(sr(:, 3), sr(:, 1), 'DisplayName', 'Slip-Ring - 6rpm');
  plot(of(:, 3), of(:, 1), 'DisplayName', 'OFF');
  hold off;
  xlabel('Time [s]'); ylabel('Velocity [m/s]');
  xlim([0, 100]);
  legend('Location', 'northeast');
#+end_src

#+NAME: fig:slip_ring_spindle_marble_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/slip_ring_spindle_marble_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:slip_ring_spindle_marble_time
#+CAPTION: Velocity as measured by the geophone located on the marble - Time domain
#+RESULTS: fig:slip_ring_spindle_marble_time
[[file:figs/slip_ring_spindle_marble_time.png]]

#+begin_src matlab
  figure;
  hold on;
  plot(sp(:, 3), sp(:, 2), 'DisplayName', 'Spindle and Slip-Ring');
  plot(sr(:, 3), sr(:, 2), 'DisplayName', 'Only Slip-Ring');
  plot(of(:, 3), of(:, 2), 'DisplayName', 'OFF');
  hold off;
  xlabel('Time [s]'); ylabel('Velocity [m/s]');
  xlim([0, 100]);
  legend('Location', 'northeast');
#+end_src

#+NAME: fig:slip_ring_spindle_sample_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/slip_ring_spindle_sample_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:slip_ring_spindle_sample_time
#+CAPTION: Velocity as measured by the geophone at the sample location - Time domain
#+RESULTS: fig:slip_ring_spindle_sample_time
[[file:figs/slip_ring_spindle_sample_time.png]]

#+begin_src matlab :exports none :tangle no
  xlim([0, 1]);
#+end_src

#+NAME: fig:slip_ring_spindle_sample_zoom
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/slip_ring_spindle_sample_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:slip_ring_spindle_sample_zoom
#+CAPTION: Velocity as measured by the geophone at the sample location - Time domain
#+RESULTS: fig:slip_ring_spindle_sample_zoom
[[file:figs/slip_ring_spindle_sample_zoom.png]]

** Frequency Domain
We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab :results none
  dt = of(2, 3)-of(1, 3);

  Fs = 1/dt; % [Hz]

  win = hanning(ceil(10*Fs));
#+end_src

Then we compute the Power Spectral Density using =pwelch= function.

First for the geophone located on the marble
#+begin_src matlab
  [pxof_m, f] = pwelch(of(:, 1), win, [], [], Fs);
  [pxsr_m, ~] = pwelch(sr(:, 1), win, [], [], Fs);
  [pxsp_m, ~] = pwelch(sp(:, 1), win, [], [], Fs);
#+end_src

And for the geophone located at the sample position.
#+begin_src matlab
  [pxof_s, ~] = pwelch(of(:, 2), win, [], [], Fs);
  [pxsr_s, ~] = pwelch(sr(:, 2), win, [], [], Fs);
  [pxsp_s, ~] = pwelch(sp(:, 2), win, [], [], Fs);
#+end_src

And finally for the relative velocity between the sample and the marble.
#+begin_src matlab
  [pxof_r, ~] = pwelch(of(:, 2)-of(:, 1), win, [], [], Fs);
  [pxsr_r, ~] = pwelch(sr(:, 2)-sr(:, 1), win, [], [], Fs);
  [pxsp_r, ~] = pwelch(sp(:, 2)-sp(:, 1), win, [], [], Fs);
#+end_src

And we plot the ASD of the measured velocities:
- figure [[fig:sr_sp_psd_marble_compare]] for the geophone located on the marble
- figure [[fig:sr_sp_psd_sample_compare]] for the geophone at the sample position

#+begin_src matlab :results none
  figure;
  hold on;
  plot(f, sqrt(pxsp_m), 'DisplayName', 'Spindle - 6rpm');
  plot(f, sqrt(pxsr_m), 'DisplayName', 'Slip-Ring - 6rpm');
  plot(f, sqrt(pxof_m), 'DisplayName', 'OFF');
  hold off;
  set(gca, 'xscale', 'log');
  set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
  legend('Location', 'southwest');
  xlim([2, 500]);
#+end_src

#+NAME: fig:sr_sp_psd_marble_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_sp_psd_marble_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_sp_psd_marble_compare
#+CAPTION: Comparison of the ASD of the measured velocities from the Geophone on the marble
#+RESULTS: fig:sr_sp_psd_marble_compare
[[file:figs/sr_sp_psd_marble_compare.png]]

#+begin_src matlab :results none
  figure;
  hold on;
  plot(f, sqrt(pxsp_s), 'DisplayName', 'Spindle - 6rpm');
  plot(f, sqrt(pxsr_s), 'DisplayName', 'Slip-Ring - 6rpm');
  plot(f, sqrt(pxof_s), 'DisplayName', 'OFF');
  hold off;
  set(gca, 'xscale', 'log');
  set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
  legend('Location', 'southwest');
  xlim([2, 500]);
#+end_src

#+NAME: fig:sr_sp_psd_sample_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_sp_psd_sample_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_sp_psd_sample_compare
#+CAPTION: Comparison of the ASD of the measured velocities from the Geophone at the sample location
#+RESULTS: fig:sr_sp_psd_sample_compare
[[file:figs/sr_sp_psd_sample_compare.png]]

#+begin_src matlab :results none
  figure;
  hold on;
  plot(f, sqrt(pxsp_r), 'DisplayName', 'Spindle - 6rpm');
  plot(f, sqrt(pxsr_r), 'DisplayName', 'Slip-Ring - 6rpm');
  plot(f, sqrt(pxof_r), 'DisplayName', 'OFF');
  hold off;
  set(gca, 'xscale', 'log');
  set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD of the relative velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
  legend('Location', 'southwest');
  xlim([2, 500]);
#+end_src

#+NAME: fig:sr_sp_psd_relative_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_sp_psd_relative_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_sp_psd_relative_compare
#+CAPTION: Comparison of the ASD of the relative velocity
#+RESULTS: fig:sr_sp_psd_relative_compare
[[file:figs/sr_sp_psd_relative_compare.png]]

** Conclusion
#+begin_important
  - The slip-ring rotation induces almost no vibrations on the marble, and only a little vibrations on the sample above 100Hz.

  - The spindle rotation induces a lot of vibrations of the sample as well as on the granite.
  - There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
    - The peak is really sharp, could this be due to magnetic effect?
    - Should redo the measurement with piezo accelerometers.
#+end_important