#+TITLE: Measurements
:DRAWER:
#+STARTUP: overview

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

#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP:   ../index.html

#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>

#+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 conditions

| *Date*       | 2017-11-17          |
| *Sensors*    | Accelerometers      |
| *Excitation* | Instrumented Hammer |
| *Location*   | Laboratory          |

Dynamics of the station is evaluated using instrumented hammer and accelerometers fixed on each stage.

*Goal*:
- Obtain a first estimation of resonance frequencies


- Measurement made in a metrology lab
- The granite is not glued to the floor
- The Y-Translation stage is powered and in closed-loop
- The spindle is not powered
- Mass is placed on top of the Hexapod (*how much?*) (figure [[fig:accelerometers]]).
- Made by Marc Lesourd on the 17th of November 2017

#+name: fig:accelerometers
#+caption: Accelerometers position
#+attr_html: :width 500px
[[file:./figs/accelerometers.png]]

#+name: fig:instrumented_hammer
#+caption: Instrumented Hammer used
#+attr_html: :width 500px
[[file:./figs/instrumented_hammer.png]]

* Measurements procedure
*3-axis Accelerometers* (specifications table [[tab:accelerometer]]) are glued on (see figure [[fig:accelerometers]]):
- Marble
- Y-Translation stage
- Tilt stage
- top of Hexapod

#+NAME: tab:accelerometer
#+CAPTION: Pieozoelectric acc. 356b18 - 3 axis
| Sensitivity          | 0.102 V/(m/s2)  |
| Measurement Range    | 4.9 m/s2 pk     |
| Frequency Range      | 0.5 to 3000 Hz  |
| resonant frequency   | >20000 Hz       |
| broadband resolution | 0.0005 m/s2 rms |

The structure is excited using an *instrumented hammer* with impacts on (see figure [[fig:instrumented_hammer]]):
- Marble
- Hexapod

* Measurement Files
Two measurements files are:
- =id31_microstation_2017_11_17_frf.mat= that contains:
  - =freq_frf= the frequency vector in Hz
  - Computed frequency response functions (see table [[tab:data_name]])
- =id31_microstation_2017_11_17_coh.mat=
  - Computed coherence

For each of the measurement, the measured channels are shown on table [[tab:meas_channels]].

#+NAME: tab:data_name
#+CAPTION: Description of the location of direction of the excitation for each measurement
| Object name  | Location | Direction |
|--------------+----------+-----------|
| frf_hexa_x   | Hexapod  | X         |
| frf_hexa_y   | Hexapod  | Y         |
| frf_hexa_z   | Hexapod  | Z         |
| frf_marble_x | Marble   | X         |
| frf_marble_y | Marble   | Y         |
| frf_marble_z | Marble   | Z         |

#+NAME: tab:meas_channels
#+CAPTION: Description of each measurement channel
| Ch. nb | Element       | Location | Direction |
|--------+---------------+----------+-----------|
|      1 | Not wired     | na       | na        |
|      2 | Accelerometer | Marble   | X         |
|      3 | Accelerometer | Marble   | Y         |
|      4 | Accelerometer | Marble   | Z         |
|      5 | Accelerometer | Ty       | X         |
|      6 | Accelerometer | Ty       | Y         |
|      7 | Accelerometer | Ty       | Z         |
|      8 | Accelerometer | Tilt     | X         |
|      9 | Accelerometer | Tilt     | Y         |
|     10 | Accelerometer | Tilt     | Z         |
|     11 | Accelerometer | Hexapod  | X         |
|     12 | Accelerometer | Hexapod  | Y         |
|     13 | Accelerometer | Hexapod  | Z         |

* Data Analysis
** Loading of the data
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
  <<matlab-dir>>
#+end_src

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

#+begin_src matlab :exports code :results none
  load('./raw_data/id31_microstation_2017_11_17_coh.mat',...
       'coh_hexa_x',...
       'coh_hexa_y',...
       'coh_hexa_z',...
       'coh_marble_x',...
       'coh_marble_y',...
       'coh_marble_z');

  load('./raw_data/id31_microstation_2017_11_17_frf.mat',...
       'freq_frf',...
       'frf_hexa_x',...
       'frf_hexa_y',...
       'frf_hexa_z',...
       'frf_marble_x',...
       'frf_marble_y',...
       'frf_marble_z');
#+end_src

** Pre-processing of the data
The FRF data are scaled with the sensitivity of the accelerometer and integrated two times to have the displacement instead of the acceleration.

#+begin_src matlab :results none
  accel_sensitivity = 0.102; % [V/(m/s2)]
  w = j*2*pi*freq_frf; % j.omega in [rad/s]

  frf_hexa_x =  1/accel_sensitivity*frf_hexa_x./(w.^2);
  frf_hexa_y = -1/accel_sensitivity*frf_hexa_y./(w.^2);
  frf_hexa_z = -1/accel_sensitivity*frf_hexa_z./(w.^2);

  frf_marble_x =  1/accel_sensitivity*frf_marble_x./(w.^2);
  frf_marble_y =  1/accel_sensitivity*frf_marble_y./(w.^2);
  frf_marble_z = -1/accel_sensitivity*frf_marble_z./(w.^2);
#+end_src

** X-direction FRF
#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_marble_x(:,  2)), 'DisplayName', 'Marble - X');
  plot(freq_frf, abs(frf_marble_x(:,  5)), 'DisplayName', 'Ty - X');
  plot(freq_frf, abs(frf_marble_x(:,  8)), 'DisplayName', 'Ry - X');
  plot(freq_frf, abs(frf_marble_x(:, 11)), 'DisplayName', 'Hexa - X');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([20, 200]); xticks([20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

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

#+NAME: fig:marble_x_frf
#+CAPTION: Response to a force applied on the marble in the X direction
#+RESULTS: fig:marble_x_frf
[[file:figs/marble_x_frf.png]]


#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_hexa_x(:,  2)), 'DisplayName', 'Marble - X');
  plot(freq_frf, abs(frf_hexa_x(:,  5)), 'DisplayName', 'Ty - X');
  plot(freq_frf, abs(frf_hexa_x(:,  8)), 'DisplayName', 'Ry - X');
  plot(freq_frf, abs(frf_hexa_x(:, 11)), 'DisplayName', 'Hexa - X');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([20, 200]); xticks([20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

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

#+NAME: fig:hexa_x_frf
#+CAPTION: Response to a force applied on the hexa in the X direction
#+RESULTS: fig:hexa_x_frf
[[file:figs/hexa_x_frf.png]]

** Y-direction FRF
#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_marble_y(:,  3)), 'DisplayName', 'Marble - Y');
  plot(freq_frf, abs(frf_marble_y(:,  6)), 'DisplayName', 'Ty - Y');
  plot(freq_frf, abs(frf_marble_y(:,  9)), 'DisplayName', 'Ry - Y');
  plot(freq_frf, abs(frf_marble_y(:, 12)), 'DisplayName', 'Hexa - Y');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([20, 200]); xticks([20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

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

#+NAME: fig:marble_y_frf
#+CAPTION: Response to a force applied on the marble in the Y direction
#+RESULTS: fig:marble_y_frf
[[file:figs/marble_y_frf.png]]

#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_hexa_y(:,  3)), 'DisplayName', 'Marble - Y');
  plot(freq_frf, abs(frf_hexa_y(:,  6)), 'DisplayName', 'Ty - Y');
  plot(freq_frf, abs(frf_hexa_y(:,  9)), 'DisplayName', 'Ry - Y');
  plot(freq_frf, abs(frf_hexa_y(:, 12)), 'DisplayName', 'Hexa - Y');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([20, 200]); xticks([20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

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

#+NAME: fig:hexa_y_frf
#+CAPTION: Response to a force applied on the hexa in the Y direction
#+RESULTS: fig:hexa_y_frf
[[file:figs/hexa_y_frf.png]]

** Z-direction FRF
#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_marble_z(:,  4)), 'DisplayName', 'Marble - Z');
  plot(freq_frf, abs(frf_marble_z(:,  7)), 'DisplayName', 'Ty - Z');
  plot(freq_frf, abs(frf_marble_z(:, 10)), 'DisplayName', 'Ry - Z');
  plot(freq_frf, abs(frf_marble_z(:, 13)), 'DisplayName', 'Hexa - Z');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([20, 200]); xticks([20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

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

#+NAME: fig:marble_z_frf
#+CAPTION: Response to a force applied on the marble in the Z direction
#+RESULTS: fig:marble_z_frf
[[file:figs/marble_z_frf.png]]

#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_hexa_z(:,  4)), 'DisplayName', 'Marble - Z');
  plot(freq_frf, abs(frf_hexa_z(:,  7)), 'DisplayName', 'Ty - Z');
  plot(freq_frf, abs(frf_hexa_z(:, 10)), 'DisplayName', 'Ry - Z');
  plot(freq_frf, abs(frf_hexa_z(:, 13)), 'DisplayName', 'Hexa - Z');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([20, 200]); xticks([20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

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

#+NAME: fig:hexa_z_frf
#+CAPTION: Response to a force applied on the hexa in the Z direction
#+RESULTS: fig:hexa_z_frf
[[file:figs/hexa_z_frf.png]]
* Results
#+begin_important
- Resonances have been identified at 45Hz and 75Hz
- However, the quality of the measurements are bad at low frequency
- New measurements should be done with Geophones
#+end_important