"Huddle test" + calibration analysis

test-bench-flexible-joints.org

@@ -601,9 +601,10 @@ Another measurement bench allowing better accuracy will be developed.
 <<sec:test_meas_probe>>
 *** Introduction                                                    :ignore:
 
-- *Load Cells*: [[file:doc/A700000007147087.pdf][FC2231-0000-0010-L]] (and  [[file:doc/FRE_DS_XFL212R_FR_A3.pdf][XFL212R]])
+#+begin_note
 - *Encoder*: [[file:doc/L-9517-9448-05-B_Data_sheet_RESOLUTE_BiSS_en.pdf][Renishaw Resolute 1nm]]
 - *Displacement Probe*: [[file:doc/Millimar--3723046--BA--C1208-C1216-C1240--FR--2016-11-08.pdf][Millimar C1216 electronics]] and [[file:doc/tmp3m0cvmue_7888038c-cdc8-48d8-a837-35de02760685.pdf][Millimar 1318 probe]]
+#+end_note
 
 *** Setup                                                           :ignore:
 The measurement setup is made such that the probe measured the translation table displacement.
@@ -748,6 +749,7 @@ However, there is some time delay of tens of milliseconds that could induce some
 :header-args:matlab+: :tangle ./matlab/probe_stiffness.m
 :END:
 <<sec:meas_probe_stiffness>>
+
 *** Introduction                                                    :ignore:
 
 #+begin_note
@@ -867,6 +869,313 @@ exportFig('figs/mahr_stiffness_f_d_plot.pdf', 'width', 'wide', 'height', 'normal
 The Millimar 1318 probe has a stiffness of $\approx 0.04\,[N/mm]$.
 #+end_summary
 
+** Force Sensor Calibration
+*** Introduction                                                    :ignore:
+
+#+begin_note
+*Load Cells*:
+- [[file:doc/A700000007147087.pdf][FC2231-0000-0010-L]]
+- [[file:doc/FRE_DS_XFL212R_FR_A3.pdf][XFL212R]]
+#+end_note
+
+There are both specified to have $\pm 1 \%$ of non-linearity over the full range.
+
+The XFL212R has a spherical interface while the FC2231 has a flat surface.
+Therefore, we should have a nice point contact when using the two force sensors as shown in Figure [[fig:force_sensor_calibration_setup]].
+
+#+name: fig:force_sensor_calibration_setup
+#+caption: Zoom on the two force sensors in contact
+#+attr_latex: :width 0.8\linewidth
+[[file:figs/IMG_20210309_145333.jpg]]
+
+The two force sensors are therefore measuring the exact same force, and we can compare the two measurements.
+
+*** 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>>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+<<matlab-init>>
+#+end_src
+
+#+begin_src matlab :tangle no
+addpath('./matlab/mat/');
+addpath('./matlab/');
+#+end_src
+
+#+begin_src matlab :eval no
+addpath('./mat/');
+#+end_src
+
+*** Analysis                                                        :ignore:
+Let's load the measured force of both sensors.
+#+begin_src matlab
+%% Load measurement data
+load('calibration_force_sensor.mat', 't', 'F', 'Fc')
+#+end_src
+
+We remove any offset such that they are both measuring no force when not in contact.
+#+begin_src matlab
+%% Remove offset
+F  = F  - mean(F( t > 0.5 & t < 1.0));
+Fc = Fc - mean(Fc(t > 0.5 & t < 1.0));
+#+end_src
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(t, F, 'DisplayName', 'FC2231');
+plot(t, Fc, 'DisplayName', 'XFL212R');
+hold off;
+xlabel('Time [s]'); ylabel('Measured Force [N]');
+xlim([0,15]); ylim([0,55]);
+legend('location', 'southeast');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/force_calibration_time.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:force_calibration_time
+#+caption: Measured force using both sensors as a function of time
+#+RESULTS:
+[[file:figs/force_calibration_time.png]]
+
+Let's select only the first part from the moment they are in contact until the maximum force is reached.
+
+#+begin_src matlab
+%% Only get the first part until maximum force
+F  = F( t > 1.55 & t < 4.65);
+Fc = Fc(t > 1.55 & t < 4.65);
+#+end_src
+
+Then, let's make a linear fit between the two measured forces.
+
+#+begin_src matlab
+%% Make a line fit
+fit_F = polyfit(Fc, F, 1);
+#+end_src
+
+The two forces are plotted against each other as well as the linear fit in Figure [[fig:calibrated_force_dit]].
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(Fc, F, '-', 'DisplayName', 'Raw Data');
+plot(Fc([1,end]), Fc([1,end])*fit_F(1) + fit_F(2), '--', 'DisplayName', 'Line Fit');
+hold off;
+xlabel('XFL212R [N]'); ylabel('FC2231 [N]');
+xlim([0,50]); ylim([0,50]);
+legend('location', 'southeast');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/calibrated_force_dit.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:calibrated_force_dit
+#+caption: Measured two forces and linear fit
+#+RESULTS:
+[[file:figs/calibrated_force_dit.png]]
+
+The measurement error between the two sensors is shown in Figure [[fig:force_meas_error]].
+It is below 0.1N for the full measurement range.
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(Fc, F - (Fc*fit_F(1) + fit_F(2)), 'k-');
+hold off;
+xlim([0,50]); ylim([-0.12, 0.12]);
+xlabel('Measured Force [N]');
+ylabel('Error [N]')
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/force_meas_error.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:force_meas_error
+#+caption: Error in Newtons
+#+RESULTS:
+[[file:figs/force_meas_error.png]]
+
+The same error is shown in percentage in Figure [[fig:force_meas_error_percentage]].
+The error is less than 1% when the measured force is above 5N.
+
+#+begin_src matlab :exports none
+figure;
+plot(Fc, 100*(F - (Fc*fit_F(1) + fit_F(2)))./Fc, 'k-');
+xlim([0,50]); ylim([-4, 1]);
+xlabel('Measured Force [N]');
+ylabel('Error [\%]')
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/force_meas_error_percentage.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:force_meas_error_percentage
+#+caption: Error in percentage
+#+RESULTS:
+[[file:figs/force_meas_error_percentage.png]]
+
+** Force Sensor Noise
+*** Introduction                                                    :ignore:
+The objective of this measurement is to estimate the noise of the force sensor [[file:doc/A700000007147087.pdf][FC2231-0000-0010-L]].
+To do so, we don't apply any force to the sensor, and we measure its output for 100s.
+
+*** 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>>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+<<matlab-init>>
+#+end_src
+
+#+begin_src matlab :tangle no
+addpath('./matlab/mat/');
+addpath('./matlab/');
+#+end_src
+
+#+begin_src matlab :eval no
+addpath('./mat/');
+#+end_src
+
+
+*** Analysis                                                        :ignore:
+Let's load the measurement data.
+
+#+begin_src matlab
+%% Load measurement data
+load('force_sensor_noise_meas.mat', 't', 'F');
+Ts = t(2) - t(1);
+#+end_src
+
+The measured force is shown in Figure [[fig:force_noise_time]].
+
+#+begin_src matlab :exports none
+%% Take last 100s
+F = F(t > t(end)-100);
+t = t(t > t(end)-100);
+
+%% Remove force offset and reset time
+F = F - mean(F);
+t = t - t(1);
+#+end_src
+
+#+begin_src matlab :exports none
+figure;
+plot(t, F)
+xlabel('Time [s]');
+ylabel('Force [N]');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/force_noise_time.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:force_noise_time
+#+caption: Measured force
+#+RESULTS:
+[[file:figs/force_noise_time.png]]
+
+Let's now compute the Amplitude Spectral Density of the measured force.
+
+#+begin_src matlab
+%% Compute Spectral Density of Measured Force
+% Hanning window
+win = hanning(ceil(1/Ts));
+
+% Power Spectral Density
+[pxx, f] = pwelch(F, win, [], [], 1/Ts);
+#+end_src
+
+The results is shown in Figure [[fig:force_noise_asd]].
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(f, sqrt(pxx));
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$N/\sqrt{Hz}$]');
+xlim([1, 1/Ts/2]); ylim([4e-5, 1e-3]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/force_noise_asd.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:force_noise_asd
+#+caption: Amplitude Spectral Density of the meaured force
+#+RESULTS:
+[[file:figs/force_noise_asd.png]]
+
+
+** TODO Force Sensor Stiffness
+*** Introduction                                                    :ignore:
+
+The objective of this measurement is to estimate the stiffness of the force sensor [[file:doc/A700000007147087.pdf][FC2231-0000-0010-L]].
+
+To do so, a very stiff element is fixed in front of the force sensor as shown in Figure [[fig:setup_meas_force_sensor_stiffness]].
+
+Then, we apply a force on the stiff element through the force sensor.
+We measure the deflection of the force sensor using an encoder.
+
+Then, having the force and the deflection, we should be able to estimate the stiffness of the force sensor supposing the stiffness of the other elements are much larger.
+
+#+name: fig:setup_meas_force_sensor_stiffness
+#+caption: Bench used to measured the stiffness of the force sensor
+#+attr_latex: :width 0.6\linewidth
+[[file:figs/IMG_20210309_145242.jpg]]
+
+From the documentation, the deflection of the sensor at the maximum load (50N) is 0.05mm, the stiffness is therefore foreseen to be around $1\,N/\mu m$.
+
+*** 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>>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+<<matlab-init>>
+#+end_src
+
+#+begin_src matlab :tangle no
+addpath('./matlab/mat/');
+addpath('./matlab/');
+#+end_src
+
+#+begin_src matlab :eval no
+addpath('./mat/');
+#+end_src
+
+*** Analysis                                                        :ignore:
+
+Let's load the measured force as well as the measured displacement.
+#+begin_src matlab
+%% Load measurement data
+load('force_sensor_stiff_meas.mat', 't', 'F', 'd')
+#+end_src
+
+#+begin_src matlab
+%% Select important part of data
+F  = F( t > 1.55 & t < 4.65);
+d  = d( t > 1.55 & t < 4.65);
+#+end_src
+
+#+begin_src matlab
+%% Linear fit
+fit_k = polyfit(F, d, 1);
+#+end_src
+
+#+begin_src matlab
+%% Force Sensor Stiffness
+fit_k(1)
+#+end_src
+
 * Bending Stiffness Measurement
 :PROPERTIES:
 :header-args:matlab+: :tangle ./matlab/bending_stiff_meas.m