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Static Measurements

Table of Contents

1 Ty Stage

All the files (data and Matlab scripts) are accessible here.

1.1 Notes

  • 5530: Straightness Plot: Yz
  • Filename: r:\home\PDMU\PEL\Measurement_library\ID31\ID31_u_station\TY\12_12_2018\linear deviation _tyz_401_points.txt
  • Acquisition date: 09/01/2019 13:49:42
  • Current date: 08/03/2019 08:46:35
  • Measurement Type: STRAIGHTNESS vertical
  • Travel Mode: Bidirectional
  • Number of Target Positions: 401
  • Number of total data pairs: 2406
  • Number of total data runs:6
  • Position Value Units: millimeters
  • Error Value Units: micrometers
Environmental Data Min Max Avg
Air Temp (C) 024,57 024,61 024,59
Air Prs (mm) 742,56 743,29 742,83
Air Hmd (%) 024,00 024,00 024,00
MT1 Temp (C)     020,00
MT2 Temp (C) 024,40 024,44 024,42
MT3 Temp (C) 024,32 024,36 024,34

In a very schematic way, the measurement is explained on figure 1. The positioning error \(d\) is measure as a function of \(x\). Because the measurement is done in a static way, the dynamics of the station (represented by the mass-spring-damper system on the schematic) does not play a role in the measure.

The obtained data corresponds to the guiding errors.

guiding_errors.png

Figure 1: Schematic of the measurement

1.2 Data Pre-processing

sed 's/\t/  /g;s/\,/./g' "mat/linear_deviation_tyz_401_points.txt" > data/data_tyz.txt
head "mat/data_tyz.txt"
Run Pos TargetValue ErrorValue
1 1 -4.5E+00 7.5377892E+00
1 2 -4.4775E+00 7.5422246E+00
1 3 -4.455E+00 7.5655617E+00
1 4 -4.4325E+00 7.5149518E+00
1 5 -4.41E+00 7.4886377E+00
1 6 -4.3875E+00 7.437007E+00
1 7 -4.365E+00 7.4449354E+00
1 8 -4.3425E+00 7.3937387E+00
1 9 -4.32E+00 7.3287468E+00

1.3 Matlab - Data Import

filename = 'mat/data_tyz.txt';
fileID = fopen(filename);
data = cell2mat(textscan(fileID,'%f  %f  %f  %f', 'collectoutput', 1,'headerlines',1));
fclose(fileID);

1.4 Data - Plot

First, we plot the straightness error as a function of the position (figure 2).

figure;
hold on;
for i=1:data(end, 1)
  plot(data(data(:, 1) == i, 3), data(data(:, 1) == i, 4), '-k');
end
hold off;
xlabel('Target Value [mm]'); ylabel('Error Value [$\mu m$]');

raw_data_tyz.png

Figure 2: Time domain Data

Then, we compute mean value of each position, and we remove this mean value from the data. The results are shown on figure 3.

mean_pos = zeros(sum(data(:, 1)==1), 1);
for i=1:sum(data(:, 1)==1)
  mean_pos(i) = mean(data(data(:, 2)==i, 4));
end
figure;
hold on;
for i=1:data(end, 1)
  filt = data(:, 1) == i;
  plot(data(filt, 3), data(filt, 4) - mean_pos, '-k');
end
hold off;
xlabel('Target Value [mm]'); ylabel('Error Value [$\mu m$]');

processed_data_tyz.png

Figure 3: caption

1.5 Translate to time domain

We here make the assumptions that, during a scan with the translation stage, the Z motion of the translation stage will follow the guiding error measured.

We then create a time vector \(t\) from 0 to 1 second that corresponds to a typical scan, and we plot the guiding error as a function of the time on figure 4.

t = linspace(0, 1, length(data(data(:, 1)==1, 4)));
figure;
hold on;
plot(t, data(data(:, 1) == 1, 4) - mean_pos, '-k');
hold off;
xlabel('Time [s]'); ylabel('Error Value [um]');

time_domain_tyz.png

Figure 4: caption

1.6 Compute the PSD

We first compute some parameters that will be used for the PSD computation.

dt = t(2)-t(1);

Fs = 1/dt; % [Hz]

win = hanning(ceil(1*Fs));

We remove the mean position from the data.

x = data(data(:, 1) == 1, 4) - mean_pos;

And finally, we compute the power spectral density of the displacement obtained in the time domain.

The result is shown on figure 5.

[pxx, f] = pwelch(x, win, [], [], Fs);

pxx_t = zeros(length(pxx), data(end, 1));

for i=1:data(end, 1)
  x = data(data(:, 1) == i, 4) - mean_pos;
  [pxx, f] = pwelch(x, win, [], [], Fs);
  pxx_t(:, i) = pxx;
end
figure;
hold on;
plot(f, sqrt(mean(pxx_t, 2)), 'k-');
hold off;
xlabel('Frequency (Hz)');
ylabel('Amplitude Spectral Density $\left[\frac{m}{\sqrt{Hz}}\right]$');
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');

psd_tyz.png

Figure 5: PSD of the Z motion when scanning with Ty at 1Hz

2 TODO Spindle

Author: Dehaeze Thomas

Created: 2019-05-14 mar. 09:52

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