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< title > Measurements< / title >
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< meta name = "author" content = "Dehaeze Thomas" / >
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< h1 class = "title" > Measurements< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org20cd7af" > 1. Experimental conditions< / a > < / li >
< li > < a href = "#org4b136ea" > 2. Measurements procedure< / a > < / li >
< li > < a href = "#org7a4e10c" > 3. Measurement Files< / a > < / li >
< li > < a href = "#orgc4e4e05" > 4. Data Analysis< / a >
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< ul >
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< li > < a href = "#org8e48582" > 4.1. Loading of the data< / a > < / li >
< li > < a href = "#orgdef23af" > 4.2. Pre-processing of the data< / a > < / li >
< li > < a href = "#org9329022" > 4.3. X-direction FRF< / a > < / li >
< li > < a href = "#orgf143ff0" > 4.4. Y-direction FRF< / a > < / li >
< li > < a href = "#org69dd2ae" > 4.5. Z-direction FRF< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgdfa9254" > 5. Results< / a > < / li >
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< div id = "outline-container-org20cd7af" class = "outline-2" >
< h2 id = "org20cd7af" > < span class = "section-number-2" > 1< / span > Experimental conditions< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< col class = "org-left" / >
< col class = "org-left" / >
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< tr >
< td class = "org-left" > < b > Date< / b > < / td >
< td class = "org-left" > 2017-11-17< / td >
< / tr >
< tr >
< td class = "org-left" > < b > Sensors< / b > < / td >
< td class = "org-left" > Accelerometers< / td >
< / tr >
< tr >
< td class = "org-left" > < b > Excitation< / b > < / td >
< td class = "org-left" > Instrumented Hammer< / td >
< / tr >
< tr >
< td class = "org-left" > < b > Location< / b > < / td >
< td class = "org-left" > Laboratory< / td >
< / tr >
< / tbody >
< / table >
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< p >
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Dynamics of the station is evaluated using instrumented hammer and accelerometers fixed on each stage.
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< / p >
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< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Obtain a first estimation of resonance frequencies< / li >
< / ul >
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< ul class = "org-ul" >
< li > Measurement made in a metrology lab< / li >
< li > The granite is not glued to the floor< / li >
< li > The Y-Translation stage is powered and in closed-loop< / li >
< li > The spindle is not powered< / li >
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< li > Mass is placed on top of the Hexapod (< b > how much?< / b > ) (figure < a href = "#orge99c284" > 1< / a > ).< / li >
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< li > Made by Marc Lesourd on the 17th of November 2017< / li >
< / ul >
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< div id = "orge99c284" class = "figure" >
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< p > < img src = "./figs/accelerometers.png" alt = "accelerometers.png" width = "500px" / >
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< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Accelerometers position< / p >
< / div >
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< div id = "org363f97a" class = "figure" >
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< p > < img src = "./figs/instrumented_hammer.png" alt = "instrumented_hammer.png" width = "500px" / >
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< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Instrumented Hammer used< / p >
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< h2 id = "org4b136ea" > < span class = "section-number-2" > 2< / span > Measurements procedure< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< p >
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< b > 3-axis Accelerometers< / b > (specifications table < a href = "#org3aa8e2c" > 1< / a > ) are glued on (see figure < a href = "#orge99c284" > 1< / a > ):
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< / p >
< ul class = "org-ul" >
< li > Marble< / li >
< li > Y-Translation stage< / li >
< li > Tilt stage< / li >
< li > top of Hexapod< / li >
< / ul >
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< table id = "org3aa8e2c" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Pieozoelectric acc. 356b18 - 3 axis< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
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< tbody >
< tr >
< td class = "org-left" > Sensitivity< / td >
< td class = "org-left" > 0.102 V/(m/s2)< / td >
< / tr >
< tr >
< td class = "org-left" > Measurement Range< / td >
< td class = "org-left" > 4.9 m/s2 pk< / td >
< / tr >
< tr >
< td class = "org-left" > Frequency Range< / td >
< td class = "org-left" > 0.5 to 3000 Hz< / td >
< / tr >
< tr >
< td class = "org-left" > resonant frequency< / td >
< td class = "org-left" > > 20000 Hz< / td >
< / tr >
< tr >
< td class = "org-left" > broadband resolution< / td >
< td class = "org-left" > 0.0005 m/s2 rms< / td >
< / tr >
< / tbody >
< / table >
< p >
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The structure is excited using an < b > instrumented hammer< / b > with impacts on (see figure < a href = "#org363f97a" > 2< / a > ):
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< / p >
< ul class = "org-ul" >
< li > Marble< / li >
< li > Hexapod< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-org7a4e10c" class = "outline-2" >
< h2 id = "org7a4e10c" > < span class = "section-number-2" > 3< / span > Measurement Files< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< p >
Two measurements files are:
< / p >
< ul class = "org-ul" >
< li > < code > id31_microstation_2017_11_17_frf.mat< / code > that contains:
< ul class = "org-ul" >
< li > < code > freq_frf< / code > the frequency vector in Hz< / li >
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< li > Computed frequency response functions (see table < a href = "#org2cde1ca" > 2< / a > )< / li >
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< / ul > < / li >
< li > < code > id31_microstation_2017_11_17_coh.mat< / code >
< ul class = "org-ul" >
< li > Computed coherence< / li >
< / ul > < / li >
< / ul >
< p >
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For each of the measurement, the measured channels are shown on table < a href = "#org6601586" > 3< / a > .
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< / p >
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< table id = "org2cde1ca" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 2:< / span > Description of the location of direction of the excitation for each measurement< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Object name< / th >
< th scope = "col" class = "org-left" > Location< / th >
< th scope = "col" class = "org-left" > Direction< / th >
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< / thead >
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< tr >
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< td class = "org-left" > frf_hexa_x< / td >
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< td class = "org-left" > Hexapod< / td >
< td class = "org-left" > X< / td >
< / tr >
< tr >
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< td class = "org-left" > frf_hexa_y< / td >
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< td class = "org-left" > Hexapod< / td >
< td class = "org-left" > Y< / td >
< / tr >
< tr >
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< td class = "org-left" > frf_hexa_z< / td >
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< td class = "org-left" > Hexapod< / td >
< td class = "org-left" > Z< / td >
< / tr >
< tr >
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< td class = "org-left" > frf_marble_x< / td >
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< td class = "org-left" > Marble< / td >
< td class = "org-left" > X< / td >
< / tr >
< tr >
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< td class = "org-left" > frf_marble_y< / td >
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< td class = "org-left" > Marble< / td >
< td class = "org-left" > Y< / td >
< / tr >
< tr >
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< td class = "org-left" > frf_marble_z< / td >
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< td class = "org-left" > Marble< / td >
< td class = "org-left" > Z< / td >
< / tr >
< / tbody >
< / table >
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< table id = "org6601586" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 3:< / span > Description of each measurement channel< / caption >
< colgroup >
< col class = "org-right" / >
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< col class = "org-left" / >
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< th scope = "col" class = "org-right" > Ch. nb< / th >
< th scope = "col" class = "org-left" > Element< / th >
< th scope = "col" class = "org-left" > Location< / th >
< th scope = "col" class = "org-left" > Direction< / th >
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< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Not wired< / td >
< td class = "org-left" > na< / td >
< td class = "org-left" > na< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Marble< / td >
< td class = "org-left" > X< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Marble< / td >
< td class = "org-left" > Y< / td >
< / tr >
< tr >
< td class = "org-right" > 4< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Marble< / td >
< td class = "org-left" > Z< / td >
< / tr >
< tr >
< td class = "org-right" > 5< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Ty< / td >
< td class = "org-left" > X< / td >
< / tr >
< tr >
< td class = "org-right" > 6< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Ty< / td >
< td class = "org-left" > Y< / td >
< / tr >
< tr >
< td class = "org-right" > 7< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Ty< / td >
< td class = "org-left" > Z< / td >
< / tr >
< tr >
< td class = "org-right" > 8< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Tilt< / td >
< td class = "org-left" > X< / td >
< / tr >
< tr >
< td class = "org-right" > 9< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Tilt< / td >
< td class = "org-left" > Y< / td >
< / tr >
< tr >
< td class = "org-right" > 10< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Tilt< / td >
< td class = "org-left" > Z< / td >
< / tr >
< tr >
< td class = "org-right" > 11< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Hexapod< / td >
< td class = "org-left" > X< / td >
< / tr >
< tr >
< td class = "org-right" > 12< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Hexapod< / td >
< td class = "org-left" > Y< / td >
< / tr >
< tr >
< td class = "org-right" > 13< / td >
< td class = "org-left" > Accelerometer< / td >
< td class = "org-left" > Hexapod< / td >
< td class = "org-left" > Z< / td >
< / tr >
< / tbody >
< / table >
< / div >
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< div id = "outline-container-orgc4e4e05" class = "outline-2" >
< h2 id = "orgc4e4e05" > < span class = "section-number-2" > 4< / span > Data Analysis< / h2 >
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< div class = "outline-text-2" id = "text-4" >
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< div id = "outline-container-org8e48582" class = "outline-3" >
< h3 id = "org8e48582" > < span class = "section-number-3" > 4.1< / span > Loading of the data< / h3 >
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< div class = "outline-text-3" id = "text-4-1" >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > load(< span class = "org-string" > './raw_data/id31_microstation_2017_11_17_coh.mat'< / span > ,...
< span class = "org-string" > 'coh_hexa_x'< / span > ,...
< span class = "org-string" > 'coh_hexa_y'< / span > ,...
< span class = "org-string" > 'coh_hexa_z'< / span > ,...
< span class = "org-string" > 'coh_marble_x'< / span > ,...
< span class = "org-string" > 'coh_marble_y'< / span > ,...
< span class = "org-string" > 'coh_marble_z'< / span > );
load(< span class = "org-string" > './raw_data/id31_microstation_2017_11_17_frf.mat'< / span > ,...
< span class = "org-string" > 'freq_frf'< / span > ,...
< span class = "org-string" > 'frf_hexa_x'< / span > ,...
< span class = "org-string" > 'frf_hexa_y'< / span > ,...
< span class = "org-string" > 'frf_hexa_z'< / span > ,...
< span class = "org-string" > 'frf_marble_x'< / span > ,...
< span class = "org-string" > 'frf_marble_y'< / span > ,...
< span class = "org-string" > 'frf_marble_z'< / span > );
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< / pre >
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< div id = "outline-container-orgdef23af" class = "outline-3" >
< h3 id = "orgdef23af" > < span class = "section-number-3" > 4.2< / span > Pre-processing of the data< / h3 >
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< div class = "outline-text-3" id = "text-4-2" >
< p >
The FRF data are scaled with the sensitivity of the accelerometer and integrated two times to have the displacement instead of the acceleration.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > accel_sensitivity = 0.102; < span class = "org-comment" > % [V/(m/s2)]< / span >
w = < span class = "org-constant" > j< / span > < span class = "org-type" > *< / span > 2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > freq_frf; < span class = "org-comment" > % j.omega in [rad/s]< / span >
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frf_hexa_x = 1< span class = "org-type" > /< / span > accel_sensitivity< span class = "org-type" > *< / span > frf_hexa_x< span class = "org-type" > ./< / span > (w< span class = "org-type" > .^< / span > 2);
frf_hexa_y = < span class = "org-type" > -< / span > 1< span class = "org-type" > /< / span > accel_sensitivity< span class = "org-type" > *< / span > frf_hexa_y< span class = "org-type" > ./< / span > (w< span class = "org-type" > .^< / span > 2);
frf_hexa_z = < span class = "org-type" > -< / span > 1< span class = "org-type" > /< / span > accel_sensitivity< span class = "org-type" > *< / span > frf_hexa_z< span class = "org-type" > ./< / span > (w< span class = "org-type" > .^< / span > 2);
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frf_marble_x = 1< span class = "org-type" > /< / span > accel_sensitivity< span class = "org-type" > *< / span > frf_marble_x< span class = "org-type" > ./< / span > (w< span class = "org-type" > .^< / span > 2);
frf_marble_y = 1< span class = "org-type" > /< / span > accel_sensitivity< span class = "org-type" > *< / span > frf_marble_y< span class = "org-type" > ./< / span > (w< span class = "org-type" > .^< / span > 2);
frf_marble_z = < span class = "org-type" > -< / span > 1< span class = "org-type" > /< / span > accel_sensitivity< span class = "org-type" > *< / span > frf_marble_z< span class = "org-type" > ./< / span > (w< span class = "org-type" > .^< / span > 2);
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org9329022" class = "outline-3" >
< h3 id = "org9329022" > < span class = "section-number-3" > 4.3< / span > X-direction FRF< / h3 >
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< div class = "outline-text-3" id = "text-4-3" >
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< div id = "orgc62d27f" class = "figure" >
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< p > < img src = "figs/marble_x_frf.png" alt = "marble_x_frf.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Response to a force applied on the marble in the X direction< / p >
< / div >
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< div id = "org6bfc7a4" class = "figure" >
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< p > < img src = "figs/hexa_x_frf.png" alt = "hexa_x_frf.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Response to a force applied on the hexa in the X direction< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgf143ff0" class = "outline-3" >
< h3 id = "orgf143ff0" > < span class = "section-number-3" > 4.4< / span > Y-direction FRF< / h3 >
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< div class = "outline-text-3" id = "text-4-4" >
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< div id = "org1460e50" class = "figure" >
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< p > < img src = "figs/marble_y_frf.png" alt = "marble_y_frf.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Response to a force applied on the marble in the Y direction< / p >
< / div >
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< div id = "org50bc3da" class = "figure" >
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< p > < img src = "figs/hexa_y_frf.png" alt = "hexa_y_frf.png" / >
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< p > < span class = "figure-number" > Figure 6: < / span > Response to a force applied on the hexa in the Y direction< / p >
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< div id = "outline-container-org69dd2ae" class = "outline-3" >
< h3 id = "org69dd2ae" > < span class = "section-number-3" > 4.5< / span > Z-direction FRF< / h3 >
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< div class = "outline-text-3" id = "text-4-5" >
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< div id = "orga24d122" class = "figure" >
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< p > < img src = "figs/marble_z_frf.png" alt = "marble_z_frf.png" / >
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< p > < span class = "figure-number" > Figure 7: < / span > Response to a force applied on the marble in the Z direction< / p >
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< div id = "orge608125" class = "figure" >
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< p > < img src = "figs/hexa_z_frf.png" alt = "hexa_z_frf.png" / >
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< p > < span class = "figure-number" > Figure 8: < / span > Response to a force applied on the hexa in the Z direction< / p >
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< div id = "outline-container-orgdfa9254" class = "outline-2" >
< h2 id = "orgdfa9254" > < span class = "section-number-2" > 5< / span > Results< / h2 >
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< div class = "outline-text-2" id = "text-5" >
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< div class = "important" id = "orgbd89935" >
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< li > Resonances have been identified at 45Hz and 75Hz< / li >
< li > However, the quality of the measurements are bad at low frequency< / li >
< li > New measurements should be done with Geophones< / li >
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< div id = "postamble" class = "status" >
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< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2020-11-12 jeu. 10:26< / p >
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