Rename footnotes

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Thomas Dehaeze 2025-02-04 14:24:00 +01:00
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@ -297,7 +297,7 @@ Using this method, an axial stiffness of $70 N/\mu m$ is found to give good resu
* Introduction :ignore:
The Nano-Hexapod struts (shown in Figure ref:fig:test_struts_picture_strut) are composed of two flexible joints that are fixed at the two ends of the strut, one acrfull:apa[fn:5] and one optical encoder[fn:6].
The Nano-Hexapod struts (shown in Figure ref:fig:test_struts_picture_strut) are composed of two flexible joints that are fixed at the two ends of the strut, one acrfull:apa[fn:test_struts_5] and one optical encoder[fn:test_struts_6].
#+name: fig:test_struts_picture_strut
#+caption: One strut including two flexible joints, an amplified piezoelectric actuator and an encoder
@ -342,7 +342,7 @@ A mounting bench was developed to ensure:
A CAD view of the mounting bench is shown in Figure ref:fig:test_struts_mounting_bench_first_concept.
It consists of a "main frame" (Figure ref:fig:test_struts_mounting_step_0) precisely machined to ensure both correct strut length and strut coaxiality.
The coaxiality is ensured by good flatness (specified at $20\,\mu m$) between surfaces A and B and between surfaces C and D.
Such flatness was checked using a FARO arm[fn:1] (see Figure ref:fig:test_struts_check_dimensions_bench) and was found to comply with the requirements.
Such flatness was checked using a FARO arm[fn:test_struts_1] (see Figure ref:fig:test_struts_check_dimensions_bench) and was found to comply with the requirements.
The strut length (defined by the distance between the rotation points of the two flexible joints) was ensured by using precisely machined dowel holes.
@ -460,7 +460,7 @@ Thanks to this mounting procedure, the coaxiality and length between the two fle
:END:
<<sec:test_struts_flexible_modes>>
A Finite Element Model[fn:3] of the struts is developed and is used to estimate the flexible modes.
A Finite Element Model[fn:test_struts_3] of the struts is developed and is used to estimate the flexible modes.
The inertia of the encoder (estimated at $15\,g$) is considered.
The two cylindrical interfaces were fixed (boundary conditions), and the first three flexible modes were computed.
The mode shapes are displayed in Figure ref:fig:test_struts_mode_shapes: an "X-bending" mode at 189Hz, a "Y-bending" mode at 285Hz and a "Z-torsion" mode at 400Hz.
@ -509,7 +509,7 @@ The mode shapes are displayed in Figure ref:fig:test_struts_mode_shapes: an "X-b
<<m-init-other>>
#+end_src
To experimentally measure these mode shapes, a Laser vibrometer[fn:7] was used.
To experimentally measure these mode shapes, a Laser vibrometer[fn:test_struts_7] was used.
It measures the difference of motion between two beam path (red points in Figure ref:fig:test_struts_meas_modes).
The strut is then excited by an instrumented hammer, and the transfer function from the hammer to the measured rotation is computed.
@ -649,7 +649,7 @@ In order to measure the dynamics of the strut, the test bench used to measure th
The strut mounted on the bench is shown in Figure ref:fig:test_struts_bench_leg_overview
A schematic of the bench and the associated signals are shown in Figure ref:fig:test_struts_bench_schematic.
A fiber interferometer[fn:4] is used to measure the motion of the granite (i.e. the axial motion of the strut).
A fiber interferometer[fn:test_struts_4] is used to measure the motion of the granite (i.e. the axial motion of the strut).
#+name: fig:test_struts_bench_leg
#+caption: Experimental setup used to measure the dynamics of the struts.
@ -1573,7 +1573,7 @@ Therefore, large $y$ misalignments are expected.
To estimate the misalignments between the two flexible joints and the APA:
- the struts were fixed horizontally on the mounting bench, as shown in Figure ref:fig:test_struts_mounting_step_3 but without the encoder
- using a length gauge[fn:2], the height difference between the flexible joints surface and the APA shell surface was measured for both the top and bottom joints and for both sides
- using a length gauge[fn:test_struts_2], the height difference between the flexible joints surface and the APA shell surface was measured for both the top and bottom joints and for both sides
- as the thickness of the flexible joint is $21\,mm$ and the thickness of the APA shell is $20\,mm$, $0.5\,mm$ of height difference should be measured if the two are perfectly aligned
Large variations in the $y$ misalignment are found from one strut to the other (results are summarized in Table ref:tab:test_struts_meas_y_misalignment).
@ -2273,10 +2273,10 @@ actuator.cs = args.cs; % Damping of one stack [N/m]
* Footnotes
[fn:7] OFV-3001 controller and OFV512 sensor head from Polytec
[fn:6] Vionic from Renishaw
[fn:5] APA300ML from Cedrat Technologies
[fn:4] Two fiber intereferometers were used: an IDS3010 from Attocube and a quDIS from QuTools
[fn:3] Using Ansys\textsuperscript{\textregistered}. Flexible Joints and APA Shell are made of a stainless steel allow called /17-4 PH/. Encoder and ruler support material is aluminium.
[fn:2] Heidenhain MT25, specified accuracy of $\pm 0.5\,\mu m$
[fn:1] FARO Arm Platinum 4ft, specified accuracy of $\pm 13\mu m$
[fn:test_struts_7] OFV-3001 controller and OFV512 sensor head from Polytec
[fn:test_struts_6] Vionic from Renishaw
[fn:test_struts_5] APA300ML from Cedrat Technologies
[fn:test_struts_4] Two fiber intereferometers were used: an IDS3010 from Attocube and a quDIS from QuTools
[fn:test_struts_3] Using Ansys\textsuperscript{\textregistered}. Flexible Joints and APA Shell are made of a stainless steel allow called /17-4 PH/. Encoder and ruler support material is aluminium.
[fn:test_struts_2] Heidenhain MT25, specified accuracy of $\pm 0.5\,\mu m$
[fn:test_struts_1] FARO Arm Platinum 4ft, specified accuracy of $\pm 13\mu m$