Rename footnotes
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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
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* Introduction :ignore:
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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].
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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].
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#+name: fig:test_struts_picture_strut
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#+caption: One strut including two flexible joints, an amplified piezoelectric actuator and an encoder
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@ -342,7 +342,7 @@ A mounting bench was developed to ensure:
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A CAD view of the mounting bench is shown in Figure ref:fig:test_struts_mounting_bench_first_concept.
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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.
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The coaxiality is ensured by good flatness (specified at $20\,\mu m$) between surfaces A and B and between surfaces C and D.
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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.
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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.
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The strut length (defined by the distance between the rotation points of the two flexible joints) was ensured by using precisely machined dowel holes.
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@ -460,7 +460,7 @@ Thanks to this mounting procedure, the coaxiality and length between the two fle
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:END:
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<<sec:test_struts_flexible_modes>>
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A Finite Element Model[fn:3] of the struts is developed and is used to estimate the flexible modes.
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A Finite Element Model[fn:test_struts_3] of the struts is developed and is used to estimate the flexible modes.
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The inertia of the encoder (estimated at $15\,g$) is considered.
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The two cylindrical interfaces were fixed (boundary conditions), and the first three flexible modes were computed.
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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.
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@ -509,7 +509,7 @@ The mode shapes are displayed in Figure ref:fig:test_struts_mode_shapes: an "X-b
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<<m-init-other>>
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#+end_src
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To experimentally measure these mode shapes, a Laser vibrometer[fn:7] was used.
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To experimentally measure these mode shapes, a Laser vibrometer[fn:test_struts_7] was used.
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It measures the difference of motion between two beam path (red points in Figure ref:fig:test_struts_meas_modes).
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The strut is then excited by an instrumented hammer, and the transfer function from the hammer to the measured rotation is computed.
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@ -649,7 +649,7 @@ In order to measure the dynamics of the strut, the test bench used to measure th
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The strut mounted on the bench is shown in Figure ref:fig:test_struts_bench_leg_overview
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A schematic of the bench and the associated signals are shown in Figure ref:fig:test_struts_bench_schematic.
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A fiber interferometer[fn:4] is used to measure the motion of the granite (i.e. the axial motion of the strut).
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A fiber interferometer[fn:test_struts_4] is used to measure the motion of the granite (i.e. the axial motion of the strut).
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#+name: fig:test_struts_bench_leg
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#+caption: Experimental setup used to measure the dynamics of the struts.
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@ -1573,7 +1573,7 @@ Therefore, large $y$ misalignments are expected.
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To estimate the misalignments between the two flexible joints and the APA:
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- the struts were fixed horizontally on the mounting bench, as shown in Figure ref:fig:test_struts_mounting_step_3 but without the encoder
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- 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
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- 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
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- 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
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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).
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@ -2273,10 +2273,10 @@ actuator.cs = args.cs; % Damping of one stack [N/m]
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* Footnotes
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[fn:7] OFV-3001 controller and OFV512 sensor head from Polytec
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[fn:6] Vionic from Renishaw
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[fn:5] APA300ML from Cedrat Technologies
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[fn:4] Two fiber intereferometers were used: an IDS3010 from Attocube and a quDIS from QuTools
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[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.
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[fn:2] Heidenhain MT25, specified accuracy of $\pm 0.5\,\mu m$
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[fn:1] FARO Arm Platinum 4ft, specified accuracy of $\pm 13\mu m$
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[fn:test_struts_7] OFV-3001 controller and OFV512 sensor head from Polytec
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[fn:test_struts_6] Vionic from Renishaw
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[fn:test_struts_5] APA300ML from Cedrat Technologies
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[fn:test_struts_4] Two fiber intereferometers were used: an IDS3010 from Attocube and a quDIS from QuTools
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[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.
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[fn:test_struts_2] Heidenhain MT25, specified accuracy of $\pm 0.5\,\mu m$
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[fn:test_struts_1] FARO Arm Platinum 4ft, specified accuracy of $\pm 13\mu m$
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