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Thomas Dehaeze 2025-02-04 15:40:27 +01:00
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@ -415,14 +415,14 @@ The "controlled" DoF of each stage (for instance the $D_y$ direction for the tra
The translation stage is used to position and scan the sample laterally with respect to the X-ray beam. The translation stage is used to position and scan the sample laterally with respect to the X-ray beam.
A linear motor was first used to enable fast and accurate scans. A linear motor was first used to enable fast and accurate scans.
It was later replaced with a stepper motor and lead-screw, as the feedback control used for the linear motor was unreliable[fn:12]. It was later replaced with a stepper motor and lead-screw, as the feedback control used for the linear motor was unreliable[fn:ustation_12].
An optical linear encoder is used to measure the stage motion and for controlling the position. An optical linear encoder is used to measure the stage motion and for controlling the position.
Four cylindrical bearings[fn:4] are used to guide the motion (i.e. minimize the parasitic motions) and have high stiffness. Four cylindrical bearings[fn:ustation_4] are used to guide the motion (i.e. minimize the parasitic motions) and have high stiffness.
**** Tilt Stage **** Tilt Stage
The tilt stage is guided by four linear motion guides[fn:1] which are placed such that the center of rotation coincide with the X-ray beam. The tilt stage is guided by four linear motion guides[fn:ustation_1] which are placed such that the center of rotation coincide with the X-ray beam.
Each linear guide is very stiff in radial directions such that the only DoF with low stiffness is in $R_y$. Each linear guide is very stiff in radial directions such that the only DoF with low stiffness is in $R_y$.
This stage is mainly used in /reflectivity/ experiments where the sample $R_y$ angle is scanned. This stage is mainly used in /reflectivity/ experiments where the sample $R_y$ angle is scanned.
@ -449,13 +449,13 @@ To precisely control the $R_y$ angle, a stepper motor and two optical encoders a
**** Spindle **** Spindle
Then, a rotation stage is used for tomography experiments. Then, a rotation stage is used for tomography experiments.
It is composed of an air bearing spindle[fn:2], whose angular position is controlled with a 3 phase synchronous motor based on the reading of 4 optical encoders. It is composed of an air bearing spindle[fn:ustation_2], whose angular position is controlled with a 3 phase synchronous motor based on the reading of 4 optical encoders.
Additional rotary unions and slip-rings are used to be able to pass electrical signals, fluids and gazes through the rotation stage. Additional rotary unions and slip-rings are used to be able to pass electrical signals, fluids and gazes through the rotation stage.
**** Micro-Hexapod **** Micro-Hexapod
Finally, a Stewart platform[fn:3] is used to position the sample. Finally, a Stewart platform[fn:ustation_3] is used to position the sample.
It includes a DC motor and an optical linear encoders in each of the six struts. It includes a DC motor and an optical linear encoders in each of the six struts.
This stage is used to position the point of interest of the sample with respect to the spindle rotation axis. This stage is used to position the point of interest of the sample with respect to the spindle rotation axis.
@ -481,7 +481,7 @@ It can also be used to precisely position the PoI vertically with respect to the
<<ssec:ustation_motion_description>> <<ssec:ustation_motion_description>>
**** Introduction :ignore: **** Introduction :ignore:
In this section, mathematical tools[fn:6] that are used to describe the motion of positioning stages are introduced. In this section, mathematical tools[fn:ustation_6] that are used to describe the motion of positioning stages are introduced.
First, the tools to describe the pose of a solid body (i.e. it's position and orientation) are introduced. First, the tools to describe the pose of a solid body (i.e. it's position and orientation) are introduced.
The motion induced by a positioning stage is described by transformation matrices. The motion induced by a positioning stage is described by transformation matrices.
@ -558,7 +558,7 @@ For rotations along $x$, $y$ or $z$ axis, the formulas of the corresponding rota
\end{subequations} \end{subequations}
Sometimes, it is useful to express a rotation as a combination of three rotations described by $\bm{R}_x$, $\bm{R}_y$ and $\bm{R}_z$. Sometimes, it is useful to express a rotation as a combination of three rotations described by $\bm{R}_x$, $\bm{R}_y$ and $\bm{R}_z$.
The order of rotation is very important[fn:5], therefore, in this study, rotations are expressed as three successive rotations about the coordinate axes of the moving frame eqref:eq:ustation_rotation_combination. The order of rotation is very important[fn:ustation_5], therefore, in this study, rotations are expressed as three successive rotations about the coordinate axes of the moving frame eqref:eq:ustation_rotation_combination.
\begin{equation}\label{eq:ustation_rotation_combination} \begin{equation}\label{eq:ustation_rotation_combination}
{}^A\bm{R}_B(\alpha, \beta, \gamma) = \bm{R}_u(\alpha) \bm{R}_v(\beta) \bm{R}_c(\gamma) {}^A\bm{R}_B(\alpha, \beta, \gamma) = \bm{R}_u(\alpha) \bm{R}_v(\beta) \bm{R}_c(\gamma)
@ -1398,7 +1398,7 @@ Therefore, from a control perspective, they are not important.
**** Ground Motion **** Ground Motion
The ground motion was measured by using a sensitive 3-axis geophone[fn:11] placed on the ground. The ground motion was measured by using a sensitive 3-axis geophone[fn:ustation_11] placed on the ground.
The generated voltages were recorded with a high resolution DAC, and converted to displacement using the Geophone sensitivity transfer function. The generated voltages were recorded with a high resolution DAC, and converted to displacement using the Geophone sensitivity transfer function.
The obtained ground motion displacement is shown in Figure ref:fig:ustation_ground_disturbance. The obtained ground motion displacement is shown in Figure ref:fig:ustation_ground_disturbance.
@ -1466,7 +1466,7 @@ exportFig('figs/ustation_ground_disturbance.pdf', 'width', 'half', 'height', 450
**** Ty Stage **** Ty Stage
To measure the positioning errors of the translation stage, the setup shown in Figure ref:fig:ustation_errors_ty_setup is used. To measure the positioning errors of the translation stage, the setup shown in Figure ref:fig:ustation_errors_ty_setup is used.
A special optical element (called a "straightness interferometer"[fn:9]) is fixed on top of the micro-station, while a laser source[fn:10] and a straightness reflector are fixed on the ground. A special optical element (called a "straightness interferometer"[fn:ustation_9]) is fixed on top of the micro-station, while a laser source[fn:ustation_10] and a straightness reflector are fixed on the ground.
A similar setup was used to measure the horizontal deviation (i.e. in the $x$ direction), as well as the pitch and yaw errors of the translation stage. A similar setup was used to measure the horizontal deviation (i.e. in the $x$ direction), as well as the pitch and yaw errors of the translation stage.
#+name: fig:ustation_errors_ty_setup #+name: fig:ustation_errors_ty_setup
@ -1564,9 +1564,9 @@ pxx_dy_dx = pxx_dy_dz;
**** Spindle **** Spindle
To measure the positioning errors induced by the Spindle, a "Spindle error analyzer"[fn:7] is used as shown in Figure ref:fig:ustation_rz_meas_lion_setup. To measure the positioning errors induced by the Spindle, a "Spindle error analyzer"[fn:ustation_7] is used as shown in Figure ref:fig:ustation_rz_meas_lion_setup.
A specific target is fixed on top of the micro-station, which consists of two sphere with 1 inch diameter precisely aligned with the spindle rotation axis. A specific target is fixed on top of the micro-station, which consists of two sphere with 1 inch diameter precisely aligned with the spindle rotation axis.
Five capacitive sensors[fn:8] are pointing at the two spheres, as shown in Figure ref:fig:ustation_rz_meas_lion_zoom. Five capacitive sensors[fn:ustation_8] are pointing at the two spheres, as shown in Figure ref:fig:ustation_rz_meas_lion_zoom.
From the 5 measured displacements $[d_1,\,d_2,\,d_3,\,d_4,\,d_5]$, the translations and rotations $[D_x,\,D_y,\,D_z,\,R_x,\,R_y]$ of the target can be estimated. From the 5 measured displacements $[d_1,\,d_2,\,d_3,\,d_4,\,d_5]$, the translations and rotations $[D_x,\,D_y,\,D_z,\,R_x,\,R_y]$ of the target can be estimated.
#+name: fig:ustation_rz_meas_lion_setup #+name: fig:ustation_rz_meas_lion_setup
@ -2274,7 +2274,7 @@ exportFig('figs/ustation_errors_model_dy_vertical.pdf', 'width', 'half', 'height
:PROPERTIES: :PROPERTIES:
:UNNUMBERED: t :UNNUMBERED: t
:END: :END:
<<sec:uniaxial_conclusion>> <<sec:ustation_conclusion>>
In this study, a multi-body model of the micro-station was developed. In this study, a multi-body model of the micro-station was developed.
It was difficult to match the measured dynamics obtained from the modal analysis of the micro-station. It was difficult to match the measured dynamics obtained from the modal analysis of the micro-station.
@ -4664,15 +4664,15 @@ Otherwise, when the limbs' lengths derived yield complex numbers, then the posit
* Footnotes * Footnotes
[fn:12]It was probably caused by rust of the linear guides along its stroke. [fn:ustation_12]It was probably caused by rust of the linear guides along its stroke.
[fn:11]A 3-Axis L4C geophone manufactured Sercel was used. [fn:ustation_11]A 3-Axis L4C geophone manufactured Sercel was used.
[fn:10]Laser source is manufactured by Agilent (5519b). [fn:ustation_10]Laser source is manufactured by Agilent (5519b).
[fn:9]The special optics (straightness interferometer and reflector) are manufactured by Agilent (10774A). [fn:ustation_9]The special optics (straightness interferometer and reflector) are manufactured by Agilent (10774A).
[fn:8]C8 capacitive sensors and CPL290 capacitive driver electronics from Lion Precision. [fn:ustation_8]C8 capacitive sensors and CPL290 capacitive driver electronics from Lion Precision.
[fn:7]The Spindle Error Analyzer is made by Lion Precision. [fn:ustation_7]The Spindle Error Analyzer is made by Lion Precision.
[fn:6]The tools presented here are largely taken from [[cite:&taghirad13_paral]]. [fn:ustation_6]The tools presented here are largely taken from [[cite:&taghirad13_paral]].
[fn:5]Rotations are non commutative in 3D. [fn:ustation_5]Rotations are non commutative in 3D.
[fn:4]Ball cage (N501) and guide bush (N550) from Mahr are used. [fn:ustation_4]Ball cage (N501) and guide bush (N550) from Mahr are used.
[fn:3]Modified Zonda Hexapod by Symetrie. [fn:ustation_3]Modified Zonda Hexapod by Symetrie.
[fn:2]Made by LAB Motion Systems. [fn:ustation_2]Made by LAB Motion Systems.
[fn:1]HCR 35 A C1, from THK. [fn:ustation_1]HCR 35 A C1, from THK.