Rework hexapod specifications + static deflection
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@ -2027,22 +2027,52 @@ The simulation is considered to be fairly realistic as the model used has been s
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* General Conclusion and Further notes
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* General Conclusion and Further notes
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<<sec:conclusion_and_further_notes>>
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<<sec:conclusion_and_further_notes>>
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** Introduction :ignore:
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** Nano-Hexapod Specifications
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** Nano-Hexapod Specifications
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Table summarizing the nano-hexapod wanted characteristics:
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<<sec:nano_hexapod_specifications>>
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*** Introduction :ignore:
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In this section are gathered all the specifications related to the nano-hexapod.
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*** Dimensions
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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The wanted dimension of the nano-hexapod are shown in Figure [[fig:nano_hexapod_size]]:
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- Diameter of the bottom platform: 300mm
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- Diameter of the top platform: 200mm
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- Maximum Height: 90mm
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#+name: fig:nano_hexapod_size
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#+caption: First implementation of the nano-hexapod / metrology reflector and sample interface
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[[file:figs/nano_hexapod_size.png]]
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*** Flexible Joints
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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Flexible joints are located at each end of the six struts.
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These flexible joints should have the following properties:
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- High Axial Stiffness: $K_a > 10^7\,[N/m]$
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- Small Bending Stiffness: $K_b < 50\,[Nm/rad]$
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- Small Torsion Stiffness: $K_t < 50\,[Nm/rad]$
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The required angular stroke has not been estimated in this study.
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It is however simple to do so as the angular motion of each joint can easily be measured in the multi-body model used to perform the simulations.
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Typical angular stroke for such flexible joints is expected.
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*** Actuators
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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The actuation part is probably the most important part of the Stewart platform.
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- Dimensions (Figure [[fig:nano_hexapod_size]]):
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- Maximum Height: 90mm
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- Diameter of the bottom platform: 300mm
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- Diameter of the top platform: 200mm
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- Stiffness:
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- Stiffness:
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- Resonances should stay between 5Hz and 50Hz for payload masses up to 50kg
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- Resonances should stay between 5Hz and 50Hz for payload masses up to 50kg
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- This corresponds to strut stiffnesses of $k \approx 10^5 - 10^6\,[N/m]$
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- This corresponds to strut stiffnesses of $k \approx 10^5 - 10^6\,[N/m]$
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- Flexible joints:
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- Axial Stiffness: $K_a > 10^7\,[N/m]$
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- Bending Stiffness: $K_b < 50\,[Nm/rad]$
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- Torsion Stiffness: $K_t < 50\,[Nm/rad]$
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- Required angular stroke: can be estimated with simulations
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- Force:
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- Force:
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- Weight: $60\,kg \rightarrow 600\,N \rightarrow 60\,N$ on each actuator
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- Weight: $60\,kg \rightarrow 600\,N \rightarrow 60\,N$ on each actuator
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- Dynamic: few Newtons
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- Dynamic: few Newtons
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@ -2054,12 +2084,60 @@ Table summarizing the nano-hexapod wanted characteristics:
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This is probably more difficult to obtain.
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This is probably more difficult to obtain.
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However, by limiting the acceleration of these stages, we may limit the dynamic tracking errors to acceptable levels
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However, by limiting the acceleration of these stages, we may limit the dynamic tracking errors to acceptable levels
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- If the chosen technology allows $\pm 50 \mu m$ that would be safer
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- If the chosen technology allows $\pm 50 \mu m$ that would be safer
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- Sensors to be included:
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-
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#+name: fig:nano_hexapod_size
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*** Sensors
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#+caption: First implementation of the nano-hexapod / metrology reflector and sample interface
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:PROPERTIES:
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[[file:figs/nano_hexapod_size.png]]
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:UNNUMBERED: t
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:END:
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A relative displacement sensor must be included in each of the nano-hexapod's legs as explained in Section [[sec:robust_control_architecture]].
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The sensors must as the following properties:
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- High bandwidth $> 1\,[kHz]$
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- Fine resolution $< 10\,[nm]$
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- Range of $> 100\,[\mu m]$
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Note that the sensor signal will have to pass through the Slip-Ring.
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This adds few constrains:
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- The sensor signal must be immune to some "electrical noise" that could be induced by the slip-ring
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- Limited number of slip-ring channels should be required for the six sensors
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Several sensor technology could be used for the nano-hexapod.
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Characteristics of those sensors are shown in Table [[tab:characteristics_relative_sensor]].
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#+name: tab:characteristics_relative_sensor
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#+caption: Characteristics of relative measurement sensors cite:collette11_review
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| Technology | Frequency | Resolution | Range | T Range |
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|----------------+------------+----------------+--------------+-------------|
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| LVDT | DC-200 Hz | 10 nm rms | 1-10 mm | -50,100 °C |
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| Eddy current | 5 kHz | 0.1-100 nm rms | 0.5-55 mm | -50,100 °C |
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| Capacitive | DC-100 kHz | 0.05-50 nm rms | 50 nm - 1 cm | -40,100 °C |
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| Interferometer | 300 kHz | 0.1 nm rms | 10 cm | -250,100 °C |
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| Encoder | DC-1 MHz | 1 nm rms | 7-27 mm | 0,40 °C |
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*** Architecture
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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** Problem of Static Deflection?
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Let's now consider the problem of static deflection when changing the payload.
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The maximum payload's mass is $50\,[kg]$, this corresponds to an added vertical force of $\approx 500\,[N]$.
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If this is to be compensated by the nano-hexapod, $\approx 100\,[N]$ should be applied by each of the nano-hexapod's actuators.
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In such case, the nano-hexapod keeps its nominal configuration.
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In practice, this could be done using the relative motion sensor included in each leg, and a feedback control keeping the legs displacements at the wanted value.
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This might not be a problem is piezoelectric stacks are used, but it is a big issue is voice coils are used.
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An alternative would be to accept that the nano-hexapod experiences some static deflection.
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With a vertical nano-hexapod stiffness $\approx 10^6\,[N/m]$, the maximum static deflection would be:
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\[ k_z \approx 10^6\,[N/m] \longrightarrow \Delta z = \frac{\Delta m g}{k_z} \approx 0.5\,[mm] \]
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This will change a little bit the architecture of the nano-hexapod but this should be too small to change significantly the dynamics.
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** Sensor Noise introduced by the Metrology
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** Sensor Noise introduced by the Metrology
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Say that is will introduce noise inside the bandwidth (100Hz)
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Say that is will introduce noise inside the bandwidth (100Hz)
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7
ref.bib
7
ref.bib
@ -63,3 +63,10 @@
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doi = {10.1016/j.jsv.2006.07.050},
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doi = {10.1016/j.jsv.2006.07.050},
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url = {https://doi.org/10.1016/j.jsv.2006.07.050},
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url = {https://doi.org/10.1016/j.jsv.2006.07.050},
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}
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}
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@techreport{collette11_review,
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author = {Collette, C and Artoos, K and Guinchard, M and Janssens, S and Carmona Fernandez, P and Hauviller, C},
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institution = {cern},
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title = {Review of sensors for low frequency seismic vibration measurement},
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year = {2011},
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}
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