From c3bd2046228bdb6480a183d4d0f3be2a43405a68 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Fri, 8 May 2020 16:31:43 +0200 Subject: [PATCH] Rework hexapod specifications + static deflection --- index.org | 108 ++++++++++++++++++++++++++++++++++++++++++++++-------- ref.bib | 7 ++++ 2 files changed, 100 insertions(+), 15 deletions(-) diff --git a/index.org b/index.org index 0c6afcb..7de4b77 100644 --- a/index.org +++ b/index.org @@ -2027,22 +2027,52 @@ The simulation is considered to be fairly realistic as the model used has been s * General Conclusion and Further notes <> +** Introduction :ignore: ** Nano-Hexapod Specifications -Table summarizing the nano-hexapod wanted characteristics: +<> +*** Introduction :ignore: +In this section are gathered all the specifications related to the nano-hexapod. + +*** Dimensions +:PROPERTIES: +:UNNUMBERED: t +:END: + +The wanted dimension of the nano-hexapod are shown in Figure [[fig:nano_hexapod_size]]: +- Diameter of the bottom platform: 300mm +- Diameter of the top platform: 200mm +- Maximum Height: 90mm + +#+name: fig:nano_hexapod_size +#+caption: First implementation of the nano-hexapod / metrology reflector and sample interface +[[file:figs/nano_hexapod_size.png]] + +*** Flexible Joints +:PROPERTIES: +:UNNUMBERED: t +:END: + +Flexible joints are located at each end of the six struts. +These flexible joints should have the following properties: +- High Axial Stiffness: $K_a > 10^7\,[N/m]$ +- Small Bending Stiffness: $K_b < 50\,[Nm/rad]$ +- Small Torsion Stiffness: $K_t < 50\,[Nm/rad]$ + +The required angular stroke has not been estimated in this study. +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. +Typical angular stroke for such flexible joints is expected. + +*** Actuators +:PROPERTIES: +:UNNUMBERED: t +:END: + +The actuation part is probably the most important part of the Stewart platform. -- Dimensions (Figure [[fig:nano_hexapod_size]]): - - Maximum Height: 90mm - - Diameter of the bottom platform: 300mm - - Diameter of the top platform: 200mm - Stiffness: - Resonances should stay between 5Hz and 50Hz for payload masses up to 50kg - This corresponds to strut stiffnesses of $k \approx 10^5 - 10^6\,[N/m]$ -- Flexible joints: - - Axial Stiffness: $K_a > 10^7\,[N/m]$ - - Bending Stiffness: $K_b < 50\,[Nm/rad]$ - - Torsion Stiffness: $K_t < 50\,[Nm/rad]$ - - Required angular stroke: can be estimated with simulations - Force: - Weight: $60\,kg \rightarrow 600\,N \rightarrow 60\,N$ on each actuator - Dynamic: few Newtons @@ -2054,12 +2084,60 @@ Table summarizing the nano-hexapod wanted characteristics: This is probably more difficult to obtain. However, by limiting the acceleration of these stages, we may limit the dynamic tracking errors to acceptable levels - If the chosen technology allows $\pm 50 \mu m$ that would be safer -- Sensors to be included: - - -#+name: fig:nano_hexapod_size -#+caption: First implementation of the nano-hexapod / metrology reflector and sample interface -[[file:figs/nano_hexapod_size.png]] +*** Sensors +:PROPERTIES: +:UNNUMBERED: t +:END: + +A relative displacement sensor must be included in each of the nano-hexapod's legs as explained in Section [[sec:robust_control_architecture]]. + +The sensors must as the following properties: +- High bandwidth $> 1\,[kHz]$ +- Fine resolution $< 10\,[nm]$ +- Range of $> 100\,[\mu m]$ + +Note that the sensor signal will have to pass through the Slip-Ring. +This adds few constrains: +- The sensor signal must be immune to some "electrical noise" that could be induced by the slip-ring +- Limited number of slip-ring channels should be required for the six sensors + +Several sensor technology could be used for the nano-hexapod. +Characteristics of those sensors are shown in Table [[tab:characteristics_relative_sensor]]. + +#+name: tab:characteristics_relative_sensor +#+caption: Characteristics of relative measurement sensors cite:collette11_review +| Technology | Frequency | Resolution | Range | T Range | +|----------------+------------+----------------+--------------+-------------| +| LVDT | DC-200 Hz | 10 nm rms | 1-10 mm | -50,100 °C | +| Eddy current | 5 kHz | 0.1-100 nm rms | 0.5-55 mm | -50,100 °C | +| Capacitive | DC-100 kHz | 0.05-50 nm rms | 50 nm - 1 cm | -40,100 °C | +| Interferometer | 300 kHz | 0.1 nm rms | 10 cm | -250,100 °C | +| Encoder | DC-1 MHz | 1 nm rms | 7-27 mm | 0,40 °C | + +*** Architecture +:PROPERTIES: +:UNNUMBERED: t +:END: + +** Problem of Static Deflection? +Let's now consider the problem of static deflection when changing the payload. + +The maximum payload's mass is $50\,[kg]$, this corresponds to an added vertical force of $\approx 500\,[N]$. + +If this is to be compensated by the nano-hexapod, $\approx 100\,[N]$ should be applied by each of the nano-hexapod's actuators. +In such case, the nano-hexapod keeps its nominal configuration. + +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. + +This might not be a problem is piezoelectric stacks are used, but it is a big issue is voice coils are used. + + +An alternative would be to accept that the nano-hexapod experiences some static deflection. + +With a vertical nano-hexapod stiffness $\approx 10^6\,[N/m]$, the maximum static deflection would be: +\[ k_z \approx 10^6\,[N/m] \longrightarrow \Delta z = \frac{\Delta m g}{k_z} \approx 0.5\,[mm] \] +This will change a little bit the architecture of the nano-hexapod but this should be too small to change significantly the dynamics. ** Sensor Noise introduced by the Metrology Say that is will introduce noise inside the bandwidth (100Hz) diff --git a/ref.bib b/ref.bib index 4c9bc14..73f8e4e 100644 --- a/ref.bib +++ b/ref.bib @@ -63,3 +63,10 @@ doi = {10.1016/j.jsv.2006.07.050}, url = {https://doi.org/10.1016/j.jsv.2006.07.050}, } + +@techreport{collette11_review, + author = {Collette, C and Artoos, K and Guinchard, M and Janssens, S and Carmona Fernandez, P and Hauviller, C}, + institution = {cern}, + title = {Review of sensors for low frequency seismic vibration measurement}, + year = {2011}, +}