40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop | ||||||||||

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Below are revised design parameters for the Stewart platform based on ground motion measurements. The goal is that the actuators should be able to exceed ground motion by a healthy factor (say, two decades in amplitude) across a range from about .1 Hz to 500 Hz. I would like to stitch together data from at least two seismometers, an accelerometer, and (if one is available) a microphone, but since today this week I was only able to retrieve data from one of the Guralps, I will use just that for now. The spectra below, spanning GPS times 1010311450--1010321450, show the Outside this band of interest, I chose the velocity requirement based on practical considerations. At high frequencies, the force requirement should go to zero, so the velocity requirement should go as The figure below shows the velocity spectrum extended to DC and infinite frequency using these considerations, and the derived acceleration and displacement requirements. As a starting point for the design of the platform and the selection of the actuators, let's assume a payload of ~12 kg. Let's multiply this by 1.5 as a guess for the additional mass of the top platform itself, to make 18 kg. For the acceleration, let's take the maximum value at any frequency for the acceleration requirement, ~6x10 (12)(1.5)(6x10 Next, the torque requirement. According to <http://www.iris.edu/hq/instrumentation_meeting/files/pdfs/rotation_iris_igel.pdf>, for a plane shear wave traveling in a medium with phase velocity c, the acceleration a(x, t) is related to the angular rate W'(x, t) through a(x, t) / W'(x, t) = -2 c. This implies that |W''(f)| = |a(f)| pi f / c, where W''(f) is the amplitude spectral density of the angular acceleration and a(f) of the transverse linear acceleration. I assume that the medium is cement, which according to Wolfram Alpha has a shear modulus of mu = 2.2 GPa and about the density of water: rho ~ 1000 kg/m The maximum of the acceleration requirement graph is, again, 6x10 (0.26) (1.5) (6x10 The quotient of the torque and force requirements is about 0.25 m, so, using some of my previous results, the dimensions of the platform should be as follows: radius of top plate = 0.25 m, radius of bottom plate = 2 * 0.25 m = 0.5 m, and plate separation in home position = sqrt(3) * 0.25 m = 0.43 m.
One last thing: perhaps the static load should be taken up directly by the piezos. If this is the case, then we might rather take the force requirement as being (10 m/s An actuator that can exert a |