Multistable Equilibrium System Design Methodology and Demonstration

[+] Author and Article Information
Carey King

Uni-Pixel Displays, Inc., Georgetown, TX 78628

Joseph J. Beaman, S. V. Sreenivasan, Matthew Campbell

Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712

J. Mech. Des 126(6), 1036-1046 (Feb 14, 2005) (11 pages) doi:10.1115/1.1799631 History: Received February 01, 2003; Revised March 01, 2004; Online February 14, 2005
Copyright © 2004 by ASME
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The three major design domains for MSE systems center on creating reliable, reconfigurable, and efficient designs with tailored impedances
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A Fabry–Perot pressure sensor with a nonlinear output/input characteristic can increase its range by designing its diaphragm with multiple stable stiffnesses
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Flow chart of design methodology for MSE systems
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The MSE example system consists of an array of stator magnets, an armature magnet, a rotating beam, and two springs
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For a given armature magnet position, the magnetic energy data is valid if the stator magnet is within the range shown by the hatched region
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(a) The desired local equilibrium curve fit parameters describe the local equilibrium positions. (b) Desired and actual quadratic curve fit approximations at the equilibrium points are used to evaluate the function.
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Experiment for obtaining Ft and Fn. For a fixed yrel,Ft is found for a given xrel. Likewise, for a fixed xrel,Fn is found for a given yrel. This data is used to calculate the magnetic potential energy change.
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A plot showing the constant yrel magnetic energy data curves used in the synthesis of the MSE positions for the example problem
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Evaluation of Eq. (16) using the finite element data produces the results plotted versus the relative x direction. There are two sets of five curves (dots and circles, respectively) that are equal when no error is present.
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The Monte Carlo mapping showing the most promising combinations of natural frequency and equilibrium position for the angular range of (0.0, 1.2). Note, due to the energy models and constraints, obtaining natural frequencies below 8 Hz and above 22 Hz seems highly unlikely.
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Monte Carlo mapping for case 2 problem
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The compliant beam shown in relaxed (solid) and bent (dashed) positions. The PRB angle and beam natural frequency were optimized.
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Monte Carlo mapping for the compliant beam. In the range of PRB angles up to 0.7 radians, the possible frequencies appear the same throughout.




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