Research Papers

Optimum Design of a Compliant Uniaxial Accelerometer

[+] Author and Article Information
Simon Desrochers

 Dassault Systèmes Inc., 393 Saint-Jacques Street, Montreal, QC, H2Y 1N9, Canadasimon.desrochers@3ds.com

Damiano Pasini

Department of Mechanical Engineering, McGill University, 3480 University Street, Montreal, QC, H3A 2A7, Canadadamiano.pasini@mcgill.ca

Jorge Angeles

Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canadaangeles@cim.mcgill.ca

In mathematical programming, a simplex is a polyhedron with the minimum number of vertices embedded in Rn(17).

Elastic isotropy in a plane means that the stiffness matrix of the structure at hand has two identical eigenvalues, as this matrix is symmetric. This means, in turn, that any vector in the same plane is an eigenvector of the stiffness matrix of the structure in all directions of the plane.

Recall that an antisymmetry condition applies when the geometry and load are symmetric and antisymmetric, respectively, with respect to an axis.

J. Mech. Des 132(4), 041011 (Apr 22, 2010) (8 pages) doi:10.1115/1.4001002 History: Received January 24, 2009; Revised December 19, 2009; Published April 22, 2010; Online April 22, 2010

This work focuses on the multi-objective optimization of a compliant-mechanism accelerometer. The design objective is to maximize the sensitivity of the accelerometer in its sensing direction, while minimizing its sensitivity in all other directions. In addition, this work proposes a novel compliant hinge intended to reduce the stress concentration in compliant mechanisms. The paper starts with a brief description of the new compliant hinge, the Lamé-shaped hinge, followed by the formulation of the aposteriori multi-objective optimization of the compliant accelerometer. By using the normalized constrained method, an even distribution of the Pareto frontier is found. The paper also provides several optimum solutions on a Pareto plot, as well as the CAD model of the selected solution.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Mass-spring system of an accelerometer

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Figure 2

Frequency response

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Figure 3

The simplicial 2 ΠΠ uniaxial accelerometer: (a) top view; (b) front view

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Figure 4

Cross-configuration mechanism

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Figure 5

Deformation along the sensitive axis

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Figure 6

Corner-filleted hinge

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Figure 7

Lamé curves for η=3

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Figure 8

Lamé curves of Eq. 3

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Figure 10

Structural model

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Figure 11

Pareto frontier

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Figure 12

Normalized Pareto frontier

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Figure 13

Pareto frontier

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Figure 15

Optimum accelerometer

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Figure 14

von Mises stress distribution

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Figure 9

Lamé curves polar coordinate for η=4




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