On Systematic Errors of Two-Dimensional Finite Element Modeling of Right Circular Planar Flexure Hinges

[+] Author and Article Information
B. Zettl, W. Szyszkowski, W. J. Zhang

Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, S7N A9V, Canada

J. Mech. Des 127(4), 782-787 (Sep 17, 2004) (6 pages) doi:10.1115/1.1898341 History: Received April 22, 2004; Revised September 17, 2004

This paper discusses the finite element method (FEM) based modeling of the behavior of typical right circular flexure hinges used in planar compliant mechanisms. Such hinges have traditionally been approximated either by simple beams in the analytical approach or very often by two-dimensional (2D) plane stress elements when using the FEM. The three-dimensional (3D) analysis presented examines these approximations, focusing on systematic errors due to 2D modeling. It is shown that the 2D models provide only the lower (assuming the plane stress state) or the upper (assuming the plane strain state) limits of the hinge’s stiffness. The error of modeling a particular hinge by 2D elements (with either the plane stress or the plane strain assumptions) depends mainly on its depth-to-height ratio and may reach up to about 12%. However, this error becomes negligible for hinges with sufficiently high or sufficiently low depth-to-height ratios, in which either the plane strain or stress states dominate respectively. It is also shown that the computationally intensive 3D elements can be replaced, without sacrificing accuracy, by numerically efficient 2D elements if the material properties are appropriately manipulated.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 5

Contours of stress σz, from no-stress (light) to high-stress (dark)

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Figure 6

(a) Stresses along path AB. (b) Strains along path AB.

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Figure 7

Stress in y direction along path OA and BC

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Figure 8

Deflection along hinge length

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Figure 9

Deformation of the xz-plane hinge center during bending

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Figure 10

Rotational stiffness as a function of b∕t ratio

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Figure 1

Piezoactuated compliant mechanism

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Figure 2

Right circular hinge used in finite element study

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Figure 3

3D finite element hinge model

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Figure 4

2D finite element model of hinge

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Figure 11

Percent errors of plane states as a function of b∕t ratio



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