Research Papers

Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges

[+] Author and Article Information
Guimin Chen

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an, Shaanxi 710071, China
e-mail: guimin.chen@gmail.com

Jialu Wang, Xiaoyuan Liu

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an, Shaanxi 710071, China

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 18, 2013; final manuscript received December 12, 2013; published online January 20, 2014. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 136(3), 031009 (Jan 20, 2014) (8 pages) Paper No: MD-13-1266; doi: 10.1115/1.4026265 History: Received June 18, 2013; Revised December 12, 2013

The flexure hinges are the most vulnerable parts in a flexure-based mechanism due to their smaller dimensions and stress concentration characteristics, therefore evaluating the maximum stresses generated in them is crucial for assessing the workspace and the fatigue life of the mechanism. Stress concentration factors characterize the stress concentrations in flexure hinges, providing an analytical and efficient way to evaluate the maximum stress. In this work, by using the ratio of the radius of curvature of the stress-concentrating feature to the minimum thickness as the only fitting variable, generalized equations for both the bending and tension stress concentration factors were obtained for two generalized models, the conic model and the elliptic-arc-fillet model, through fitting the finite element results. The equations are applicable to commonly used flexure hinges including circular, elliptic, parabolic, hyperbolic, and various corner-fillet flexure hinges, with acceptable errors. The empirical equations are tractable and easy to be employed in the design and optimization of flexure-based mechanisms. The case studies of the bridge-type displacement amplifiers demonstrated the effectiveness of the generalized equations for predicting the maximum stresses in flexure-based mechanisms.

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Fig. 1

Schematics of a conic flexure hinge and an elliptical-arc-fillet flexure hinge (with the positive directions for the loads shown according to the sign convention in Ref. [26]). For the conic flexure hinge, the cutout depth d is equivalent to parameter c in Ref. [14].

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Fig. 2

A conic cutout and its polar coordinates

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Fig. 3

Finite element model of a conic flexure design

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Fig. 4

Tension stress concentration factor for conic flexure hinges

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Fig. 5

Bending stress concentration factor for conic flexure hinges

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Fig. 6

An ellipse and the eccentric angle φ

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Fig. 7

Finite element model of a elliptic-arc-fillet flexure design

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Fig. 8

Tension stress concentration factor for elliptic-arc-fillet flexure hinges

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Fig. 9

Bending stress concentration factor for elliptic-arc-fillet flexure hinges

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Fig. 10

A bridge-type displacement amplifier

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Fig. 11

Contour plot of the stress distribution in the displacement amplifier using conic flexure hinges predicted by ANSYS

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Fig. 12

Contour plot of the stress distribution in the displacement amplifier using elliptic-arc-fillet flexure hinges predicted by ANSYS



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