0
Technical Briefs

Bistable Compliant Mechanisms: Corrected Finite Element Modeling for Stiffness Tuning and Preloading Incorporation

[+] Author and Article Information
A. G. Dunning1

Department of BioMechanical Engineering, Faculty of Mechanical Engineering,  Delft University of Technology, Delft 2628 CD, The Netherlandsa.g.dunning@tudelft.nl

N. Tolou

Department of BioMechanical Engineering, Faculty of Mechanical Engineering,  Delft University of Technology, Delft 2628 CD, The Netherlandsn.tolou@tudelft.nl

P. P. Pluimers

Department of BioMechanical Engineering, Faculty of Mechanical Engineering,  Delft University of Technology, Delft 2628 CD, The Netherlandsp.j.pluimers@student.tudelft.nl

L. F. Kluit

Department of BioMechanical Engineering, Faculty of Mechanical Engineering,  Delft University of Technology, Delft 2628 CD, The Netherlandsl.f.kluit@tudelft.nl

J. L. Herder

Department of BioMechanical Engineering, Faculty of Mechanical Engineering,  Delft University of Technology, Delft 2628 CD, The Netherlandsj.l.herder@tudelft.nl

1

Corresponding author.

J. Mech. Des 134(8), 084502 (Jul 10, 2012) (6 pages) doi:10.1115/1.4006961 History: Received November 28, 2011; Revised May 31, 2012; Published July 10, 2012; Online July 10, 2012

Bistable straight-guided buckling beams are essential mechanisms for precision engineering, compliant mechanisms, and MEMS. However, a straightforward and accurate numerical modeling have not been available. When preloading effects must be included, numerical modeling becomes an even more challenging problem. This article presents a straightforward numerical model for bistable straight-guided buckling beams, which includes preloading effects as well. Adjusting the bistable force–displacement characteristic by variation of design parameters and preloading is also investigated. Both lumped compliance and distributed compliance are considered in this work. In order to validate the model, measurements have been performed. It was shown that a small precurvature of bistable straight-guided buckling beams is crucial to avoid convergence into higher order buckling modes in nonlinear analysis of ANSYS™ and to obtain reliable results. Transient analysis using ANSYS™ with subsequent preloading and motion displacements can incorporate preloading effects. Moreover, the model correction allows accurate description of the increased symmetry and energy efficiency of the bistable behavior in case of increasing (in order of effectiveness) the initial angle and preloading for the case of distributed compliance. This behavior was observed by increasing the initial angle, thickness, and length of the rigid segment for the case of lumped compliance.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Configuration and definition of geometry parameters of the bistable straight-guided buckling beams (left half) for (a) case I and (b) case II. The beams have a very small curvature (1/R); the end tips are fixed at an initial angle (θ(r) ); in the center (right at the figure) the beams are constraint in x-translation and rotation about z-axis; for preloading effects (case II) the beams are preloaded over a distance (u) along the x-axis; the beams are loaded with a y-displacement (δ) in the center.

Grahic Jump Location
Figure 2

Deformated shape of the bistable straight-guided buckling beams for case II: with initially straight beams (without curvature) the deformed shape converged into a higher buckling mode (dotted); with a small curvature in the initial beams the deformed shape has the right solution (dashed)

Grahic Jump Location
Figure 3

Typical behavior of the force–displacement characteristic of a bistable mechanism; point a is the first stable point; at point b, the force exerted on the mechanism is at its maximum; point c is the unstable equilibrium position, where the bistable mechanism snaps and produces a force in the same direction as the travel range; this force is the largest at point d; point e is the second stable position of the beams; the area of the curve for Fpos and Fneg is the energy needed to put in the mechanism (Ein ) or the energy produced by the mechanism (Eout ), respectively

Grahic Jump Location
Figure 4

Flow chart of the subsequent transient analysis; the data of the preloaded initial shape (time interval 1) are used to solve the analysis for the deformed structure (time interval 2); the data of the deformed structure together with the prescribed displacement give the final results

Grahic Jump Location
Figure 5

Top view of the measurement set-up: The force–displacement characteristic of mechanisms was determined by measuring actuation force (Fact ) and displacement (Xact ) from relaxed position to the second stable position and vice versa; the angle and preloading were adjusted by a rotational stage mounted on a linear stage

Grahic Jump Location
Figure 6

Results of the experiments and the ANSYS™ simulations for three typical cases: (1) with initial curvature (solid), (2) without initial curvature (dashed), (3) with initial curvature and preloading (dotted)

Grahic Jump Location
Figure 7

Results of the evaluation ratios determined with ANSYS™ analysis for varying design parameters for case I (a, c, e) and case II (b, d, f), normalized to the largest value of each ratio

Grahic Jump Location
Figure 8

Results of the evaluation ratios determined with ANSYS™ analysis for varying the preloading in case II, normalized to the largest value of each ratio

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In