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

Abstract

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.

Stress relaxation insensitive designs for metal compliant mechanism threshold accelerometers

“…The resulting equations are solved numerically by applying a given displacement to the beams, and calculating the forces that result. Note that more complex models have also been developed for similar bistable mechanisms [16,17] but we have found the more simple model is sufficient for understanding most of the performance variations we measured.…”

On the infinitely-stable rotational mechanism using the off-axis rotation of a bistable translational mechanism

“…Nonlinear FEA (Dunning et al, 2012), however, can accurately predict post-buckling behaviour of bistable mechanisms as well as accurate stress values without any assumptions as mentioned above, which surpasses these fast numerical methods in Kim and Ebenstein (2012), Holst et al (2011) and Zhang and Chen (2013). In addition, nonlinear FEA can analyse off-axis characteristics that these methods in Kim and Ebenstein (2012), Holst et al (2011) and Zhang and Chen (2013) cannot deal with.…”

“…Different from the above reported works in Lassooij et al (2012), Chen and Lan (2012), Hansen et al (2007), Dunning et al (2012), Kim and Ebenstein (2012), Holst et al (2011) and Zhang and Chen (2013) which employ the primary translation to achieve finite multi-stable statuses, this paper studies on the multistable off-axis rotation behaviour of the bistable translational mechanism in order to obtain an infinitely-stable rotational mechanism. This off-axis rotation behavior with multistable points has also potential applications in human joint rehabilitative devices, dynamic and static balancing of machines, and human mobility-assisting devices (Hou and Lan, 2013) when combining with a positive stiffness spring.…”

“…The beam length was set up to L = 50 mm with the in-plane thickness T = 1 mm, out-ofplane depth B = 5 mm, inclined angle θ = 10 • and Young's Modulus E = 2.4 GPa. In order to avoid the high-order buck- ling with high peek force and high stress, an optimised slight curvature (1/1000 mm −1 ) (Dunning et al, 2012) was applied to the beam, which is trivial in comparison to the beam length but is enough to perturb the beam to buckle at lower bending modes (Fig. 1b).…”

“…Unlike the traditional ways of using locking mechanisms and detents, a compliant mechanism based multistable mechanism obtains multistability through the storage and release of potential energy stored in their flexible members during post-buckling. This paper focuses on bistable translational mechanisms using fixed-clamped beams (Lassooij et al, 2012;Chen and Lan, 2012;Hansen et al, 2007;Dunning et al, 2012;Kim and Ebenstein, 2012;Holst et al, 2011;Zhang and Chen, 2013), rather than using the fixed-pinned (Qiu et al, 2004) and the pinned-pinned beams (Sonmez and Tutum, 2008) that are hard to manufacture monolithically. There are mainly two methods to design the fixed-clamped bistable translational mechanism (Dunning et al, 2012).…”