Micro Accelerometer with Mechanically Nonlinear Self-Limited Bistable Suspension
Thursday, November 12, 2009, 6:00 pm, Room Hall 3
We report on operational principle, modeling and design of an electrostatically actuated accelerometric device with mechanically nonlinear suspension element. The device incorporates a proof mass actuated by a parallel-plate electrode and attached to a substrate by initially curved beams in such a way that both electrostatic and inertial forces are directed along the beam. In accordance with the exact extensible elastica and approximate reduced order models of the beam used for the analysis, the deformation of an initially curved slender beam subjected to an end force can be subdivided into two stages - the "bending" stage associated mainly with the straightening of the beam and the "tension" stage corresponding to elongation of the almost straight beam. Since the stiffness of the beam at the first stage is significantly lower than at the second stage, the force–displacement dependence of this kind of suspension is of self-limiting type and the beam can be viewed, in a sense, as one directional constraint. Application of nonlinear electrostatic force results in electrostatic (pull-in) instability followed by the steep increase in the straightened beam stiffness preventing contact with the electrode and resulting in appearance of an additional stable configuration and bistability of the beam.
In this research we present two operational principles for measuring the acceleration - the pull-in voltage monitoring and the resonance frequency shift monitoring. The pull-in voltage approach is based on the (found to be close to linear) dependence between the pull-in voltage and the acceleration, while the self-limiting characteristic of the suspension prevents undesirable from the reliability point of view contact between the proof mass and the actuation electrode. The resonance frequency approach is based on the monitoring of the resonant frequency shift appearing due to acceleration and significantly enhanced in the vicinity of the pull-in instability points. Model results show that using suggested approach significant improvement, comparing to conventional designs with linear flexures, in the device performance could be achieved and µg resolution combined with extended dynamic range are feasible for relatively simple architecture and well established silicon on insulator (SOI) based fabrication process.