Shai Shmulevich

Reversing the action of thermoelastic bimorphs using selective directional stiffeners

We present for the first time ever, a method for reversing the response of thermoelastic bimorph actuators, without changing the order of their layers. Our device is constructed from a flat stage that is suspended on three thermoelastic bimorph spiral arms. We demonstrate that the thermoelastic response of the spiral bimorphs can be affected by using directional stiffeners. We show that with no stiffeners, the thermoelastic response naturally displaces the stage downwards by 7μm. Stiffeners that are angled at 45° relative to the spiral tangent, enhance this response by a factor of 3, and increase the downward displacement to 23μm. Surprisingly, stiffeners which are angled at -45°, completely reverse the direction of the response, and result in an enhanced upward displacement of 23μm.

Selective Stiffening for Producing a Mass-Fabrication Compatible Motion Conversion Mechanism

We present a mechanism that converts in-plane to out-of-plane motions, which is fully compatible with mass-fabrication processes. By using selective stiffening, we induce coupling between in-plane and out-of-plane responses of the mechanism. The conversion ratio is constant (i.e., linear response), and it can be easily tailored by the number of stiffeners used in an otherwise unchanged design planform. The linearity of the motion conversion and the possibility to tailor it, are demonstrated experimentally using dedicated test devices. As a specific example of application, we use the motion conversion mechanism to achieve a parallel out-of-plane motion of a flat stage, which is driven by in-plane comb-drives.

On the quality of quality-factor in gap-closing electrostatic resonators

We present analytic expressions for three common measures of the dynamic response in gap-closing electrostatic resonators. We show that peak gain, peak sharpness and logarithmic decrement are distinctively different and are not equal to the quality-factor of the unloaded system. We experimentally validate our theoretical predictions by characterizing the dynamic response of test devices. The significance of this work is that it clarifies the correct way in which the performance of MEMS resonators should be reported to avoid ambiguity.

Mass-fabrication compatible mechanism for converting in-plane to out-of-plane motion

We present a mechanism that converts in-plane to out-of-plane motion, which is fully compatible with standard mass-fabrication methods. The mechanism harnesses the well-established in-plane actuation achieved by comb-drives, and converts it to out-of-plane motion. The motion conversion ratio is constant (i.e. linear conversion), and it can be easily tuned by adding or subtracting modular elements, in an otherwise unchanged design planform. We experimentally demonstrate the linearity of the mechanism, and use dedicated test devices to show the tunability of the conversion ratio. With a different test device, we demonstrate parallel out-of-plane motion of a flat stage. The measurements of this device show good agreement with model predictions.

Tuning the first instability window of a MEMS Meissner parametric resonator using a linear electrostatic anti-spring

We demonstrate frequency tuning of the first instability window of a MEMS Meissner parametric resonator. Our parametric resonator includes a transducer which provides a negative electrostatic stiffness that is not affected by motion. We therefore refer to this transducer as a linear anti-spring. We achieve parametric excitation by time-modulation of this negative electrostatic stiffness. Our design is rather robust to fabrication tolerances. In contrast, most state-of-the-art MEMS parametric resonators are either detrimentally affected by a nonlinear electrostatic stiffness, or are far more sensitive to fabrication tolerances.

A MEMS Implementation of a Classic Parametric Resonator

We present a microelectromechanical systems realization of a classic parametric resonator. This parametric resonator is ideal in the sense that the electrostatic stiffness, which may be time modulated, is not affected by motion. We also present a simple, efficient, and intuitive model of parametric excitation. This model predicts the minimal modulation amplitude required to obtain an unbounded response in a parametric system with linear damping. We show experimental results in which the system is operated as a Meissner resonator.

A Gap-Closing Electrostatic Actuator With a Linear Extended Range

We present for the first time a gap-closing electrostatic actuator with a linear extended range. We achieve this by designing a nonlinear spring which exactly counteracts the nonlinear effects of electrostatic attraction forces in gap-closing actuators. We demonstrate this on test devices with an initial gap of g=22μ. The initial response up to a deflection of g/4 is stable and is inevitably nonlinear, but beyond this point we demonstrate good linearity up to a displacement of 85% of the nominal gap.

Dynamically-balanced folded-beam suspensions

We present a complete methodology for designing a new folded-beam suspension which responds as a linear spring at the fundamental resonance. This is in sharp contrast to the response of standard folded-beam suspensions. The static response of the standard folded-beam suspension is linear over a wide range of motions. But, surprisingly, the dynamic response of the standard folded-beam suspension is strongly nonlinear for small motion amplitudes that are larger than the width of the flexure beams. We have previously shown experimental evidence of this problem with the standard suspension. In contrast, the stiffness of the new dynamically balanced folded-beam suspension is not affected by motion amplitude. In the present work we show new experimental evidence demonstrating that the new design solves this problem.

Dynamically Balanced Folded-Beam Suspensions for Resonators

The standard folded-beam suspension is often used in electrostatic comb-drive resonators with the intention of achieving a system with a linear response. However, we show that the harmonic response of the standard folded-beam suspension is not linear at the fundamental resonance frequency of the system. Specifically, we show that at the fundamental resonance frequency, the stiffness of the suspension increases monotonically with increasing motion amplitude. We show that even though the suspension is intended to respond as a linear spring, it is actually designed to do so only in static loading. We present a solution to the problem in the form of a new dynamically balanced folded-beam suspension. This suspension is designed such that at the fundamental frequency of the system, its response is linear, and its stiffness is unaffected by motion. The methodology for designing this suspension is fully detailed. We experimentally demonstrate the viability of the new design.

The electromechanical response of a self-excited MEMS Franklin oscillator

We present a self-excited MEMS Franklin oscillator, which responds in steady state vibrations when subjected to a sufficient dc voltage. The system is constructed from an electrostatically-floating rotor, which sequentially transfers charge between a source and drain electrodes. We present a comprehensive analysis of the electromechanical response of the system. Our analysis shows that current flows from the source to drain only when the rotor is in transition. Surprisingly, at contact of the rotor with either the source or the drain electrodes, there is no current in the system, and the charge transfer mechanism is essentially a recombination of opposite charges. This means that although we drive our system by 30 to 70 Volts, the contacts are essentially cold switching. Our experimental measurements of the dynamic response of the system are in good agreement with our model predictions.