An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.

Dynamic pull-in of parallel plate and torsional electrostatic MEMS actuators.

Arch-shaped microelectromechanical systems (MEMS) have been used as mechanical memories, micro-relays, micro-valves, optical switches and digital micro-mirrors. A bi-stable structure, such as an arch, is characterized by a multivalued load deflection curve. Here we study the symmetry breaking, the snap-through instability and the pull-in instability of a bi-stable arch-shaped MEMS under static and dynamic electric loads. Unlike a mechanical load, the electric load is a nonlinear function of the a priori unknown deformed shape of the arch. The nonlinear partial differential equation governing transient deformations of the arch is solved numerically using the Galerkin method and a time integration scheme that adaptively adjusts the time step to compute the solution within the prescribed tolerance. For the static problem, the displacement control and the pseudo-arc-length continuation methods are used to obtain the bifurcation curve of the arch's displacement versus a load parameter. The displacement control method fails to compute the arch's asymmetric deformations that are found by the pseudo-arc-length continuation method. For the dynamic problem, two distinct mechanisms of the snap-through instability are found. It is shown that critical loads and geometric parameters for instabilities of an arch under an electric load with and without consideration of mechanical inertia effects are quite different. A phase diagram between a critical load parameter and the arch height is constructed to delineate different regions of instabilities. We compare results from the present model with those from a continuum mechanics based approach, and with results of other models and experiments available in the literature.

https://imechanica.org/files/SMS_Das_Batra_preprint.pdf

Symmetry breaking, snap-through and pull-in instabilities under dynamic loading of microelectromechanical shallow arches

In this study, influences of intermolecular forces on the dynamic pull-in instability of electrostatically actuated beams are investigated. The effects of midplane stretching, electrostatic actuation, fringing fields, and intermolecular forces are considered. The boundary conditions of the beams are clamped-free and clamped-clamped. A finite-element model is developed to dis- cretize the governing equations, and Newmark time discretization is then employed to solve the discretized equations. The static pull-in instability is investigated to validate the model. Finally, dynamic pull-in instability of cantilevers and double-clamped beams are studied considering the Casimir and van der Waals effects. The results indicate that by increasing the Casimir and van der Waals effects, the effect of inertia on pull-in values considerably increases.

Dynamic pull-in instability of electrostatically actuated beams incorporating Casimir and van der Waals forces

Application of homotopy analysis method in studying dynamic pull-in instability of microsystems

Large-amplitude non-linear vibrations of micro- and nano-electromechanical resonant sensors around their primary resonance are investigated. A comprehensive multiphysics model based on the Galerkin decomposition method coupled with the averaging method is developed in the case of electrostatically actuated clamped-clamped resonators. The model is purely analytical and includes the main sources of non-linearities as well as fringing field effects. The influence of the higher modes and the validation of the model is demonstrated with respect to the shooting method as well as the harmonic balance coupled with the asymptotic numerical method. This model allows designers to investigate the sensitivity variation of resonant sensors in the non-linear regime with respect to the electrostatic forcing.

/pdf/computational-and-quasi-analytical-models-for-non-linear-1zm1o9shsl.pdf

Computational and quasi-analytical models for non-linear vibrations of resonant MEMS and NEMS sensors

This study is devoted to providing precise predictions of the dc dynamic pull-in voltages of a clamped?clamped micro-beam based on a continuous model. A pull-in phenomenon occurs when the electrostatic force on the micro-beam exceeds the elastic restoring force exerted by beam deformation, leading to contact between the actuated beam and bottom electrode. DC dynamic pull-in means that an instantaneous application of the voltage (a step function such as voltage) is applied. To derive the pull-in voltage, a dynamic model in partial differential equations is established based on the equilibrium among beam flexibility, inertia, residual stress, squeeze film, distributed electrostatic forces and its electrical field fringing effects. The method of Galerkin decomposition is then employed to convert the established system equations into reduced discrete modal equations. Considering lower-order modes and approximating the beam deflection by a different order series, bifurcation based on phase portraits is conducted to derive static and dynamic pull-in voltages. It is found that the static pull-in phenomenon follows dynamic instabilities, and the dc dynamic pull-in voltage is around 91?92% of the static counterpart. However, the derived dynamic pull-in voltage is found to be dependent on the varied beam parameters, different from a fixed predicted value derived in past works, where only lumped models are assumed. Furthermore, accurate closed-form predictions are provided for non-narrow beams. The predictions are finally validated by finite element analysis and available experimental data.

https://ir.nctu.edu.tw:443/bitstream/11536/8207/1/000260263900008.pdf

DC dynamic pull-in predictions for a generalized clamped–clamped micro-beam based on a continuous model and bifurcation analysis

A novel low-torque ball re-positioning scheme based on a sliding-mode ball observer is developed in this study with the aim to precisely reside the rolling ball inside an automatic balancer system (ABS) to its desired position – 180 degree opposite to the inherent imbalance of the rotating system which the ABS is attached to. In this way, the ABS is capable of substantially reducing radial vibrations of the rotating system for a decent balancing. For preliminary feasibility, the case of a single ball is considered in this study. The first step is to establish the dynamic model of the system, which is followed by the analysis to ensure stability of the desired ball position. The second step is to forge a sliding-mode observer for estimating on-line position and velocity of the ball. With ball estimation capability, a low-torque speed regulator that essentially generates a series of speed drops to the neighborhood of suspension resonance is proposed to overcome practical ball rolling friction for residing the ball at the desired position. The design characteristic of low-torque required for the regulator is particularly suited to most of commercial spindle motors which can only output limited torques at high speeds. Finally, simulations and experiments are conducted for a benchmark problem of optical disc drives in order to verify the effectiveness of the proposed scheme of the sliding-mode observer and the low-torque speed regulator.

/pdf/a-novel-low-torque-ball-re-positioning-scheme-based-on-a-3uheixna72.pdf

A novel low-torque ball re-positioning scheme based on a sliding-mode ball observer for an automatic balancer system

This study is devoted to evaluate the performance of an automatic ball-type balance system (ABB) installed in optical disk drives (ODD) with consideration of the rolling friction between the balancing balls and the ball-containing race of the ABB. Researches have been conducted to study the performance of the ABB by investigating the nonlinear dynamics of the system; however, the rolling friction model adopted was a simple stick-slip type, which does not reflect the true contact dynamics between rolling balls and their races, leading to an inaccuracy in predicting ABB performance. In this study, a complete dynamic model of the ABB including a detailed rolling friction model based on contact mechanics is established. The method of multiple scales is then applied to formulate a scaled model to find all possible steady-state ball positions and analyze stabilities. It is found that possible steady-state residing positions of the ball inside the race are multiple and form continuous ranges. Numerical simulations and experiments are conducted to verify the validness of the theoretical findings. The obtained results are used to predict the level of residual vibration, with which the guidelines on dimension design and material choices of the ABB are distilled to achieve desired performance.Copyright © 2004 by ASME

Effects of Rolling Friction of the Balancing Balls on the Automatic Ball Balancer for Optical Disk Drives

— The objective of this study is to design a novel cone-shaped lens cap on LEDs in order to achieve high optical efficiency in an ultra-thin directly lit RGB LED backlight unit (BLU) for large-sized LCD TVs. The use of the novel lens cap could play the role of a diffuser, a low light-efficiency component in a BLU, in order to gain higher efficiency and simultaneously provide satisfactory uniformity in light distribution. The novel cone-shaped lens is coated with aluminum on the outside surface of the cone for mirroring effects to reflect most of the LED emitted light horizontally and then reflect the light at the BLU boundaries, and then, finally to the output plane. In this way, bright spots on the output plane of the BLU can be avoided, leading to increased uniformity. Simulations were conducted to design and optimize varied aspects of the designed lens and BLU, including the cone angle of the proposed lens and the LED spacing (pitch). To further achieve color balance, a known Genetic Algorithm is used to search for the optimal angular placement of each RGB LED, resulting in better color balance. Finally, a prototype BLU for large-sized 37-in. LCD TVs with the proposed lens was built to verify the expected performance.

A novel lens cap designed for the RGB LEDs installed in an ultra‐thin and directly lit backlight unit of large‐sized LCD TVs

This study develops a highly-efficient light-guide plate for edge lighting backlight module that has no optical films. The light guide plate is designed to control the angle of the incident rays to the top surface from light source, to get the highest uniformity of intensity for thin edge lighting backlight system applications. The micro-prisms of pyramidal shape on the top surface can highly-efficient collimate with the light rays. Another micro-prism of v-cut shape on the bottom surface can reflect the incident light into the front direction and mixing the rays in the lightguide plate with the high uniformity. A novel design concept of the v-cut is the regular density varies of the cut in the LGP. The modeling simulation program, employing a Monte Carlo method based on TracePro software, has optimized the shape of the pyramidal micro-prisms on the top surface and the density distribution condition of the v-cut micro-prisms on the bottom surface, also the multiple scattering characteristics. The two types of the micro-prisms at the top and bottom surface can be highly recommended for the uniformity of the brightness via the optimal design process. Future work is warranted on improving the optical efficiency by using light-emitting diodes as a light source. The backlight module will allow us to increase the optical efficiency and to lower the total cost in portable LCD applications. The study confirms that a uniformity of brightness can be achieved without using any optical films, resulting in a high uniformity of 84%.

C.-W. Chiu

Papers

DC dynamic pull-in predictions for a generalized clamped–clamped micro-beam based on a continuous model and bifurcation analysis

A novel low-torque ball re-positioning scheme based on a sliding-mode ball observer for an automatic balancer system

Effects of Rolling Friction of the Balancing Balls on the Automatic Ball Balancer for Optical Disk Drives

A novel lens cap designed for the RGB LEDs installed in an ultra‐thin and directly lit backlight unit of large‐sized LCD TVs

Design of a highly-efficient light guide plate for the edge lighting backlight module