Repulsive Force Actuators Research Articles

Bifurcation analysis of the levitation force MEMS actuators

This paper investigates the nonlinear dynamic behavior of a repulsive force actuator from the bifurcation perspective in the cases of primary and principal parametric resonances. The studied model consists of a specific configuration that produces out-of-plane repulsive (levitation) force. The governed equation of motion around static equilibrium is described in the form of a generalized forced Mathieu equation holding quadratic and cubic nonlinearities. While the particular system of interest is one with generated levitation force, the results can be applied to a wide class of MEMS in which the governing equation of motion is classified as the forced Mathieu equation. Coordinate transformation of the systems’ analytical solution from polar to Cartesian is done to preclude the singularity in origin. The frequency response is studied, and analytical expressions for equilibrium positions as fixed points are presented. Assessing the Jacobian matrix, the stability of each branch is examined, and the critical detuning values are defined in which the bifurcations occur. This criterion is then used to border the regions and illustrate the phase portraits of picked points within the regions. The results graphically show that inducing system by the initial conditions corresponding to the fixed points, triggers constant amplitude as well as angle, which ends up with periodic motion. Moreover, the outcome proves that perturbation analysis merely captures the periodic motions and fails to detect quasi-periodic motions. Our analysis provides a platform for further understanding of the repulsive electrostatic force, which is highly nonlinear. The results can be deployed in designing sensors with a wider detection range in which the amplitude jump is measured near the pitchfork bifurcation of principal parametric and cyclic fold bifurcation of primary resonances.

Static and dynamic characterization of micro-electro-mechanical system repulsive force actuators

This paper presents the static and dynamic response characterization of an electrostatic micro-electro-mechanical system mirror driven by repulsive force. The experimental analysis of the static response in different seasons of the year indicates that the capillary force caused by the thin layer of water underneath the mirror is the dominant factor for variation in the lifting threshold of the applied voltage. Dynamic characterization of the mirror reveals a large natural frequency of 2.6 kHz at the increasing rate of 8 Hz/V, indicating a four-fold increase compared to a previous design. This high natural frequency with an almost linear increase is desired for fast speed scanners and interferometers with high tunability benefited from the simplified signal processing circuit. Since the amplitude of the repulsive force micro-structure is no longer restricted to any geometrical limitation, the non-dimensionalizing parameters are chosen so that the nonlinear terms are small enough in order that the perturbation method is applicable in the vicinity of both primary and principal parametric resonances. The analytical analysis shows the way for inserting a bookkeeping parameter in a simple manner based on the evaluation of the magnitude of order in which the pre-assumed value is further validated by experimental results. The results of our investigations can be used to analytically evaluate the static and dynamic behavior of the system and have important applications in the design of various devices such as filters, interferometers, and switches.

Theoretical and experimental investigations of the primary and parametric resonances in repulsive force based MEMS actuators

This work demonstrates an efficient approach to excite primary and parametric resonances of a Microelectromechanical system (MEMS) based repulsive force actuator. The electrostatic micro-actuator design consists of a particular arrangement of the actuating electrodes to create a repulsive like force, offering, therefore, a higher traveling range and eliminating pull-in instability. A generalized form of forced Mathieu equation of motion is first formulated and afterward a perturbation analysis, through the Method of Multiple Scales (MMS), is carried out to find an approximate analytical solution of the micro-actuator dynamic response. The steady-state response is subsequently acquired and then compared with experimental results in the vicinity of the microsystem's natural frequency (primary resonance) and then around twice the same frequency (principal parametric resonance). MMS based frequency, force, and transition curves are obtained for both cases with clearly shown distinct regions bordered by lines in which the bifurcation points are well traced. The results show that the parametric excitation actuation can be more efficient, requiring less power as compared to the primary resonance excitation. Moreover, unlike the classical method where the structure is vulnerable to the dynamic pull-in instability, this design provides a larger amplitude of motion while protecting the structure from any dynamic pull-in instability. The ability of this design in exciting both the parametric and primary resonances can be advantageous for several applications ranging from micro-resonator based logic system to memory-based micro-devices. Besides, this study provides an analytical tool for designing MEMS sensors with higher resolutions as the amplitude of the micro-system is no longer restricted to any geometrical limitation.

Large aperture surface-micromachined rotating micromirror with the majority of dimples removed

This paper presents a surface-micromachined repulsive-force driven 1D rotating micromirror with a large aperture (1 mm). Two rotating beams are located on the bottom side of the mirror plate, while two repulsive-force actuators are connected to two middle sides to push the mirror plate up for out-of-plane rotation. Thus, no complex self-assembly structure is required to raise the mirror plate for rotation as most conventional surface-micromachined rotating micromirrors do. In order to increase the yield rate for the large aperture micromirror and avoid dimples used for preventing stiction during fabrication, six post-fabrication melted supporting beams are used along the circumference to increase the stiffness in fabrication, which are electrically melted and broken after fabrication to restore the initial stiffness. Only 12 dimples in the center of mirror plate are used for preventing operational stiction. The mirror’s reflectivity is increased to 25% from 20% after removing the majority of dimples. 36 prototypes are fabricated and tested and none of them suffer from stiction problem. The 6.3° optical rotation is achieved with a settling time of 26 ms.

Post-Fabrication Melting Procedure With I-Shaped Beams for Stiction-Free Release of 2-D Surface-Micromachined Micromirrors Equipped With Repulsive-Force Actuators

This paper presents a post-fabrication melting procedure with an I-shaped beam design to solve the problem of stiction in surface-micromachined 2-D micromirrors equipped with repulsive-force actuators. This design adds extra I-shaped beams to the free-standing mirror plate to increase its stiffness about one thousandfold and allow it to survive the wet release process. Then, those beams are melted and broken electrically on-chip after fabrication to restore the original stiffness. With the aid of repulsive force, the I-shaped beam design can use a low current for melting. A high current was used in the previously presented T-shaped fusible tether beam design, but it causes splattering and residue. The I-shaped beam design has been successfully applied to a repulsive-force 2D micromirror that is integrated with head-up display and stiction is eliminated. The modeling, simulation, and prototyping processes are presented, and the ways in which it can be used in a general surface-micromachined free-standing structure to eliminate stiction are discussed. [2017-0299]

Parametric resonance of a repulsive force MEMS electrostatic mirror

We investigate the nonlinear dynamic behavior of an electrostatic MEMS mirror. The MEMS mirror is driven by repulsive force actuators, which avoid pull-in instability and enable large travel ranges. In parallel-plate actuators, the force on the structure is toward the substrate limiting the range of motion to the capacitor gap. Unlike parallel-plate, repulsive force actuators push the mirror away from the substrate not limiting the motion. The highly nonlinear nature of the repulsive force and the large motions create unique characteristics that differ from parallel-plate actuators. Repulsive force actuators show linear natural frequency hardening with increased DC voltages unlike parallel-plate ones that have frequency softening. A large parametric resonance is another attribute of repulsive force actuators as the limitations of a small gap and pull-in instability are eliminated. To simulate the system response, we use a lumped parameter model with linear and cubic stiffness modulated by the excitation voltage that causes parametric resonances. Using the shooting technique, we obtained simulations that agree well with the nonlinear responses observed in our experiments. As the limitation of a small gap is overcome, the electrostatic force triggers large principal parametric resonances with amplitudes as large as the primary resonance. The parametric resonance is more pronounced at low DC excitation levels when geometric nonlinearities are not significant (axial stress is low). While the initial gap is only 2μm, under parametric resonance, our one-millimeter diameter mirror reaches ±43μm at 1.2kHz when the excitation level is as low as VDC=40V, VAC=1V in a vacuum. The ability to achieve parametric resonances with repulsive force actuation can serve and improve the signal-to-noise ratio and speed in various applications such as confocal microscopy.

Research on ultra-fast vacuum mechanical switch driven by repulsive force actuator.

In order to meet the fast operation demands of DC circuit breakers, a high-speed vacuum mechanical switch (VMS) driven by a repulsive force actuator is focused. To improve the drive speed and energy conversion efficiency (ECE) of the actuators, the dynamic characteristics of the double sided coil repulsive force actuators are investigated, and two generalized optimization design methods focusing on the aspect ratio of the driving coils (defined as ARF) and the electrical parameters (defined as EF) are developed. FEM simulation models' simulation and tests of VMS prototypes are conducted to verify the optimization methods. Results prove that the ARF method could improve the ECE of a VMS from 1.05% to 7.55%, and EF method could improve ECE of the same VMS from 1.05% to 6.61%, the combination of ARF and EF could improve the value of VMS's ECE to 10.50%, thus proving the validity and accuracy of the optimization methods.

Micromirror based virtual image automotive head-up display

A micromirror based virtual image head-up Display (HUD) system for automobile is presented. This auto-HUD includes a micromirror laser vector scanning display module, a projection screen, a reflective mirror and a transparent reflector for generating the virtual image. The display module integrates a micromirror driven by four repulsive-force actuators, a laser, the driving and control circuits and a double concave lens. The prototype of the micromirror HUD is fabricated and installed in a car model. Its performance is tested. The micromirror HUD is superior over the conventional HUD in terms of viewing angle, cost and size.

Novel automated microassembly mechanism based on on-chip actuators

The development of a novel automated microassembly mechanism based on on-chip actuators is described. The assembly mechanism utilizes repulsive-force actuators to flip surface-micromachined two-dimensional structures out-of-plane and assemble them in a vertical position. The assembly mechanism is suitable for wafer-level multidevice batch assembly without external interference. Prototypes were fabricated using the PolyMUMPs surface micromachining technology, then tested. The strength of the assembled structures in terms of withstanding external acceleration was calculated and experimentally measured. The measured results showed the assembly strength of 7 g for prototype 1 and 8 to 11 g for prototype 2.

A Study on Semi-Active Magnetic Bearing Position-Controlled by Piezoelectric Actuators

This paper investigates non-contact hybrid bearings that use permanent magnets for repulsive force and piezoelectric actuators for position-control. A structurally-improved hybrid bearing is presented. First, the concept of the hybrid bearing is briefly introduced along with previous test results. Then, the newly devised bearing with a decreased gap between rotor and stator is designed and analyzed with FEM to optimize the magnetic forces. Finally, a prototype bearing using the proposed mechanism is fabricated and a control method is discussed.

Experimental verification of an out-of-plane repulsive-force electrostatic actuator using a macroscopic mechanism

A macroscopic mechanism is developed to verify a repulsive-force electrostatic actuator, which consists of an array of fixed finger electrodes and an array of moving finger electrodes. The actuator is able to generate an asymmetric electric field surrounding the top and bottom surfaces of each moving finger electrode to push the moving finger up and away from the fixed fingers. The macroscopic mechanism consists of a macro repulsive force actuator, a high voltage power supply, a z-stage, a high precision balance and a LCR meter. The force and capacitance characteristic curves of the actuator are obtained using the macro mechanism. The 3-stage force (repulsive, zero and attractive forces) of the actuator is verified, as well as the effects of the moving finger width on the actuator’s performance. Experimental tests show that the macro repulsive-force actuator can generate a repulsive force of 3,000 μN with a maximum gap of 9.5 mm for generating a repulsive force.

Design, Modeling, and Demonstration of a MEMS Repulsive-Force Out-of-Plane Electrostatic Micro Actuator

An analytical model is developed for a two-layer repulsive-force out-of-plane micro electrostatic actuator by using conformal mapping techniques. The model provides the means to establish the performance characteristics in terms of stroke and generated force of the actuator and is used to develop design and optimization rules for the actuator. Numerical simulations were conducted in order to verify the analytical model. A simple physical model is also presented that explains the mechanism for generating the repulsive force. A Multi-User-MEMS-Processes repulsive-force out-of-plane rotation micromirror is developed to experimentally verify the analytical model and to demonstrate the repulsive-force actuator's capability of driving large-size rotation plates by using surface micromachining technology. Experimental measurements show that the repulsive-force rotation micromirror with a size of 312 mum times 312 mum achieved a mechanical rotation of 0deg-2.1deg at a dc driving voltage of 0-200 V. The micromirror achieved an open-loop settling time of 2.9 ms for a mechanical rotation of 2.3deg and an open-loop bandwidth of 150 Hz (-3 dB).

Performance assessment of a multi-level repulsive-force out-of-plane microelectrostatic actuator

A multi-level repulsive-force out-of-plane microelectrostatic actuator is proposed in this paper. The actuator uses a repulsive force instead of an attractive force and thus avoids the pull-in effect associated with conventional parallel-plate microelectrostatic actuators. The multi-level repulsive-force actuator is modelled, and the performance of an example design of the actuator is presented through numerical simulations. Simulation results show that the multi-level actuator can output a stroke much larger than that of a two-layer repulsive-force actuator when subject to the same voltage.