The first objective of this dissertation is to present hybrid numerical-analytical approaches and reduced-order models to simulate microelectromechanical systems (MEMS) in multi-physics fields. These include electric actuation (AC and DC), squeeze-film damping, thermoelastic damping, and structural forces. The second objective is to investigate MEMS phenomena, such as squeeze-film damping and dynamic pull-in, and use the latter to design a novel RF-MEMS switch. In the first part of the dissertation, we introduce a new approach to the modeling and simulation of flexible microstructures under the coupled effects of squeeze-film damping, electrostatic actuation, and mechanical forces. The new approach utilizes the compressible Reynolds equation coupled with the equation governing the plate deflection. The model accounts for the slip condition of the flow at very low pressures. Perturbation methods are used to derive an analytical expression for the pressure distribution in terms of the structural mode shapes. This expression is substituted into the plate equation, which is solved in turn using a finite-element method for the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors. We apply the new approach to a variety of rectangular and circular plates and present the final expressions for the pressure distributions and quality factors. We extend the approach to microplates actuated by large electrostatic forces. For this case, we present a low-order model, which reduces significantly the cost of simulation. The model utilizes the nonlinear Euler-Bernoulli beam equation, the von K´arm´an plate equations, and the compressible Reynolds equation. The second topic of the dissertation is thermoelastic damping. We present a model and analytical expressions for thermoelastic damping in microplates. We solve the heat equation for the thermal flux across the microplate, in terms of the structural mode shapes, and hence decouple the thermal equation from the plate equation. We utilize a perturbation method to derive an analytical expression for the quality factor of a microplate with general boundary conditions under electrostatic loading and residual stresses in terms of its structural mode shapes. We present results for microplates with various boundary conditions. In the final part of the dissertation, we present a dynamic analysis and simulation of MEMS resonators and novel RF MEMS switches employing resonant microbeams. We first study microbeams excited near their fundamental natural frequencies (primary-resonance excitation). We investigate the dynamic pull-in instability and formulate safety criteria for the design of MEMS sensors and RF filters. We also utilize this phenomenon to design a low-voltage RF MEMS switch actuated with a combined DC and AC loading. Then, we simulate the dynamics of microbeams excited near half their fundamental natural frequencies (superharmonic excitation) and twice their fundamental natural frequencies (subharmonic excitation). For the superharmonic case, we present results showing the effect of varying the DC bias, the damping, and the AC excitation amplitude on the frequency-response curves. For the subharmonic case, we show that if the magnitude of the AC forcing exceeds the threshold activating the subharmonic resonance, all frequency-response curves will reach pull-in. / Ph. D.

<p>The objectives of this investigation were to experimentally and numerically assess the performance of a ball bearing supported turbocharger (TC). Turbochargers are mechanical devices used to improve the efficiency of modern engines. Using ball bearings improves the TC efficiency, and represents one of many evolving high-speed applications for ball bearings.</p> <p>The experimental objectives of this investigation were to design and develop a turbocharger test rig (TTR) to measure the shaft whirl of the rotating assembly and the axial and frictional loads experienced by the bearing cartridge. The TTR contains a ball bearing TC which was instrumented and operated under a variety of test conditions including rotational speeds up to 55,000 rpm. In order to measure the axial loads on the compressor and turbine sides, customized sensors were designed, fabricated and integrated into the TC housing. The anti-rotation (AR) pin, which normally prevents the bearing cartridge from rotating, was replaced with a custom-made sensor to measure frictional losses in the bearing cartridge.  These sensors were designed to minimally affect the operation of the TC. Proximity probes were initially installed on the compressor side and later on the turbine side to monitor shaft whirl using targets attached to the ends of the impellers. An assembly to record axial shaft motion with a proximity probe was also developed. Axial load and motion results indicated that the compressor side bears most of the axial load. As the backpressure or the speed of the TC increased the axial load also increased. Frictional measurements from the AR pin sensor demonstrated low power losses in the ball bearing cartridge. For certain shaft speed ranges, the data from the sensors illustrated periodic trends in response to subsynchronous whirl of the shaft.</p> <p>The numerical modeling objectives of this investigation were to characterize the dynamics of the ball bearing supported TC. In this TC, the compressor, turbine and shaft are supported by a bearing cartridge composed of back-to-back angular contact ball bearings. The cartridge is supported by squeeze film dampers (SFDs) and is prevented from rotation by the AR pin. To achieve the objectives, first an equivalent bearing model was developed to investigate the bearing dynamics and whirl of the TC rotating assembly. The TC bearing cartridge was modeled with a single deep groove ball bearing (DGBB) using the discrete element method. The SFD which supports the bearing was modeled with a bilinear spring and damper. A DGBB was used because it can support axial load in both directions. This model was then extended to include a flexible shaft represented by tetrahedral finite elements and supported by an ACBB cartridge. After this model was used to reproduce the whirl from the test rig, the bearing internal geometry and SFD properties were adjusted to determine their effect on shaft whirl. Wear and damage criteria were also developed to evaluate the simulation results. The best simulation result was obtained with a small clearance in the bearing and with a stiffer SFD. The clearance was necessary as the shaft and bearing deform at high speeds, preloading the bearing.</p> <p>The best simulation result was found to have reduced sliding and limited variation in contact force, which should lead to reduced friction and improved overall life. This study demonstrates the importance of taking the bearing system into account while designing a TC or other high speed mechanical system, as the bearing and SFD properties can have a significant impact on the system performance.</p>

With the advent of micro and nano electromechanical systems (MEMS/NEMS), there has been rapid development in the design and fabrication of sensitive resonant sensors. Sensitivity of such devices depends on the resonant frequency and the quality factor (Q). The Q of these devices are dependent on process induced prestress in the structural geometry, interaction with the external environment, and the encapsulation method. For high frequency sensors operating in air and under encapsulation condition, the Q is dominated by structural and fluid-structure interaction losses. In this thesis, we set out to study the dominant energy dissipative mechanisms that are constituent of the experimentally observed loss (Q-factor) in two specific test geometries—uncapped and capped circular MEMS drumhead resonators. Considering the importance of various factors, we consider four important problems pertaining to the uncapped as well as capped resonators. In the first problem, the most important factors perhaps are the acoustic radiation losses emanating from the annular plate, and the effect of added mass effect on the natural frequencies of the annular plate. The second problem is to investigate the dominant contribution of squeeze film losses and acoustic radiation losses with respect to various natural frequencies of the annular plate. The third problem is to consider the effect of prestress on the natural frequencies of the annular plate and its associated fluid-structure interaction losses (quality factors due to squeeze film damping and acoustic radiation losses). The fourth problem is to study the dominant fluid-structure interaction losses and structural losses that are constituent of experimentally measured Q-factors of the encapsulated annular plate (conceptual representation of MEMS device under packaged conditions). In the first problem, we study the mode dependent acoustic radiation losses in an uncapped drumhead microresonator which is represented by a annular circular plate fixed at its outer edge, suspended over a fixed substrate. There are two main effects which are associated with such systems due to the fluid-structure interaction. First is the “added mass effect,” which reduces the effective resonance frequency of the structure. The second is the acoustic radiation loss from the top side of the resonator, that affects the quality factor of the vibrating structure. In deriving the analytical solution, we first obtain the exact mode shapes of the structure ignoring any effect of the surrounding fluid (air) on the mode shape. Subsequently, we use these mode shapes to study the effect of the surrounding fluid on the associated natural frequencies and the Q-factor. The effect of “added mass” on the frequencies of the structure is found to be negligible. However, the acoustic radiation losses found to be significant. Additionally, we found that the variation in Qac over the first few modes (< 40 MHz) is marked with a local maximum and a minimum. Beyond this range, Qac increases monotonically over the higher frequency modes. It is also found that such kind of variation can be described using different acoustics parameters. Finally, comparing the acoustics radiation loss based quality factor with the experimental results for the uncapped drumhead resonator, the acoustic damping dominates only at higher modes. Therefore, our second problem forms the basis of finding other fluid-related damping. In the second problem, we explore the fluid losses due to squeeze film damping in the uncapped drumhead micro resonator. In this case, the squeeze film loss is due to the flow of the fluid film between the bottom surface of the annular plate and the fixed substrate. Based on the literature survey, it is found that the squeeze film damping reduces with increase in the air-gap thickness and the operating frequencies respectively. However, the squeeze film effect can not be ignored at lower frequencies. In order to investigate the contribution of squeeze film damping in uncapped resonator, we determine squeeze-film damping based quality factor Qsq corresponding to different modes of the resonators using FEM based software, ANSYS. On comparing Qsq with the experiments, we found that Qsq matches well with the experiments corresponding to the lower modes. Therefore, it is found that Qsq dominates at low frequencies (< 20 MHz) and Qac plays significant role at high frequencies (> 40 MHz). Both types of damping should be considered while modeling the fluid damping in uncapped resonator. In the next study, we discuss the effects of prestress on the resonant frequencies and quality factor. In the third study, we discuss the applicability of thin-plate theory with prestress and membrane theory in computing the frequencies and quality factor due to acoustic and squeeze film losses in the uncapped drumhead resonator. In the first two studies, although the quality factor due to acoustic losses and the squeeze film captures the correct trend of the experimental results, there is a mismatch between the experimental and theoretical frequencies computed with added mass effect. In order to improve the computation of frequencies corresponding to measured modes, we first used membrane theory to predict the frequencies, and finally we quantify that there exists discrepancy between computed and the corresponding experimental frequencies with error of about 8–55%. Since, both the membrane as well as thin plate theory without prestress do not correctly model the frequencies, we used the thin plate theory with prestress. For a prestress level of 96 MPa, we found the match between the computed frequencies and the corresponding quality factors with the measured values. However, we also found that there exists strong dependence of prestress on the acoustic radiation loss, with decrease in the acoustic loss based quality factors with increase in the prestress level. In the subsequent problem, we focus on the computation of losses in capped drumhead resonator which leads to a design possibility of improving the quality factor by containing the acoustic radiation losses. In the fourth problem, we study the structural and fluid-structure interaction losses which are dominant constituent of net Q-factor observed in experiments due to encapsulation of uncapped drumhead resonator. Essentially, the geometry of the capped resonator constitutes upper and lower cavities subjected to fluid-structure interaction losses on both sides of the annular plate. The dominant fluid-structure interaction loss is found to be due to squeezing action acting simultaneously in the upper and lower cavities. However, as we go to the higher modes, squeeze film damping become very small and the damping due to structure related losses such as clamping and thermoelastic losses becomes significant. We found the thermoelastic damping to be the dominant source of structural damping at higher resonant modes, whereas, the clamping losses are found to be relatively smaller. Finally, on comparing the net quality factor with the experimental results, we observed that the squeeze film losses are dominant at lower frequencies, and thermoelastic losses dominate at the higher frequencies. However, there remains some discrepancy between theoretical and experimental Q-factors particularly over higher frequency range. Such discrepancy may be due to some unaccounted factors which may be explored to improve the modeling of damping in capped resonators. The emphasis of this work has been towards developing a comprehensive understanding of different dominant dissipative mechanisms, classified into the fluid-structure interaction and the structural losses, that are constituent of the Q-factor at various resonant modes of uncapped and capped drumhead resonators.

Squeeze Film Dampers (SFD) provide viscous damping in rotor bearing systems to reduce lateral vibration amplitudes and to isolate mechanical components. Aircraft engine shafts, often supported on roller bearings, operate at high rotational speeds and are susceptible to large amplitude shaft whirl due to rotor imbalance. SFDs aid to reduce such large whirl amplitudes while also eliminating rotor instabilities. he current work quantifies experimentally the forced performance of two parallel squeeze SFDs separated by a central groove. Force coefficients are identified in a specialized SFD test rig constructed to undergo similar operating and loading conditions as in jet engines. Of interest is to quantify the effect of a central feed groove on the forced performance of SFDs and to validate predictions from a computational tool. The test rig comprises of an elastically supported bearing structure and one of two journals. Tests are conducted on two open ends SFDs, both with diameter D and nominal radial clearance c; each damper with two parallel film land lengths L= 1/5 D and 2L, separated by a feed groove of width L and depth 3/4 L. ISO VG 2 grade lubricant oil flows into the central groove via 3 orifices, 120 degrees apart, and then through the film lands to finally exit to ambient. In operation, a static loader pulls the bearing to various static off center positions with respect to the stationary journal, and electromagnetic shakers (2,200 N) excite the test system with single frequency loads over a frequency range to generate rectilinear, circular and elliptical orbits with specified motion amplitudes. A frequency domain method identifies the SFD mechanical parameters, viz., stiffness, damping, and added mass coefficients. The long damper generates 7 times more direct damping and 2 times more added mass compared to the short length damper. The damping coefficients are sensitive to the static eccentricity (up to 50 percent c) while showing lesser dependency on the amplitude of whirl motion (up to 20 percent c). On the other hand, added mass coefficients are nearly constant with static eccentricity and decrease with higher amplitudes of motion. The magnitudes of identified cross-coupled coefficients are insignificant for all imposed operating conditions for either damper. Large dynamic pressures recorded in the central groove demonstrate the groove does not isolate the film lands by merely acting as a source of lubricant, but contributes to the generation of large added mass coefficients. The recorded dynamic pressures in the film lands and central groove do not evidence lubricant vapor or gas cavitation for the tested static eccentricities and amplitudes of motion. The direct damping coefficients for both dampers are independent of excitation frequency over the frequency range of the tests. Predictions derived from a novel SFD computational tool that includes flow interactions in the central groove and oil supply orifices agree well with the experimental force coefficients for both dampers. The current work advances the state of the art in SFDs for jet engines.