We present studies on squeeze film effects in dynamic MEMS devices with a special emphasis on the development of compact analytical models. First, the efficacy of lumped parameter modelling of dynamic MEMS devices is illustrated in MATLAB/SIMULINK software environment using a MEMS gyroscope and a MEMS microphone as examples. This is followed by a comparative study of equivalent electrical circuit models for a MEMS microphone wherein the importance of accurate extraction of lumped mass, stiffness and damping is brought into focus. In this context, a need for an in depth study of squeeze film behaviour in MEMS structures is highlighted and a strong motivation is drawn for the development of compact squeeze film models. A 2D analytical model for estimating squeeze film damping and spring force in perforated MEMS structures is presented. The governing equations based on isothermal compressible Reynolds equation are derived by considering an approximate circular pressure cell around a hole which is representative of the spatially invariant pressure pattern over the interior of the flow domain. The advantages and limitations of the solution are discussed with relevance to MEMS structures. Next, a comprehensive analytical model for 3D MEMS structures that includes effects of compressibility, inertia, and rarefaction in the flow between two parallel plates forming the squeeze region as well as the flow through perforations is developed. A modified Reynolds equation that includes the unsteady inertial term is derived from the Navier-Stokes equation to model the flow in the circular cell and the losses through the holes are modelled using Poiseuille flow. Rarefaction effects in the flow through the air-gap as well as the holes are accounted for by considering the slip boundary conditions. The analytical results are compared with extensive numerical simulations carried out using full 3-D Navier-Stokes equation solver in a commercial simulation package (ANSYS-CFX). We show that the analytical solution performs very well in tracking the net force up to the first resonant frequency of the entrapped air.

The goal of the current study was to develop a computational framework for modelling the coupled fluid-structure interaction problem of squeeze films often encountered in MEMS devices. Vibratory MEMS devices such as gyroscopes, RF switches, and 2D resonators often have a thin plate like structure vibrating transversely to a Fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping to the vibrating plate. For accurate modelling of the squeeze film effect, one must account for the coupled fluid-structure interaction. The majority of prior works attempting to address the coupled problem either approximate the mode shape of the vibrating plate or resort to cumbersome iterative solution strategies to address the problem in an indirect way. In the current work, we discuss the development of a fully coupled finite element based numerical scheme to solve the 2D Reynolds equation coupled with the 3D plate elasticity equation in a single step. The squeeze film solver so developed has been implemented into a commercial FEA package NISA as part of its Micro-Systems module. Further, extending on a prior analytical work, the effect of variable ow boundaries for an all sides clamped plate on squeeze film parameters has been thoroughly investigated. The developed FEM based numerical scheme has been used to validate the results of the prior analytical study. The developed numerical scheme models the 2D Reynolds equation thus limiting the model to account for the effects of the fluid volume strictly confined between the structure and the substrate. To study the effect of surrounding fluid volume ANSYS FLOTRAN simulations have been performed by numerically solving the full 3D Navier Stokes equation in the extended fluid domain for the different flow boundary scenarios. Cut-off frequencies are established beyond which one can consider a 2D fluid domain without considerable loss of accuracy. First, a displacement based finite element formulation is presented for the 2D Reynolds equation coupled with the 3D elasticity equation. Both lower order 8 node and higher order 27 node 3D elements are developed. Only a single type of 3D element is used for modelling along with a 2D fluid layer represented by the \wet" face of the 3D structural domain. The results from our numerical model are compared with experimental data from literature for a MEMS cantilever. The results from the 27 node displacement based elements show good agreement with published experimental data. The results from the lower order 8 node displacement based elements however show huge errors even for relatively fine meshes due to locking issues in modelling high aspect ratio structures. This limits the implementation of the displacement based solver in commercial FE packages where the available mesh generators are generally restricted to lower order 3D elements. In order to overcome the limitations faced by lower order elements (primarily locking issues) in modelling high aspect ratio MEMS geometries, a coupled hybrid formulation is developed next. A thorough performance study is presented considering both the hybrid and displacement based elements for lower order 8 node and higher order 27 node ele- ments. The optimal element choice for modelling squeeze film geometries is determined based on the comparative studies. The effect of element aspect ratio for hybrid and displacement based elements are studied and the superiority of hybrid formulation over displacement based formulations is established for lower order 8 node elements. The coupled hybrid nite element formulation developed for lower order elements is implemented in the commercial FEA package NISA. The implementation scheme to integrate the developed coupled hybrid 8 node squeeze film solver into the commercial FEA package is discussed. The pre-integration analysis and subsequent requirement gaps are first investigated. Based on the gap analysis, certain GUI modifications are undertaken and parser programs are developed to re-format data according to NISA input requirements. Certain special features are included in the package to aid in post processing data analysis by MEMS designers such as \frequency sweep" and \node of interest" selection. As a case study for validation, we also present the modelling of a MEMS cantilever and show that the simulation results from our software are in good agreement with experimental data reported in the literature. Finally as a case study, an extension of a prior analytical work, which studies the effect of varying flow boundaries on squeeze film parameters, is discussed. Explanations are provided for the findings reported in the prior analytical work. The concept of using variation in flow boundaries as a frequency tuning tool is introduced. The analytical results are validated with the coupled numerical scheme discussed before, by considering imposed mode shape for an all sides clamped plate as prescribed displacement to the fluid domain. The simulated results are used to study the intricacies in squeeze film damping and stiffness variations with respect to spatial changes in the fluid flow boundary conditions. In particular, it has been shown that the boundary venting conditions can be used effectively to tune the dynamic response of a micromechanical structure over a fairly large range of frequencies and somewhat smaller range of squeeze film damping. Next, the effect of the surrounding fluid volume for various venting conditions is studied. ANSYS FLOTRAN is used to solve for the full 3D Navier Stokes equation over the extended fluid domain. Results from the extended domain study are used to determine cut-off frequencies beyond which one need not resort to an extended mesh study, and yet be within 5% accuracy of the full extended mesh model.

This thesis presents the design and analysis for development of a Capacitive Micromachined Ultrasonic Transducer (CMUT), a novel sensor and actuator, aimed at replacing the conventional piezoelectric transducers for air-coupled ultrasonic imaging applications. These CMUTs are fabricated using the silicon micromachining technology wherein all fabrication is done on the surface of a silicon wafer by means of thin-film depositions, patterning with photolithography and etching. The main emphasis of this study is on developing analytical models that serve as effective design tools for the development of these devices. A desirable goal of such study is to create reasonable mathematical models, obtain analytical solutions, wherever possible, for various measures of transducer performance and provide design aids. A logical start is the lumped parameter modeling wherein the explicit dependence of the physical parameters on the spatial extent of the device is ignored. The system lumped parameters, such as the equivalent stiffness, the equivalent mass, and the equivalent damping are extracted from reasonable analytical or numerical models and subsequently used in the static and dynamic analysis of the device. Useful predictions are made with regard to the key transducer parameters, such as, the pull-in voltage, the static deflection, the dynamic response and the acoustic field produced. The modeling work presented embodies two main objectives: (i) it serves to provide direction in the design phase, and, (ii) it serves to aid in the extraction of critical parameters which affect the device behavior. Comparison of the results with the more rigorous FEM simulations as well as with those present in the existing literature assure that the developed models are accurate enough to serve as useful design tools. The distributed parameter modeling is presented next. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electro-elastic coupling aspect in the design of these devices. An approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear, is presented. The model is based on the Kirchhoff-Love assumptions that the plate is thin and the deflections and slopes are small. The classical thin-plate theory is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. This theory is used to determine the static deflection of the CMUT membrane due to a DC bias voltage. The thin-plate electro-elastic equation is solved using the Galerkin weighted residual technique under the assumption that the deflections are small in comparison to the thickness of the plate. The results obtained are compared to those obtained from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations. A simple analytical formula, which gives fairly accurate results (to within 3% of the value predicted by ANSYS simulations) for determination of the pull-in voltage, is also presented. As stated, this formula accounts for the elastic deflection of the membrane due to the coupled interaction with the electrostatic field. The effect of vacuum sealing the backside cavity of a CMUT is investigated in some detail. The presence or absence of air inside the cavity has a marked effect upon the system parameters, such as the natural frequency and the pull-in voltage. The possibility of using sealed CMUT cavities with air inside at ambient pressure is explored. In order to estimate the transducer loss due to the presence of air in the sealed cavity, the squeeze film forces resulting from the compression of the trapped air film are evaluated. Towards this end, the linearized Reynolds equation is solved in conjunction with the appropriate boundary conditions, taking the flexure of the membrane into account. From this analysis, it is concluded that, for a sealed CMUT cavity, the presence of air does not cause any squeeze film damping even when the flexure of the membrane is taken into account (the case of a rigid plate is already known). Although the emphasis of the study undertaken here is not on the physical realization of a working CMUT, a single cell as well as a linear array based on the design presented here, were fabricated (in a foundry elsewhere) in order to verify some of the most fundamental device parameters from experimental measurements. The fabricated devices have been characterized for their resonant frequency, quality factor, and structural integrity. These tests were conducted using the laser Doppler vibrometer and the Focused Ion Beam milling. Having investigated thoroughly the behavior of a single cell, we proceed to demonstrate how these cells can be arranged optimally in the form of an array to provide a comprehensive ultrasonic imaging system. A thorough analysis of the requirements for the array architecture is undertaken to determine the optimal configuration. The design constraints that need to be taken into account for CMUT arrays, especially for NDE applications, are presented. The main issue of designing an array consisting of a large number of CMUT cells required for producing a pressure wave of sufficient strength which is detectable upon reflection from the desired location even after suffering severe attenuation resulting from propagation in various media is addressed. A scalable annular array architecture of CMUT cells is recommended based on the analysis carried out.

Most modern engines utilise pistons with an offset gudgeon pin. In internal combustion engines, the offset is to the major thrust side of the piston. The piston thrust side is the part of the piston perpendicular to the gudgeon pin that carries the majority of side loading during the power stroke. Primary reason for having the gudgeon pin positioned eccentrically is to prevent the piston from slamming into the cylinder bore after the connecting rod journal passes the top dead centre. This phenomenon is referred to as piston slap, and is more pronounced in compression ignition and high performance engines due to higher combustion pressure than that of commercial spark ignition engines. The coming together of the piston and the bore results in scuffing, at best, or, catastrophic failure at worst. Clearance space between bore and piston is filled by a lubricant film. The main role of the lubricant is to separate the piston and bore by reacting to the applied load. Investigating the above problem requires a holistic approach, whereby a dynamic three degree-of-freedom piston model is coupled with a lubrication model to represent the actual system. The dynamic model determines the motion of the piston in combined axial, lateral and rotation about the gudgeon pin. The reactive forces due to lubricant films on the major and minor thrust sides of the piston play significant roles in piston dynamics and are evaluated by either quasi-static or transient solution of the lubricant contact conjunctions. The novel quasi-static analysis is carried out in the sense of its detailed approach, including many key practical features. not incorporated in other analyses, hitherto reported in literature. These features include first and foremost the development of a specific contact mechanics model for evaluation of conforming contacts for piston skirt against liner or bore. The quasi-static analysis includes many practical feature not encountered in other literature on the subject, such as detailed surface irregularities and modification features, and with thermal distortion. The analysis has been extended to thermohydrodynamics, as well as micro-hydrodynamics, all with high computational mesh densities, and robust methods of solution in space and time domains, including effective influence Newton-Raphson method and linear acceleration integration scheme. The transient tribo-elasto-multi-body dynamics problem includes physics of motion study from film thickness prediction and secondary motion evaluation of the order of micrometers and minutes of arc to large rigid body dynamics, including simultaneous solution of the contact problem at both major and minor thrust sides. Such a comprehensive solution has not hitherto been reported in literature. The thesis discusses many aspects of piston dynamics problem, through the broad spectrum of vehicle manufacture, with many pertinent practical engineering issues. In particular, it provides solutions for high performance Formula 1 racing engines. This is the first ever comprehensive analysis of piston tribodynamics for this range of engines at very high combustion pressures. This study has shown the paramount influence of profile of piston in promoting lubrication between the contiguous bodies, as evident from the pattern of lubricant flow through the contact. Deformation of the bodies increases the volume of lubricant in the contact. During the reversal in direction of piston motion, when the entraining velocity momentarily cases and reversal takes place, the load is held by an elastic squeeze.

Gear rattle is caused by engine torsional vibration (engine order response) imparted to the transmission components, further causing the gears to oscillate within their functional backlashes. These oscillations lead to the repetitive impact of gear teeth, which lead to noisy responses, referred to as gear rattle. The lack of in-depth research into the effect of lubricant on gear rattle has been identified as a deficiency in the previous research in rattle. The aim ofthe current work is to address this shortcoming. The thesis outlines a new approach in investigating the problem of idle gear rattle. The approach is based on the assumption that under idling condition the teeth-pair impact loads are sufficiently low and the gear speeds are sufficiently high to permit the formation of a hydrodynamic lubricant film between the mating gear teeth. This film acts as a non-linear spring-damper that couples the driver and the driven gears. A torsional single-degree of freedom model is used in the development of the theory. The model is then expanded into a seven-degree of freedom torsional model and finally into an Il-degree of freedom model that also includes the lateral vibrations of the supporting shafts. The Il-degree of freedom model is based on a real life transmission that is also used in experimental studies to validate the model. It is found that lubricant viscosity and bearing clearance (lubricant resistance in squeeze) play important roles in determining the dynamics of the system and its propensity to rattle. At low temperatures, the lateral vibrations of the shafts, carrying the gears interfere with the gear teeth impact action. The severity of rattle is determined by the relationship between the entraining and squeeze film actions of the hydrodynamic film. When the latter dominates, the system can rattle more severely. The numerical results are found to correlate well with the experimental findings obtained from vehicle tests in a semi-anechoic chamber and also with those from a transmission test rig in the powertrain laboratory.

Tests are performed on a flexure-pivot-pad tilting-pad bearing with a series integral squeeze film damper in load-between-pads configuration, with both active and locked damper. The damper effects are negated when locked, resulting in a flexure-pivot-pad bearing only. Experimental tests provide static performance data and dynamic stiffnesses from which rotordynamic coefficients are extracted. The following two excitation schemes are implemented: (1) multi-frequency, single direction excitation and (2) single-frequency, rotating load excitation (or "circular excitation"). The XLTRC2 Rotordynamics Software Suite provides stiffness and damping coefficient, eccentricity, and power loss predictions for the locked damper bearing. Test conditions include the rotor-speed range of 4000-12000 rpm and the unit-load range of 0-862 kPa (0-125 psi). Dynamic tests utilizing the multi-frequency excitation for the locked and active damper bearing configurations both show that the real portion of the dynamic stiffness is well modeled by a quadratic curve fit, and the imaginary portion representing the damping is a linear function of excitation frequency. This means that frequency independent coefficients can be obtained when an added mass term is included. While stiffness coefficients are lower for the active damper bearing, damping coefficients remain almost constant between the locked and active damper configurations. A simulation shows that, although the damping coefficients do not change significantly, the reduced stiffness provided by the damper results in greater effective damping. Static performance tests for the locked and active damper bearing indicate low cross-coupling, as shown by the eccentricity and low attitude angle measurements. Pad metal temperature measurements show a smaller temperature differential along the pad arcs for the active damper bearing, than observed for the locked damper case. Frictional power loss is estimated based on lubricant temperature rise and does not differ significantly for the two bearing configurations.

Squeeze Film Dampers (SFDs) are employed in high-speed Turbomachinery, particularly aircraft jet engines, to provide external damping. Despite numerous successful applications, it is widely acknowledged that the theoretical models used for SFD design are either overly simplified or incapable of taking into account all the features such as cavitation, air entrainment etc., affecting the performance of a SFD. On the other hand, experimental investigation of flow field and dynamic performance of SFDs can be expensive and time consuming. The current work simulates the flow field inside the dynamically deforming annular gap of a SFD using the commercial computational fluid dynamics (CFD) code Fluent and compares the results to the experimental data of San Andrés and Delgado. The dynamic mesh capability of Fluent and a User Defined Function (UDF) was used to replicate the deforming gap and motion of the rotor respectively. Two dimensional simulations were first performed with different combinations of rotor whirl speed, operating pressures and with and without incorporating the cavitation model. The fluid used in the simulations was ISO VG 2 Mobil Velocite no. 3. After the successful use of the cavitation model in the 2D case, a 3D model with the same dimensions as the experimental setup was built and meshed. The simulations were run for a whirl speed of 50 Hz and an orbit amplitude of 74 μm with no through flow and an inlet pressure of 31kPa (gauge). The resulting pressures at the mid-span of the SFD land were obtained. They closely agreed with those obtained experimentally by San Andrés and Delgado.

In der vorliegenden Arbeit wird ein neuer mikromechanischer Drehratensensor nach dem Stimmgabelprinzip vorgestellt. Die mechanische Sensorstruktur wird mit Hilfe der Bulkmikromechanik hergestellt und arbeitet nach dem elektrostatischen Wirkprinzip. Um große Amplituden zu erreichen, werden mechanische Koppelschwingungen ausgenutzt. In der Arbeit wird allgemein auf Entwurfsprozeß, Modellierung und Simulation mikromechanischer Strukturen eingegangen. Es wird die gemeinsame Lösung gekoppelter Felder mit Hilfe der Netzwerkmethode (PSpice) und die partitionierte Lösung mittels Online-Simulatorkopplung (ANSYS–PSpice) vorgestellt. Ein wesentlicher Bestandteil der Arbeit ist die Untersuchung der viskosen Luftdämpfung mikromechanischer Elemente mit engen Bewegungsspalten. Es werden verschiedene Möglichkeiten der vereinfachten Berechnung gezeigt.

Typical aero-engine assemblies have at least two nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. As a result, the flexible casing structures become highly sensitive to the vibration excitation arising from the High and Low pressure rotors. Lowering vibrations at the aircraft engine casing can reduce harmful effects on the aircraft engine. Inverse problem techniques provide a means toward solving the unbalance identification problem for a rotordynamic system supported by nonlinear SFD bearings, requiring prior knowledge of the structure and measurements of vibrations at the casing. This thesis presents two inverse solution techniques for the nonlinear rotordynamic inverse problem, which are focused on applications where the rotor is inaccessible under operating conditions, e.g. high pressure rotors. Numerical and experimental validations under hitherto unconsidered conditions have been conducted to test the robustness of each technique. The main contributions of this thesis are:• The development of a non-invasive inverse procedure for unbalance identification and balancing of a nonlinear SFD rotordynamic system. This method requires at least a linear connection to ensure a well-conditioned explicit relationship between the casing vibration and the rotor unbalance via frequency response functions. The method makes no simplifying assumptions made in previous research e.g. neglect of gyroscopic effects; assumption of structural isotropy; restriction to one SFD; circular centred orbits (CCOs) of the SFD. • The identification and validation of the inverse dynamic model of the nonlinear SFD element, based on recurrent neural networks (RNNs) that are trained to reproduce the Cartesian displacements of the journal relative to the bearing housing, when presented with given input time histories of the Cartesian SFD bearing forces.• The empirical validation of an entirely novel approach towards the solution of a nonlinear inverse rotor-bearing problem, one involving an identified empirical inverse SFD bearing model. This method is suitable for applications where there is no adequate linear connection between rotor and casing. Both inverse solutions are formulated using the Receptance Harmonic Balance Method (RHBM) as the underpinning theory. The first inverse solution uses the RHBM to generate the backwards operator, where a linear connection is required to guarantee an explicit inverse solution. A least-squares solution yields the equivalent unbalance distribution in prescribed planes of the rotor, which is consequently used to balance it. This method is successfully validated on distinct rotordynamic systems, using simulated data considering different practical scenarios of error sources, such as noisy data, model uncertainty and balancing errors. Focus is then shifted to the second inverse solution, which is experimentally-based. In contrast to the explicit inverse solution, the second alternative uses the inverse SFD model as an implicit inverse solution. Details of the SFD test rig and its set up for empirical identification are presented. The empirical RNN training process for the inverse function of an SFD is presented and validated as a part of a nonlinear inverse problem. Finally, it is proved that the RNN could thus serve as reliable virtual instrumentation for use within an inverse rotor-bearing problem.

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