Stewart McWilliam

A preliminary investigation of thermo-elastic damping in silicon rings

Zeners model for thermo-elastic loss, when applied to uniform beams undergoing flexural vibrations, gives theoretical predictions of mechanical Q-factor that often agree well with experimental measurements. The use of silicon ring resonators in MEMS devices is now becoming increasingly common. This paper considers the application of Zeners theory to thin, circular rings and presents a simple expression for the Q-factor associated with in-plane flexural modes of vibration. The theoretical predictions are shown to be in good agreement with experimental measurements for a practically relevant range of ring sizes. The relationships between ring dimensions, ambient temperature and Q-factor are explored.

Optimization of a cantilever microswitch with piezoelectric actuation

This paper considers MEMS microswitches with piezoelectric-film actuation. A mathematical actuator model is established that accounts for normal stress at the piezo-substrate interface, in addition to shear stress. This model gives more accurate predictions for relatively thicker piezoelectric layers. Maintaining adequate contact force between switch electrodes is important in ohmiccontact switches, but parallel contact geometry is also important in switches that provide capacitive coupling between the signal lines. Furthermore, ‘off-state’ isolation is governed by electrode gap when open. The presented mathematical model demonstrates the relationships between these factors and the switch geometry. Optimum conditions are derived.

A geometric parameter study of piezoelectric coverage on a rectangular cantilever energy harvester

This paper proposes a versatile model for optimizing the performance of a rectangular cantilever beam piezoelectric energy harvester used to convert ambient vibrations into electrical energy. The developed model accounts for geometric changes to the natural frequencies, mode shapes and damping in the structure. This is achieved through the combination of finite element modelling and a distributed parameter electromechanical model, including load resistor and charging capacitor models. The model has the potential for use in investigating the influence of numerous geometric changes on harvester performance, and incorporates a model for accounting for changes in damping as the geometry changes. The model is used to investigate the effects of substrate and piezoelectric layer length, and piezoelectric layer thickness on the performance of a microscale device. Findings from a parameter study indicate the existence of an optimum sample length due to increased mechanical damping for longer beams and improved power output using thicker piezoelectric layers. In practice, harvester design is normally based around a fixed operating frequency for a particular application, and improved performance is often achieved by operating at or near resonance. To achieve unbiased comparisons between different harvester designs, parameter studies are performed by changing multiple parameters simultaneously with the natural frequency held fixed. Performance enhancements were observed using shorter piezoelectric layers as compared to the conventional design, in which the piezoelectric layer and substrate are of equal length.

Development of micromachined RF switches with piezofilm actuation

Current developments in RF systems require high-performance switches for applications including signal routing, impedance matching and adjustable gain amplifiers. The use of micro-switches to replace traditional semiconductor components is increasingly common, because of their advantages in terms of electrical isolation and power loss. This paper reports on a research program relating to the development of a silicon micro-machined RF micro-switch that uses thin-film piezoelectric material for actuation. Piezoelectric actuation has potential advantages over electrostatic actuation in terms of achievable forces and simplicity of structural design. This paper gives an overview of the design and analysis of a prototype switch. The design concept, based on a cantilevered silicon beam or plate, is described. A low order mathematical model, incorporating the mechanical and electrical characteristics of the switch and the interaction between the silicon structure and the piezo-drive is summarized. This allows the basic behavior of the switch to be quantified, and provides a useful tool for design and optimization purposes. The outline design and manufacture/processing of a prototype switch is discussed.

A statistical analysis of first and second order vessel motions induced by waves and wind gusts

Abstract A closed form series solution for the combined first and second order response probability density function has been derived in terms of the eigen values and eigen vectors of the matrix arising in a discretised Kac-Siegert analysis. The first term of the resulting series corresponds to the assumption that the first and second order response are statistically independent, while subsequent terms depend upon the joint cumulants of the response. The applicability of the method is investigated by comparison with time domain simulation. The results suggest that a good estimate of the probability density function may be obtained from the first term of the series and that a limited number of eigen values will suffice. Consequently, it may be deduced that the need to calculate the forementioned eigen vectors is obviated and the eigen problem reduced.

Extreme values of first- and second-order wave-induced vessel motions

A recently developed expansion for the joint probability density function of two variables has been used to develop a means of determining the mean up-crossing rate of a combined first- and second-order random process. The first term in the series corresponds to the assumption that the response displacement and velocity processes are statistically independent, and further terms depend upon the joint displacement-velocity cumulants. The extreme statistics are then determined using the Poisson assumption of up-crossings. The accuracy of the method is examined by comparing the results with time domain simulation, and it is found that the displacement and velocity are, to a good approximation, statistically independent for the examples studied.

Optimization of piezoelectric cantilever energy harvesters including non-linear effects

This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations.

Review and comparison of different support loss models for micro-electro-mechanical systems resonators undergoing in-plane vibration

Several approaches for calculating support loss in micro-electro-mechanical system resonators undergoing in-plane vibration are reviewed. In each of them, the support is approximated as a semi-infinite domain. The first approach is analytical and models the support as a semi-infinite thin plate. This is compared with two different finite element approaches that introduce artificial boundaries to their finite domain. In order to absorb outgoing waves and model the infinite support, a perfectly matched layer method and the use of infinite elements are considered. Simple test cases are studied and the results for the support losses predicted by the different methods are compared. It is shown that each of the methods yields similar trends. Using the developed analytical model, a parametric study is performed on the support losses of a ring-based resonator. General strategies for improving the quality factor by reducing support losses are provided.

Piezoelectric energy harvesting for tyre pressure measurement applications

Piezoelectric energy harvesters have been proposed as a means of supplying electrical power to remote tyre pressure monitoring systems. This solution avoids problems of battery replacement and allows the tyre pressure monitoring system to be self-powered. In this paper, a previously developed theoretical model is used to predict the electric output and mechanical responses of a cantilever beam energy harvester embedded within a car tyre. The radial deformation of the tyre is considered to provide base excitation to the energy harvester, and a bump stop is incorporated into the harvester design to limit the vibration amplitude and maintain the structural integrity of the harvester. The simulation results show that the harvester achieves maximum power output, with or without the stop, when the harvester location coincides with the tyre contact patch. It is also found that the average power output is reduced when a bump stop is used, but the bending stress in the cantilever reduces significantly as the displacement of the beam is limited. A comparison with published experimental results indicates good levels of agreement. The model developed can be used as a design tool to optimize the performance of energy harvesters in tyre applications, where a compromise between power generation and structural integrity is required.

Novel Optimization Technique for Variation Propagation Control in An Aero-Engine Assembly

This paper presents a novel optimization technique in straight-build assembly to control variation propagation. The optimization technique is developed by minimizing the eccentricity stage by stage in the assembly. The straight-build assembly model is derived from connective assembly models, easily expressing the part-to-part relationships. Any measurement error or process error in the assembly can be easily incorporated in the model. This approach can be also used to predict the final assembly quality while the design is still at the conceptual stage. The straight-build assembly is validated by using statistical analysis through two case studies: a simple identical cylindrical-component assembly and a practical non-identical cylindrical-component assembly. The variation propagation can be reduced significantly for the straight-build assembly, compared to the direct-build assembly without optimization. The results show how the variation propagation control is related to process noise and measurement accuracy. The simulation results also show that minimal variation can be achieved at reduced cost by properly selecting the accuracy of measurement, according to process procedures. The information obtained provides a practical and useful approach for design engineers. The potential applications of the straight-build assembly are also illustrated.