Mary C. Pugh

A finite volume method and experimental study of a stator of a piezoelectric traveling wave rotary ultrasonic motor

Piezoelectric traveling wave rotary ultrasonic motors are motors that generate torque by using the friction force between a piezoelectric composite ring (or disk-shaped stator) and a metallic ring (or disk-shaped rotor) when a traveling wave is excited in the stator. The motor speed is proportional to the amplitude of the traveling wave and, in order to obtain large amplitudes, the stator is excited at frequencies close to its resonance frequency. This paper presents a non-empirical partial differential equations model for the stator, which is discretized using the finite volume method. The fundamental frequency of the discretized model is computed and compared to the experimentally-measured operating frequency of the stator of Shinsei USR60 piezoelectric motor.

Time-Dependent Finite-Volume Model of Thermoelectric Devices

Thermoelectric modules are an important alternative to heat engines in the harvesting of waste heat. Electrical-thermal analogs are often employed when studying heat conduction and this approach can be extended to develop a model for thermoelectric effects. In this article, the coupled thermoelectric partial differential equations are discretized using the finite-volume method; the discretization respects the coupling between the heat sink and the thermoelectric material. The new model is especially useful when an accurate picture of transients in a thermoelectric device is required. Results from the 1-D finite-volume model are shown to agree with experimental results as well as 3-D simulations using COMSOL.

A Dynamic Model of a High Temperature Arc Lamp

High temperature, high pressure arc lamps are used to thermally process semiconductor wafers. An accurate dynamic model that links radiation output to current input would facilitate the design of a power circuit that optimizes energy transfer to the arc. A finite volume arc model was derived using averaging of the energy balance equation over spatial domains. The space averaging approach accurately models the partial differential equation form of the energy balance equation, as tested with both steady state and transient arc currents, including high energy pulses with a current amplitude range from 400 A to 40 kA and a pulse width of a millisecond or less.

A Dynamic Model of a High-Temperature Arc Lamp

High-temperature high-pressure arc lamps are used to thermally process semiconductor wafers. An accurate dynamic model that links the radiation output to the current input would facilitate the design of a power circuit that optimizes energy transfer to the arc. In this paper, a dynamic arc model is derived using averaging of the energy balance equation over spatial domains. This space averaging approach (the “finite-volume method”) accurately models the energy balance equation, as tested with both steady and transient arc currents, including high-energy pulses with a current amplitude range from 400 A to 27 kA and a pulsewidth of a millisecond or less.

Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times), and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers is also studied, for early time transients at reactive electrodes and for nonreactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

Modeling of composite piezoelectric structures with the finite volume method

Piezoelectric devices, such as piezoelectric traveling-wave rotary ultrasonic motors, have composite piezoelectric structures. A composite piezoelectric structure consists of a combination of two or more bonded materials, at least one of which is a piezoelectric transducer. Piezoelectric structures have mainly been numerically modeled using the finite element method. An alternative approach based on the finite volume method offers the following advantages: 1) the ordinary differential equations resulting from the discretization process can be interpreted directly as corresponding circuits; and 2) phenomena occurring at boundaries can be treated exactly. This paper presents a method for implementing the boundary conditions between the bonded materials in composite piezoelectric structures modeled with the finite volume method. The paper concludes with a modeling example of a unimorph structure.

Modeling of piezoelectric devices with the finite volume method

A partial differential equation (PDE) model for the dynamics of a thin piezoelectric plate in an electric field is presented. This PDE model is discretized via the finite volume method (FVM), resulting in a system of coupled ordinary differential equations. A static analysis and an eigenfrequency analysis are done with results compared with those provided by a commercial finite element (FEM) package. We find that fewer degrees of freedom are needed with the FVM model to reach a specified degree of accuracy. This suggests that the FVM model, which also has the advantage of an intuitive interpretation in terms of electrical circuits, may be a better choice in control situations.

Time dependent finite volume model of thermoelectric devices

Thermoelectric modules are an important alternative to heat engines in the harvesting of waste heat. Electrical-thermal analogues are often employed when studying heat conduction and this approach can be extended to develop a model for thermoelectric effects. The coupled thermoelectric partial differential equations are discretized using the finite volume method; the discretization respects the coupling between the heat sink and the thermoelectric material. The new model is especially useful when an accurate picture of transients in a thermoelectric device is required. Results from simulations using the model are presented and validated experimentally.

Modelling and optimizing a system for testing electronic circuit boards

In this article we consider a difficult combinatorial optimization problem arising from the operation of a system for testing electronic circuit boards (ECB). This problem was proposed to us by a company that makes a system for testing ECBs and is looking for an efficient way of planning the tests on any given ECB. Because of its difficulty, we first split the problem into a covering subproblem and a sequencing subproblem. We also give a global formulation of the test planning problem. Then we present and discuss results pertaining to the covering and sequencing subproblems. These results demonstrate that their solution yields testing plans that are much better than those currently used by the company. Finally we conclude our article by outlining avenues for future research.