Novel performance analysis techniques with application to the scaling properties of silicon micromotor structures

Abstract

<p>An output coefficient extracted from motor design sizing calculations is cast into a form whereby it can be implemented as an actuation independent measure of performance. The way in which this measure scales for both electrically actuated motors and magnetically actuated motors is investigated. An engineering process for judging the advantages and disadvantages of each actuation scheme as it applies to particular motor designs is discussed. The performance capabilities of an electrically actuated variable capacitance motor are compared to those of a magnetically actuated alternative using the output coefficient as a comparative measure. A transition point is estimated which represents the scale at which the benefits of electrical actuation over magnetic actuation put electrically actuated devices in the realm of practical consideration. The two axis or dq0 method of analysing conventional magnetically actuated machines is extended and applied to the topology of an electrically actuated variable capacitance silicon micromotor. A "conventional" finite element technique is used to obtain estimates for the direct axis and quadrature axis synchronous capacitive susceptances. The energy based formulation employed eliminates the need to extract self and mutual phase capacitances and produces the desired axis capacitances directly. This novel method brings attention to higher order harmonics in the direct axis and quadrature axis charge waveforms. A physical explanation based on positive, negative and zero sequence phase charge is derived accounting for the observed rotor position-dependent characteristics. A dual bounds approach is applied to a typical two-dimensional micromotor structure. The direct axis capacitance is computed for the conditions of maximum stator pole-rotor pole overlap with the excitation EMT placed in two "extreme" conditions. The first condition is placement along the rotor's direct axis and the second condition is placement along the rotor's quadrature axis. Quadrilaterals are used to discretize a ninety degree (electrical) section of a silicon micromotor structure with a stator pole to rotor pole ratio of three to two. Two separate discretizations are considered, one for each of the stator EMF conditions previously noted. A method in which the same quadrilateral discretization can be used for both the upper and lower capacitance bound is presented. The notion of a stationary solution for the method of dual bounds is shown to exist. A simple two-dimensional example is given in order to illustrate how the linear equations are derived and to bring to out the ability to control the coupling of the resultant linear equations. Substantial computational savings, especially in the three-dimensional case can be realized (when compared to the finite element method) and warrant future examination and application in both electrically actuated and magnetically actuated problems. The encouraging two-dimensional results lead to a full three-dimensional extension of the theory, in particular, the development of novel geometrical constructs necessary for dual bound analysis. Formal methods for determining the placement of equipotential slices and flux tube walls inside fundamental cuboid structures are presented. Actual numerical results are presented for two simple three-dimensional constructs. A discretization process is given that shows how a complete three-dimensional silicon micromotor model can be discretized using the geometrical primitives derived in this thesis.</p>