Shape design of a MEMS device by Schwarz‐Christoffel numerical inversion and Pareto optimality

Abstract

Purpose

This paper sets out to provide a numerical procedure for field analysis and shape design for a class of MEMS devices.

Design/methodology/approach

The proposed numerical procedure for field analysis relies on numerical inversion of Schwarz‐Christoffel (SC) transformations for doubly‐connected regions: the geometry of a given micromotor is mapped into an annulus, where the non‐radial field excited by the transformed electrodes is computed. In turn, the shape design relies on the definition of non‐dominated solution according to the Pareto optimality conditions.

Findings

The SC approach proposed here allows the designer to evaluate both driving torque and radial force characteristics of the device with suitable accuracy within short CPU times. In turn, this allows one to perform repeated field analyses for a large number of feasible geometries and to use enumerative approaches to design optimization. By this means, a 3D objective space is investigated to identify the optimal shape of an electrostatic micromotor, subject to prescribed constraints.

Originality/value

To the best of one's knowledge, the combination of SC transformations and Pareto optimality is an unprecedented method for MEMS design. In particular, it is expected that the proposed SC tools will supply a fast and accurate computation to compare or supplement results from FEM tools, when a large number of geometries should be analysed. This could be particularly useful in the preliminary steps of a design procedure for a given class of devices.

Citation

Costamagna, E., Di Barba, P. and Savini, A. (2008), "Shape design of a MEMS device by Schwarz‐Christoffel numerical inversion and Pareto optimality", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 4, pp. 760-769. https://doi.org/10.1108/03321640810878162