Evaluation of energy dissipation mechanisms in vibrational microactuators

The energy dissipation characteristics of beam-shaped microactuators are analytically evaluated here as a first step in establishing a design method that minimizes their energy consumption. The energy dissipation by airflow force is calculated by using the Navier-Stokes equation and its accuracy is verified by comparing it with experimental results. Additionally, the dissipations due to squeeze force, internal friction, and support loss are respectively calculated by using a Reynolds equation, structural damping theory, and a two-dimensional theory of elasticity. The final formulas, obtained in simple and closed forms so that they can easily be used in the actual design process, are then used to evaluate the relationships between beam size and dissipation ratio for silicon cantilevers, Permalloy cantilevers, and Permalloy spiral springs. Finally,the indicial responses of a Permalloy cantilever is calculated and the relationship between beam size and settling time is clarified.