Design of ideal circular bending actuators for high performance micropumps

This paper presents an investigation of ideal geometry and material parameters of piezo-driven axisymmetric unimorph actuators for micropump applications. Based on Classic Laminated Plate Theory, closed form expressions for the transverse and radial displacement under diverse loads are derived for two types of unimorph actuators. The general approach allows an application of this theory to almost arbitrary actuator geometries. Using analytical and numerical methods, both actuators are optimized to achieve maximum stroke volume at predefined pressure conditions. In this process, strikingly simple expressions are found, constituting the theoretical maximum stroke volume of a circular bender type actuator. The optimization is complemented by a non-linear FEM study that confines the scope of the the analytical results. In summary, the optimization procedure presented in this paper facilitates the design of piezoelectrically driven unimorph diaphragm actuators by providing generic design rules regarding materials and geometrical dimensions.