Modelling and Optimal Design of Multilayer Cantilever Microactuators
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U10.11.1
Modelling and Optimal Design of Multilayer Cantilever Microactuators L.H. Han, T. J. Lu Department of Engineering, University of Cambridge Trumpington Street, Cambridge CB2 1PZ, UK ABSTRACT Thermal expansion is an important actuation mechanism for microelectromechanical system (MEMS). We investigate multi-layered cantilever microactuators actuated by resistive heating with an electric current. The actuator consists of films and sandwiched microheaters. An electrothermal-elastic model for characterizing microactuators is developed. The general analytical expressions relating tip deflection with an applied electric field, temperature change, the film thickness and the applied load at the tip are obtained. The large deflection is considered in the model. The width effect of the cantilever is also investigated using 3D finite element analysis. Based on the analytical solutions and a mixed variable programming (MVP) algorithm, the optimal design of the actuators is presented. The algorithms optimize simultaneously with respect to the number of films and the material choice from a list of candidate materials. The minimum weight and maximum deflection are chosen as the design objectives. INTRODUCTION Thermal expansion is an important actuation mechanism for microelectromechanical system (MEMS). The bimorph structure has been successfully implemented in MEMS applications [1][2] [3]. In practical cases, a bimorph actuator may contain additional layers (such as heating elements, bonding and insulation layers etc). For macroactuators, Timoshenko’s bimetal model [4] is sufficient for determining the quasi-static behavior of the bimorph actuator since the additional layers are relatively thin and can be ignored. However, for microactuators, the additional layer may have a comparable thickness with respect to the active layer, the bimorph model is invalid. Moreover, due to the manufacturing difficult for a single layer stress-free thick film, the layers of a bimorph actuator may be made by stacking multiple thin films. Therefore, more general multimorph models are required for the actuator design. In this paper, the electrothermal-elastic model for multilayer cantilever actuators is developed. The optimal design of multimorphs is presented. THEORY When an electrical current I is applied to an m-layer multimorph cantilever beam (Fig. 1), resistive heating occurs. The thermal expansion will induce the beam bending. The tip deflection can be obtained by the electro-thermal and thermal-elastic analyses. Electro-Thermal analysis To calculate the temperature distribution, a one-dimensional conduction model [5] is employed since the films are thin. The temperature variation of the beam with respect to time and position is as follows:
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n ∂T ∂qx p 2 R (1) ∑ ρi ci Ai ∂t = ∂x − hp (T − T0 ) + I L i =1 Where Ai = Bti is the cross-section area of the ith layer with the density ρi , specific heat cip and the convection heat transfer coefficient h , R is the resistance of the heating layer, n ∂T qx = ∑ K i
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