Ž . Sensors and Actuators 81 2000 285–289 www.elsevier.nlrlocatersna Modelling and analysis of a magnetic microactuator a, ) a a b b ´ b D. de Bhailıs , C. Murray , M. Duffy , J. Alderman , G. Kelly , S.C. O Mathuna ´ ´ a PEI Technologies, UniÕersity College, Prospect Row, Lee Maltings, Cork, Ireland b National Microelectronics Research Centre, UniÕersity College, Prospect Row, Lee Maltings, Cork, Ireland Abstract This paper describes the operation of a magnetic microactuator. A prototype device consisting of a Nd–Fe–B permanent magnet, a silicon membrane and an electroplated copper coil is used to verify models and to predict the deflection of the magnetic microactuator. The analysis of this device involves the investigation of its electromagnetic and mechanical behaviour using analytical methods and finite Ž . element analysis FEA . A design procedure for a magnetic microactuator is also outlined. The prototype device was characterised and the measured results compared to the theoretical data. Results show that the deflection of the device may be predicted to an accuracy of 20%. q 2000 Elsevier Science S.A. All rights reserved. Ž . Keywords: Finite element analysis FEA ; Magnetic microactuator; Silicon membrane 1. Introduction In the development of actuating devices, various driving mechanisms are under investigation, including electromag- netic, electrostatic, chemical, piezoelectric and thermop- wx neumatic actuation 1 . In recent years, electromagnetic actuators have generated considerable interest due to the desirable characteristic of having the ability to produce large forces which allows the design of devices with large deflection. Electromagnetic actuation also has the advan- wx tage of contactless movement 2 . This property can be utilised in environments where safety is critical and where it is important that an actuator has the capability of self-test. The possibility of reducing power consumption in mag- netic actuators by using high aspect ratio coils makes electromagnetics an attractive choice of driving principle w x 3,4 . Both electromagnetic and mechanical analyses are re- quired to fully characterise an electromagnetic actuator. In terms of the mechanical performance of such a device, the main parameters of interest are the generated magnetic force and the deflection of the pumping membrane. This paper deals with the design for deflection of a magnetic microactuator. ) Corresponding author. 2. Operating principle Fig. 1 shows a schematic of the components of a magnetic microactuator. The device should consists of a substrate, a coil, magnetic material, and a moveable mem- brane. When a current is applied to the coil, a magnetic field is generated which interacts with the magnetic field of the permanent magnet to produce a force. This force acts on the membrane thereby causing it to deflect. The parameters on which the deflection of the microac- tuator is dependent are outlined in Fig. 2. The deflection primarily depends on the magnetic force generated by the coil and the magnet, and the restoring force of the mem- brane. The magnetic force is given by the magnetic field of the coil, the strength of the magnet and the volume of the magnet. It is also dependent on the position of the magnet along the central axis. The restoring force of the membrane is related to the mechanical properties of the material and the geometry of the material. The contribution of each of the parameters is outlined in the following analysis. 2.1. Magnetic field of coil The magnetic field generated by the conductors is mod- elled using analytical formulae and FEA. The analytical equation for the magnetic field generated by a circular coil 0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. Ž . PII: S0924-4247 99 00176-4