A hybrid full-Lagrangian technique for the static and dynamic analysis of magnetostatic MEMS

Abstract

Magnetostatic microelectromechanical systems (MEMS) are based on the electromagnetic interactions between magnetic microstructures and active (coils) or passive (permanent magnets) magnetic field sources. They offer distinct advantages at the micrometer scale in strength, polarity and distance of actuation, when compared to other methods of actuation in MEMS. For proper understanding and detailed exploration of magnetostatic MEMS, it is important to have a reliable and efficient physical level simulation tool. In this paper, we propose an efficient technique, namely the hybrid full-Lagrangian technique for the static and dynamic analysis of magnetostatic MEMS. In this technique, the magnetostatic analysis needed to compute the magnetostatic force acting on the microstructure is performed using a hybrid BIE/Poisson approach. The Poisson equation is solved for the interior magnetostatic domains and the boundary integral equation (BIE) formulation of the potential equation is solved for the exterior magnetostatic domain and the different domains are coupled through interface conditions. A Lagrangian description of all the physical domains (magnetostatic, mechanical and fluidic) is used to eliminate geometry updates and rediscretization. The Lagrangian formulation along with the hybrid approach makes the proposed technique much more efficient than conventional tools for the analysis of magnetostatic MEMS. The new technique is used to simulate several magnetostatic MEMS switches and relays and validated by comparing numerical simulation results with experimental data. Dynamic analysis of a magnetostatic MEMS switch is performed using the new technique.

Sensing and Actuation in MEMS

“…The generated force F z in the vertical direction z can be approximated in this case as [39][40][41][42] where M z is the magnetization, V m is the volume of the magnet, and B z is the vertical magnet flux density generated by the coil. Usually, more accurate estimation of this force requires finite-element analysis and more complicated models [43]. Electromagnetic-magnetic interaction between a magnet and a coil has been also explored for power generation and energy harvesting [44][45][46].…”

Statistical Analysis and Yield Enhancement of MEMS Devices by Considering Multi-Process Variations

“…Various physical fields, such as electrical, mechanical and fluidic, are required to accurately model their interactions for such devices. Advances in numerical simulations and underlying multi-fields understanding have greatly improved the pace of devices modeling [1][2]. Unfortunately, assumptions have been made in these works that properties of the devices are all deterministic.…”