Topology optimization of 2D in-plane single mass MEMS gyroscopes
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RESEARCH PAPER
Topology optimization of 2D in-plane single mass MEMS gyroscopes Daniele Giannini1 · Francesco Braghin1 · Niels Aage2 Received: 29 December 2019 / Revised: 27 February 2020 / Accepted: 30 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we apply the topology optimization method to the design of MEMS gyroscopes, with the aim of supporting traditional trial and error design procedures. Using deterministic, gradient-based mathematical programming, the approach is here applied to the design of 2D in-plane single mass MEMS gyroscopes. We first focus on a benchmark academic case, for which we present and compare three different formulations of the optimization problem, considering typical industrial requirements. These include the maximization of the response of the sensor’s structure to the external angular rate, target resonant frequencies and minimum or constrained material usage. Also, a minimum length scale is imposed to the geometric features in order to ensure manufacturability, and an explicit penalization of grey elements is proposed to improve convergence to black and white layouts. Once the suitability of the method has been assessed, the formulation associated with the lowest computational cost, i.e. the one considering static estimations of the resonant frequencies, is applied to the design of a real-world MEMS gyroscope, targeting different resonant frequencies. Keywords Topology optimization · Single mass MEMS gyroscopes · Eigenfrequencies tuning · Harmonic response · Coriolis force · Minimum length scale
1 Introduction The market of inertial micro electro mechanical systems (MEMS) has grown at a spectacular rate in the last two decades. This kind of devices includes sensors such as accelerometers and gyroscopes, originally developed for military and space-related utilities but now found in a multitude of everyday products. For example, airbagrelease sensors and electronic stability control are now standard in all new cars. Also, activity monitoring of pacemaker patients and stabilization of platforms such as transport robots, drones and cameras are now improving our quality of life through the use of inertial MEMS devices. But, probably, the most interesting application is the motion sensing integrated into consumer electronics Responsible Editor: Emilio Carlos Nelli Silva Daniele Giannini
[email protected] 1
Department of Mechanical Engineering, Politecnico di Milano, Via G. La Masa 1, 20156 Milan MI, Italy
2
Centre for Acoustic-Mechanical Micro Systems, Department of Mechanical Engineering, Technical University of Denmark, Nils Koppels All´e, Building 404, DK-2800 Kgs. Lyngby, Denmark
(mobile phones, game controllers, toys etc.), personal navigation systems and other human-machine interfaces. The introduction of inertial MEMS into new application areas is a trend that is still gaining momentum (Kempe 2011). Potential markets of growth are expected through the evolution of sensors for wearable electronics, mobile health-care
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