a Monte Carlo Investigation M. Bagherinia, S. Mariani, A. Corigliano - PowerPoint PPT Presentation

Dipartimento di Ingegneria Civile e Ambientale Stochastic Effects on the Dynamics of a Resonant MEMS Magnetometer: a Monte Carlo Investigation M. Bagherinia, S. Mariani, A. Corigliano Dipartimento di Ingegneria Civile e Ambientale Politecnico di Milano, Italy

2 2 Magnetometers: engineering motivation The earth magnetic field as a vector quantity X,Y, Z components Orientation determination Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

3 Working principle The external magnetic fields Change of the resonating system configuration ( displacement, eigen-frequency) Static Plate Static Plate ELECTRICAL MEASUREMENT Mems Structure Mems Structure The magnetic field component is defined as a function of the configuration change Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Design requirements 4 Some Designs In The Literature Design Demands Herrera-May et al 1 High sensitivity 1 2 3 2 Process limitations Behraad Bahreyni 1 2 3 3 Mechanical acceleration filtering VTT technical research center 1 2 3 The goal of our designs Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

New design ideas (Capacitive parallel plates) 5 5 v i g B z c acceleration g Displacement due to magnetic field v Displacement due to acceleration Absence of acceleration Presence of acceleration Mechanical acceleration filtered out Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Multi-physics modeling 6 i l Hamilton’s principle Thermo electro magneto mechanical problem Joule effect Lorentz force and eddy current Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Multi-physics modeling 7 Applying Galerkin method to Hamilton’s principle First Eigen mode Clamped - Clamped One degree of freedom equivalent system (Duffing nonlinear equation) Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Multi-physics modeling 8 Maximum amplitude of oscillation is given by the solution of Current frequency Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Multi-physics simulation 9 To check the model, Ansys multi-physics simulations were performed Static thermo-electro-structural analysis Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Multi-physics simulation 10 , Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Parameter optimization 11 Sensitivity (Maximum amplitude) Sensor’s performance Power consumption (Minimum electrical resistance) To have an optimal device, we perform a multi objective optimization procedure, consisting of a structural objective function (Z Max ) and an electrical objective function (R elec ) h l Optimal h , l of the multi-physics solution for the fundamental component Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Optimal design for dynamic compliance 12 Unconstrained objective function Constrained objective function (red line), and optimal path followed by the minimization algorithm (black dotted line) Except for the first iterations that move from a point violating the prescribed equality constraint, the optimizer provides a set of feasible solutions to the arising sub-problems. It finally ends with the expected global minimum h=2 μ m, l=580.9 μ m Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Optimal design for power consumption 13 Unconstrained objective function Constrained objective function (red line), and optimal path followed by the minimization algorithm (black dotted line) Except for the first iterations that move from a point violating the prescribed equality constraint, the optimizer provides a set of feasible solutions to the arising sub-problems. It finally ends with the expected global minimum h=3.8 μ m, l=798.1 μ m Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Uncertainty assessment of sensors performance 14 Sources of uncertainty in the model and probability density functions (PDFs) Young’s modulus -10 x 10 1.5 E data Normal Lognormal Inverse gaussian Maximum Weibull 1 likelihood Rician Density E distribution 0.5 0 1.4 1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 RVE of polysilicon Data 11 x 10 PDF of E Over etching uncertainty in beam width due to process (uniform PDF) Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Uncertainty assessment of sensors performance 15 Monte Carlo simulation: effect of uncertainties on Z Max around the optimal values h distribution E distribution 200 400 100 200 0 0 2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 1.35 1.4 1.45 1.5 1.55 1.6 1.65 -6 11 x 10 x 10 number of occurrence -11 amplitude histogram x 10 500 3 amplitude 2 0 1 1 1.5 2 2.5 2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 amplitude h -11 -6 x 10 x 10 -11 -11 x 10 x 10 3 amplitude 3 amplitude 2 2 1 1.8 2.4 1.6 2.3 1 2.2 1.4 2.1 1.2 2 1.35 1.4 1.45 1.5 1.55 1.6 1.65 11 -6 x 10 x 10 E h E 11 x 10 Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems

Planned activities 16  Validate the multi-physics model by a commercial FEM code (either Ansys or Comsol)  Adopt a topology optimization approach to find the optimal shape of the base component (to search for the optimal shape, not only beam shaped structures, but also tapered, curved and any other arbitrary shape)  Performing the experimental tests on the devices Eurosime2013 - A. Corigliano, M. Bagherinia, M. Bruggi, S. Mariani, E. Lasalandra . www.stru.polimi.it/mems