The present work investigates the potential of the finite element method (FEM) in the design process of magnetic Micro-Electro-Mechanical-Systems (MEMS). The magnetic forces and torques acting on a magnetic body are of great importance in wireless actuating principles. Good models are required to allow for precise and predictable motion of the magnetic body. However, analytical results are only available for simple geometries and experiments are often time consuming and may have a certain number of uncertain parameters that may influence the results. Numerical methods, and in particular the finite element method, offer the possibility to study a magnetic body with known material properties in a well defined environment.
Consequently, in this work, a method is proposed to calculate the net body torque on arbitrarily shaped bodies in a homogeneous magnetic field using the commercial finite element software Ansys . In addition, a procedure to de- termine the demagnetization factors of these bodies is given. The code is first validated by the known analytical results for an ellipsoid. As an application, the demagnetization factors, as well as the net magnetic torque on brick shaped bodies and the IRIS Microrobot are calculated. A method is proposed to predict the torque acting on the Microrobot analytically. However, experimental results are necessary to confirm this method.
Furthermore, Ansys is used to model magneto-structural coupling that is, the motion and deformation of a magnetic body due to an external magnetic field. Two devices are presented (as case studies rather than as actual design concepts), the magnetic resonator and the magnetic scratch drive actuator (MSDA). A quasi- analytical model for the static deflection of the magnetic resonator is given and good agreement with the finite element model is obtained. The MSDA is modeled to show the potential of Ansys in modeling MEMS devices, as additional to the coupling effects, contact elements and spring elements are introduced. Again, experimental results are required.
Table of Contents
1 Introduction
1.1 Scope of the Thesis
1.2 Structure of the Report
2 Theoretical Considerations
2.1 Magnetostatics
2.2 Magnetic Force and Torque
2.3 Analytical Model
3 Finite Element Model
3.1 Introduction to the Finite Element Method
3.2 ANSYS and the Maxwell Stress Tensor
3.3 The Meshing
3.4 Boundary Conditions
3.5 Material Properties
3.6 Finite Elements
3.7 Scripting
4 Demagnetization Factors and Magnetic Torque
4.1 Demagnetization Factors
4.2 Magnetic Torque
4.3 Saturation Effects
5 Coupled Magneto-Structural Analysis
5.1 Overview
5.2 Implementation of Magneto-Structural Coupling
5.3 Magnetic Resonator
5.4 Magnetic Scratch Drive Actuator
6 Summary and Outlook
Objectives and Topics
The work investigates the application of the finite element method (FEM) for designing 3D magnetic Micro-Electro-Mechanical-Systems (MEMS), focusing on calculating magnetic forces and torques acting on arbitrarily shaped bodies, as well as modeling magneto-structural coupling in specific micro-devices.
- Finite element method (FEM) application for magnetic MEMS
- Calculation of demagnetization factors and magnetic torques
- Magneto-structural coupling modeling in Ansys
- Performance analysis of magnetic resonators and actuators
- Validation of numerical approaches against analytical models
Excerpt from the Book
2.1 Magnetostatics
The behavior of electromagnetic fields as well as their interactions with matter are described by Maxwell’s equations, which in the differential form are given by
Gauss’s Law ∇·D = ρ
Gauss’s Law for Magnetics ∇·B = 0
Faraday’s Law of Induction ∇×E = −dB/dt
Ampère’s Law ∇×H = J + dD/dt
where H and E are the magnetic and electric field respectively, D and B are the electric and magnetic flux density, and ρ and J are the free electric charge and free current density.
We will consider the special case with no electrical charges (ρ = 0), no electric fields (E = 0), no currents (J = 0) and static fields (d(•)/dt = 0). Then Maxwell’s equations reduce to
∇·B = 0
∇×H = 0
Summary of Chapters
1 Introduction: Provides an overview of magnetic MEMS and the thesis scope, highlighting the challenge of fabricating 3D magnetic structures and the need for numerical modeling.
2 Theoretical Considerations: Outlines Maxwell’s equations, magnetic material properties, and derived expressions for calculating net magnetic forces and torques.
3 Finite Element Model: Details the implementation of the finite element method in Ansys, including meshing strategies, boundary conditions, and material property settings.
4 Demagnetization Factors and Magnetic Torque: Presents the numerical calculation of demagnetization factors and magnetic torques, validated against analytical ellipsoid models.
5 Coupled Magneto-Structural Analysis: Investigates the magneto-mechanical coupling in a magnetic resonator and a scratch drive actuator using iterative FEM simulations.
6 Summary and Outlook: Synthesizes the findings of the thesis and suggests future directions for validating the numerical methods through experimental results.
Keywords
Magnetic MEMS, Finite Element Method, Magneto-structural coupling, Ansys, Maxwell stress tensor, Demagnetization factors, Magnetic torque, Microrobot, Magnetic resonator, Scratch drive actuator, Magnetostatics, Simulation, Numerical analysis, MEMS design, Microactuation
Frequently Asked Questions
What is the core focus of this research?
The work focuses on using the finite element method to accurately predict the magnetic forces and torques acting on micro-scale 3D magnetic structures, which is crucial for the development of wireless MEMS actuators.
Which application area is particularly highlighted?
The study specifically uses the IRIS Microrobot as a case study, exploring its potential application in medical fields like eye surgery where predictable motion is essential.
How is the finite element model validated?
The numerical code is validated by comparing the calculated torque and demagnetization factors for simple prolate ellipsoids against well-established analytical formulas.
What software is utilized for the simulations?
The research primarily utilizes the commercial finite element software Ansys for both static magnetic analysis and coupled magneto-structural simulations.
How is the interaction between magnetic and structural fields managed?
The coupling is implemented through an iterative indirect (sequential) process, where magnetic loads are transferred to the structural environment and the mesh is updated accordingly until convergence.
What are the primary modeling limitations?
The study notes that current results are numerical and require experimental validation; it also identifies challenges in modeling complex contact and nonlinear material behavior.
Why are standard analytical models insufficient for this work?
Analytical solutions are generally limited to very simple geometries, whereas the proposed MEMS devices often feature complex, non-ellipsoidal 3D shapes that require numerical methods.
How do the researchers handle material saturation?
Saturation effects are studied by incorporating a nonlinear BH curve, generated using a modified Langevin function, into the finite element model to observe deviations from linear behavior.
What is the role of the "Equivalent Ellipsoid" in this work?
The equivalent ellipsoid serves as a reference geometry, allowing researchers to map complex structures like the microrobot or bricks to a known shape to approximate magnetic behavior analytically.
What specific devices are used to demonstrate magneto-structural coupling?
The study tests the coupling method on a magnetic resonator and a magnetic scratch drive actuator to demonstrate potential optimization pathways for MEMS devices.
- Quote paper
- Zoltan Nagy (Author), 2006, Numerical Approaches To 3D Magnetic MEMS, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/183339
