Mathematical Modelling and Simulation of Magnetostrictive Materials by Comsol Multiphysics
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1 Presented at the COMSOL Conference 2008 Hannover COMSOL Confernce 05/11/2008 Mathematical Modelling and Simulation of Magnetostrictive Materials by Comsol Multiphysics M. Bailoni 1, Y.Wei 2, L. Norum 3 1 University of Trieste, guest at Norwegian University of Science and Technology (NTNU) 2, 3 NTNU Department of Electric Power Engineering, Trondheim, NORWAY 1 bailoni@elkraft.ntnu.no, 2 yingkang.wei@sintef.no, 3 norum@ntnu.no, 1
2 Outline Motivation History and Physical behavior Functions and applications o Sensors o Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Problems Conclusion 2
3 Motivation make tool to achieve for a quantitativies analysis the relation magneto-mechanical Particuliarities of the material: - high density of available energy - long life time - prospective for new type of energy conversion 3
4 Outline Motivation History and Physical behavior Functions and applications o Sensors o Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Problems Conclusion 4
5 History and Physical behavior History: - Discovered on 1842 James Joule - Giant magnetostrictive 1960 USA Navy Physical behaviour: - Apply magnetic field H 5
6 History and Physical behavior - Internal domains alignment - Changing in shape changing in magnetic field 6
7 History and Physical behavior - Reversible cycle and magneto-mechanical coupling diagram 7
8 Outline Motivation History and Physical behavior Functions and applications o Sensors o Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Problems Conclusion 8
9 Functions and applications Sensors and actuators: Coil electrical energy magnetic energy Magnetostrictive rod magnetic energy mechanical energy. Possibility to recover energy from waste 9
10 Outline Motivation History and Physical behavior Functions and applications o o Sensors Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Problems Conclusion 10
11 Mathematical modelling The constitutive magnetostriction equations are: S = relative deformation of the shape Δl l the compliance at constant magnetic field magnetic field (induction) S = η T + d H ( H ) stress T is the forces per unit of area B= d T + μ H ( T ) piezomagnetic strain constant permeability at constant stress is the magnetic filed (intensity) 11
12 Mathematical modelling By making some mathematical steps the model will be: ( με 2 ρd 2 ) T d T H H = σ + ( με ρη) + μσ H d t μ t t μ t T T H = ρη + ρd x t t Considering harmonic analysis: H = ω kt % + ω k % H T 2 x = ω GT % + ω G% H k% 1 k% 2 G% G% 1 2 d = = iμσ d + ω μ ( ρη με ) i ( ρd μ ε) = ρσ = ρd μ 2 μ σ ω 12
13 Mathematical modelling Iterative evaluation for the parameters 13
14 Outline Motivation History and Physical behavior Functions and applications o Sensors o Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Problems Conclusion 14
15 Modelling in Comsol Multiphysics Model related to the mathematical one for the simulation 15
16 Modelling in Comsol Multiphysics Induction flux lines 16
17 Modelling in Comsol Multiphysics Auxiliary 2D geometry and meshing 17
18 Outline Motivation History and Physical behavior Functions and applications o Sensors o Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Results and problems Conclusion 18
19 Results and problems Full harmonic excitation simulation 19
20 Results and problems 3D model problem 20
21 Outline Motivation History and Physical behavior Functions and applications o Sensors o Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Results and problems Conclusion 21
22 Conclusion Comsol can solve this problem Stress depend of H and time Tractive and compressive efforts located top and bottom Future work: -transient analysis -complete and detailed simulation 22
23 23 Thank you!
24 24 Mathematical modelling
25 25 Mathematical modelling
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