Mathematical Modelling and Simulation of Magnetostrictive Materials by Comsol Multiphysics

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 www.ntnu.no

Outline Motivation History and Physical behavior Functions and applications o Sensors o Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Problems Conclusion 2 www.ntnu.no

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 www.ntnu.no

History and Physical behavior History: - Discovered on 1842 James Joule - Giant magnetostrictive 1960 USA Navy Physical behaviour: - Apply magnetic field H 5 www.ntnu.no

History and Physical behavior - Internal domains alignment - Changing in shape changing in magnetic field 6 www.ntnu.no

History and Physical behavior - Reversible cycle and magneto-mechanical coupling diagram 7 www.ntnu.no

Functions and applications Sensors and actuators: Coil electrical energy magnetic energy Magnetostrictive rod magnetic energy mechanical energy. Possibility to recover energy from waste 9 www.ntnu.no

Outline Motivation History and Physical behavior Functions and applications o o Sensors Actuators Energy conversion Mathematical modelling Modelling in Comsol Multiphysics Problems Conclusion 10 www.ntnu.no

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 www.ntnu.no

Mathematical modelling By making some mathematical steps the model will be: ( με 2 ρd 2 ) 2 2 2 T d T H H = σ + ( με ρη) + μσ + 2 2 H d t μ t t μ t 2 2 2 T T H = ρη + ρd 2 2 2 x t t Considering harmonic analysis: H = ω kt % + ω k % H 2 2 2 1 2 2 T 2 x = ω GT % + ω G% H 2 2 1 2 k% 1 k% 2 G% G% 1 2 d = = iμσ d + ω μ ( ρη με ) i + 2 2 ( ρd μ ε) = ρσ = ρd μ 2 μ σ ω 12 www.ntnu.no

Mathematical modelling Iterative evaluation for the parameters 13 www.ntnu.no

Modelling in Comsol Multiphysics Model related to the mathematical one for the simulation 15 www.ntnu.no

Modelling in Comsol Multiphysics Induction flux lines 16 www.ntnu.no

Modelling in Comsol Multiphysics Auxiliary 2D geometry and meshing 17 www.ntnu.no

Results and problems Full harmonic excitation simulation 19 www.ntnu.no

Results and problems 3D model problem 20 www.ntnu.no

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 www.ntnu.no

23 www.ntnu.no Thank you!

24 www.ntnu.no Mathematical modelling

25 www.ntnu.no Mathematical modelling