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MacMMems : Macro Modeler for Magnetic Mems

Graphical interface

IHM MacMMems

Modeling method

MacMMems is a modelling tool dedicated to the magnetic microsystem design. It is based on magnetostatic modelling with symbolic calculation of integrals :
Biot and Savart (for conductors):
Biot & Savart
Coulombian equivalence (for magnets) :
Equivalence Coulombienne with and
Forces and torques are then defined by integral expressions of the fields created by each sources.

Semi-analytical modelling

MacMMems is an equation generator, indeed, it produce a semi-analytical model which can be used by CADES framework for simulation or optimisation needs.

Application exemple : optimization of a magnetic µ-switch


  • 4 fixed magnets
  • 1 mobile magnet
  • 4 conductors

Design specifications

  • 14 parameters to optimize
  • 12 parameters to contrain
  • To keep a force during displacement > 0.5 µN
  • To ensure a choc resistance < 15 G
  • To minimize copper losses

Finite elements comparison

In the case of simple geometries, analytical method are better than numerical ones due to numerical noise brought by meshing. Computation time is also better (1h30 vs 10 secondes for the analytical model)


Sensitivity computation is automatically generated by CADES Framework leading to gradient based optimization algorithm use.
The optimized solution answer specifications, minimizing impulsionnal switching power to 31W.

Dynamic study

The generated model is defined as a software component and can be easilly plugged into other environnements like Matlab/Simulink


  • P. Pham-Quang, B. Delinchant, J.-L. Coulomb, “Reliability-based design optimization using local sensitivity with application to magnetic nano switch”, Journal of Applied Electromagnetics and Mechanics, IOSPress, ISSN 1383-5416, Volume 43, Number 1-2 / 2013
  • H. L. Rakotoarison, V. Ardon, O. Chadebec, B. Delinchant, S. Guerin, J. L. Coulomb Formal Sensitivity Computation of Magnetic Moment method, IEEE Transactions on Magnetics, vol. 44,  Issue 6,  June 2008 Page(s):1014 - 1017
  • H. Chetouani, B. Delinchant, G. Reyne, Efficient modeling approach for optimization of a system based on passive diamagnetic levitation as a platform for bio-medical applications, COMPEL, Vol 26, Issue: 2, pp, 345 - 355, 2007
  • H. L. Rakotoarison, J. P. Yonnet, B. Delinchant Using Coulombian approach for Modeling Scalar Potential and Magnetic Field of a Permanent Magnet with Radial Polarization, IEEE Transactions on Magnetics., Vol. 43,  Issue 4, april 2007, pp 1261-1264, ISSN: 0018-9464
  • H. Rostaing, J. Stepanek, B. Delinchant, J. Delamare, O. Cugat « Conception, modélisation et prototypage d'un micro-relais bistable magnétique » revue internationale de génie électrique (RIGE). 2005, vol 8 n_5-6, pp. 703-724


These results are from collaborations between MAGE and µSystems teams. MacMMems was used during collaborations with industrial partener (CEDRAT, CEA/LETI, Schneider Electric).


Date of update November 22, 2018

Université Grenoble Alpes