page_title: Electropermanent magnet
section_title: Magnetic circuit analysis
hierarchical_section_title: Electropermanent magnet / Magnetic circuit analysis
caption_attribution_description: English: Detailed and simplified schematic of the EPM's magnetic circuit.
context_page_description: An electropermanent magnet or EPM is a type of permanent magnet in which the external magnetic field can be switched on or off by a pulse of electric current in a wire winding around part of the magnet. The magnet consists of two sections, one of "hard" magnetic material and one of "soft" material. The direction of magnetization in the latter piece can be switched by a pulse of current in a wire winding about the former. When the magnetically soft and hard materials have opposing magnetizations, the magnet produces no net external field across its poles, while when their direction of magnetization is aligned the magnet produces an external magnetic field.
  Before the electropermanent magnet was invented, applications needing a controllable magnetic field required electromagnets, which consume large amounts of power when operating. Electropermanent magnets require no power source to maintain the magnetic field. Electropermanent magnets made with powerful rare-earth magnets are used as industrial lifting magnets to lift heavy ferrous metal objects; when the object reaches its destination the magnet can be switched off, releasing the object.
context_section_description: Using a magnetic circuit analysis we can represent a simple EPM using the following schematic:
  We present two permanent magnets made of different materials (AlNiCo and NdFeB) and the soft magnet is made of Hiperco. An additional segment of hiperco is shown to close the circuit and obtains better calculated results. An air gap is included (One for each side of the EPM) for calculating the magnetic flux and field generated in the air as function of the gap distance. This will lead to obtain an expression of the EPM's force (exerted over the additional segment of hiperco) as a function of the separation distance.
  For the calculation of the values of the components in the circuit we will assume that all the areas in the flow have the same dimensions. If the selected magnets had a cylindrical shape then the area of the flow for the magnets will be   and the hiperco blocks will have a square section of side  in order to have the same area.
  For the AlNiCo magnet we can calculate the magnetomotive force (MMF), the reluctance  and the magnetic flow over that magnet as:
  For the NdFeB magnet we can calculate the magnetomotive force (MMF), the reluctance  and the magnetic flow over that magnet in the same way:
  Expressions for the reluctance  of the gap and the hiperco can be also generated:
  But the magnetic circuit can be simplified by using electric source transformations and considering all the hiperco in only one big reluctance (mainly because the value of those small pieces of reluctance are negligible compared with the reluctance of the permanent magnets). A simplified version of the magnetic circuit was presented on the right in the picture above:
  An equivalent reluctance () can be calculated to replace the magnets:
  For the equivalent MMF, there are going to be two different values. One when the EPM is ON and both flows are in the same direction (addition):
   EPM ON:
  And another one when the EPM is OFF and the magnetic fluxes are in opposite direction (subtraction)
   EPM OFF:
  Knowing the value of the MMF for the two stages of the EPM and the equivalent components, we can continue calculating the magnetic flux and the magnetic flux density (B):
  The original formula for force between two magnetized surfaces without fringing is well known, and presented below. In the formula the force is divided by 2. Since we are going to calculate the force for the two areas corresponding to the gaps then the equation to calculate the force as a function of the gap distance looks like:
caption: Detailed and simplified schematic of the EPM's magnetic circuit.
exif: {}