diff --git a/MagneticForces/magnets.pro b/MagneticForces/magnets.pro index 3421498848cd9eb7e1c424d4b8056ba1c6ff251a..7e73f2ddf8d7ef2f4a17929ed55d2b6c0c361282 100644 --- a/MagneticForces/magnets.pro +++ b/MagneticForces/magnets.pro @@ -2,7 +2,8 @@ Tutorial 9 : 3D magnetostatic dual formulations and magnetic forces Features: - - Dual 3D magnetostatic formulations + - 3D Magnetostatics + - Dual vector and scalar magnetic potentials formulations - Boundary condition at infinity with infinite elements - Maxwell stress tensor and rigid-body magnetic forces @@ -24,12 +25,12 @@ in the problem decription below, irresective of whether they are truly permanent magnets or ferromagnetic barrels. - The tutorial model proposes the both dual 3D magnetostatic formulations: + The tutorial model proposes both dual 3D magnetostatic formulations: the magnetic vector potential formulation with spanning-tree gauging, and the scalar magnetic potential formulation. The later is rather simple in this case since, as there are no conductors, the known coercive field hc[] is the only source field "hs" one needs - to represens the magnetic field: + to represent the magnetic field: h = hs - grad phi , hs = -hc. @@ -45,19 +46,22 @@ which is a material dependent function of the magnetic induction "b" field. Exactly like we computed the heat flux "q(S)" through a surface "S" using a special auxiliary function "g(S)" associated with that surface - in the tutorial "Tutorial 5 : thermal problem with contact resistances", + in "Tutorial 5 : thermal problem with contact resistances", the magnetic force acting on a rigid body in empty space can be evaluated as the flux of the Maxwell stress tensor through that surface. There is one auxiliary function "g(SkinMagnet~{i}) = un~{i}" - for each magnet and the resultant magnetic force acting on "Magnet~{i}" + for each magnet, and the resultant magnetic force acting on "Magnet~{i}" is given by the integral: f~{i} = Integral [ TM[{b}] * {-grad un~{i}} ] ; - It should be insisted on the fact that the Maxwell stress is discontinuous - on material discontinuities, and that magnetic forces on rigid bodies - only depend on the Maxwell stress tensor of empty space and - on the "b" and "h" field distribution on the outer side of "SkinMagnet~{i}". + It should be insisted on the fact that the Maxwell stress tensor + is always discontinuous on material discontinuities, + and that magnetic forces acting on rigid bodies + only depend on the Maxwell stress tensor of empty space, + and on the "b" and "h" field distribution, + on the external side of "SkinMagnet~{i}" + (the side of the surface in contact with air). "{-grad un~{i}}" in the above formula can be regarded as the normal vector to "SkinMagnet~{i}" @@ -69,7 +73,7 @@ which is much smaller than "AirBox". To speed up the computation of forces, a special domain "Vol_Force" for force integrations is defined, which contains only - the layers "layer~{i}" of alla magnets. + the layers "layer~{i}" of all magnets. */ Include "magnets_common.pro"