In the Quadrupole motor/generator (and also other project like the LRK project on the openvolta website), I have been using the PMs (permanent magnets) in the same fashion as M. Flynn and Dr. Lipo however, in the rotor, not into the stator.
If we have 2 PMs having the same dipole facing each other, a repelling force is produce. However, if you put a block between each, it will concentrate the magnetic flux within this block and if the block in not saturated of magnetic flux, then the PMs will stick to the block. If close the loop, each blocks will have a single pole, they will emulate a homo-polare magnet.
The advantage of doing this is adding force. So if you have both magnet with a unit 1 force, adding them face to face with dipole alike, you'll get 2 forces of unit! Right?.. No! you will get 4 forces of units!
A bit of math!
No, we are not going back to school but if we need to understand how we get 4 times more force, we have to know about one basic equation.Note that the equation is valid only for cases in which the effect of fringing is negligible and the volume of the air gap is much smaller than that of the magnetized material (less then 5mm).
The mechanical force between two nearby magnetized surfaces can be calculated with the following equation.
F = μ0 H2 A / 2
where:
F is the force, N (Newton),
A is the area of each surface, in m2,
H is their magnetizing field, in A/m,
μ0 is the permeability of space, which equals 4π×10−7 T·m/A
Since we are dealing with magnets, it is easier to use the following equation:
F = B2 A / 2μ0
where:
B the flux density, in T (Tesla).
An easier way to express this is: F = 400 000 B2 A.
Proof of concept:
As show here, the magnet is on the left side inserted in the 2 parts to create the core and the attracted armature on the right side. The airgap is 1 mm.
One part core is 40 mm x 100m x 20mm depth. The total area A = 40mm x 20mm x 2 poles= 1 600 mm2. The area has a flux density of approximately 0.4 T.F = 4 000 000 x 0.42x 0.001 6 = 102.4 N
If we verify with FEMM (finite element method software), the computed value is 108.1 N, which it is normal since the exact flux density is 0.411856 T.
If 2 PMs are put in parallel has shown here, we can see that the field density in the core and the armature has increased. If we use the same equation, one would think that since we have 2 PMs, we just have to multiply by 2 the force where 2 x 115 N = 203N. This not correct.
Since we have 2 PMs which faces the same dipole, the equation should therefore be restated to reflect this physical aspect. Therefore, F = 400 000 x (2B)2 x A. So the true value of this attracting force will now be F = 400 000 x (2 x 0.4)2 x 0.001 6 = 409.6 N. So, 409.6 N / 102.4 N gives up to 4 time the initial force!The magic is here, since we do have 2 PMs, we have two times the flux density (T); 2 x 0.4 = 0.8 T. Then the square root of 0.8 is 0.64 T. So basically what we are doing here if we assume that on magnet as 1 unit of force (1force x 2) x (1force x 2), we can now see that we quadrupled the force if we look only the components "2".
The results with FEMM yields to 431.6 N. Again 431.6 N / 108.1 N = 3.992 N, rounds up to 4 time more force.
The Quadrature
The quadrature is basically an arrangement of magnet that focuses the magnetic field in the centre of the quadrature. This is also know as a quadrupole magnet. This basic idea is use from which it inspired to design the rotor
The rotor
The Quadrupole motor / generator utilizes the PMs in parallel the quadrature, like the quadrature magnet technique to concentrate the magnetic flux within segment. When looping the segments with a PMs, the active production of torque is 4 time higher than using magnet only.
