The software used is CST STUDIO SUITE 2014.

Here is how the model looks

Dimensions are in meters. All magnets are taken to have relative permeability 1.1 and remanence B=1.4 T,

which approx. corresponds to N33 grade NdFeB magnets.

Figure 1 The inner magnet highlighted

Figure 2. The middle magnet highlighted

Figure 3. The outer magnet highlighted

The geometry is parameterized with the following parameters:

The parameters are ordered by radii.

innerR1 - Inner radius of the Inner magnet

innerR2 - Outer radius of the Inner magnet

innerR3 – Outer radius of the plurality of magnets around the Inner magnet.

…

h – Height of the model

Figure 4 Magnetization vectors for arrays of magnets

Figure 5. Magnetization of the Inner magnet

Figure 6. Magnetization of the Middle magnet

Figure 7. Magnetization of the Outer magnet

Figure 8. Meshed model

Notice “Comp. forces on groups of touching shapes” above. If 2 bodies touch, they are treated as a single

body. Forces acting on such bodies are summed up and reported as a single force exerted to one body.

Below is the full text from the screenshot above (we computed forces and torques only at one angle of

rotation).

Settings for force and torque calculation:

Coordinate system for torque axis and origin: Global

-------------------------------------------------------------------------------------

Torque axis origin:

Global coordinates:

x: +0.000000

y: +0.000000

z: +0.000000

-------------------------------------------------------------------------------------

Torque axis:

Global coordinates:

x: +0.000000

y: +0.000000

z: +1.000000

-------------------------------------------------------------------------------------

The following objects are equivalent to background material and will be ignored:

zero force objects =

-------------------------------------------------------------------------------------

force object group 1 =

component1:solid2

component1:solid2_1

component1:solid2_2

component1:solid2_3

component1:solid2_4

component1:solid2_5

component1:solid2_6

component1:solid2_7

component1:solid2_8

component1:outer

component1:solid2_9

Fx: -5.5213e+005 N

Fy: +2.9436e+005 N

Fz: +6.9208e+004 N

|F|: +6.2951e+005 N

Torque: +9.0675e+008 Nm

-------------------------------------------------------------------------------------

force object group 2 =

component1:solid1

component1:solid1_1

component1:solid1_2

component1:solid1_3

component1:solid1_4

component1:solid1_5

component1:solid1_6

component1:solid1_7

component1:solid1_8

component1:inner

component1:solid1_9

Fx: +3.9693e+005 N

Fy: +4.2547e+005 N

Fz: -1.3155e+005 N

|F|: +5.9656e+005 N

Torque: -9.4417e+008 Nm

-------------------------------------------------------------------------------------

force object group 3 =

component1:middle

Fx: -1.4974e+005 N

Fy: -1.9314e+005 N

Fz: +7.4248e+005 N

|F|: +7.8166e+005 N

Torque: +4.3287e+006 Nm