**2.1. The equivalent coil currents approximation**

In the equivalent coil currents approximation, a ring-shaped permanent magnet, magnetised in the axial direction, is assumed to exist by the set of circular coil currents located at the outer and inner side surfaces of the ring-shaped permanent magnet [4]. The directions of currents in the outer and inner equivalent coils are inversed with each other, describing the axial magnetization of the permanent magnet, as shown in Figure 2. The magnitude of these equivalent side currents is determined so as to coincide with the measured magnetic field density at the pole surface of the permanent magnet in relation to the number of the assumed equivalent coils.

Figure 3 shows the analytical model based on the equivalent side currents model. The outer and inner diameters and the height of the ring-shaped permanent magnets are represented as *dso*, *dsi* and *hs* for the stator magnet and *dro*, *dri* and *hr* for the rotor magnet, respectively. The angle *θ* is the tilt angle of the rotor magnet. The origin is set at the centre of the stator magnet. The stator magnet is located in the horizontal *x*–*y* plane and *z*-axis is set as the vertical direction along the axis of the stator magnet. The numbers of the equivalent side currents in both the rotor and stator magnets, indicated as one and three in Figure 3, are decided considering both the accuracy of the calculated results and the required time for computation.
