## 3 Model Verification  
Physical experiments were performed for the numerical model verification. The experimental stand constructed for the purpose of the torque measurement is presented in Figure 2. It consists of servo amplifier (Mitsubishi Electric MR-J4-200A-RJ), servo motor (Mitsubishi Electric HG-SR152), fastening element 1 for the first half-clutch fastening on motor axis, fastening element 2 for the second half-clutch stationary fastening, and an intermediate of 8 mm thickness for the assurance of parallel placement of the discs and for assurance of a required air-gap length. The equipment was sourced from Mitsubishi Electric (Tokyo, Japan). The servo motor is equipped with the optical encoder in the feedback loop ensuring 0.01\({}^{\circ}\) angle resolution. The nominal torque of the motor is 7.2 Nm and its measurement resolution is 0.072 Nm. During the experiment, one half-clutch was firmly fixed to the stationary experimental stand, the other to the shaft of the servo motor. Torque of the servo motor was gradually increased and recorded. The intermediate during the experiment was removed. The maximal torques were obtained for displacements close to 15\({}^{\circ}\), which match theoretical value for clutches having 6 pole-pairs. Theoretically the maximum torque is obtained at angular displacement \(\delta_{Tmax}=360^{\circ}/(4\cdot p)\), where \(p\) denotes the number of pole pairs [19]. This angular displacement (15\({}^{\circ}\)) here and, in further presented simulations, was used for the maximum torque calculations. A Tinius Olsen H10 KT experiment machine with a Tinius Olsen 500 N force sensor (type: DBBMTOL-500N) was used for measurements of the coupling's axial force (see Figure 3). The equipment was sourced from Tinius Olsen (Horsham, PA, USA). A brushless motor with a half-clutch mounted on its shaft was fixed tight. The other half-clutch was pulled by the machine by gradually increasing the force. Both half-clutches were separated by an 8 mm intermediate in the initial position. Force values causing clutch abruption were recorded. Measurements were repeated for different interacting pole pairs, followed by an assessment of averages and standard deviations. Gravitation force acting on the pulled half-clutch and on its fixing equipment was taken into consideration and excluded from the results. This way, three versions of magnetic couplings, distinguished from each other by the height of motor side half-clutch magnets, were evaluated. Theoretically, the maximum axial force is for the case of 0\({}^{\circ}\) degree angular displacement [19]. Zero angular displacement is a natural position of an unloaded magnetic clutch. Zero angular displacement was used for the maximum axial force evaluation both for experimental measurements and in further simulations. Ferromagnetic material in the close proximity to magnets affects the distribution of a magnetic field, and consequently, mechanical characteristics of a magnetic coupling. Since one half-clutch of the experimentally evaluated coupling was fixed to a brushless motor with ferromagnetic housing, it was considered in the model (see Figure 4). A comparison of experimental and simulation results was carried out for all three structures of the analyzed magnetic couplings. The height of the load side half-clutch magnets for all the cases was constant and equal to 3 mm. The other structure parameters of the magnetic couplings were also identical. However, the heights of the motor side half-clutch magnets were different (Table 1). The supports of the investigated couplings are made out of non-ferromagnetic material. Figure 2: Test stand for torque measurement. Figure 4: Magnetic clutch 3D model geometry for experimental verification; (**a**) 3D view (**b**) projection. Figure 3: Test stand for axial force measurements. The obtained experimental (see Figure 5) and simulation results indicate the adequacy of the numerical model (see Tables 1 and 2).