## 4 Results
### Influence of Backings Material  
Ferromagnetic backings create conditions for easier magnetic flux circulation, i.e., implements a stronger magnetic link between half-clutches of a coupling. For particular applications, it is relevant to reduce the total weight of a system. This could be achieved by using backings made from a lighter non-ferromagnetic material. Sometimes it is relevant to minimize the weight only of one half-clutch.  
Figure 8: The maximum axial force \(F_{am}\) dependencies on parameter \(\Delta h_{m}\) for different air-gap lengths; (**a**) coupling with ferromagnetic backings; (**b**) coupling with non-ferromagnetic backings.  
Figure 7: The maximum torque \(T_{m}\) dependencies on the difference parameter \(\Delta h_{m}\) for different air-gap lengths; (**a**) case of couplings with ferromagnetic backings; (**b**) case of couplings with non-ferromagnetic backings.  
To investigate the quantitative dependence of the maximum torque and the maximum axial force on material of backings, simulations were accomplished for cases of the coupling's structures with two non-ferromagnetic material backings (\(T_{m0}\), \(F_{m0}\)), with one ferromagnetic backing, with one non-ferromagnetic material backing (\(T_{m1}\), \(F_{m1}\)), and with two ferromagnetic material backings (\(T_{m2}\), \(T_{m2}\)). I The considered coupling had identical half-clutches (\(\Delta l_{m}=0\)). Other parameters of the coupling are presented in Table 3. The results are presented in Figure 9a,b.  
The results show that the maximum torque is lower by approximately 20% for the case of the coupling with one non-ferromagnetic backing and by approximately 36% with both non-ferromagnetic backings in comparison to the case of the coupling, having both backings made from a ferromagnetic material. The dependence of the torque ratio indicates the weak dependence on air-gap length. The maximum axial force ratios indicate the higher sensitivity to the air-gap length and tend to decrease in response to increasing air-gap length.  
This research was performed aiming to evaluate how ferromagnetic backings with a shrouding shape (see Figure 10b) influence the maximum torque and the maximum axial force.  
The obtained results are presented in Figure 11a,b. Ferromagnetic backings having a shrouding shape decrease both the maximum torque and the maximum axial force of the coupling. There is noticeable tendency of the ratio \(T^{\prime}{}_{msh}/T_{m}\) reduction with increasing air-gap length. Here \(T^{\prime}{}_{msh}\) denotes the maximum torque of the magnetic clutch with backings having a shrouding shape, and \(T_{m}\) denotes the maximum torque of clutch having backings of a non-shrouding shape. The influence of the shrouding effect is less significant on axial  
Figure 10: Geometry of coupling: (a) non-shrouding backings (b) shrouding backings.  
Figure 9: Dependencies of mechanical characteristics of coupling on material of its backings; (a) the maximum torque dependencies; (b) the maximum axial force dependencies.  
force than on torque. Similarly, the influence of shrouding effect on the maximum axial force is higher for higher lengths of the air-gap.  
Since backings with a shrouding shape have significant negative effect on the maximum torque, it is not recommended to use ferromagnetic backings of this form in the structure of couplings. If shrouding is necessary, it is recommended to use backings composed from both ferromagnetic and non-ferromagnetic material parts. Parts of the backings which shroud magnets could be manufactured from non-ferromagnetic material and the parts in the region under (above) magnets out of ferromagnetic material.