## 4 Results
### Influence of the Air-Gap Length between Adjacent Magnets  
Influence of the air-gap length between adjacent magnets (see Figure 12) on the maximum torque and the maximum axial force of the coupling was analyzed, assuming the constant volume of magnets. Identical half-clutches (\(\Delta h_{m}=0\)) were analyzed in the research. The cross-sectional area of magnets is  
\[S_{m}=\pi\Big{(}R_{o}^{2}-R_{i}^{2}\Big{)}-2 pl_{adj}(R_{o}-R_{i}), \tag{10}\]  
Figure 11: Dependencies on ferromagnetic backing forms; (**a**) the maximum torque dependencies; (**b**) the maximum axial force. Figure 12: Geometry of a single half clutch of the coupling. where \(l_{adj}\) is the air-gap length between adjacent magnets \(\left(l^{\prime}_{adj}=0.1\text{ mm}\right)\), and \(S^{\prime}_{m}\) is the area when \(l_{adj}=l^{\prime}_{adj}\). The rest of parameters were set as listed in Table 3.  
The volume of a single half-clutch magnet is  
\[V^{\prime}_{m}=S^{\prime}_{m}h^{\prime}_{m}, \tag{11}\]  
where \(h_{m}\) is height of magnets \(\left(h^{\prime}_{m}=5\text{ mm}\right)\) (see Figure 6). To sustain the same volume of the magnets while increasing the air-gap length \(l_{adj}\) between magnets, the parameter \(h_{m}\) was chosen according to the expression  
\[h_{m}=\frac{V^{\prime}_{m}}{S_{m}}. \tag{12}\]  
The obtained results are presented in the Tables 5 and 6. For the case of coupling with ferromagnetic backings, the air-gap length \(l_{adj}\) has a minor influence on torque in the considered range. Torque of the coupling with non-ferromagnetic backings is more sensitive to the value of \(l_{adj}\) in comparison to the case of the coupling with ferromagnetic backings. For the case, higher torque values were obtained for higher \(l_{adj}\) values. The maximum axial force of the coupling is more sensitive to the air-gap length between adjacent magnets for the case of the structure with ferromagnetic backings. geometry options, magnetic characteristics of backings material, specificity of backings form and air-gap length between adjacent magnets on the maximum torque and the maximum axial force of the coupling are covered. Research of magnets' height difference in different half-clutches of couplings revealed that the maximum torque and the maximum axial force values decrease in a nonlinear manner in response to the increasing difference. The sensitivity of the maximum torque and the maximum axial force to the difference is larger in the upper ranges of the difference. The results of torque ratios of the coupling with identical and with diverse half-clutches exhibit low sensitivity to air-gap length between the half-clutches, especially for a case of a coupling with ferromagnetic backings. In contrast to torque, for the case of coupling with ferromagnetic backings, the axial force exhibits a higher sensitivity to the air-gap length between half-clutches, especially in the upper range of the considered diversities. Research of the influence of backing material on the mechanical characteristics of couplings revealed that the maximum torque is lower by approximately 20% for the case of coupling with single non-ferromagnetic backing and by approximately 36% for the case of coupling with both non-ferromagnetic backings in comparison to the case of coupling with both ferromagnetic material backings. It was determined that the maximum torque ratios of the structure with a single ferromagnetic backing or with both non-ferromagnetic backings to the torque of the structure with both ferromagnetic backings has a minor influence on air gap length. The maximum axial force ratios in comparison to the maximum torque ratios exhibit a higher sensitivity to the air-gap length and continuously decrease in response to increasing air-gap length. Research of a backings shape's influence on mechanical characteristics showed that ferromagnetic backings, which partially shroud magnets, decrease both the maximum torque and the maximum axial force significantly. The shrouding effect decreases the maximum axial torque by approximately 20%.