## 3 Topological Diversity and Structural Design in Magnetic Gear Systems
### Design Parameters of Magnetic Gears  
Geometric characteristics play a crucial role in determining the gear ratio and torque performance of magnetic gears (MGs). Similar to mechanical gear systems, the gear ratio in MGs defines the relationship between the input and output speeds. However, instead of using the number of mechanical teeth, MGs utilize the number of magnetic pole pairs [46]. To better understand the structural differences and torque transmission principles between mechanical and magnetic gears, Figure 5 presents a comparative illustration of the typical configurations of both systems. Figure 4: Representation of the drive gear system and torque transmission. In a magnetic gear, the number of magnets on the inner rotor is denoted by nPM\(-\)in, and the number of magnets on the outer rotor is denoted by nPM\(-\)out. The number of modulators on the carrier is given by:  
\[n_{sp}=\frac{n_{PM-int}}{2}+\frac{n_{PM-out}}{2} \tag{1}\]  
is defined as follows. The gear ratio is:  
\[g_{r}=\frac{\frac{n_{PM-int}}{2}+\frac{n_{PM-int}}{2}}{\frac{n_{PM-in}}{2}} \tag{2}\]  
is expressed as follows. The highest gear ratio is achieved when the outer rotor is held stationary [47; 48]. One of the key design parameters in magnetic gears is the configuration of the rotating components, namely the rotor, carrier, and modulator, and whether these components are fixed or allowed to rotate. This configuration directly affects both the gear ratio and the overall mechanical behavior of the system [49]. Figure 6 schematically illustrates various coaxial magnetic gear configurations based on different combinations of rotating parts. As shown in Figure 6, the gear ratio varies depending on the selected fixing strategy. For a magnetic gear with 14 outer magnets, 6 inner magnets, and 10 modulators on the carrier, the gear ratio is observed to change as follows: when the modulator ring is fixed, gr = 7/3; when the outer rotor is fixed, gr = 10/3; and when the inner rotor is fixed, gr = 10/7. As seen, the highest gear ratio is achieved when the outer rotor is fixed, making this configuration particularly suitable for low-speed and high-torque applications. Depending on which component is fixed, both the gear ratio and torque transmission vary, enabling optimization according to the specific design objectives of the system. Emerging geometrical variations such as conical coa  
Figure 5: Structures of a mechanical gear (**left**) and a permanent magnet magnetic gear (**right**). Figure 6: Coaxial magnetic gears based on rotating components: configurations where (from (**left**) to (**right**)) the carrier is fixed, the outer rotor is fixed, and the inner rotor is fixed. unique design advantages, particularly for axial space-constrained environments, although they introduce new challenges in flux modulation and mechanical alignment [50]. In addition to gear ratio optimization, the magnet arrangement and the selection of a magnet material must be carefully considered to enhance system efficiency and torque output. The Halbach array, widely utilized in magnetic gear systems, enhances the magnetic flux density within the air gap by arranging magnets according to a specific magnetization pattern, while simultaneously minimizing leakage flux on the yoke side. Figure 7 illustrates a typical Halbach magnet configuration and the corresponding magnetic flux distribution. Several studies in the literature have demonstrated, through finite-element analysis (FEA), that employing a Halbach array in the outer rotor significantly improves the magnetic focusing effect. After modulation, the magnetic flux peaks were observed to align with the pole pairs on both the inner and outer rotors [51]. Particularly in outer rotor designs incorporating Halbach magnetization, the magnetic flux steering capability is markedly enhanced, leading to an overall improvement in torque performance [52; 53]. Although FEA provides highly accurate results, it requires substantial computational resources, especially in iterative or parametric design processes.