## 3 Topological Diversity and Structural Design in Magnetic Gear Systems
### Design Parameters of Magnetic Gears
\begin{table}
\begin{tabular}{c c c c c} \hline
**Permanent Magnet** & **Hc (kA/m)** & **Br (T)** & **BHmax (kJ/m3)** & **Tc (\({}^{\circ}\)C)** \\ \hline Alnico & 40–140 & 0.6–1.4 & 10–88 & 700–860 \\ Ferrite & 120–300 & 0.2–0.4 & 10–40 & 450 \\ NdFeB & 750–2000 & 1.0–1.4 & 200–400 & 310–400 \\ SmCo & 600–2000 & 0.8–1.1 & 150–240 & 720 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of different types of permanent magnets [59]. beyond material properties, design optimizations also play a decisive role in determining performance parameters such as torque density. Therefore, the following section will address the concept of torque density in magnetic gears and the present studies aimed at its enhancement. Various design optimization efforts have been conducted to increase the volumetric torque density in magnetic gear systems. For example, using a slotted magnetic modulation ring in the carrier structure has led to improvements in static torque performance. Figure 8 illustrates the structure of a coaxial magnetic gear (CMG) with a slotted modulation ring. In a study conducted using a finite-element analysis (FEA), the ratio of permanent magnet pole pairs was set at 1:4.25, and the static torque was found to increase by approximately 4-4.12% compared to conventional coaxial magnetic gears (CMGs). Furthermore, torque ripple was reduced by 72.28% and 69.84%, while iron loss and eddy current loss decreased by 8.91% and 66.57%, respectively [60]. These design improvements, aimed at increasing the torque density, offer significant opportunities for enhancing the mechanical performance of magnetic gear systems. However, thermal effects also represent a critical aspect of the design, just as important as mechanical parameters in ensuring long-term system reliability. In this context, the following section examines the thermal behavior and thermal management strategies in magnetic gear systems in detail. Thermal effects in magnetic gear systems become a critical engineering consideration, especially in compact designs targeting high torque density. As system dimensions increase and the air gap between the input and output rotors narrows, the surface area available for convection decreases. This leads to increased thermal resistance and complicates effective system cooling. The thermal load generated by core losses and eddy currents becomes more pronounced under such conditions. In particular, the high electrical conductivity of permanent magnet materials significantly increases eddy current losses, leading to severe heating. The literature shows that, with an increasing rotational speed, these losses and the resulting system temperature also rise [61; 62]. This temperature increase may cause thermal deformation in components and degradation of magnetic materials, thus threatening system reliability. For example, in a magnetic gear system designed for integration into a 6 MW wind turbine operating at 12.5 rpm, analyses showed that the heat generated from magnetic losses could be effectively managed using an axial airflow cooling system [63]. In this study, magnetic losses were calculated through analytical modeling, while heat transfer was analyzed using a thermal network model and the finite-element method (FEM). A more recent study conducted mutual heat transfer analysis using 3D flow and conduction/convection methods in a fully laminated magnetic gear system. The average outer rotor temperature was estimated with an error of 2.5 K lower than that obtained using a simple conduction model [64]. Eddy currents in magnetic gear systems are a significant source of heat, primarily due to the high electrical conductivity of permanent magnet materials. Analytical and  
Figure 8: Structure of a coaxial magnetic gear with a slotted magnetic modulation ring [60]. semi-analytical models have been developed to predict these losses in related rotating machines, such as permanent magnet synchronous machines [65] and induction motors [66], providing valuable insights into their behavior under various operating conditions.