Analytical Formulation for Optimisation of Torque Density in Magnetic Gears

Energy efficiency is a very important consideration in vehicle design today. Minimizing weight would go a long way in this direction, as it directly contributes up to 75% of fuel consumption. Mechanical gearboxes and transmissions are components that add significantly to vehicle weight. For example, the mass of typical automotive transmissions ranges from 40 to 200 kg, depending on the size of the vehicle. In recent years, magnetic gears (MG) have gained attention as realistic alternatives to mechanical gears. MGs operate without contact, where torque amplification, reduction, and transmission are achieved through the interaction of magnetic fields, which allows for lighter designs. For practical use in automotive vehicles, MGs must be capable of transferring sufficient amounts of torque. To maintain being compact and lightweight, the torque density of the MG must be maximized. Hence, the MG needs to be designed in such a way so as to achieve high flux concentration. Torque density analysis of MGs is not trivial, and often, some trade-offs between accuracy and computational cost is required. Several methods of analysis have been used by various researchers, including Finite Element Analysis, Reluctance Network Analysis (RNA), the Quasi 3D Analytical Method, and Genetic Algorithms (GA). In this work, we examine these methods and present an analytical formulation that relates MG torque to its physical parameters. Understanding such relationships could help optimise future MG designs such that torque density can be maximised.