Analytical solution to magnetic field distribution of a parallel magnetised rotor with cylindrical or ring-type permanent magnet

Ultra-high-speed permanent magnet synchronous motors (PMSMs) usually use bipolar rotors with ring permanent magnets (PMs) or cylindrical PMs which are magnetised in parallel. The stator of the motor is first simplified as a slotless stator, and an analytical solution to the flux density distribution in the motor is obtained by solving the Laplace's equation in the regions of PM and airgap. Then, by introducing the two-dimensional relative permeance function, the slotting effects on the radial flux density are also included. Finally, rotors with different types of PMs are studied by the presented analytical method and the finite-element analysis. In addition, experiments are also performed to verify the results of the analysis. This analytical solution can be used to determine the open-circuit flux density of PMSMs which have a parallel magnetised rotor with cylindrical or ring-type PM. With the analytical solution, the dimensionless magnetic flux density in the airgap could also be derived and can be used to calculate the sizes of different rotors with the same airgap flux density easily.