A compact expression for cogging torque considering both radial and tangential fields for surface-mounted PM motors

Cogging torque is due to the interaction between a magnet's magnetomotive force and a slotted stator or rotor structure. In this paper, a compact equation for cogging torque is presented for surface-mounted permanent magnet motors. This equation has four terms of field interactions involving tangential and radial components of airgap flux density. These four terms are considered as sources of cogging. Variations of these sources with pole embrace are examined. In earlier publications, closed-form expressions for pole embrace corresponding to the minimum cogging were presented considering only radial fields. In this paper, an attempt is made to recognize the influence of tangential fields in cogging. The compact form given here distinctly reflects the significance of both radial and tangential field components. Furthermore, to study the trends of cogging sources with pole number and airgap radius, simplified expressions for harmonic content of field components are derived using the first-order binomial approximation. The analysis on cogging presented in this paper helps in determining search domains in which optimum embrace for minimum cogging can be found when both the radial and tangential field components are considered.