Influence of Slot and Pole Number Combinations on Cogging Torque in PM Machines with Tooth Bulge and Rotor Eccentricity

With the aid of vector analysis and finite element method, this paper investigates the influence of tooth bulge and static/dynamic rotor eccentricities on cogging torque of permanent magnet (PM) machines having various slot/pole number combinations ($Ns/ 2 p$), e.g. $2 p=Ns \pm m$ where m is an integer (including $2 p=Ns \pm 1$ and $2 p=Ns \pm 2), Ns/ 2 p=12$/8, and $Ns/ 2 p=12$/4. It is firstly found that m greatly influences the interaction of two tolerances on cogging torque. The degree of interaction is reduced with the increase of m, and it is larger in “ $-m$” than in “ $+m$” machines. Secondly, for the machines having $2 p=Ns-m$, there is a weakening interaction of cogging torque when the static eccentric rotor is close to outward bulged teeth, whilst there is a strengthening interaction of cogging torque when the static eccentric rotor is close to inward bulged teeth, but vice versa for $2 p=Ns+m$ machines. However, cogging torques due to dynamic rotor eccentricity and tooth bulge always have a strengthening interaction wherever the relative location of the dynamic eccentric rotor and bulged teeth is.