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

With the aid of vector analysis and finite element method, this paper investigates the influence of slot and pole number combinations on cogging torque in permanent magnet (PM) machines with interactive effects between tooth bulge and rotor eccentricity, accounting for various slot/pole number combinations (
N_s
/2
p
), e.g., 2
p
=
N_s
±
m
where
m
is an integer (including 2
p
=
N_s
± 1 and 2
p
=
N_s
± 2),
N_s
/2
p
= 12/8, and
N_s
/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
m
, and it is larger in “−
m
” than in “+
m
” machines. Secondly, for the machines having 2
p
=
N_s
−
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
=
N_s
+
m
machines. However, in both 2
p
=
N_s
±
m
machines, cogging torques due to dynamic eccentricity and tooth bulge always have a strengthening interaction. The measured cogging torques of the prototypes verify the predicted results.