Page 186 - Electric Drives and Electromechanical Systems

180 Electric Drives and Electromechanical Systems

which is related to the motor’s mechanical angular velocity, u m , by,

u s
u m ¼ (6.24)
p
In order for the torque angle to be kept constant (and hence for the stator’s ampere
distribution to be kept in synchronism with the rotor), use is made of a vector or field-
oriented controller; this requires a resolver or a similar high-performance position-
measurement system to be fitted to the motor.

6.2.2 Voltage characteristics
The emf of a sinusoidally wound brushless motor can be determined in a manner which
is similar to that used for the determination of the torque relationships. For the same
elemental group of conductors in a machine with p - pole pairs, the contribution to the
back emf of an elemental portion of the winding is given by,
BðqÞlu m N sin pq dq
de ¼ (6.25)
2
Using the flux relationship given in Eq. (6.21) and integrating, the r.m.s. phase emf is
given by,

rBlu m p
b
E p ¼ p ffiffiffi (6.26)
2 2p
p ffiffiffi
where the line-to-line voltage by 3E p .
6.2.3 Torque-speed characteristics

An ideal motor was considered in the analysis above; in practice, the construction of the
stator windings, and particularly the effect of the stator’s slots, has a significant effect on
the motor’s performance and characteristics. In addition, the location of the magnets,
either mounted on the surface or within the body of the rotor, has to be considered in
detail. It is normal to undertake a detailed modelling of this type of motor using
electromagnetic CAD packages (Hendershot and Miller, 1994). If the analytic method
considered above is extended to include the effects of the construction of the windings, it
can be shown that the r.m.s. phase emf is given by

E p u s j m
p ffiffiffi (6.27)
2
and the output torque is given by,
p ffiffiffi
3ppI 2j m sin b
T ¼ (6.28)
8
The flux linkage provided by the rotor-mounted magnets is given by,
(6.29)
j m ¼ kN p B m