Hardware Reference
In-Depth Information
4.2.8 Conditions of Magnetic Field for Producing Am-
pere's Torque
Asexplainedinsection4.2.2,therotating fi eld can be generated by either
mechanically rotating the rotor or electrically changing the current between
pole-pairs. Moreover, it is explained in section 4.2.3 that the EM torque in
an electric motor is produced by the interaction between the rotor fi eld and
the stator fi eld. Can all the stator and rotor fi elds interact to generate the
EM torque? What are the necessary conditions for these fi elds to generate the
torque?
Both the stator and rotor can produce magnetic fi eld in the airgap. The
total airgap fi eld is
X
X
B g (θ,t)=B r (θ,t,δ r )+B s (θ,t,δ s )=
r m (θ,t,δ r )+
s n (θ,t,δ s ), (4.64)
m
n
where, the r m and s n are the m th order rotor harmonic and the n th order
stator harmonic fi elds, respectively. The reference positions of the rotor and
stator are δ r and δ s , respectively.
If these harmonic fi elds rotate in space at speeds of Ω rm and Ω sn respec-
tively, then these harmonics can be expressed as
r m (θ,t,δ r )=R m sin[m(Ω rm t −θ+δ rm )+δ r ],
(4.65)
s n (θ,t,δ s )=S n sin[n(Ω sn t −θ+δ sn )+δ r ],
(4.66)
where, δ rm and δ sn are the reference positions of the harmonics r m and s n ,
respectively.
The energy of the magnetic fi eld in the airgap is
Z
Z
W g = gl c r
0
B g dθ = gl c 0
2
B g dθ,
(4.67)
0
0
where,
l c
:effective length of the motor (see Figure 4.9),
r
: average radius of the airgap,
µ 0
: permeability of air,
g
: width of the airgap, and
ν 0
: the inverse value ofµ 0 , known as the reluctivity of air.
(4.68)

Search WWH ::

Custom Search