Hardware Reference
In-Depth Information
Figure 4.36: The output EMF from the brushes of commutation system (for a
single coil).
In this circuit, R
a
and L
a
are the resistance and inductance of the armature
winding, respectively. The external voltage applied on the terminals of the
winding is V , while the back-EMF produced in the motor operation is E.The
dynamics of this equivalent circuit model of DC motor can be expressed as
V = i · R
a
+ L
a
di
dt
+ E.
(4.58)
In the steady state, the input current is constant and the above equation
reduces to
V = i · R
a
+ E.
(4.59)
The conversion between the electro-magnetic power P
em
and the mechan-
ical power P
me
is possible because of the existence of the back-EMF. The
relationship between these two powers can be expressed as
P
em
= P
me
⇔
E · I = T
em
· Ω.
(4.60)
Further explanation on conversion between P
em
and P
me
is given in sec-
tion 4.3.10.
One can easily deduce from equations 4.47 and 4.60 that,
½
T
em
= K
t
· I,
E = K
e
· Ω.
(4.61)
This implies that the torque constant (K
t
) and back-EMF constant (K
e
)ofa
motor have the same magnitude when SI units are used.
