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.