0195136047.pdf

602 ROTATING MACHINES

The schematic arrangement of a shunt motor is shown in Figure 13.4.8(a). For a given applied

voltage and field current, Equations (13.4.4) and (13.4.3) can be rewritten as

Te=KaφIa=KmIa (13.4.9)

Ea=Kaφωm=Kmωm (13.4.10)

BecauseVt=Ea+IaRa,orIa=(Vt−Ea)/Ra, it follows that

Te=

KmVt

Ra

−

Km^2 ωm

Ra

(13.4.11)

Pem=EaIa=Teωm=

VtKmωm

Ra

−

K^2 mω^2 m

Ra

(13.4.12)

The forms of the torque–armature current, speed–torque, and speed–power characteristics for a

shunt-connected dc motor are illustrated in Figure 13.4.9.

The shunt motor is essentially a constant-speed machine with a low speed regulation. As

seen from Equation (13.4.8), the speed is inversely proportional to the field flux, and thus it can

be varied by controlling the field flux. When the motor operates at very low values of field flux,

however, the speed will be high, and if the field becomes open-circuited, the speed will rise rapidly

beyond the permissible limit governed by the mechanical structure. In order to limit the speed to

a safe value, when a shunt motor is to be designed to operate with a low value of shunt-field flux,

it is usually fitted with a small cumulative series winding, known as astabilizing winding.

The schematic diagram of a series motor is shown in Figure 13.4.8(b). The field flux is directly

determined by the armature current so that

Te=KaφIa=KIa^2 (13.4.13)

and with negligible armature resistance,

Vt=Ea=Kaφωm=KIaωm (13.4.14)

Te=

Vt^2

Kω^2 m

(13.4.15)

Pem=ωmTe=

Vt^2

Kωm

(13.4.16)

and the speed–power curve is a rectangular hyperbola. The forms of the torque–armature current,

speed–torque, and speed–power characteristics for a series-connected dc motor are also illustrated

Shunt Shunt

Shunt

Series

Series

Series

Armature current

Torque

Torque

Speed

Power

Speed

Compound

Figure 13.4.9Characteristic curves for dc motors.