Speed and torque control  (Page 2/19)

$E_a=K_f{I}_f{\omega }_m$ ( 10.3)

where $I_f$ is the average field current, ${\omega }_m$ is the angular velocity in rad/sec, and $K_f=K_a{P}_d{N}_f$ is a geometric constant which depends upon the dimensions of the motor, the properties of the magnetic material used to construct the motor, as well as the number of turns in the field winding.

• The electromagnetic torque is given as

$T_{\text{mech}}=\frac{E_a{I}_a}{{\omega }_m}=K_f{I}_f{I}_a$ (10.4)

and the armature current is given by

$I_a=\frac{V_a-E_a}{R_a}$ (10.5)

• Setting the motor torque equal to $T_{\text{load}}$ , solve for ${\omega }_m$

${\omega }_m=\frac{V_a-I_a{R}_a}{K_f{I}_f}=\frac{V_a-\frac{T_{\text{load}}{R}_a}{K_f{I}_f}}{K_f{I}_f}$ (10.6)

• From Eq. 10.6, recognizing that the armature resistance voltage drop $I_a{R}_a$ is generally quite small in comparison to the armature voltage $V_a$ , for a given load torque, the motor speed will increase with decreasing field current and decrease as the field current is increased.
• The lowest speed obtainable is that corresponding to maximum field current (the field current is limited by heating considerations); the highest speed is limited mechanically by the mechanical integrity of the rotor and electrically by the effects of armature reaction under weak-field conditions giving rise to poor commutation.
• Armature current is typically limited by motor cooling capability. In many dc motors, cooling is aided by a shaft-driven fan whose cooling capacity is a function of motor speed. Under constant-terminal-voltage operation with varying field current, the $E_a{I}_a$ product, and hence the allowable motor output power, remain substantially constant as the speed is varied. A dc motor controlled in this fashion is referred to as a constant-power drive.
• Torque, however, varies directly with field flux and therefore has its highest allowable value at the highest field current and hence lowest speed.
• Field-current control is thus best suited to drives requiring increased torque at low speeds.

Armature-Circuit Resistance Control: Armature-circuit resistance control provides a means of obtaining reduced speed by the insertion of external series resistance in the armature circuit.

• It can be used with series, shunt, and compound motors; for the last two types, the series resistor must be connected between the shunt field and the armature, not between the line and the motor.
• Depending upon the value of the series armature resistance, the speed may vary significantly with load, since the speed depends on the voltage drop in this resistance and hence on the armature current demanded by the load.
• The disadvantage of poor speed regulation may not be important in a series motor, which is used only where varying-speed service is required or can be tolerated.
• A significant disadvantage of this method of speed control is that the power loss in the external resistor is large, especially when the speed is greatly reduced.
• Armature-resistance control results in a constant-torque drive because both the field-flux and, to a first approximation, the allowable armature current remain constant as speed changes.
• A variation of this control scheme is given by the shunted-armature method, which may be applied to a series motor, as in Fig. 10.3a, or a shunt motor, as in Fig. 10.3b.