In all dc motors equations (1) to (4) hold, where V is the applied d.c. voltage, E is the motor back e.m.f. at speed N and field flux ø,Ia, is the value of the armature current which gives motor torque T, If
is the field current and Kf
, K,and Kt
are called the flux, speed and torque constants respectively. R is the series resistance of the motor and is equal to either the armature resistance alone or to the sum of armature (Ra) and field (Rf)resistances, depending on the type of motor connection used.
The performance of the motor can be readily derived from the above equations. For example, equations (1) and (2) show that the motor speed is roughly proportional to supply voltage V, ignoring secondary effects due to voltage drop caused by armature current, provided that motor flux does not also vary in the same manner with voltage. This can be satisfied with series and separately excited machines, but not with shunt field windings in which the current is determined by the supply voltage and field resistance. Therefore shunt motors cannot be used for speed control using supply-voltage variation.
The methods by which a d.c. motor can be started, controlled and stopped will now be examined with reference to some typical power semiconductor control circuits.
Depending on the type of supply, either a form of controlled rectification or d.c. line control may be used. Figure below shows a system which uses a unidirectional thyristor converter to control the voltage applied to the motor armature. The field may be supplied either from a separate bridge rectifier, or as in Figure, where diodes D1 and D2 are used to pass current to both the armature and the field. The field is supplied by the diode bridge D1-D2-D4-D5. Although this circuit
economises on the number of devices used, the ratings of diodes D1 and D2 have been increased, and for large machines a separate field rectifier system is to be preferred.
For many applications, however, especially in battery vehicles, only a d.c. supply is present, and the motor must now be driven by some form of chopper arrangement.
Referring to the load voltage waveform, suppose that at time to thyristor TH1 is fired. The load voltage rises to VB and power is supplied to the motor. From a previous cycle C was charged to VB-E with plate a positive, where E is the motor back e.m.f. at this speed. When TH1 is fired the capacitor resonates with L and recharges with plate b positive, so that when TH2 is fired, thyristor TH1 is reverse biased by VB-E and turns off. Motor current flows in D2 and C charges to VB with plate a positive, the voltage drop in D2 being ignored, the load voltage being zero as at t2. On light loads the inductive load current will decay to zero, the current flowing against the motor back e.m.f., before TH1 is refired. When this occurs, say at t3, the capacitor will discharge through D1 and its voltage will fall to VB-E. The motor back e.m.f. has therefore had two effects.
First, it has distorted the load voltage waveform between heavy loads and light loads. Since the magnitude of the load voltage is determined by its waveform this means a change in the motor voltage and hence its speed, even though the firing period of the thyristors has been unaltered. This is not serious and can be compensated for by using closed-loop speed control. A much more serious effect of the back e.m.f. has been a reduction in the available thyristor commutation voltage, and although this voltage is reduced most on light loads, when commutation is least demanding, it is a disadvantage of this circuit. A much better solution is to replace D1 by a thyristor, which turns off as soon as capacitor resonance has been completed, and so prevents the motor back e.m.f. from affecting the capacitor voltage.