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Characteristics of DC Motors – Shunt, Series and Compound Motors
The performance of a DC motor is given by the relation among the armature current, torque and speed. These relations are given graphically in the form of curves, which are called as characteristics of DC motors. These characteristics show the behaviour of the DC motor under different load conditions.
Following are the three important characteristics of a DC motor
Torque and Armature Current Characteristics
It is the graph plotted between the armature torque (τa) and the armature current (Ia) of a DC motor. It is also known as electrical characteristics of the DC motor.
Speed and Armature Current Characteristics
It is the graph plotted between the speed (N) and the armature current (Ia) of a DC motor. This characteristic curve is mainly used for selecting a motor for a particular application.
Speed and Torque Characteristics
The graph plotted between the speed (N) and the armature torque (τa) for a DC motor is known as the speed-torque characteristics. It is also known as mechanical characteristics of DC motor.
Characteristics of DC Shunt Motor
The shunt motors are the constant flux machines i.e. their magnetic flux remains constant because their field winding is directly connected across the supply voltage which is assumed to be constant.
Torque and Armature Current Characteristics
The armature torque in a DC motor is directly proportional to the flux and the armature current, i.e.,
$$\mathrm{\tau_{a}\:\varpropto\:\varphi I_{a}}$$
In case of a shunt motor, the flux is also constant. Therefore,
$$\mathrm{\tau_{a}\:\varpropto\:I_{a}}$$
Hence, the torque and armature current characteristics of DC shunt motor is straight line passing through the origin (see the figure). The shaft torque is less than the armature torque which is represented by the dotted line.
From the characteristics, it can be seen that a very large current is required to start a heavy load. Thus, the shunt motor should not be started on heavy loads.
Speed and Armature Current Characteristics
The Speed of a shunt DC motor is given by,
$$\mathrm{N\:\varpropto\:E_{b}}$$
$$\mathrm{\because \:E_{b}\:=\:V\:-\:I_{a}R_{a}}$$
$$\mathrm{\therefore \:N \:\propto\:(V\:-\:I_{a}R_{a})}$$
For a DC shunt motor, the back EMF and flux both are constant under normal operating conditions. Therefore, the speed of a shunt motor will remain constant with respect to armature current as shown by dotted line.
However, when the load is increased, the back EMF and flux decreases due to the drop in armature resistance and armature reaction respectively. Although the back EMF decreases somewhat greater than the flux so that speed of motor decreases slight with the increase in load (as line AB).
Speed and Torque Characteristics
This is the curve plotted between the speed and the torque for various armature currents. It can be seen that the speed of the shunt motor decreases as the load torque increases.
Characteristics of DC Series Motor
In a DC series motor, the field winding is connected in series with the armature and hence carries the full armature current. When the load on shaft of the motor is increased, the armature current also increases. Hence, the flux in a series motor increases with the increase in the armature current and vice-versa.
Torque and Armature Current Characteristics
In a DC motor,
$$\mathrm{\tau_{a}\:\propto\:\varphi I_{a}}$$
$$\mathrm{Upto\:magnetic\:saturation,\varphi \:\propto\: I_{a};\:so\:that\:\tau_{a}\:\propto\:I_a^2}$$
$$\mathrm{After\:magnetic\:saturation,\: φ\:becomes\:constant\:so\:that,\:\tau_{a}\:\propto\:I_{a}}$$
Therefore, up to magnetic saturation, the armature torque is directly proportional to the square of the armature current. Hence, the torque versus armature current curve upto magnetic saturation is a parabola (part OA of the curve).
After the magnetic saturation, the armature torque is directly proportional to the armature current. Hence, torque versus armature current curve after magnetic saturation is a straight line (Part AB of the curve).
From the torque versus armature current curve, it is clear that the starting torque of a DC series motor is very high.
Speed and Armature Current Characteristics
The speed of a DC series motor is given by,
$$\mathrm{N\:\propto\:\frac{E_{b}}{\varphi};\:Where,\:E_{b}\:=\: V-I_{a}(R_{a}+R_{se})}$$
With the increase in the armature current, the back EMF is decreased due to the ohmic drop in armature and series field resistances whereas the flux is increased. Although, the resistance drop is very small under normal operating conditions and can be neglected, thus,
$$\mathrm{N\:\propto\:\frac{1}{\varphi}\:\propto\:\frac{1}{I_{a}};\:Up\:to\:magnetic\:saturation.}$$
Hence, up to magnetic saturation the speed versus armature current curve is a hyperbola while after the magnetic saturation, the flux becomes constant and hence the speed
Speed and Torque Characteristics
The speed torque characteristics of a DC series motor can be obtained from its speed-armature current and torque-armature current characteristics as follows
For a given value of Ia determine τa from the torque-armature current curve and N from the speed-armature current curve. This will give a point (τ,N) on speed-torque curve. Repeat this procedure for different values of armature current and determine the corresponding values of speed and torque (τ1, N1), (τ2, N2) etc.
When these points are plotted on the graph, we obtain the speed and torque characteristics of a DC series motor as shown in the figure.
It is clear from the characteristics that the series motor has high torque at low speed and vice-versa. Thus, the series DC motor is used where high starting torque is required.
Important – At no-load, the armature current is very small and so is the flux. Hence, the speed increases to a dangerously high value which can damage the machine. Therefore, a series motor should never be started on no-load.
Characteristics of Cumulative Compound DC Motor
A cumulative compound DC motor is the one in which the series field aids the shunt field i.e. both are in same direction.
Torque and Armature Current Characteristics
When the armature current is increased, the series field increases whereas the shunt field remains constant. As a result, the total flux in the machine is increases and hence the armature torque.
Speed and Armature Current Characteristics
When the load is increased, the armature current is also increased which increases the flux per pole. Consequently, the speed of the motor decreases with the increase in the load. Therefore, a cumulative compound motor has poor speed regulation.
Speed and Torque Characteristics
For a given armature current, the torque of a cumulative compound motor is greater than that of a shunt motor but less than that of a series motor. 
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