In my previous article (Click here to read the article) I have discussed that DC motors are still used where we want speed control. Today we will see the different types of DC motors based on the arrangements of Filed and Armature windings.

Before we jump into types of DC motors we should understand the equivalent circuit of a DC motor. As we know, there is a Field Winding and an Armature Winding. The Field winding will have inductance and resistance, therefore we can represent Field Winding as an inductor and resistor. There is an internally generated voltage (Motional EMF in Conductor) in Armature Winding; therefore, we can represent it as a voltage source. Further, there will be resistance offered by Armature Winding. The equivalent circuit can be given as,

Where,

E_{A} = Internally generated EMF

L_{F} = Field Inductance

R_{F} = Field Resistance

R_{A} = Armature Resistance

You may think that there should be Inductance offered by Armature Winding. It is true that there will be inductance, and there will be a voltage drop at it. The voltage drop of an inductor depends on the rate of change of current. In steady-state, the rate of change of current is negligible so the voltage drop will be negligible. Therefore, it is not shown in the circuit. The Field Inductance is shown because the Field Resistance is varied for controlling the speed of the motor. It changes the current in the winding. Therefore, the rate of change in current will not be negligible this time. So, therefore, the Field Inductance is shown in the circuit.

The internally generated voltage (Motional E.M.F) is directly proportional to flux generated and the speed of armature (Rotor).

Where,

E_{A} = Internally generated EMF

ω = Speed of Armature (Rotor)

ф = Magnetic Flux

K = Motor Constant

We have also seen in the previous article,

Where,

I_{A} = Current in Armature

# Types of DC Motor:

The major types of dc motors classified according to the arrangement of Armature and Field winding are given below,

- Separately Excited DC Motor
- Shunt DC Motor
- Series DC Motor
- Compounded DC Motor

## Separately Excited and Shunt DC Motors:

In Separately Excited Motor, the Field Winding and Armature are excited from separate sources. Therefore, there are two sources, one for Armature and the other for Field Winding.

Where,

V_{T} = Terminal Voltage

V_{F }= Voltage of Field Source

I_{A} = Armature Current

I_{F} = Field Current

Other terms have the same meanings.

The loop equation of Armature can be written as,

A Shunt Dc motor has Field Winding in parallel with the Armature Winding. Therefore, there is only one source from which the current is divided into the Armature branch and Field branch. Consider the following circuit,

The loop Equation of Armature can be written as,

Here,

In both the equations are identical, only the magnitude of armature current is different, which can be controlled by applied Voltage (V_{T}). In the Separately Excited motor, it is very clear that the Field and Armature current are independent of each other. While in Shunt motor, the Field Winding and Armature are parallel. In a parallel connection, the current is independent of the resistance in other branches. The current depends on the branch resistance and applied voltage. Let’s consider the following circuit,

The Current in the Resistor R_{1} will be,

The current is independent of the value of R_{2}.

Hence, in both the arrangements the Field Current is independent of Armature Winding. We will see in other types; Field Current will be dependent on Armature Winding. If the Field current is independent, the flux produced will independent of Armature Current. This is the reason that both types are discussed together because both have the same characteristics.

### The relation between Speed and Torque:

The terminal voltage of both the motors can be given as,

As

And,

Putting both the values of I_{A} and E_{A} in eq (1),

From the obtained equation we can see that the speed of the motor decreases with the increase in the Torque induced. The speed is inversely proportional to the Flux. Hence we can control the speed of the motor by changing the flux. The relation between the speed and torque is linear if all the other factors are constant. But in reality, the armature reaction reduces the flux which increases the speed and the relationship becomes non-linear. To control this, we can use the Compensating Winding. This motor is used where we want good speed regulation and adjustable speed.

## Series DC Motor:

In Series Motor the Field Winding and Armature are in series with each other. In a series circuit, the current is the same in all the connected components. The current depends on the values of all components. If the value of one component is changed when the current is changed. Here, in series motor, the Field Current is the same as Armature Current. Hence, the magnetic flux produced will depend on the Armature Current. We can say that the Flux is the function of Armature Current which can be written as,

Where ‘k’ is the constant of proportionality.

The equivalent circuit can be drawn as,

The labels have the same meaning as described above.

The loop equation will be,

Here again, the voltage is drop at Field Winding is neglected as it will be negligible in the Steady-state (Normal Operating Condition).

### The relation between Speed and Torque:

The Induced Torque depends on the Flux and the Armature current i.e.

But as stated earlier,

Therefore,

This tells that the Torque induced is directly proportional to the square of Armature current.

Further,

Putting in eq (2),

The equation of terminal voltage can be written as,

Putting the value of E_{A},

Putting the values,

From the above equation, we can say speed is inversely proportional to the square root of the induced torque. By plotting the above equation by using typical values we get,

The speed of Series DC motor is theoretically infinite when Induce torque is zero. In actual the torque can never be zero due to losses. Therefore, at no load, the speed is very high which can damage the motor as well. So wherever the Series motor is installed, care must be taken, that it should not be unloaded at any time accidentally or deliberately. Generally, the Series motor can run at twice the rated speed. Therefore, the torque should not below as much to produce speed more than twice of the rated speed.

The torque is directly proportional to the square of the current, therefore it can produce more torque than any other DC motor for the same amount of current. It is used in the application where high torque is needed.

## Compounded DC Motor:

In Compounded motors, the Field is connected in parallel and series as well. The equivalent circuit can be given as,

Where,

L_{FS} = Series Field Inductance

L_{FP} = Parallel (Shunt) Field Inductance

R_{FS} = Series Field Resistance

R_{FP} = Parallel (Shunt) Field Resistance

Other symbols have the same meanings.

Again in steady-state, the voltage drop across inductance will be negligible, therefore, we will not include its voltage in the loop equation.

The loop (KVL) equation of armature can be written as,

But,

Therefore,

Since there are two Fields the net Field can be additive (cumulative) and subtractive (differential). Therefore, we can classify Compounded DC Motors into two types,

- Cumulatively Compounded DC Motors
- Differentially Compounded DC Motors

### a) Cumulatively Compounded DC Motors:

The Cumulatively Compounded DC motors are those in which the net field is additive. The magnetomotive force is the sum of both the Fields. The equation of magnetomotive force can be given as,

Where,

F_{F} = Net Magnetomotive Force of Fields

F_{FS} = Magnetomotive Force of Series Field

F_{FP} = Magnetomotive Force of Parallel (Shunt) Field

The additive characteristic is achieved when the current or leaves the dotted terminal of both the Fields.

### a) Differentially Compounded DC Motors

In Differentially Compounded DC motors, the net Field is the difference of Shunt and Series Fields.

It is achieved when the current enters from the dotted terminal in one of the Fields and leaves from the dotted terminal of the other.

We can arrange the Shunt (Parallel) connection in two ways,

- Long-shunt Connection
- Short-shunt Connection

### i. Long-shunt Connection:

### ii. Short-shunt Connection:

### The relation between Speed and Torque:

We will discuss the relation in Cumulatively and Differentially Compounded DC motors separately.

#### a) Cumulatively Compounded DC Motor:

Cumulatively Compounded DC Motors have the features of both the Series and Shunt Motor. It can give more torque on less amount of current like Series Motors. It does not attain over speed when unloaded thus behaving like Shunt Motors. We have seen earlier, in parallel connection, the current in a branch is independent of the other branch. Therefore, the shunt field draws current which is independent of the armature current. So at the start of the motor, the armature current will be low and therefore the current in the Series Field will be low as well. But the current in Shunt Field will be constant. Hence, at light load, the motor will behave as Shunt Motor. The shunt current remains constant as long as the shunt resistance is constant and the current of armature increases if the load is increased. When the Armature Current exceeds the Shunt Current the motor behaves as Series Motor.

#### b) Differentially Compounded DC Motors:

The speed-torque relationship of a differentially compounded motor is unstable. To understand this let’s get back the equation that we have studied in the relative heading.

The net force is the difference between the shunt field force and the series field source. At no load, the shunt field force is dominant. When the load increases the armature current increases, which increases the series field source. Due to an increase in the series field force, the net force is decreased. This means the net flux is decreased. Due to the decrease in the flux, the speed of motor increases. The speed increases drastically as the load increases making the motor unstable. This is the reason this motor is not suitable to use.

To start this motor safely the series field is shorted due to which the motor behaves as a shunt motor. Otherwise, it can damage itself. The difference of the field can be negative because after some time the series field force increases more than the shunt field force. This changes the direction of the torque of the motor. Due to change in rotation, the rotor is locked for some time and motor draws excessive current which can damage the winding.