**Torque and Speed Equations**

For a d.c. motor >> Torque is directly proportional to the product of **Armature current** and **main flux**.

Now Φ is the flux produced by the field winding and is proportional to the current passing through the field winding.

Similarly the back emf produced in the armature is given by >>

As we know >> V = E_{b} + I_{a} R_{a}

>> E_{b} = V – I_{a} R_{a}

Speed equation becomes :

These relations play an important role in understanding the various characteristics of different types of motors.

**DC Motor Characteristics**

The performance of a d.c. motor under various condition can be judged by the following characteristics :

- Torque – Armature current characteristics
- Speed – Armature current characteristics
- Speed – Torque characteristics

**Characteristics of DC Shunt Motor**

**Torque – Armature current characteristics :**

For a constant values of R_{sh} and supply voltage V >> **I _{sh} is also constant and hence flux is also constant.**

The equation represents a straight line, passing through the origin as shown in the figure. Torque increases linearily with armature current. It is seen that armature current is decided by the load, So as load increases >> Armature current increases >> Increasing the torque developed linearly.

To generate high starting torque, this type of motor requires a large value of armature current at start. This may damage the motor hence d.c. shunt motors can develop moderate starting torque and hence suitable for such applications where starting torque requirement is moderate.

**Speed – Armature current Characteristics :**

So as load increases >> The armature current increases and hence drop I_{a} R_{a} also increases.

Hence for constant supply voltage, V – I_{a} R_{a} decreases and hence speed reduces. But as R_{a} is very small, for change I_{a} in from no load to full load, drop I_{a} R_{a} is very small and hence drop in speed is also not significant from no load to full load.

In d.c. shunt motor >> Speed regulation is order of 5 to 10 % from no load to full load >> That’s why d.c. shunt motor is also called as a constant drive motor.

**Speed – Torque Characteristics :**

So from these 2 equations we can conclude that Speed and Torque both has a linear relationship. This characteristics is similar to speed – Armature current characteristics.

This curve shows that the speed almost remains constant through torque changes from no load to full load conditions.

**Characteristics of DC Series Motor**

**Torque – Armature current Characteristics :**

In case of series motor the series field winding is carrying the entire armature current. So flux produced is proportional to the armature current.

** **

The torque in case of series motor is proportional to the square of the armature current. This relation is parabolic in nature as shown in the figure.

As load increases, armature current increases and torque produced increases proportional to the square of the armature current upto a certain limit.

As the entire Armature current passes through the series field, there is a property of an electromagnet called saturation, may occur. Saturation means though the current through the winding increases, the flux produced remains constant. Hence after the saturation the characteristics take the shape of straight line as flux becomes constant.

**These types of motors can produce high torque for small amount of armature current hence series motor are suitable for the applications which demand high starting torque.**

**Speed – Armature current Characteristics :**

From the speed equation we get >>

Now the values of R_{a} and R_{se} are so small that the effect of change in I_{a }on speed overrides the effect of change in V – I_{a} R_{a} – I_{a} R_{se} on the speed.

Hence in the speed equation, E_{b} ≈ V and can be assumed constant. So speed equation reduces :

So speed – armature current characteristics is rectangular hyperbola as shown in the figure.

**Speed – Torque Characteristics :**

In case of series motors,

Hence we can write,

Thus as torque increases when load increases, the speed decreases. **On no load, torque is very less and hence speed increases to dangerously high value.**

Thus the nature of the speed – torque characteristics is similar to the nature of the speed – armature characteristics.

**Why Series motor is never started on No load?**

It is seen earlier that motor armature current is decided by the load. On light load or no load, the armature drawn by the motor is very small.

In case of a dc series motor, and on no load armature current is small hence flux produced is also very small.

According to the speed equation,

So on very light load or no load as flux is very small, the motor tries to run at dangerously high speed which may damage the motor mechanically. This can be seen from the speed – armature current and the speed – torque characteristics that on low armature current and low torque condition motor shows a tendency to rotate with dangerously high speed.

For this reason it is not selected for belt drives as breaking or slipping of belt causes to throw the entire load off on the motor and made to run motor with no load which is dangerous.

**Practically pure d.c. series motors are not used, instead of them Compound motor is used.**

**Characteristics of DC Compound Motor**

Compound motor characteristics basically depends on the fact whether the motor is cummultively compound or differential compound. All the characteristics of the compound motor are the combination of the shunt and series characteristics.

Cummulative compound motor is capable of developing large amount of torque at low speed just like series motor. However** it is not having a disadvantage of series motor even at light or no load. **

So cummulative compound motor can run at a reasonable speed and will not run with dangerously high speed like series motor, on light or no load condition.

In differential compound motor, as two fluxes oppose each other, the resultant flux decreases as load increases, thus the machine runs at a higher speed with increase in load. **This property is dangerous as on full load, the motor may try to run with dangerously high speed. So differential compound motor is generally not used in practice. **

The exact shape of these characteristics depends on the relative contribution of series and shunt field windings. If the shunt field winding is more dominant then the characteristics take the shape of the shunt motor characteristics. While if the series field winding is more dominant then the characteristics take the shape of the series characteristics.