Electrical – Relation between torque and speed in a dc motor(say dc shunt motor)

Conceptually, you have to think about this slightly differently. The way I think you are thinking about this is kind of like torque in a vehicle. A car with more torque is going to accelerate more quickly and is associated with an increase in speed. In other words, you press on the gas pedal to increase the speed and you need torque to do that.

However, when you are talking about the relationship between speed and torque of a DC motor, then you have to think about it differently. For a given motor with a constant input voltage, the speed of the motor is going to be determined by the load on the motor shaft. For a given load, the only way to increase the speed is to increase the voltage. And this increase in speed will require some more torque to accelerate but after it reaches its new speed, the torque will back off to its original torque (unless, of course, the load is dependent on speed - like in a fan).

So maybe a better way for you to think about it is instead of saying "Torque and speed in a DC motor are said to be inversely proportional" you say "For a given voltage, torque and speed in a DC motor are said to be inversely proportional." A speed-torque curve that you see on data sheets is only valid for the rated voltage and the motor will operate on that curve. So if torque goes up, the speed will follow that curve and go down.

The basic principle is simple - torque is proportional to armature current * magnetic flux. In a permanent magnet or shunt wound motor you can assume that flux is constant, so torque is just proportional to current.

However this does not take into account internal friction, windage, and magnetic losses. When the motor is running free these losses cause it to draw a no-load current (Io). Subtracting Io from total current draw leaves you with the portion that produces output torque.

Power = rotational speed x torque. As more load is applied the motor draws more current, which increases torque. However as current flows through the windings their resistance causes the effective voltage to drop, so speed decreases. Below 50% rpm the power output will also decrease, reaching zero at stall.

In a series wound motor the situation is different, because flux is not constant. With no load a series wound motor will speed up until friction and windage losses match the internal torque supplied by Io. This rpm could be very high, perhaps even high enough to destroy the motor. When a load is applied the resulting torque is proportional to current squared, because both armature and field currents contribute to magnetic force.