A series-connected de motor is designed to operate with a...

A series-connected de motor is designed to operate with a variable load. The resis$\operatorname{tances} R_{A}$ and $R_{F}$ are negligible. To attain high efficiency, the motor has been designed to have very small rotational losses. For a load torque of $100 \mathrm{Nm}$, the machine runs at its maximum rated speed of 1200 rpm. a. Find the speed for a load torque of 300 $\mathrm{Nm}$. b. What is the no-load speed? What are the potential conscquences of having the load become disconnected from the motor without disconnccting the de source?

A series-connected de motor is designed to operate with a variable load. The resis$\operatorname{tances} R_{A}$ and $R_{F}$ are negligible. To attain high efficiency, the motor has been designed to have very small rotational losses. For a load torque of $100 \mathrm{Nm}$, the machine runs at its maximum rated speed of 1200 rpm.
a. Find the speed for a load torque of 300 $\mathrm{Nm}$. b. What is the no-load speed? What are the potential conscquences of having the load become disconnected from the motor without disconnccting the de source?

Key Concepts

Series-connected DC Motor

A series-connected DC motor is a type of motor in which the field winding is connected in series with the armature. This configuration means that the same current flows through both the armature and the field winding, which causes the field flux to vary with the load current. This characteristic leads to a unique performance curve, particularly an increase in speed when the load decreases, since lower current reduces the flux and thereby increases the speed for a given applied voltage.

Speed-Torque Characteristic

The relationship between speed and torque in a series-connected DC motor is highly nonlinear. Under load conditions, the torque produced is proportional to the square of the armature current, and the motor speed inversely depends on the flux. As the load increases, the motor draws more current, which increases the flux and reduces the speed. Conversely, if the load decreases, the current drops causing a reduction in flux and potentially resulting in an excessively high no-load speed.

No-load Speed

No-load speed refers to the speed of the motor when no external mechanical load is applied. In a series-connected DC motor, the current becomes very small under no-load conditions, leading to a significant drop in field flux. This reduced flux causes the motor to run much faster than its rated speed, which can be dangerously high and lead to mechanical or thermal issues if not controlled properly.

Motor Runaway and Control Safety

When the load is disconnected from a series-connected DC motor without disconnecting the supply, the motor may accelerate uncontrollably—commonly known as runaway speed. This condition is dangerous because the excessive speeds can result in mechanical failures, insulation breakdown, or other forms of damage that compromise both the motor's integrity and safety. Proper control measures and protection circuits are essential to mitigate these risks during fault conditions or load removal.

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