Suppose that a shunt-connected machine operates at 800 rpm...

Suppose that a shunt-connected machine operates at 800 rpm on the linear portion of its magnetization characteristic. The motor drives a load that requires constant torque. Assume that $R_{A}=0 .$ The resistances in the field circuit are $R_{F}=50 \Omega$ and $R_{\mathrm{adj}}=$ $25 \Omega$. Find a new value for $R_{\text {adj }}$ so that the speed becomes 1200 rpm. What is the slow. cst speed that can be achicved by varying $R_{\text {ad }} ?$

Key Concepts

Speed-Flux Relationship

In a DC motor, the back electromotive force (EMF) is largely determined by the speed and the field flux. Since back EMF balances the applied voltage, any decrease in flux (achieved by increasing series field resistance) will lead to an increase in speed for a constant armature voltage. This inverse relationship between flux and speed is critical when making adjustments to achieve either higher or lower speeds in practical applications.

Magnetization Characteristic (Linear Region)

The magnetization characteristic of a DC machine shows the relationship between the field current and the produced magnetic flux. Operating in the linear portion of this curve is important because it implies a direct proportionality between field current and flux, which simplifies analysis and ensures predictable motor behavior when adjusting the field circuit. Deviations from the linear region could lead to nonlinear performance and complicate control strategies.

DC Shunt Motor Operation

DC shunt motors are characterized by having their field and armature windings in parallel. In these machines, the speed is nearly constant because the field current is stable; however, when additional control means are introduced, such as varying the resistance in the field circuit, the motor’s speed can be adjusted. This concept is critical when considering the effects of changing the field circuit parameters on motor performance.

Field Flux and Its Control

The magnetic flux in the motor’s field is directly related to the field current, and in a shunt motor, this current can be altered by changing the resistance in the field circuit. By increasing or decreasing the resistance, the field flux is weakened or strengthened respectively, which in turn impacts the motor’s speed. This adjustment is essential for speed control, particularly when a motor is required to operate at different speeds under load.

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