Understanding DC Machine Main Field Flux Distribution

In a DC machine, the main magnetic field is produced by the field windings placed on the stator poles. This magnetic field crosses the air gap and enters the armature (rotor), which is where the voltage is induced.

The shape of this main field flux distribution across the armature periphery is a crucial aspect of DC machine design and performance. It determines the nature of the induced voltage in the armature conductors.

Factors Influencing Flux Distribution Shape

The shape of the flux distribution is primarily determined by two factors:

• The geometry of the stator poles, especially the pole shoes.
• The variation in the length of the air gap between the stator poles and the armature surface.

Why the Shape is Typically Trapezoidal

Let's consider a typical DC machine pole structure:

The poles have a core and a wider pole shoe. The pole shoe serves to distribute the flux more evenly over a larger area of the armature surface beneath it. The air gap length between the pole face (underside of the pole shoe) and the armature surface is generally made uniform over the central portion of the pole shoe. However, as you move towards the edges of the pole shoe, the air gap length increases rapidly.

The magnetic flux density (\(B\)) in the air gap is inversely proportional to the reluctance of the air gap. The reluctance is directly proportional to the length of the air gap. So, where the air gap is short, the flux density is high, and where the air gap is long, the flux density is low.

• Under the central part of the pole shoe, the air gap is relatively uniform and short. This results in a region of relatively uniform and high flux density. This corresponds to the flat top of the trapezoidal shape.
• As you move away from the center towards the pole tips (edges of the pole shoe), the air gap length increases. This causes the flux density to decrease. This corresponds to the sloping sides of the trapezoidal shape.
• In the region between the poles (interpolar region), the air gap is very large, and the flux density is very low, ideally close to zero. This corresponds to the base of the trapezoidal shape.

Plotting the flux density along the armature periphery results in a shape that is approximately trapezoidal.

Comparing Shapes

• Peaky: A peaky distribution would imply the flux density is highest at one point and tapers off sharply, not typical for standard DC machine pole shoes designed for flux spreading.
• Saddle shape: A saddle shape indicates a dip in flux density, often caused by armature reaction under load, not the basic no-load main field flux shape.
• Triangular: A triangular shape would suggest a flux density that linearly decreases from a peak, implying a different pole design or air gap variation than typically found in standard DC machines.
• Trapezoidal: This shape accurately reflects the effect of the uniform air gap under the pole face and the increasing air gap at the pole edges, which is characteristic of standard DC machine pole design.

Therefore, the shape of the main field flux distribution in a standard DC machine under no-load conditions is trapezoidal.

Revision Table: DC Machine Flux Concepts

Additional Information: Factors Affecting Flux Distribution

While the basic main field flux distribution is trapezoidal, several factors can influence the actual flux pattern in a DC machine:

• Armature Reaction: When the armature carries current (i.e., the machine is loaded), it produces its own magnetic field. This armature field interacts with the main field, distorting the flux distribution. It tends to weaken the main field at one end of the pole and strengthen it at the other end, shifting the neutral axis. Under load, the resultant flux distribution becomes non-trapezoidal, often skewed or saddle-shaped depending on the load and machine design.
• Saturation: If the magnetic core material (poles, yoke, armature core) becomes saturated at high flux densities, the flux distribution can become flatter at the top than an ideal trapezoid.
• Interpoles: Smaller poles placed between the main poles, connected in series with the armature. They generate a commutating flux that counteracts the armature reaction flux in the interpolar region, aiding commutation. The interpoles affect the flux distribution mainly in the region between the main poles.
• Compensating Windings: Windings embedded in slots in the main pole faces, connected in series with the armature. They directly oppose the armature reaction flux under the pole face, keeping the flux distribution under the main pole closer to the ideal trapezoidal shape even under load.

Understanding the basic main field flux distribution shape is fundamental before analyzing the effects of armature reaction and other factors.