6.3 DC Motor and Generator Theory

DC Motor and Generator Theory in Aviation

Direct current (DC) machines are fundamental to aircraft electrical systems, serving as starter motors, actuators, fuel pump drives, and electrical power generators. Modern turbine-powered aircraft frequently utilize a combined unit known as a starter-generator. During engine starting, this unit acts as a DC motor, drawing heavy current from the battery or auxiliary power unit (APU) to crank the turbine to its self-sustaining speed. Once the engine is running, the aircraft control circuitry automatically switches the unit's configuration so that it operates as a generator, supplying $28\text{ VDC}$ to the electrical buses and recharging the batteries. Understanding the construction, physics, and control of DC machines is crucial for aircraft maintenance technicians who must troubleshoot power generation and actuation systems.

Physical Construction of a DC Machine

Whether operating as a motor or a generator, the basic physical construction of a DC machine is identical. It consists of the following primary components:

• Stator (Field Frame or Yoke): The outer iron frame that provides structural support and houses the field windings (or permanent magnets). The field windings are wound around soft-iron pole pieces to produce the main magnetic field.
• Rotor (Armature): The rotating core made of laminated steel sheets (to reduce eddy currents) containing slots. Copper conductors (armature windings) are wound through these slots. It is within these conductors that the generator voltage is induced or the motor force is developed.
• Commutator: A cylindrical assembly of copper segments mounted on the rotor shaft but insulated from the shaft and from each other by thin sheets of mica. The ends of the armature coils are connected to these segments. In a generator, the commutator acts as a mechanical rectifier, converting the alternating current (AC) induced in the rotating loops into direct current (DC) at the brushes. In a motor, it acts as a mechanical inverter, reversing the direction of current in the armature coils as they rotate to maintain a continuous, unidirectional torque.
• Brushes: Soft carbon or graphite blocks held by spring pressure against the rotating commutator. They form the sliding electrical contact between the rotating armature and the external stationary circuit.

Generator Action and Fleming's Right-Hand Rule

Generator action is based on Faraday's law of electromagnetic induction. When an external mechanical force (such as an aircraft engine accessory gearbox) rotates the armature conductors through the stator's magnetic field, an EMF is induced in the conductors. The induced voltage in a single conductor is given by:

$e = B \cdot l \cdot v \cdot \sin(\theta)$

Where $B$ is the magnetic flux density, $l$ is the length of the conductor in the field, $v$ is the velocity, and $\theta$ is the angle at which the conductor cuts the magnetic lines of force. The maximum voltage is induced when the conductor moves perpendicular to the magnetic field ($\theta = 90^\circ$).

Fleming's Right-Hand (Generator) Rule

To determine the direction of the induced conventional current in a generator conductor:

1. Extend the thumb, index (fore) finger, and middle finger of your right hand mutually perpendicular to each other.
2. Point your Index finger in the direction of the magnetic field (North to South).
3. Point your Thumb in the direction of the Motion of the conductor.
4. Your Middle finger will point in the direction of the induced Current flow.

Memory Tip: Remember G-R (Generator = Right hand).

Motor Action, Back EMF, and Fleming's Left-Hand Rule

Motor action is based on the physical force exerted on a current-carrying conductor when placed inside a magnetic field. This force is described by:

$F = B \cdot I \cdot l \cdot \sin(\theta)$

Fleming's Left-Hand (Motor) Rule

To determine the direction of force and motion in a motor conductor:

1. Extend the thumb, index, and middle finger of your left hand mutually perpendicular to each other.
2. Point your Index finger in the direction of the magnetic field (North to South).
3. Point your Middle finger in the direction of the applied Current (conventional flow).
4. Your Thumb will point in the direction of the resulting Force or Motion of the conductor.

Memory Tip: Remember M-L (Motor = Left hand).

Back EMF ($E_b$)

When a DC motor rotates, its armature conductors cut the magnetic lines of force of the stator field. By Faraday's law, this motion induces a voltage inside the armature. According to Lenz's law, this induced voltage must oppose the applied supply voltage. This voltage is called back EMF (or counter EMF, $E_b$). The relationship between supply voltage ($V$), armature current ($I_a$), and armature resistance ($R_a$) is:

$V = E_b + I_a \cdot R_a \implies I_a = \frac{V - E_b}{R_a}$

Back EMF serves as a self-regulating governor for the motor. At the exact instant of starting, the armature is stationary (speed = 0), meaning $E_b = 0$. Consequently, the starting current is extremely high, limited only by the very low resistance of the armature windings:

$I_{start} = \frac{V}{R_a}$

As the motor accelerates, the rotating conductors cut the magnetic field faster, generating a larger back EMF. This back EMF opposes the supply voltage, automatically reducing the armature current to a normal, safe operating level. To prevent damage from excessive starting current, large aircraft DC motors use current-limiting starting resistors that are bypassed once the motor builds sufficient speed and back EMF.

Commutation and Armature Reaction

Armature Reaction

When a DC machine is loaded, the current flowing through the armature windings creates its own magnetic field. This armature field distorts and weakens the main magnetic field produced by the stator. This effect is armature reaction.

Armature reaction shifts the Magnetic Neutral Axis (MNA) — the plane where no voltage is induced in the conductors. In a generator, the MNA shifts in the direction of rotation. In a motor, the MNA shifts opposite to the direction of rotation. If the brushes remain at the physical neutral axis, they will contact commutator segments connected to coils that are still cutting magnetic flux, causing heavy sparking at the brushes, which damages the commutator.

Solutions to Armature Reaction

1. Brush Shifting: Moving the brushes to align with the shifted MNA. This is only effective for constant-load machines because the MNA shift varies with armature current.
2. Interpoles (Commutating Poles): Small auxiliary poles placed between the main stator poles. The interpoles are wound with heavy wire and connected in series with the armature, so their magnetic strength varies with load. They produce a field that cancels the armature reaction in the commutating zone, allowing the brushes to remain in the physical neutral position.

Worked Exam Calculation Scenario

Problem: An aircraft $28\text{ VDC}$ fuel boost pump motor has an armature resistance ($R_a$) of $0.12\ \Omega$. During normal operation at full speed under load, the motor draws a current of $25\text{ Amperes}$. Calculate:

1. The voltage drop across the armature resistance during operation.
2. The back EMF ($E_b$) generated by the motor at running speed.
3. The starting current ($I_{start}$) if the motor is connected directly to the supply without a starting resistor.

Step 1: Calculate the voltage drop across the armature. $V_{drop} = I_a \cdot R_a = 25\text{ A} \times 0.12\ \Omega = 3.0\text{ Volts}$

Step 2: Calculate the back EMF ($E_b$). $E_b = V - I_a \cdot R_a = 28\text{ V} - 3.0\text{ V} = 25.0\text{ Volts}$

Step 3: Calculate the starting current ($I_{start}$). At the instant of start, speed is 0, so $E_b = 0$: $I_{start} = \frac{V}{R_a} = \frac{28\text{ V}}{0.12\ \Omega} \approx 233.3\text{ Amperes}$

Analysis: The starting current ($233.3\text{ A}$) is over $9$ times the normal operating current ($25\text{ A}$), demonstrating the extreme electrical stress on startup and the critical role of back EMF in regulation.

Exam Traps and Tips

• Armature Current is always AC internally: A classic exam trap is asking whether the current flowing within the armature windings of a DC generator is AC or DC. The answer is always AC. The commutator is what converts it to DC for the external circuit.
• Brush Shift Direction: Remember the difference in MNA shift. A generator shifts forward (with rotation); a motor shifts backward (against rotation).
• Starter-Generator dual roles: When operating as a starter, it is a series-wound motor (high starting torque). When operating as a generator, it behaves as a shunt-wound machine (constant voltage regulation).