MC-B3 · DC motor torque & speed

Torque and Speed of the DC Motor

A spinning armature also generates. Its back-EMF opposes the supply and sets the speed. Vary the field flux, watch where the speed goes, and confirm a result that runs against intuition.

Weaken the field flux — where does the speed go?

The back-EMF Eb = kΦN nearly balances the terminal voltage, so the speed is N = (V - IaRa)/(kΦ). Lower the flux slider. Noting that Φ sits in the denominator, predict first where the speed will go.

Field flux ΦΦ = 1.00

Slide for continuous flux. The curve is the speed N.

Speed set by the back-EMF balance

N = (V - IaRa)/(kΦ) = 1500 rpm

Lowering the flux seems to slow it, but the opposite is true. Since Eb = kΦN must oppose a nearly constant terminal voltage, a smaller Φ forces a larger N to keep the balance.

Lower Φ — N goes?

Misaligned

Back-EMF is the latch that limits current

A motor’s armature also spins in the flux and generates. This back-EMF Eb = kΦN opposes the supply, so the armature current is Ia = (V - Eb)/Ra. The larger the back-EMF, the smaller the current. At the instant of starting N = 0, so Eb = 0 and the current surges to V/Ra. That is why large motors use a starting resistance to hold down the initial current.

ObserveEb = kΦN

The back-EMF is flux times speed.

ChooseIa = (V - Eb) / ?

The armature current is the leftover voltage over the armature resistance.

Torque is flux times current

A conductor carrying current in flux feels a force F = BIl. Summing the torque of all armature conductors gives T = kΦIa. When the load rises, the speed dips slightly, the back-EMF falls by that much, Ia = (V - Eb)/Ra grows, and the torque rises to a new balance. This self-regulation, the motor matching its load, is thanks to the back-EMF.

On your ownT = ?

The torque is flux times armature current.

Three handles to set the speed

N = (V - IaRa)/(kΦ) offers three handles. Field control lowers Φ to push the speed above rated (constant power, high speed). Voltage control lowers V to bring the speed widely below rated (constant torque). Resistance control adds a series resistance in the armature to slow it, but that resistance dissipates and the efficiency is poor. All three are just which term of the same one equation you touch.

Fill inN = (V - IaRa) / ?

The speed is the back-EMF divided by the flux.

Back to the first screen

Lowering the flux sped the motor up because the back-EMF Eb = kΦN must balance the nearly constant terminal voltage. As Φ shrinks in the denominator, N grows to keep that balance. In the same N = (V - IaRa)/(kΦ), lowering V slows it, and adding series resistance to grow IaRa slows it too. The torque is T = kΦIa, flux times current, and when the load changes the back-EMF adjusts the current automatically to match the torque. Every behaviour of the DC motor hangs on this one back-EMF balance.

The DC motor: the spinning armature’s back-EMF Eb = kΦN opposes the terminal voltage, so the armature current is Ia = (V - Eb)/Ra, the speed N = (V - IaRa)/(kΦ), and the torque T = kΦIa. With Φ in the denominator, weakening the field raises the speed. Speed control is the three handles V, Φ and R of the same equation.

Once you hold this balance

The back-EMF balance is the root of every DC-motor characteristic. Whether the field is wired in series or in parallel changes the relation between Φ and Ia, giving the different torque-speed curves of series, shunt and compound motors. The next unit covers the external characteristic and voltage build-up of the same machine run as a generator (MC-B4). There too the starting point is Eb = kΦN.