Universal motor: why a series-wound motor runs on AC and DC

Series winding: field and armature in one circuit

A DC series motor connects the field winding in series with the armature through the commutator and brushes. The flux Φ is produced by the field current, and the torque is the product of flux and armature current:

T = k × Φ × I

Below magnetic saturation Φ is proportional to I, so

T ∝ I²

The torque therefore does not depend on the sign of the current. Reverse the supply polarity of a DC series motor and both flux and armature current reverse, so the direction of rotation does not change. The same thing happens on AC at every half cycle.

Why it also works on alternating current

On AC the current reverses direction 100 times a second at 50 Hz. Since flux and armature current reverse at the same instant, each half cycle produces torque in the same direction. The instantaneous torque is proportional to i(t)², so it is never negative. It pulsates between zero and twice its mean value at 2f, 100 Hz on a 50 Hz supply, which is why these motors hum, and the inertia of the rotor smooths the resulting speed.

To work on AC the machine needs a laminated field core, to limit eddy-current losses from the alternating flux, in addition to the commutator. The windings also have reactance on AC, which they do not have on DC, so at the same RMS voltage less voltage is left to balance the back-EMF. A universal motor therefore runs slower on AC than on DC at the same voltage, and the power factor is below 1. Many motors have a tapped field winding to compensate.

Speed: very high, and the series characteristic

The back-EMF is E = k × Φ × ω. In steady state E is roughly the supply voltage minus the resistive drop, so

ω ≈ (V − I × R) / (k × Φ)

When the load increases, the current rises, the flux rises and the speed falls steeply: a series motor has high torque at low speed, which is why it suits tools that need power to start. Without load the current falls, the flux weakens, and the speed has to rise to produce the same back-EMF. There is nothing in the machine to limit it except friction and fan losses, so an unloaded series motor can run away to destructive speeds.

Illustration. On a 230 V supply, a motor at full load runs at 15 000 rpm with Φ = 1 and E ≈ 200 V (a 30 V resistive drop). If the load torque falls to 1/16 of that, the current falls to 1/4 and (unsaturated) the flux to 1/4, while the resistive drop falls to 7.5 V and E rises to about 222 V. The speed becomes about 15 000 × (222 / 200) / 0.25 ≈ 67 000 rpm. In practice windage and the fan of a small tool limit the speed, and universal motors are never run unloaded or coupled by a belt that could slip off.

The same property is the reason for the very high speeds of 10 000 to 30 000 rpm in tools: for a given power, a faster motor is smaller and lighter, and a gearbox or fan loads it.

Controlling the speed with a triac

Because speed rises with the effective voltage, universal motors are easy to control with a triac dimmer-type circuit. The triac is fired at an angle α after each zero crossing, and the RMS voltage on the motor is

V_eff = V × √(1 − α / π + sin 2α / (2π))

At α = 0 the motor receives full voltage, at α = 90° it receives about 71% of V (162 V from a 230 V supply), and at α = 180° it receives nothing. Many variable-speed drills, blenders and sewing machines work this way, often with feedback from a tachometer to hold speed under load. The price is a lower power factor and some electrical noise on the line.

Brushes, sparking and where it is used

The commutator reverses the armature current in each coil as it passes the brushes. The coil being switched has inductance, so the current does not stop at once and the brush and segment spark. Sparking grows with the armature current and with speed, and on AC there is also a transformer EMF in the commutated coil. The result is brush wear, commutator blackening, radio interference and, in the worst case, a ring of fire around the commutator. Interference suppressors (capacitors and chokes) are standard in appliances.

Brushes are the wearing part of a universal motor and set its life, from a few hundred hours in heavily used tools to several thousand in appliances. Brushless designs with an electronically commutated motor are replacing them where cost allows.

• Power tools: drills, angle grinders, circular saws, routers, where high torque at start and low weight matter
• Vacuum cleaners: high speed drives the fan, and a triac can adjust the suction
• Kitchen appliances: blenders, mixers, food processors
• Hair dryers, sewing machines and small garden tools

Typical ratings run from a few watts to about 1 kW (some above). For continuous high-power duty, induction motors and brushless motors are more efficient and quieter.

How the simulator models the universal motor

The simulator solves a series circuit with one RMS current I and a back-EMF in phase with it (the commutator makes the motor act like a resistance). With winding resistance R and reactance X (zero on DC, scaled with frequency on AC), the supply voltage satisfies

V² = (R × I + E)² + (X × I)²

The flux uses the same saturating function as the DC series motor simulator. The model is calibrated so the nameplate gives exactly rated speed and current at rated voltage and load. The current for a given load is found by search, and the speed follows from the back-EMF. Locked-rotor current is V / √(R² + X²).

The triac uses the V_eff formula above. The torque ripple plot uses T(t) = T_mean × (i(t) / I_rms)², and the brush sparking indicator is a qualitative number from current and speed. If the raw speed passes 1.5 times rated the model reports runaway, and the displayed speed is limited to 3 times rated.

Limits: the instantaneous flux does not follow current (an RMS approximation is used), and commutation currents and harmonics on the line are not modelled.

Try it in the universal motor simulator

In the universal motor simulator, pick a template: power drill (600 W), vacuum cleaner (1000 W) or kitchen mixer (300 W).

• Set Supply type to DC, note the speed, then switch to AC at the same voltage. The speed is lower and the power factor falls below 1; the Speed–torque chart draws both curves.
• Check the Current and torque over two supply cycles chart: on AC the current reverses, but the torque (proportional to i²) stays positive and pulsates at 2f. The Torque ripple (2f) readout gives its frequency. On DC both lines are flat.
• Lower the Mechanical load towards 0%. The speed climbs and then the runaway warning appears, with the displayed speed capped.
• On AC, raise the Triac firing angle from 0° towards 180°. Its hint gives the motor voltage (RMS) and its percentage of the supply, and the speed falls. The control is hidden on DC.
• Raise the load and watch the Brush sparking indicator move from Low to Moderate to Heavy, with sparks at the brushes in the 3D scene.

The same machine, with the same torque direction, works on both supplies; only the speed and the power factor change.

Try it in the simulator