Electric motors: permanent-magnet and induction

Hal's trial van has been on its courier route for three weeks when Marcus Bell, who drives it, brings it back with a complaint. Between about 55 and 65 km/h (35 and 40 mph), he hears a high whine that rises and falls with speed, louder when he accelerates and almost gone when he coasts. "The old van had noises too," he says, "but they were engine noises. I don't know what this one is telling me." Marty smiles. "Electric drive units are quiet, so every small noise stands out. Before we decide whether this one is a problem, Kiran is going to learn how the motor works."

This lesson explains how electric traction motors make torque, the two main types, permanent-magnet synchronous motors and induction motors, how motors behave across their speed range, the sensors that tell the inverter where the rotor is, how motors are cooled, and how a technician separates normal drive unit sounds from faults.

How a motor makes torque

Every electric motor works by the force between magnetic fields. The stator, the stationary outer part, holds copper windings arranged in three phases. When the inverter sends three-phase alternating current through them, the windings make a magnetic field that rotates around the stator. The rotor, the turning part inside, has a magnetic field of its own, and it is pulled around by the rotating stator field. The strength of the pull, the torque, depends on the strength of the two fields and the angle between them; the inverter controls both by controlling the current in each phase.

Running the same machine in reverse makes it a generator. When the vehicle's momentum drives the rotor faster than the stator field, the machine converts mechanical energy into electrical energy, and the inverter sends it back to the battery. That is regenerative braking, the subject of a later lesson. In an electrified vehicle, "motor" and "motor-generator" mean the same machine.

The first equation links power, torque and speed: power in watts equals torque in newton-metres times angular speed in radians per second. The second gives the electrical frequency the inverter must produce, in hertz, for a motor with p poles turning at n revolutions per minute.

Permanent-magnet synchronous motors

Most electric vehicles and hybrids use a permanent-magnet synchronous motor, often shortened to PMSM. Its rotor carries strong rare-earth magnets, usually neodymium-iron-boron, set inside slots in a laminated steel core. Because the rotor's field comes from the magnets, the stator's current does not have to create it, which makes the motor very efficient, often above 95 percent over much of its range, and compact for its power. The rotor turns at exactly the speed of the stator's rotating field, in step with it, which is what synchronous means.

The magnets bring two consequences that matter to technicians. First, whenever the rotor turns, its magnets generate a voltage in the stator windings, called back electromotive force. A towed electric vehicle with its drive wheels on the ground can generate high voltage in its motor, which is why makers specify flatbed towing or wheel dollies, and why a disconnected motor cable can still be live if the wheels turn. Second, the magnets' field is always present, so at high speed the inverter must weaken it with an opposing current, called field weakening, to keep the back voltage below the battery voltage.

Some makers use a variation with less magnet material, or with none: a wound-rotor synchronous motor, also called an externally excited motor, makes its rotor field with a winding fed through brushes or a contactless transformer, avoiding rare-earth magnets at some cost in efficiency.

Induction motors

An induction motor's rotor has no magnets and no connections. It is a cage of aluminium or copper bars joined by rings at each end, set in a laminated core. The stator's rotating field induces currents in the bars, and those currents make the rotor's field. Because induction needs relative movement, the rotor always turns slightly slower than the field; the difference, called slip, is a few percent. Induction motors are rugged, cheap and contain no rare-earth metals, and they make no back voltage when the inverter is off, so they drag less when coasting. They are a little less efficient than permanent-magnet motors at light loads. Some dual-motor vehicles use a permanent-magnet motor on one axle for efficient cruising and an induction motor on the other for extra power when needed.

Torque and power across the speed range

An electric motor can deliver its maximum torque from standstill, which is why electric vehicles accelerate so briskly from a stop. Torque stays at its maximum up to the base speed, where the motor's back voltage reaches the limit the inverter can supply. Above base speed, the motor runs in its constant-power region: torque falls as speed rises, so that power stays roughly constant until the top speed. Because a motor makes useful torque across such a wide range, most electric vehicles need only a single fixed reduction gear, as Kiran saw in Dr. Singh's drive unit in the drivetrain course.

# Torque, power and speed: a traction motor's curve, and the wheel torque through the reduction gear
import math
t_max = 310.0          # newton-metres, available up to base speed
p_max = 150.0          # kilowatts
base = p_max * 1000 * 60 / (2 * math.pi * t_max)
ratio = 9.0            # single reduction gear
tire_m = 0.335         # loaded tire radius, metres
print(f"base speed: {base:,.0f} rpm")
for n in (1000, 3000, base, 6000, 9000, 12000):
    torque = t_max if n <= base else p_max * 1000 * 60 / (2 * math.pi * n)
    power = 2 * math.pi * torque * n / 60 / 1000
    road = n / ratio * 2 * math.pi * tire_m * 60 / 1000
    print(f"{n:6,.0f} rpm: {torque:5.0f} N m, {power:5.1f} kW, wheel torque {torque * ratio * 0.97:5.0f} N m, road speed {road:5.0f} km/h")

base speed: 4,621 rpm
 1,000 rpm:   310 N m,  32.5 kW, wheel torque  2706 N m, road speed    14 km/h
 3,000 rpm:   310 N m,  97.4 kW, wheel torque  2706 N m, road speed    42 km/h
 4,621 rpm:   310 N m, 150.0 kW, wheel torque  2706 N m, road speed    65 km/h
 6,000 rpm:   239 N m, 150.0 kW, wheel torque  2084 N m, road speed    84 km/h
 9,000 rpm:   159 N m, 150.0 kW, wheel torque  1389 N m, road speed   126 km/h
12,000 rpm:   119 N m, 150.0 kW, wheel torque  1042 N m, road speed   168 km/h

Rotor position sensors

To control the current in each phase, the inverter must know exactly where the rotor is, many thousands of times a second. Most traction motors use a resolver, a small rotary transformer on the motor shaft. The inverter feeds its primary winding with an excitation signal, typically a sine wave of several kilohertz, and two secondary windings, set at 90 degrees to each other, return sine and cosine signals whose amplitudes vary with the shaft angle. Resolvers are rugged and tolerate heat and vibration. Some motors use Hall-effect or inductive position sensors instead. After a motor, resolver or inverter is replaced, many systems need an offset learn, a scan tool procedure that teaches the inverter the exact angle between the resolver and the rotor's magnets; skipping it can cause rough operation or a no-ready condition.

A resolver fault usually sets a code and puts the vehicle into a reduced-power mode or prevents it from moving. A technician checks the resolver's windings for resistance and for shorts to the motor housing with the system de-energized, following the maker's procedure, and inspects the connector for coolant or water, which is a common cause.

Cooling the motor

A motor that is 95 percent efficient still turns 5 percent of its power into heat in its windings, its steel and its magnets. At 150 kilowatts, that is 7.5 kilowatts. Motors are cooled by coolant through a jacket around the stator, by oil sprayed directly on the windings and rotor, or by both, and the heat is usually shared with the inverter's cooling loop and sometimes used to warm the battery or the cabin. Magnets lose strength if they overheat, so the inverter limits power when the motor temperature climbs, much as the BMS limits the battery. Low coolant or a failed pump shows first as reduced power on long climbs, such as the highway west of Calgary (Denver) into the mountains.

Marcus's whine

Kiran and Marty drive the van with the scan tool recording motor speed and a vibration app on a tablet recording the sound. The whine peaks at about 60 km/h (37 mph). They compare its frequency with the drive unit's possible sources: the motor's electrical frequency and its harmonics, and the gear mesh frequencies of the two-stage reduction gear, which Kiran calculates from the tooth counts in the service information.

# Which part of the drive unit is whining? Compare the noise frequency with motor and gear frequencies
motor_rpm = 4500
poles = 8
z_input, z_inter1 = 19, 59         # first gear stage tooth counts
z_inter2, z_output = 21, 64        # second gear stage
noise_hz = 1425
motor_hz = motor_rpm / 60
electrical = poles * motor_rpm / 120
stage1 = motor_hz * z_input
inter_hz = motor_hz * z_input / z_inter1
stage2 = inter_hz * z_inter2
sources = {"motor shaft": motor_hz, "electrical frequency": electrical, "electrical x6 (slot harmonic)": electrical * 6,
           "stage 1 gear mesh": stage1, "stage 2 gear mesh": stage2}
for name, f in sources.items():
    print(f"{name:30} {f:8.0f} Hz{'  <- matches the noise' if abs(f - noise_hz) / noise_hz < 0.03 else ''}")

motor shaft                          75 Hz
electrical frequency                300 Hz
electrical x6 (slot harmonic)      1800 Hz
stage 1 gear mesh                  1425 Hz  <- matches the noise
stage 2 gear mesh                   507 Hz

The noise matches the first stage's gear mesh frequency, not the motor. Gear mesh whine at a particular speed, louder under drive torque and quieter when coasting, is common on electric drive units, because there is no engine noise to cover it. Kiran checks the service information and finds a bulletin for this van: the drive unit's software has an update that changes the inverter's torque ramp in that speed range to reduce the gear whine, and if the noise remains above a stated level after the update, the gearbox is replaced under warranty. The leasing company's dealer performs the update the next week, and Marcus reports that the whine is now barely noticeable.

Not every drive unit noise is so benign. A grinding or growling that changes with speed may be a bearing; a clunk on changing from drive to regeneration may be a worn mount or excessive gear backlash; a loud whine with a warning light may be a motor or inverter fault. And an electric vehicle with a failing bearing can be harder to hear than a gas vehicle, because the bearing's noise blends with tire noise. The vibration order methods from the drivetrain course work here too.