Brushless DC motor design for a small car

In this case study of the design of a 45 kW motor¹ commissioned for a small family hatchback – the Rover Metro Hermes – the unit was to give rated power from 3600–12 000 rpm at a terminal voltage of 150 V AC. The unit has been tested on a dynamometer over the full envelope of performance and methods for improving the accuracy of measurement are discussed below. The results presented show a machine with high load efficiency up to expectations and the factors considered are important in minimizing losses.

3.3.1 BRUSHLESS MOTOR FUNDAMENTALS

A key aspect of motor design for improved performance is vector control, which is the resolution of the stator current of the machine into two components of current at right angles. Id is the reactive component which controls the field and Iq is the real component which controls the power. Id and Iq are normally alternating currents. In this example, Fig. 3.3, the machines being considered are of the rare-earth surface-mounted magnet type with a conventional 3 phase stator and a rotor consisting of a magnetic flux return with a number of motor pole magnets mounted on it. The open loop characteristics of the machine are considered as follows: if the shaft of the motor is driven externally to 12 000 rpm a voltage of 260 V will be recorded, (a). In this condition with full field at maximum speed, iron losses will be high and the stator will heat up very quickly. At this operating point the motor could supply about 135 kW of power. However, this is not the purpose of the design, (b).

VOLTAGE 260 V 1666 Hz

SPEED 12000 rpm

VOLTAGE

SPEED 4600 5600

Eq 260 V d x q

lq x q 35 V

Id Is

Iq V out 150

V ø LAGGING POWER FACTOR TORQUE

SPEED BASE3600 4600 5600

LEADING LEADING Pf UNITY Pf

The torque–speed requirement for a typical small vehicle is shown to be constant torque to base speed (around 3600 rpm) then constant power to 12 000 rpm. This assumes a fixed ratio design speed reducer. During the first region the voltage rises with speed. In the second region the voltage is held constant at 150 V by deliberately introducing a circulating current – Id which produces 152 V at 12 000 rpm to offset the 260 V produced by the machine, to leave 150 V at the machine terminals. The circulating current produces this voltage across the inductance of the machine winding. It also produces armature reaction which weakens the machine field; total field = armature reaction + permanent magnet field gives a lower air gap flux and lower iron losses. This mode of operation is known as vector control. What happens if we reverse the direction of Id? Theoretically we strengthen the field. However, with a surface mounted magnet motor the machine slows down due to the effect of the circulating current on the machine inductance. However, the torque per amp of Iq current remains constant.

If we supply the motor from a square wave inverter we observe some interesting phenomena when we vary the position of the rotor timing signals. In the correct position the stator current is very small. When the current lags the voltage the motor slows and produces current with sharp spikes and considerable torque ripple. When the current leads the voltage the motor runs faster and produces a near sine wave with smooth torque output. It is the field weakening mode we wish to use in our control strategy, (c).

3.3.2 MOTOR DESIGN: METHOD OF MEASUREMENT

In the following account details are given of the motor design, Fig. 3.4, and of the predicted and measured efficiency maps. The measured efficiency maps were carried out using a variable DC link voltage source inverter. Polaron conducted the trials with two waveforms: a square wave with conduction angle 180° and a square wave with harmonic reduction, conduction angle 150°, the purpose being to assess the effects of the harmonics on motor performance, (a).

a = 150° audible a = 180° audible

SPEED V I P noise V I P noise

1000 29V 7.3A 75W 52dB 28V 12.4A 72W 54dB

2000 55V 8.1A 216W 54dB 55V 12.8A 216W 54dB

3000 82.6V 8.4A 396W 56dB 84V 13.2A 405W 55dB

4000 113V 9.12A 540W 56dB 110V 13.6A 630W 56dB

5000 138V 9.12A 765W 58dB 137V 13.8A 900W 57dB

6000 150V 25A 990W 59dB 150V 24A 1080W 58dB

8000 150V 87A 1440W 60dB 150V 84A 1800W 63dB

10000 150V 122A 2250W 67dB 150V 123A 2700W 69dB

Fig. 3.4 Motor design data: (a) XP1070 machine data; (b) no-load losses (machine only).

Stack OD 220 mm Stator mass 14.1 kg

Stack ID 142.5 mm Rotor mass 4.12 kg

Length 80.5 mm Total mass 34 kg

Overall length 140.5 mm Rotor inertia 0.016 kg m²V

Pole number 16 Thermal resistance 0.038°C/Watt

Peak torque 200 Nm Thermal capacity 6000 joules/°C

Motor constant km RMS 3.03 Nm/sqr (W) Rotor critical speed 21 000 rpm Motor constant km DC2 89 Nm/sqr (W) Nominal speed 12 000 rpm Electrical time constant 10.4 millisecs Back EMF at 12 000 rpm = 260 V Mechanical time constant 1.9 millisecs Winding resistance 0.096 ohm

Friction 0.171 Nm Winding inductance 100 microhenries

Motor torque constant 0.3 Nm/A Vector control voltage 150 V Winding star connected RMS line to line

(a)

(b)

The measurement of electrical input power is accurately achieved using the ‘three wattmeter’

method. Measurement of mechanical power is more difficult. Polaron found it necessary to mount the motor into a swing frame with a separate load cell to obtain accurate results at low torque.

Even so, other problems such as mechanical resonances and beating effects at 50 Hz harmonics require care in assessing results. The operating points were on the basis of maximum efficiency below 150 V AC terminal voltage.

Results are in the form of three efficiency maps which give predicted and measured performance on both waveforms. The losses in this type of motor are dominated by resistance at low speed and iron losses at high speed. What the results show is that low speed performance was accurately predicted but high speed performance was less efficient especially at light load. The reason for this is that the iron loss at 10 000 rpm, no-load, should be about 1000 W, sine wave, (b). With 150 V terminal voltage the measured figure was 2200 W. The following paragraphs discuss the factors affecting this result but it is believed that the main contributors are larger than expected hysteresis losses due to core steel not being annealed, and larger than expected eddy current losses because of lower than specified insulation between laminations.

Annealing causes oxidation of the surface of the steel, leading to improved interlayer insulation.

Polaron subsequently coat the laminations with epoxy resin then clamp them in a fixture to form a solid core for winding.

3.3.3 MOTOR DESIGN FACTORS AFFECTING MACHINE EFFICIENCY

For the stator the important factors are: (i) shape of lamination – optimized lamination has a much larger window than 50 Hz induction motor lamination and a bigger rotor diameter relative to the stator diameter; (ii) use of high nickel steels is counteracted by poor thermal conductivity. Thin silicon steel with well-insulated laminations gives best results. Laminations should be annealed and not subjected to large mechanical stresses. The core can be a slide fit in casing at room temperature as expansion due to core heating soon closes the gap. Stator OD should be a ground surface; (iii) winding must be litz wire and vacuum impregnated to ensure good thermal conductivity.

Varnish conducts 10 times the heat of air gap.

For the rotor the main ones are: (i) if magnets are thick (10 mm in this case) mild steel flux return is satisfactory; (ii) magnets are unevenly spaced to remove cogging torque; (iii) individual poles must not contain gaps between magnet blocks making up the pole. Such gaps lead to massive high frequency iron losses. This can be checked by rotating the machine at lower speed and observing the back-EMF pattern. If there are sharp spikes in the wave form the user will have problems with losses.

3.3.4 MOTOR CONTROL

Battery operated drives must make optimum use of the energy stored in the battery. To do this, the efficiency of both motor and driveline are critically important. This is especially true in vehicle cruise mode typically two-thirds speed one-third maximum torque, therefore Polaron proposed to build a drive with two control systems: (i) current source control in constant torque region and (ii) voltage source operation in constant power region. At 45 kW 6000 rpm we would expect I_L 175 A, V_AC 150 V; inverter switching loss 10 kHz, 1.8 kW; converter saturated loss 0.9 kW, using PWM on the windings and IBGT devices.

If, however, we use a square wave at the machine frequency, Fig. 3.5, and the machine operates with a leading power factor, the switching losses are greatly reduced for additional iron loss, of 225 W, at top speed. The inverter efficiency increases from 94% to 97%. In the low speed constant torque region there is no alternative to using PWM in some form.

Fig. 3.5 Motor line current waveforms.