Out on the road
A vehicle has 60 cm external diameter wheels, so it moves about 2m for each wheel rotation. A 180 km/h (50 m/s, 112 mph) speed corresponds to 25 wheel turns per second. At each wheel turn, the 24 magnets are passing in front of each wire, alternatively north and south. The electric current has to be inverted in the wires for each polarity inversion, in order to keep the same direction of the driving forces (see previous figure). The current pulse periods corresponds to 1/12 of a wheel turn. At the maximum speed of 180 km/h, the minimum period is 3.33ms (300 Hz max), easily achievable with existing power MOSFETs.
When the space between magnets is in front of the wires (red for instance), the current in these wires has to be stopped, before being inverted. The “complementary” wires (green for instance) are in front of the magnets, with current flowing, in order to keep the torque constant. The phase difference (positive or negative) between red and green wires depends on the motion direction (forward or backward).
A magnetic field sensor (Hall-effect type, for instance) is joined to the axle to determine the relative position of the magnets and wires, and thus commands the current switching.
Each stack generates a driving torque, Γ = 0.27 * I
When the wheel runs at a "pulsation," ω, a counter-electromotive force (CEMF) = E, is generated on the wires:
E = 0.27 * ω
(E * I product is the electrical equivalent of the mechanical power Γ * ω)
At 180 km/h (ω = 2 * 3.14 * 25 = 157), E = 42V.
At a speed v (km/h), E(v) = 0.23 * v.
Electronic gearbox performance at varying speed
At start up, E = 0. The series resistance of the wires and the switches is the only limiting factor for the current in the stacks. The 12 stacks are connected in series, powered by a 130V battery.
A maximum of 28 switches are connected in series (a conservative approach, with one switch at each end of each stack). The switches between two stacks have a DC command, while the switches at the ends of the network are switching to the two poles of the battery, in order to invert the current in the net.
The 28 switches have a total series resistance of about 5.6 Ω (the conservative approach includes the series resistance of the battery and of the connections). The current flowing through the 12 stacks is about 20A, generating a maximum starting torque of 260 Nm (four wheel drive).
In order to control this torque, it is possible:
To power only two wheels (torque divided by 2);
To power only one network (red or green, torque divided by 2);
Or control the duration of the current pulses (Pulse Width Modulation).
When the vehicle speeds up, the CEMF voltage increases, and reduces the flowing current:
I = (Vbat – E) / R
At 45 km/h (28 mph), the CEMF voltage on each stack is 10.5V, and thus on the 12 stacks in series, 126V—approaching the battery voltage value. The current flowing through the stacks starts to become negative for speeds faster than 45 km/h, and the motor acts as a generator.
The wheel motors also act as brakes. All the current generated by regenerative braking is used to charge the battery. No additional circuitry is needed.
In order to brake at speeds slower than 45 km/h, it is necessary to short circuit the stacks into a resistor. The braking energy is lost. Using it to recharge the battery would require additional circuitry, that may be worthless, as this energy is relatively small (0.5 * M * v2
). [Ed. Note: Previous calculation for energy corrected from original posted text.]
Part 2 of this feature covers applications at higher, more practical speeds and manufacturability.
Roland Marbot is principal at EZ Consulting, firstname.lastname@example.org.