Electric hub motor improves EV range: Part 1 – Technology basics
Most of the electric cars currently available are using brushless permanent magnet (PM) motors. These motors have very good characteristics, but their control circuitry consumes a lot of power, that may require liquid cooling. This wasted energy is taken from the energy stored in the battery, reducing the range of the car.
For hybrid vehicles using series power train technology (the combustion engine drives an electrical generator charging the battery), this waste of energy translates into a reduction of the miles covered per gallon of gas.
This series describes the concept of a brushless DC motor with an "electronic gearbox," requiring an almost lossless control circuitry. This translates into improved range, which is also increased by a nearly 100% regenerative braking energy recovery, as well as reduced manufacturing cost and better reliability.
The motor described here is designed to fit into the wheels of a 4WD car. The same concept can be used for implementations of a centralized electrical motor with mechanical transmission. Other implementations of the concept can be considered.
Motor and gearbox basics
The axle of the motor is fixed, with no transmission of any mechanical energy from the vehicle to the wheels (which allows for simplified shock absorbers and improvement of the energy transmission yield). The stator of the motor, "tied" to the axle, is made of printed circuits with copper electric wires. The rotor of the motor is made of magnets and is joined to the rim of the wheel, turning around the axle.
The described motor is made up of a dozen “stacks.” Each stack is 5-mm thick, and is made of a disk of magnets, 3-mm thick, and a printed-circuit disk, 1.8-mm thick, with a 0.2-mm gap between the stator and rotor.
Below is a front view (top) and side view of the motor.
The magnet disks consist of 24 magnets, oriented as radial segments with a magnetization in the direction of the thickness of the disk. These segments occupy 50% of the area of the disk (non-adjacents) and are polarity alternated (N-S magnet, S-N magnet, N-S, S-N, etc). External diameter of the disk is 40 cm; internal diameter is 10 cm. Each magnet segment is 15 cm long.
A 1 Tesla (T) magnetic field can be generated in the air gap of this configuration (2-mm gap for 3 mm magnet thickness) using neodymium rare-earth materials.
Motor calculations
The following computations are done with a 0.6-T field, in order to be conservative or allow the use of cheaper magnets.
Printed circuit disks are made of two networks, each made of 24 radial wires (shown in red and green in the previous figures), connected as “serpentines.” The series resistance of the wires is assumed to be the resistance of the radial axes, as the circular connections can be designed sufficiently thick for essentially zero resistance. The cross section of the radial wires is 2 mm2 (4 mm large x 0.5-mm thick) in the center part of the disk, up to 8 mm2 (16 mm x 0.5 mm) in the outer part.
The twin networks are powered with 90° phase difference, as shown below, in order to maintain the motor torque during the switching time of the current on the complementary phase.
The length of the 24 wires is 24 * 15 cm = 3.6m. The rotation force on these wires is:
This force is applied in the middle of the wires, at a distance from the axis of 12.5 cm. The motor torque per stack is
The total motor torque generated by the 12 stacks is:
A 30A current generates a mechanical torque of 97.2 Nm.
A vehicle driven by four wheels has a total driving torque of 390 Nm, when 30A is flowing through all stacks. This corresponds to the driving torque of existing high-performance cars.
A 15-cm copper wire, with a cross section varying between 2 mm2 and 8 mm2 has a resistance of 6 µΩ. Assuming that interconnections between radial wires have a negligible resistance, the total resistance of a printed circuit disk wire is 24 * 6 = 0.145 mΩ.
A 30A current flowing through this wire generates a 4.5 mV voltage drop, and 130 mW power dissipation. The total power dissipation for the 12 stacks of a wheel, when 30A are flowing in all disks is 1.6W.
All wires of all stacks are connected to the command circuitry, located close to the axle. Each wire is connected to an electronic switch, with a series resistance of 0.2 Ω (conservative number, in order to take into account unexpected parasitic resistances). This switch represents the major contribution in the estimated total resistance of the electric circuit, and generates most of the joule losses (carefull selection of these MOS transistors has a direct impact on the energetic yield of the system). 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:
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:
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 (M * v2).
Part 2 of this feature covers applications at higher, more practical speeds.
Roland Marbot is principal at EZ Consulting, marbot.roland@neuf.fr.
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