# EV Tech 101

Electric Vehicle Technology is an enormous area of study. As time permits, I hope to distill some of what I've learned and share it here.

## Motor Types

Several types of motors have been used in electric vehicles over the years.

Brushed DC (forklifts, early electric cars)

Brushless DC (Toyota Prius)

Induction (Tesla Model S, GM EV1)

Permanent Magnet Synchronous / AC (Ford Focus, Nissan Leaf, BMW i3)

Switched Reluctance (maybe Hyundai?)

Synchronous Reluctance (Tesla Model 3)

Different types of motors have different design tradeoffs. These may include efficiency, power density, mass, controller complexity, cost of materials, manufacturing cost, lifespan, noise, speed range, thermal considerations, starting torque, and so on.

I will focus on brushless DC (BLDC) motors here because that is what's currently being used for trials motorcycles.

A BLDC motor approximates the operation of a simple brush-type DC motor, except that it's actually powered by a 3-phase alternating current that is being created by the controller.

## Motor Characteristic Curves

The chart below illustrates some general trends exhibited by DC motors. In the graph, the Y-axis is speed and the X-axis is torque. Although this is a standard way to present such data for electric motors, it appears quite odd to the uninitiated.

Regardless, several important concepts may be seen with a bit of study:

Credit: UCSD

Torque is linearly proportional to current (red line).

Speed decreases linearly with increasing load (blue line).

Efficiency is very low at low speeds (green line).

Maximum power output occurs when both speed and torque are optimized (yellow line).

Stall current and stall torque are both large and occur at zero speed (dashed vertical line).

This adjacent graph presents just the torque-speed relationship. Note that the speed axis has been swapped with the torque axis from the prior graph. This is a “better” representation, at least for those of us used to seeing plots for internal combustion engines.

Note that the origin of this graph does not necessarily start at zero torque and zero speed.

The maximum continuous torque will be subject to a thermal limit.

Credit: Boucher

## Why No Gearbox?

Why don't most EVs use a gearbox? I guess the simple answer is that it's because they don't need one. The latest version of Mecatecno's Dragonfly even eliminated the gearbox that was part of its original design.

It's certainly been demonstrated that an electric motorcycle does not require a gearbox. There are obviously savings in weight, cost, and complexity but I always assumed a smaller electric motor could be used if you had a gearbox.

Then I realized that a gearbox introduces an extra complication for an electric vehicle. It has to do with the motor's back EMF.

## Back EMF

Back EMF is one of the most fundamental concepts to understand regarding electric motors. EMF stands for electromotive force, which is a bit of a misnomer since it is not a force in the true physics sense. The term was coined in about 1799 by Volta (inventor of the chemical battery) and has stuck with us. Think of EMF as voltage, because it is voltage.

All motors simultaneously act as generators while they are running. Back EMF is the voltage that is produced due to this generating action. Back EMF has the opposite polarity of the voltage that is powering the motor.

Back EMF increases linearly with motor speed. A motor attains its maximum speed when its back EMF equals its supply voltage. Back EMF is often written BEMF.

To visualize BEMF in action, consider a simple DC motor operating under load at a constant voltage.

Imagine the load is suddenly reduced (your motorcycle gets some air, for example).

The required torque will be smaller than the torque that was being delivered.

The speed of the motor will increase due to reduced torque demand.

Being proportional to speed, BEMF increases.

With an increase in BEMF, armature current will decrease.

Recall that torque is proportional to armature current.

Torque decreases until it becomes sufficient for the load.

Likewise, if a DC motor is suddenly loaded (say when encountering deep sand), the load will cause a decrease in speed. Due to a reduction in speed, BEMF will decrease which allows more armature current to flow. An increase in armature current causes torque to increase to meet the load requirement.

## The EV as a System

An electric vehicle is designed as a system with a motor, battery, and controller all rated for a particular voltage. The problem I see is if the motor gets “overspun” (operated at a speed greater than that normally restricted by its back-EMF) the ratings of the controller and battery could be exceeded.

Although it seems less likely with a trials bike, it's certainly a possibility with a road racer or a motocrosser – come into a corner, drop a few gears, let the clutch out, and allow the motor to “catch up.” There might be minimal “engine braking” and racers would experiment to see what worked best.

Back in 2011 - 2012, Brammo built an electric MX bike with a gearbox. I know early electric road racers used a gearbox as well. With a fully automatic gearbox, it would be a simple matter to disallow an over-speed condition. Likewise, a manual gearbox could electronically inhibit a downshift under adverse conditions.

## Motor Torque

The formula for torque in an electric motor varies as the product of rotor diameter squared times rotor length.

T = k * D² * L (where k is a constant dependent on several factors, including current)

Increasing the length (L) of the rotor produces a proportional change in torque (T).

Whereas torque is proportional to rotor diameter (D) squared. One factor in this relationship is simply due to the change in the length of the lever arm. The other factor is that as the diameter changes, so does the circumference and therefore the space available for magnets. These two linear factors combine to produce a squared change.

## Torque Constant (Kt)

The constant of motor torque (Kt) is numerically the torque produced divided by armature current. The units are Newton-meters / Ampere. Torque is partly determined by the number of winding turns on the armature and the strength of the magnets.

## Velocity Constant (Kv)

The constant of motor velocity (Kv) is a measure of the speed at which the motor runs when one volt is applied with no load attached. The units are rpm/volt. (Not to be confused with “kV,” the abbreviation for kilovolt.) The Kv rating of a motor is the ratio of the motor’s unloaded rpm to the peak voltage.

## Power, Speed, Torque Relationship (SI units)

Power = Torque * Speed / (30/π)

Torque = (30/π) * Power / Speed

Units: Power in watts, Torque in Nm, Speed in rpm. Note that 30/π = approximately 9.55

## Battery Current ≠ Motor Current

Battery current is not the same as motor phase current. The battery current is DC, whereas the motor current is AC. Power is calculated differently in an AC circuit than in a DC circuit.

## Electrical vs. Mechanical RPM

Electrical RPM is often abbreviated ERPM

ERPM = mechanical RPM * number of pole pairs

Mechanical RPM = ERPM / number of pole pairs

The number of “pole pairs” is one-half the number of magnets

## Energy Stored in a Motor

Electric motors can store energy via:

Winding inductance (dependent on current)

The inertial mass of the rotor (dependent on angular velocity)

This presents a problem when testing a controller on the bench. Laboratory power supplies are usually designed only to source current, not sink it. This means that any regenerative power recovered has nowhere to go, raising the voltage of the DC-bus capacitors beyond their ratings. Destruction of the controller's switching transistors follows.

Energy is also stored in the kinetic motion of any attached load (the vehicle, for example).

## Power Cell vs. Energy Cell

Lithium-ion cells may be optimized to allow a high discharge current (a power cell) or to store maximum energy per unit volume and/or unit mass (an energy cell) but not both simultaneously.

Multiple parameters influence the design tradeoffs, such as:

Electrode coating weight, porosity, particle size, carbon content, and binder content.

Current collector coating composition and thickness.

Size and number of connection tags.

## Counting Coulombs

The coulomb is named in honor of the French engineer Charles-Augustin de Coulomb (1736 - 1806). It represents the unit for electrical charge, equal to 1 ampere flowing for 1 second.

Coulomb counting provides a method of estimating a battery's state of charge (SoC). This is accomplished by measuring current flow and numerically integrating that current over time. The method only provides a relative change in state of change, so the battery is typically fully charged as a reference point. Current leaving the battery decreases its SoC and current entering the battery increases its SoC.

1 ampere-hour equals 3600 coulombs.