Articles, Issue 46 - Autumn 2012

Full Acceleration

A clear dynamic benefit of electric traction for vehicular use, especially in comparison to internal combustion engines is that they produce very high torque from zero rpm.  Additionally electric motors do not need a clutch to move a vehicle off from stationary and also, in theory, can function without the need for a gearbox with changeable ratios, thus saving weight and cost of several major components found in a conventional vehicle powertrain.  These advantages, combined with their potential to improve noise, vibration and harshness (NVH) of a vehicle, make them attractive, especially with the environmental benefits of zero tailpipe emissions.

In concert with the general characteristics of electric motors, many electric motor-propelled vehicles are implied to have high performance due to the very high installed torque quoted.  This is especially the case with ‘wheel’ and ‘hub-motor’ configurations.  An example is the Lotus Evora 414E REEVolution, a range extended electric vehicle (REEV), which has individual motors with a single-ratio reduction gearbox for each driven rear wheel, these motors each producing 500 Nm and 150 kW (combined they produce 1,000 Nm and 300 kW).

Both the motors are bolted to a single transmission housing, and from this it could be imagined that the motors are coupled together directly, in fact they have completely separate single-stage reduction gearsets and therefore each wheel is individually-driven (hence the use of the term ‘wheel motor’).  This negates the requirement for a differential and facilitates the use of torque vectoring via direct motor control as a vehicle dynamic control strategy.  Together with the deletion of a stepped-ratio transmission, this vehicle therefore has a much-simplified drivetrain from battery to wheel.

To illustrate the attraction of an EV or REEV drivetrain, Fig. 1 shows the maximum performance torque curves for the Evora 414E and a production Evora S, which has a 3.5 litre supercharged V6 engine with 400 Nm and 258 kW (345 bhp).

Fig. 1: Combined torque output from Evora 414E electric drivetrain versus certified performance for Evora S internal combustion engine

In Fig. 1 the shape of the electric motor performance curve from 2,900 rpm onwards is a rectangular hyperbola: the motors each produce their maximum power of 150 kW (300 kW combined) from this speed up to their maximum rotational speed of 8,000 rpm.

The electric motors installed in the 414E together produce more torque over the entire speed range than the combustion engine, and from this one might imply their performance in vehicle would be far superior, having as they do 1,000 Nm over a very wide speed range versus the 400 Nm that the spark-ignition engine produces at its peak.

However, reality is somewhat different.  The historical development of the internal combustion engine (ICE), and with it the necessary transmission technologies to provide driveability, means that the real situation is much more complicated.  The effect of employing changeable gear ratios is to increase the torque delivered to the wheels (at the cost of reducing the vehicle speed range that the gear can be used over).

Fig. 2: Cascade curves for Evora 414E electric drivetrain versus Evora S with internal combustion engine and stepped-ratio gearbox

If one plots the so-called ‘cascade curves’ for the two vehicles, which take into account the individual gear ratios, final drive ratios and the tyre rolling radius for each, a better comparison can be made.  Such cascade curves give the thrust (or tractive force) available at the wheels for each gear versus the associated vehicle speed, shown in Fig. 2.

Fig. 1 shows that in 1st gear and up to 40 mph (64 km/h) the Evora S produces more thrust at the wheels than the 414E.  One can also see an illustration of a more general point about in-gear performance insofar as, for the Evora S, there is always more thrust available in a lower gear (if it is safe to use it), and so for maximum performance the engine should be fully revved-out; conversely if the curves were to cross, it would be worth changing up to gain more thrust (and hence acceleration).  From this, one can readily discern how tuning an engine for more high-speed power at the expense of mid-range torque generally produces better standing-start performance in a vehicle.  More specifically for the case under consideration, as soon as the driver has to change out of first gear in the Evora S, the 414E potentially has better performance, a situation compounded by the time taken to disengage drive using the clutch, change gear and reengage drive, a process which necessarily incurs a time penalty in a standing-start acceleration run.

It is thrust which pushes any vehicle along, and this metric of course allows road vehicles to be compared with boats or aircraft.  The latter case is interesting because power is a function of force times velocity; thus, while a jet engine produces thrust it requires the aircraft to be moving for it to produce power.  While this may seem a technicality as far as road vehicles are concerned, it is interesting to note that an aircraft with its brakes on producing maximum thrust for take-off is actually producing no power; similarly, doubling the speed of an aircraft for any given thrust doubles its power.

Fig. 3: Cascade curves of Figure 2 corrected for vehicle mass

Gearing allows a road vehicle’s power to be converted into thrust and an easy connection to be made between the two.  However, as far as performance is concerned, one has to bring in the effects of mass, and dividing the thrust by the mass provides a better metric for in-vehicle performance.  Although it is accepted that since it ignores drag, rolling resistance and gradient this is a somewhat simplistic approach versus full vehicle performance modelling, it does at least permit an important vehicle attribute to be factored in.  The mass-corrected cascade curves for the cases under discussion are shown in Fig. 3.

In Fig. 2 and Fig. 3 the corollary of an important early choice during the 414E project is evident.  The vehicle effectively ‘runs out’ of gearing at 131 mph (211 km/h) while having surplus power – this is illustrated by the facts that the maximum speed of the Evora S is 178 mph (287 km/h), the two vehicles have fundamentally the same aerodynamics, and the 414E has an additional 20 kW.  One can ‘correct’ this by altering the reduction gearbox ratio from 4.588 to 3.377.  The effects of this theoretical change are shown in Fig. 4, where the 414E now reaches the same maximum speed of 178 mph as the Evora S.  However, the maximum thrust has been reduced and now the comparison is much closer (excepting that 1st gear in the Evora S now provides almost twice the thrust per unit mass).  Note that the position of the rectangular hyperbola is the same, since the motors produce the same power; the difference is that the motors now start producing peak power at 64 mph (103 km/h) instead of 47.5 mph (76.5 km/h).

Fig. 4: Mass-corrected cascade curve for 414E adjusted to permit the same maximum vehicle speed as a production Evora S

These observations explain why EVs sometimes use two-speed gearboxes in order to minimize the amount of installed torque necessary to accelerate the vehicle at low speed.  Such gearboxes also help with gradeability: another reason for IC-engined vehicles having low 1st gears is to allow them to produce the thrust necessary to move up steep gradients.  This is a requirement which EVs will also have to meet in the marketplace.  Of course, adopting any form of change-ratio gearbox will put cost back into the vehicle, but since motor prices increase as they provide higher torque, the cost-benefit ratio could easily still be favourable.

Fig. 5: Mass-corrected cascade curve for 414E adjusted for 25% derate compared to production Evora S

The final point to make is that often the torque and power quoted for an electric powertrain is the maximum it can deliver before it has to down-rate due to thermal issues, which could be due to the motor, battery or power electronics.  This is the reason why the 414E is geared as it is: at a certain point dependent on time, temperature and power generated, it down-rates, and in fact maximum vehicle speed is delivered at that condition.  Assuming a down-rate of 25%, the cascade curves of Fig. 3 become those of Fig. 5.  Here the performance of the vehicle drops below that of the Evora S essentially throughout the speed range (if the engine is being revved-out).  Once temperatures have stabilized, the full performance becomes available again.

While some turbocharged ICEs now offer ‘overboost’ functions where for a short period of time extra torque is available, the certified performance is usually the minimum available, and so is the opposite situation of what is claimed for electric drive trains.  This is where the true advantages of combustion engines come to the fore: the engine of the Evora S will deliver the same performance as long as there is fuel in the tank and it also takes less than five minutes to refill.  Doing this, with modern durability sign off criteria, the ICE will deliver full performance for literally months.  Decarbonizing the fuel permits this to be done with carbon-neutrality and at a final vehicle cost that the customer can afford.  This is why ICEs will continue to be the primary propulsion in the automotive scene for years to come, with EVs having a specific role to fill in short distance, urban environment situations, and REEVs permitting longer journeys to be undertaken unencumbered by range anxiety.

Author: Jamie Turner

About lotusproactive

Lotus proActive is an e-magazine published quarterly by Lotus Engineering, covering engineering articles, industry news and articles from within Group Lotus (Cars, Engineering, Originals and Racing).


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