ajdelange

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It's pretty much a given that two motors on the rear wheels (or the front wheels) will eliminate that differential. It would serve no purpose and would be useless cost, weight and additional friction.
A differential has 3 shafts. Two motors plus two half shafts = 4 shafts - one too many.
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Much of limited access road driving these days involves speeding up and slowing down often, alas, to the point of having to come to a complete stop or crawl. In such cases intertial load is, if briefly, the biggest load. Also in hilly terrain you have to put potential (gravitional) energy into the load. That can be appreciable. But we have regen! Much of the inertial and potential energy we invest is returned to us if we can keep our feet off the friction brake pedal. Regen isn't 100% efficient so more weight does impose a penalty but it is a small one.

Now if you take your anvil collection up to your mountain cabin it's going to cost you kWh but, provided you take it home with you when you leave you will get most of that back. There is somewhere a quarry located at elevation. Their product (rocks) get hauled to a processing plant at lower elevation. The trucks are electric. They are never charged.
That's a really cool concept. That'll never happen with ICE trucks.
 

JBee

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Traction is not reduced at low wheel rpm. It's dependent upon the coefficient of friction between the tires and the road surface and the amount of weight on the tire.
Traction is not reduced at low wheel rpm. It's dependent upon the coefficient of friction between the tires and the road surface and the amount of weight on the tire.
Sorry I should use stricter terminology. Tractive force would be better...depending on which version you use. ;)

However, technically traction is not normally linear through velocity (tyre deformation vs centripetal force etc) and the coeffcient or friction can change by temperature too - hence tyre temperature being critical for adhesion in all motor sports. Temperature also increases with load and typically increases whilst accelerating too as the power goes down. Downforce from airflow also increases with velocity that in turn also increases traction. There's also a moment as the vehicle pitches backwards from acceleration etc. The acceleration of a vehicle consists of dynamic values not static ones whilst it increases in velocity, although static ones at each point are easier to compute.

Just to clarify what I mean about the adhesion limit for those that are interested; wheel slippage happens when wheel drive force exceeds the force the tyre contact patch can deliver to the ground.

?u=https%3A%2F%2Ftse4.mm.bing.net%2Fth%3Fid%3DOIP.jpg


Force = Mass x Acceleration and therefore force and acceleration are related. So if vehicle acceleration is proportional to power (W=Nm/s at the wheels) / (velocity x mass) then the time component dictates how much power can applied to accelerate the vehicle at any one point, meaning the faster (velocity is distance / time) you go the more power it takes to achieve the same rate of acceleration. Another way to look at it the adhesion limit is to imagine the size of the tyre contact patch in relation to time, in that in the same unit of time the tyre patch creates a larger patch area whilst moving then whilst stationary, allowing for more power to be applied in that same time. For example if your car can break tyre adhesion and cause wheel spillage with 50kW at 20kmh it would take 100kW to break adhesion at 40kmh. Hence the power that can be applied at low wheel rpm is less than at high rpm. This is why it's critical on launch to match traction with drive force, which Tesla can obviously easily do through motor control and monitoring wheel slip. This is also what dragsters refer to as "hookup". Without that it would just sit there and shred the tyres instead. Which is fun but won't get you far! :cool:
 

JBee

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We don't know this to be true. No one has torn apart a Plaid powertrain yet. I would bet it's not true, either :/

-Crissa
I'm pretty sure that Tesla will use identical rear drive motors on the Plaid drivetrain and because of that can neglect having a rear differential. There is a cost/packing/weight/manufacturing advantage plus it improves vehicle performance as this also helps to use torque vector control for steering under high acceleration maneuvers, both straight and around corners when approaching adhesion limits.

In the CT this would be the equivalent of having a "locked rear diff" in a 4X4, that will still allow you to turn, and unlike most ABS/ESP controllers in ICE cars will allow individual wheel acceleration and deceleration control to create yaw effect similar to a tank turning. The beauty of having this level of control is that the vehicle can actively avoid approaching the adhesion limit instead of just trying to recover from it.

This will also be better for off-road and in sand etc, in that the rotational speed differential between the wheels when turning can be maintained whilst applying even torque over at least 3 of the wheels. The forth wheel can only really be retarded using the brakes. Obviously, because of the EV drivetrain are with separate front and rear motor controllers, a middle differential is unnecessary, and so is a middle diff lock. In saying that a front differential lock, or a LSD would be nice.

I like my off-road vehicle 4x4 not 3x4. :p
 

ajdelange

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Another thing I failed to mention with respect to how torque is distributed is that the controllers can monitor slip and thus control traction to a greater extent. Traction increases linearly with slip up to about 20%, Above that it falls off (wheels spin). As the controller can measure slip they can keep it in that linear region below 0.2. Should a wheel spin (s > 0.2) the controller can instantaneously bring it back into the linear region by removing motor torque. Thus I expect that the CT will apply maximum torque (the most the mechanical parts can tolerate reduced by an appreciable safety margin) up to the point where maximum power is being drawn at which point the power limits of the motor/inverter dominate rather than the torque limits. This results in a traction curve like this one.


traction1.jpg



This curve ("AC Motor Control and Electric Vehicle Applications 2d Ed.", Kwang Hee Nam, CRC Press, 2019) is the one that will get you to 60 mph fastest provided, of course, that the substrate is cooperative. As the 0 - 60 number is pretty important to a manufacturer i think we can be confident that his design (including choice of tire) is going to allow him to reproduce this curve closely. As acceleration is linearly proportional to thrust which is in turn proportional to slip he'll want to operate his drive train as close to the peak of the slip curve (a little below 0.2) as he can. As an aside this is why people who can't resist coming out of every traffic light like A. J. Foyt find their tires don't last very long. He'll also try to set things up so that omega b (in the graph) is at 60 mph or very close to it.

It is based on this curve that I calculate 0.938 g for the CT in the torque limited region (below 60 mph). If it weighs 2500 kg that would require 23.0 kN thrust. If it weighs 3000 kg then 27.5 kN would be needed. On a slippery substrate (icy road) obviously the slip curve is different and will not allow that kind of thrust to be developed. The break point would be reached at a much lower level. Also note that I have neglected rolling resistance and drag in these back of the envelope calculations. For the mathematically inclined I considered the first term in the first equation (13.20) only*. Clearly if I included the other two terms the acceleration would not be constant in the torque limited region and the velocity would not increase linearly with time but as the solution to that differential equation. To make 60 in 2.9 seconds would require more thrust than the numbers I have given.

I don't know if it is worth mentioning but as the power taken from the motor is the product of its torque and rpm we observe that no power is drawn at the beginning of the run and that as speed increases, under the simple model, linearly with time so does the power. The power vs time curve would be linear from 0 up to the power limit up to 60 mph and flat at the power limit thereafter.

*mv is the mass of the vehicle, Te is motor torque, gdr is gearing ratio, eta is drive train efficiency, rw is wheel radius.
 
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HaulingAss

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I'm pretty sure that Tesla will use identical rear drive motors on the Plaid drivetrain and because of that can neglect having a rear differential. There is a cost/packing/weight/manufacturing advantage plus it improves vehicle performance as this also helps to use torque vector control for steering under high acceleration maneuvers, both straight and around corners when approaching adhesion limits.

In the CT this would be the equivalent of having a "locked rear diff" in a 4X4, that will still allow you to turn, and unlike most ABS/ESP controllers in ICE cars will allow individual wheel acceleration and deceleration control to create yaw effect similar to a tank turning. The beauty of having this level of control is that the vehicle can actively avoid approaching the adhesion limit instead of just trying to recover from it.

This will also be better for off-road and in sand etc, in that the rotational speed differential between the wheels when turning can be maintained whilst applying even torque over at least 3 of the wheels. The forth wheel can only really be retarded using the brakes. Obviously, because of the EV drivetrain are with separate front and rear motor controllers, a middle differential is unnecessary, and so is a middle diff lock. In saying that a front differential lock, or a LSD would be nice.

I like my off-road vehicle 4x4 not 3x4. :p
All good points. Except I'm not sure how important the last one is to actual off-road performance. Especially in an EV that has a more balanced weight distribution that a front-engine vehicle.

With an EVs more balanced weight distribution, you are likely to be ascending a steep incline when you need maximum traction. Thus the rear wheels are doing ~80% of the work. This means a little light brake application (by computer) to the slipping front wheel is all that's required to make it 4x4 instead of 4x3. Done correctly, this is actually more effective than most LSD's and has important safety (on icy roads), efficiency (on tight, high traction trails) and tire wear advantages (in most situations where you might want to use a locking differential) over a front differential lock.

In fact, with the correct traction control programming for off-road, braking the slipping wheel of an open differential will provide better traction performance than having the differential locked any time the front wheels are turned in any direction other than straight. The drivetrain binding that always occurs to various degrees when using a locking differential is far from ideal and yet, for some reason, many off-road enthusiasts swear it is the holy grail. Probably because it's the best thing they have ever had access to.

Technology changes, locking differentials are going the way of the ICE engine. And the dodo bird.
 

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A differential has 3 shafts. Two motors plus two half shafts = 4 shafts - one too many.
To be accurate, it is possible for a differential to be incorporated into the rear drive train (as it is in my Model 3) but then there is no point in having two motors on the same axle, better to just combine the two motors into one longer motor. That's why the Cybertruck (and any of the plaid powertrains) will not have a rear differential.
 

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Not being able to power both wheels with a single motor would make it less efficient.

-Crissa
You wil notice that Tesla will never design a vehicle with two rear motors and no front motor. That is so the front motor can take over for efficiency reasons under light loads.

What would reduce efficiency is to have an unnecessary differential. It's bad for weight, cost and efficiency. Not going to happen. Differentials are left over from the age of ICE vehicles and will be going the way of the dodo bird.
 

ajdelange

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What would reduce efficiency is to have an unnecessary differential. It's bad for weight, cost and efficiency. Not going to happen. Differentials are left over from the age of ICE vehicles and will be going the way of the dodo bird.
I figured out how to do it. You put a motor on each of the two output shafts of a differential. The differential combines the power from the two and transfers it to what is normally considered the input shaft. That is coupled to the input shaft of a second differential whose output shafts go to the wheels. So not only do you have one differential. You have two. Now where's my patent attorneys's card?
 

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I figured out how to do it. You put a motor on each of the two output shafts of a differential. The differential combines the power from the two and transfers it to what is normally considered the input shaft. That is coupled to the input shaft of a second differential whose output shafts go to the wheels. So not only do you have one differential. You have two. Now where's my patent attorneys's card?
The Tesla differentials are inline (there is no need for the right angle input shaft). This means, if you wanted to, with two motors, you could just put one motor on either side of the differential and power one motor or both. But I can't think of a use case where it would make any sense to do this as it would eliminate the possibility of controlling the torque distribution between the rear wheels. So the differential would be eliminated allowing the torque applied to each wheel to be controlled independently.

1623018276787.png
 

ajdelange

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So the input is the flange?
 
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