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Model S is a 2WD .... If this is rear wheel drive, what happens to the differential gear between the set of wheels at the rear? Are these differential gears replaced entirely by electronics? If so, is the differential gear business in danger?

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No.

The differential gear business is not in danger because of electric cars. All electric cars from reputable manufacturers use differentials, mainly for two reasons:

  1. Using a differential allows to have one bigger electric motor instead of two smaller ones, resulting in economies of scale
  2. Differential is a very sure way to guarantee that equal torque is distributed to both wheels. Imagine what could happen if you have two electric motors powering left and right wheels, and accelerating hard, and suddenly, one of the motors fails. The car turns violently to the left or right. Imagine a car turning to left on right-hand side traffic, or a car turning to right on left-hand side traffic. The results could be fatal.

Differentials have been used in cars for a long amount of time and we know it is practically impossible for a differential to fail in a way that lots of torque goes to one wheel and no torque goes to another wheel. It's an important safety mechanism.

I estimate that of these reasons, reason (2) is the most important. Never underestimate the safety considerations in building cars. Using electronics, you could try to write a very complex computer program that tries to guarantee that both wheels get equal torque in all conditions, but in such a safety critical environment, it is very hard to build a computer program that does so in all circumstances, including various faults. Even simpler less safety-critical environments such as electronic throttle control have had bugs, such as Toyota's ETCS-i system.

I would not trust my life on an electronically emulated differential!

I'm sure you'll find that Tesla uses differentials as well. However, the center differential is eliminated in 4WD models, meaning there are different front and rear motors. The center differential is not safety critical, so it is easy to eliminate.

Edit: Oh, and forgot to mention that I don't think there are any manufacturers of just differentials. Many companies manufacture more components than just differentials. For example, Aisin Seiki has built the transaxle of Toyota Prius that includes two electric motors in an electronically controlled CVT system. So, if Toyota chooses to use two motors per axle on a new Prius, Aisin Seiki will surely be happy to provide these two motors!

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