Too Busy For Words - the PaulWay Blog

Fri 26th Nov, 2010

Electronic Differential

One of my interests, congruent to my Electric Motorbike Without A Spiffy Name project, is to build an electric go-kart. One different from the usual ones you can see on youtube doing burnouts and beating mustangs in drag races thanks to their gigantic quantities of torque. This one is to have (dah dah daaah!) two motors.

No, stay with me, it's more interesting than that.

You see, this may show my lack of go-karting purism but I hate the fixed rear axle that most standard go-karts use. This is engineering simplicity but sharp turns require a 'drifting' technique to skid the rear wheels or you lose most of your revs and with the usual tiny motors that's hard to put back. It's also completely different from driving a car, so while kids might not know any better most adults have to learn a new technique for cornering at odds with their usual experience. Cars, of course, have a mechanical differential to distribute the power between the rear wheels - the torque applied to each wheel is the same, so the wheel with less resistance goes faster.

And there's your other problem. Because as far as I can see what you actually want is the torque appled to be in inverse proportion to the ratio of the wheel speeds. In equations this looks like:

total_rpm         = left_wheel_rpm + right_wheel_rpm
left_wheel_power  = right_wheel_rpm / total_rpm
right_wheel_power = left_wheel_rpm  / total_rpm
The left wheel and right wheel power are fractions - they add up to 1; see them as percentages if you like. What this means in practice is that when going straight both wheels get the same amount of power; when cornering the inside wheel gets more power; when one wheel slips power is decreased to it until it grips again. So both wheels will maintain traction around a corner and each wheel gets the maximum amount of power it can take. You can still spin the wheels by applying so much throttle that the wheel with the most grip will still spin, but you are much more likely to have complete traction all the way around.

This isn't really new. Most cars with electric motors - and even the massive trucks that haul hundreds of tonnes of ore in mines (which are driven by multi-megawatt electric motors powered by onboard diesel generators) - get designed to provide differential torque. Once you've got that control it's a no-brainer, it's a simple matter of programming.

What I want to do is to make a simple box that takes the hall effect sensors from two brushless DC motors and works out the RPM on each motor. It then takes the throttle information and outputs two throttles, one for each motor controller, plus feed-through links to the hall effect sensors. This would make it a simple drop-in part for go-karts, cars and anything else. It would also make it completely independent of the amount of power the controllers are supplying to the motor. There's also the possibility to use different power curves, ignore wheel stall, rev limit the motors, provide interactive feedback to the driver, and more.

(I did a bit of editing on the Wikipedia page on electronic differentials because most of the writing showed the original author's lack of familiarity with the English language, and sounded a bit like advertising for a particular company who was mentioned at the bottom of the page. The irony was that their web site hasn't been working since 2007 according to, so while their system-on-chip drop-in solution might have been wonderful it also wasn't enough to keep them going. And I really hate articles that use IEEE members-only articles as references.)

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