Wednesday, February 4, 2009

TBs TechTips 20 - Limited Slip Differentials

Recently Sariel presented an idea for a Limited Slip Differential at his new website.

It is a simple adaptation usable into driving axles of vehicles, which automatically locks the differential whenever a slip situation occurs. It happens in vehicles for instance when a wheel from a axle, driven by a differential, loses contact with the ground or slips. In such situation the standard differential transfers all the torque to that wheel, making it turning free while the other keeps stopped. As result, the entire axle stops, which may easily stop the vehicle completely.

Sariel's automated solution, uses a second pair of semi-axles, attached to the main ones on the differential, which also connect to a pair of cams.
While the vehicle keeps both wheels rotating at the same speed the cams won't lock each other. If wheels speed differ, cams will lock after some time, the differential blocks and both wheels will run at equal speeds.

For a complete and detailed description of this mechanism in its own author words, please refer to the original description in the article linked above.
Below an image illustrating the mechanism and one video, where you may see the principles in action.

Because of its simple design, this locking mechanism may actuate after short periods of different wheel rotation speeds e.g. while the vehicle turns. However it shouldn't cause any problem since the wheels speed difference is very small, while you get safe from the slipping situations.

To improve this situation and reduce solutions sensitivity to small speed differences, BS user 'Memory' (Jacob) shown his own improvement suggestion where cams are geared to move slower.
He just added a third pair of semi-axles with an 1:3 gear reduction (8z to 24z gears), which would increase the tolerance to the speed differences caused by steering, to give the same example.

The only drawback is that while tolerance gets increased, it also takes longer for the cams to move apart after them to have engaged.

Learn more about, at HowStuffWorks:
- How Differentials Work
- Clutch-type Limited Slip Differential

Learn more about, at Wikipedia:
- Limited Slip Differential


Anonymous said...

This is a very elegant solution to a common problem. Of course, on real vehicles the solutions are far more advanced. Instead of a mechanism that locks after a given relative displacement (number of turns of one wheel relative to the other), can anyone think of something that locks based on relative angular velocity?

Anonymous said...

I was thinking that if the 2 locking arms were replaced with another differential, then when one axle turned more than the other, the outer shell would spin (or stop spinning depending on how it's set up)and maybe that could be used to lock the system until both axles started moving again.

Anonymous said...

Not a big difference between this and a solution with no differential at all, I would say. This differential works only for a while and requires you to drive left, right, left, right. If you are turning more to one side (driving on a circuit), this works like a vehicle without a differential...

It's quite funny, adding a mechanism to a differential to bypass its biggest drawback, while (by the way) disabling also its only asset and, in fact, its meaning :)

Anonymous said...

The problem with this kind of locking is that it´s gonna lock even in no slip situation, if you turn the same side for a little time.

It can be esay to make a LSD based on relative speeds maybe the easier way is to use 2 diferentials where the second is "inverted" so its angular speed is the difference between wheels angular speeds. Now you just have tomake it "lockable" in function of this second diferential own speed

TechnicBRICKs said...

It is clearly stated in the post and even more at Sariel's original article, the limitation you have pointing out, here.

The 2nd differential addition, is really something to try.

Alex Campos said...

Yeah, I thought about that problem too, when on average one of the wheels turns more than the other (like, like Anonymous 2 said, on a circuit).

I think locking the differential based on speed instead of displacement is indeed more efficient, and possible using LEGO, but much more complicated... it would involve weights that, when spinning fast enough, would rise and lock the differential. I don't have easy access to LDraw where I'm currently at, so I can't explain better what I mean.

Anyway, another solution is to, instead of not allowing the differential to slip when one of wheels is lifted, simply not allowing the wheel to be lifted! Unless slippery ground (like mud or ice) is under the wheels, the differential will never slip when using a pendular suspension. For example, if one were to motorise the 8284 Tractor, its differential would never slip on uneven ground because its front axle is pendular.

TechnicBRICKs said...

Even pendular suspensions, may have their limitations at very rugged terrain.

Anonymous said...

I like this solution, but I was thinking of a different one with a rubber band between the two sides. You could have a wedge belt wheel on one side of the diff connected to a bush (that is connected to the other via gears). You get a small amount of slip before the band tightens.

The band will even its tension eventually.


Dornbi said...

I am a perfectionist and do not really like the interlocking solution. For example, it does not work if the vehicle is on a closed track. However, Sariel also presents a clutch in one of his other posts that seems to be feasible: it allows some slip but not without limits.

stuj1984 said...

This id the best LSD implementation I have seen. The actual principal is simple, using rubber bands!

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