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I've read somewhere that transfer cases (on 4x4 vehicles) split the power from front to rear, but don't do it equally. Something along a 60% rear/40% front (though I'm sure it could be any percentage as set by the manufacturer). My question is:
TLDR : Planetary center differential with viscous coupling.
EDIT : This is wrt center differential transfer case and not traditional 4X4 transfer case , since the question is about torque biasing which precludes the latter.
I understand that differentials are a huge topic and there are many clever solutions in the realm of torque biasing. I'l post one such solution more as a seed answer. Please edit and add details.
Planetary/epicyclic gearboxes , with the engine driving the Planet gears, the ring (outer sleeve?) connected to the rear differential and the sun gear connected to the front differential. This configuration allows for -
1. Our primary requirement of both the differentials needing to rotate at different speeds under normal use.
2. Torque biasing - Depending on the tooth ratio's of the planetary, ring and sun gear, the desired ratio can be designed. (50:50 , 60:40 etc)
This, however would still be limited by the maximum traction available in either of the front/rear differential. In complete loss of traction, it would function just like an open differential at the center.
This can be solved by having a viscous coupling (Fergusson Viscous Coupling) between the front and rear axles, that would in effect 'limit' the allowable slip between the two.
Electro-mechanical solutions are also used to control the viscous pressure to adapt the slip ratio (or degree of lock) as per requirement.
Other solutions use clutches.
Torsen center differentials employ worm gear principle to function as an LSD.
While researching an answer for another post I came across this. The Audi Crown Gear Central Differential splits power between the front and rear 40/60.
This is accomplished by a quazai differential/planetary gear set. If you know how a differential works the explanation is a little easier. The power comes in through what you could call the spider gears. The trick is that the spider gear pushes on the front side gear in a different place than the rear side gear. This gives a different torque output to the front and rear axles while maintaining the same speed.
