From the last article on this subject, we know that a planetary differential is capable of distributing torque unequally to its outputs based on its design. We discovered that torque split is constant for any rate of speed and irrespective of which output rotates faster, neglecting the viscous coupling (VCU) action– but what sets this ratio? Can it be changed? How can we easily determine the design torque split of a planetary differential?
Despite how complicated it looks, the ratio of a planetary differential is simple to find. When the ring gear is the input, as with the 3000GT/Stealth AWD center differential, the ratio of the sun gear to the ring gear gives us the proportion of input torque supplied to the sun gear output. In other words if we have a ring gear with 100 teeth, a sun gear with 40 teeth and the ring gear is the input, the sun gear receives 40/100 or 40% of the input torque. If 10ft-lbs is the input torque, 4ft-lbs is applied to the output (neglecting friction).
And the torque supplied to the planet carrier? That’s the remaining 60% in this example, or 6ft-lbs.
Let’s look at a model of the actual 3/S center differential. If the stock sun gear is 27 teeth and the ring gear is 60 teeth, we find a ratio of 27/60 to the sun gear (front output), or 45% of the available torque. The remaining 55% goes through the planet carrier to the center output shaft and to the rear wheels.
What if we wanted to change this ratio? Someone with the knowledge and resources to cut his own gears could modify the factory center differential with a new sun gear and a redesigned planet carrier (the original planet gears could be reused). Such a modified differential could achieve significant changes in torque split just by adding or subtracting three teeth from the sun gear:
And so a rear-biased 60:40 ratio is hardly out of reach. For someone going to the effort of fabricating a new sun gear and modified planet carrier, more radical torque splits are a minor design change away. Getting a radical 65% of drive torque to the rear wheels could be done with a 21-tooth sun gear!
What about the planet gears? Believe it or not, the planet gears have no effect on the torque split of the differential — none. The factory center differential has 13-tooth planet gears, but the following differentials have the same torque split ratio:
In fact, the outer planet gears can even be different sizes than the inside planet gears without having any effect on torque split. Remember: the ratio of the ring gear to the sun gear alone determines torque split.
So why not make the planet gears as small as possible to shrink the differential down? Besides approaching a practical limit to how few teeth a gear can have and still make good contact with another gear, the simplest answer is strength. Because drive torque is still transmitted through the planet gears, they need to be large enough to carry the load.
That’s the long and short of it. Anybody want to machine some gears?
