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Diffs & LSDs - Part 1 - Types of Differentials

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In my opinion, it is best to keep differentials and limited-slip devices as separate in your mind as possible. Yes, certain types of differentials have limited-slip devices built in, but you can still think about the two functions separately and I believe that it helps to do so. This thread will only concern the types of differentials. A separate thread will discuss the ways that slip can be limited.

The main purpose of a differential is to allow the two outputs to rotate at different speeds while still allowing each to receive at least some of the torque. Differentials are needed when the car is turning because -- assuming no tire slip -- the inside wheels turn slower than the outside wheels and the rear wheels turn slower than the front wheels. If you did not have a differential, your car would not want to turn and would suffer significant tire-wear when it was forced to turn.

There are three main types of differential. The first is the one that most people are already familiar with: the spider-type. Inside the carrier is a spider (i.e., an X-shaped piece) with at least two gears on it. The legs of the spider are firmly connected to the carrier so that the spider spins (end over end) when the carrier spins. The gears on the spider mesh with the side-gears on the output shafts. When such a diff is not differentiating, the spider- and side-gears do not rotate relative to each other. Instead, the rotation of the carrier is simply transmitted through the spider to the spider-gears to the side-gears. When differentiating, the spider-gears rotate (on the legs of the spider) while the entire carrier turns, causing one side-gear to rotate faster than the carrier and the other side-gear to rotate slower than the carrier. (In the extreme, one side-gear can be stationary and the other side-gear can turn twice as fast as the carrier.)

Side issue: Because all of the torque being transmitted from the carrier to the side-gears goes through the spider-gear to side-gear interfaces, many people upgrade cars that came with only two spider-gears to having four spider-gears, halving the force being transmitted through any one interface. In the DSM world, you will sometimes see these called "Speed Design diffs," since Speed Design makes a nice four-spider upgrade for our center differential. This is important because the center diff in an AWD DSM is one the weakest points in the drivetrain.

The second type of differential is the planetary-type. As above, the input is through the outer carrier, but in this case there are no spiders. Instead, inside the outer carrier is an inner carrier with some gears on it, and inside the inner carrier is a sun-gear. The route from the outer carrier (which has an inward-facing ring gear on it) to the sun goes like this: the outer ring meshes with a planet-gear mounted on the inner carrier. This planet meshes with another planet that is also mounted on the inner carrier. The inner planet then also meshes with the sun. This is difficult to explain without a picture (and does not appear to be well-understood by very many people), so I provide a jpg below. In this picture, the green ring is the inward-facing ring-gear on the outer carrier, the dark-blue heavy ring is the inner carrier with two light-blue planets, and the red disk is the sun-gear. Note that most planetary-type diffs have at least two pairs of planets (and usually three), but I have only included one pair because I'm a lazy sod.


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The way that a planetary diff works is best understood by considering extreme situations. First, let's think about the situation where the car is going straight ahead and no tires are slipping. In this case, the planets do not rotate on the shafts that hold them onto the inner carrier. So the outer ring turns the inner carrier and the inner carrier turns the sun. Since the inner carrier is one of the outputs and the sun is the other output, this forces the two outputs to rotate at the same speed as the input.

Now consider the situation where the inner carrier (which, again, is one of the outputs) is not turning at all. Now the outer ring rotates the outer planet which rotates the inner planet which rotates the sun. The speed at which the sun rotates relative to the outer ring depends on the relative numbers of teeth on the outer ring and the sun-gear. This assumes that the two planets are the same size, which is usually true. If the outer ring has 60 teeth and the sun has 20 teeth, then the sun spins three times as fast as the outer ring. Note how this is different from the spider-type diff. In a spider, when one output is stationary, the other always turns twice as fast as the input. In a planetary-type diff, it depends on the gearing inside the diff and can be some ratio other than 2:1. In my example with 60 input teeth and 20 teeth on the sun, the ratio when the inner carrier is stationary is 3:1. This is going to be very important.

The other extreme is when the sun-gear is stationary. Because of some neat algebra, when the planets are equal-sized, the effective number of teeth on the inner carrier is the difference between the number of teeth on the ring and the number of teeth on the sun, regardless of how many teeth are on the planets. So the inner carrier in my example has effectively 40 teeth. So when the sun-gear is stationary, the carrier will turn 1.5 times as fast as the ring. (To be pedantic, note how this is, again, different from the fixed 2:1 ratio that you get from a spider-type diff.)

OK, then, when the diff is not differentiating, the two outputs turn the same speed as the input, but when it is differentiating, something quite odd will happen. So what? Well, this matters because the output speeds (when other output is stationary) is what determines the torque-split of the differential (assuming no limited-slip device). So a spider-type diff produces an equal torque split (i.e., 50/50), because the output speeds (when the other side is stationary) are equal. But the planetary-type diff in my example provides a 2:1 torque split (i.e., 33/67), because one output turns twice as fast as the other. In particular, because the sun-gear turns twice as fast as the carrier (when the other is stationary), the sun-gear is only getting half as much torque. Recall here that torque is inversely proportional to rotational speed.

The last type of differential is the helical-type. This also needs a picture, but this time I'll be really lazy and just steal one:


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For the purposes of this thread, which only concerns differentials and does not concern limited-slip devices, the only things that matter about this differential are the numbers of teeth on the horizontal worm-like pinions that connect the two output shafts and the numbers of teeth on the side-gears. With regard to the pinions, these are the same at both ends (as they have to be, since the thin end of one pinion meshes with the thick end of the other pinion). With regard to the side-gears, these are equal to each other. Because of these equalities, this type of diff gives a 50/50 torque split (when nothing is limiting slip).

More generally, these differentials are a lot like spider-types when it comes to how torque is transmitted from the input to the outputs. The carrier turns the pinions (which are really in pairs, even if that is hard to see in the picture) and the pinions turn the side-gears. When the differential is not differentiating, the pinions do not spin on their own central axes, so the two outputs turn the same speed. If one output is stationary, then the pinions spin such that the output that is turning rotates twice as fast as the input. It's all quite similar to a spider-type diff.

But to get us ready for the limited-slip discussion, let me try to amplify on the picture. The pinions are in pairs (just like the planets in a the second type of diff). The wide-teeth end of a pinion meshes with one side-gear and also with the narrow-teeth end of its partner pinion. The narrow-teeth end of a pinion only meshes with the wide-teeth end of its partner; it does not mesh with a side-gear. Therefore, if you asume that the carrier is held stationary (maybe because the car is in gear with the engine off), if you rotate one input, the side-gear on that side will rotate the wide-teeth end of one pinion in the opposite direction which will rotate the partner pinion in the original direction which will rotate the other output side-gear in the opposite direction. And, again, because the two side-gears must have the same number of teeth, the outputs will turn the same speed (albeit in opposite directions) when you do this, which is another way to demonstrate that the diff produces a 50/50 torque split (when no limited-slip device is active).

Note that this is a Type-2 Torsen diff. A Type-2 R is similar but has an extra bit related to the limited-slip behavior of these diffs. Other types exist, but they are not used in our cars.

- Jtoby
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