Diffs & LSDs - Part 2 - Types of Limited Slip

[jtmcinder]

The great thing about differentials is that they allow the two outputs to rotate at different speeds which is important when cornering. The downside of differentials is that they allow the two outputs to rotate at different speeds which can be a problem when you try to accelerate straight ahead. In particular, if one of the outputs has less grip than the other output (or, more accurately, if one output exceeds the available grip before the other output), the engine's torque will gravitate to the output with less grip, following the path of least resistance. The result is a lot of blue tire smoke and not much acceleration.

To combat this, one adds a limited-slip device to the differential. There are three ways that this is done in DSMs.

The LSD that comes stock in the center of AWD DSMs (as well as the rear of many AWDs) is a viscous coupling (aka vicious coupling). These have two sets of plates in close proximity but separated by a silicone fluid. One set of plates is connected to one of the outputs. The other set of plates is either connected to the other output or the carrier getting the input. The key point is that the plates rotate relative to each other when the differential is allowing one output to rotate faster (or slower) than the other output.

When the plates within a VC spin at different speeds, a resisting torque is produced by the viscous fluid between the plates. In a simple world, the larger the difference in the speeds between the two sets of plates, the more resisting torque is produced. However, the function relating the speed difference to the amount of torque is sub-linear and almost as bad as a square-root function.

Fortunately, the silicone juice gains viscosity as it is heated, which adds more resisting torque. Even more, it also expands as it is heated. At first, this expansion causes more of the plates to be in the fluid, so these two changes both increase the resisting torque. However, at some point, the expansion of the fluid will cause direct metal-to-metal contact within the VC (which is why half the plates have holes and half do not), often producing enough grip to lock it solid. This happens rather suddenly and it is often referred to as the "hump phenomenon." When this occurs, all relative motion between the plates usually stops and the fluid begins to cool and, at some point, the VC will release.

The main problems with this type of LSD are that it is outrageously non-linear and also subject to the effects of initial conditions (e.g., the previous temp of the fluid and diff housing), so it is not what you want in a competition car because it is very harc to predict. It is also relatively slow to react, given that heating must occur before the hump phenomenon locks the diff. That is why the new Evo doesn't have a VC. Nor does the STi, for that matter.

The second main type of LSD that you find in DSMs is the modified clutch-pack (which I believe is also called a Salisbury but is more often just called a Kaaz amoung DSMers because Kaaz makes a good one for our cars). These also have two sets of plates, but they are not separated by a silicone fluid. Instead, they are in direct contact and are therefore more like the clutch between the flywheel and transmission. And also like a "normal" clutch, the pressure between the plates changes. But unlike a VC, which reacts to differences in output speeds, the modified clutch-pack reacts to the amount of torque being transmitted through the differential. To explain this requires another stolen picture:

[jtmcinder]

First, please note that the modified clutch-pack can only be added to (or, more accurately, incorporated within) a spider-type differential. With that in mind, note in the picture the end of one of the spiders sticking out through a hole that is V-shaped on one side. That V-shape is the key.

When the carrier is turned by the engine, the torque must be transferred to the legs of the spider to get to the outputs. When the outputs have some grip, they resist having torque transmitted to them. So the grip of the outputs wants to keep the spider from turning and the torque from the engine wants to turn the carrier. This causes the ends of the legs of the spider to push against the sides of the holes in which they are held. That side-force hits the V-shape and is "bounced" at a 90-degree angle and becomes force that tries to pry the two sides of carrier apart. This prying force is what presses the plates of the LSD against each other, locking the diff.

In summary, the amount of locking torque (which resists allowing the two outputs from rotating at different speeds) depends on the amount of torque being transmitted from the carrier to the spider (or v.v.). This is why these LSDs are said to lock as a function of the amount of transmitted torque.

One complication to this is that the V-shaped holes do not have to be symmetrical. They can be steeper on one side than the other; in fact, they can be steep on one side and flat on the other. This allows the diff to lock more when torque is transmitted from the carrier to the spider than from the spider to the carrier. When this trick is not used -- such that the Vs is symmetrical and the LSD locks equally in both directions -- it is a 2-way diff. If it locks more when the engine is turning the wheels than when the wheels are turning the engine, but still locks a little in the latter direction, it is a 1.5-way diff. If one side of the V is flat, such that it only locks when the engine is driving the wheels, it is a 1-way diff.

The third type of LSD that you find in DSMs is the helical type (aka Torsen; aka ATB, for automatic torque-biasing; aka Quaife, since they make the good ones). These cannot be added to a spider like a VC or modified clutch-pack and cannot be combined with a planetary-type diff, because the limited-slip device is part of the differential, itself. Let's bring back that picture from the diffs thread:

[jtmcinder]

Recall from the diffs thread how power is transmitted from the carrier (input) to the side-gears (outputs): the carrier swings the pinions around with it and the pinions turn the side-gears. Now look very closely at the angled (helical) cut of the side-gears. Note especially how they are mirror-images of each other. This is the key to a Type-2 helical LSD.

Obeying the red arrows drawn around the output shafts, assume that the carrier is being rotated such that the side closer to you is going up. Now focus on the pinion in the foreground -- the one that has the wide teeth on the right and is meshed with the right axle. Because the force transmitted between gears must be at a right angle to the mesh and these are helical-cut gears, when this pinion tries to rotate the right side-gear the pinion will also be forced towards the center of the diff (i.e., to the left in the picture). However, because the other side-gear is a mirror image and the partner of the visible pinion is trying to rotate the left side-gear, the partner pinion will also be forced towards the center (i.e., to the right). But the two pinions are meshed to each other, so they cannot move relative to each other.

If the two outputs have equal grip such that both receive their full 50% of the input torque, then the two partners in each pair of pinions will be pushing towards the center the exact same amount. The net effect, in this case, is nothing interesting.

But imagine what happens when one output doesn't have enough grip to use up its 50% of the torque (and wants to just spin wildly and make pretty blue smoke, instead). In this case, the output shaft with less grip will not push back as hard against the input torque as the side with good grip. (Quaife likes to talk about "reflected torque" which I kind of like and kind of dislike, so I won't use this too often.) Under these conditions, the pair of pinions do not have equal amounts of sideways force inside the diff, so they both move sideways together (away from side with higher grip) and grind against one end of the pockets that they're in. This grinding makes it harder for the pinions to rotate within their pockets, so they resist the differentiating behavior that occurs only when the pinions rotate.

In summary, Type-2 helical LSDs lock as a function of the difference in the amounts of torque being transmitted to each of the outputs. When the outputs are equal, the side-forces on the pinions are equal and there is no resistance to differentiation. When the outputs are unequal (or, more accurately, when the reflected torques are unequal), the pinions have unequal side-forces and wedge against one end of their pockets and, therefore, resist differentiation.

How much this type of diff can lock is mostly a function of the angle of the cut of the helical gears. If they are nearly flat, the side-forces stay low and it won't lock very hard. If the angles are steep, the side-forces can get quite high and it can lock pretty well. The way that this is usually described is in terms the maximum ratio of output torques that the LSD can produce, with 4:1 being pretty good. (In contrast, however, note that a modified clutch-pack can lock absolutely solid, which allows for an infinite ratio of outputs.)

Side issue: be careful about reading too much into (or being too literal about) the names that companies use for their differentials and limited-slip devices. The 45/55-split diff that Subaru uses is called the VTD for "variable torque differential," which can easily make you think that it can change the torque split. Well, it can't. It is a planetary-type diff geared for a 45/55 split and that is all it will ever be. Yes, when the limited-slip device kicks in the entire package behaves otherwise, but the diff itself is always a 45/55. Same sort of thing applies to Torsens as described by Quaife's advertizing literature. It is called both an "automatic torque-sensing" (ATS) diff and an "automatic torque-baising" (ATB) diff. The first part seems OK, in that it does "sense" a difference in reflected torques, but the second part can be misleading. It seems to make people think that it actualy reroutes input torque to the output with more grip in some magical way. Well, maybe that is one of the ultimate effects, but what it really does in order to achieve this is to lock up (to some extent), just like any other limited-slip device.

Side, side note: There is a differential & limited-slip combo that actually reroutes torque in a manner that is almost magical (at least it does something that is a lot closer to the name given to a Quaife): viz., the automatic yaw controller in late-model Evo8s. It does this by doing something very close to what happens inside an automatic transmission when it shifts gears. But just because such a device does exist doesn't mean that a Quaife can do this, too. And I can't see anyone trying to install the AYC from an Evo in a DSM, so I am way off-topic.

One last point about helical-type limited-slip devices: they only work if both outputs reflect at least some torque. In one side has zero grip and reflects nothing, the shaft on that side will spin like crazy, instead. This is why there is a second version of the Type-2 Torsen which includes a preload between the two side-gears. This version has the downside of never being a completely open diff (for cornering), but has the benefit of not returning to being open when one wheel is suddenly lifted off the ground while you are trying to accelerate. This is the Type-2 R. Unfortunately, I don't think that they are available for DSMs. And, yet, it could be argued that if you are lifting a wheel while accelerating in a DSM, your drivetrain isn't your main problem. But that shall be saved for another day and another thread.

Finally, there is also a low-tech approach to limiting slip that is available for our cars: the "insert" (aka Phantom Grip). This is a small, spring-loaded block that is installed on the spider and drags/rubs/grinds against the spider's gears, which makes it harder for them to turn. (Recall, here, that the gears on them legs of the spider only turn when one output is turning faster than the other.) Thus, these devices also act as a limited-slip device.

One positive about "inserts" is how they are a little like modified clutch-packs in that they resist slip more when more torque is being transmitted through the diff (although it should be notes that this behavior is two-way by definition, so the increase in slip-limiting occurs under braking as much as under power). This is true because the spider's gears are pressed inwards against the "insert" when torque is being transmitted.

The negatives of "inserts" are two-fold: most are not very strong, so they can't limit slip very much, and they are acting in a way that (from the engineers at Mitsu's point of view) misuses and/or abuses the gears on the spider. Also, if an "insert" breaks, the little pieces will probably take your diff before you can get the car stopped and, possibly, before you even realize it broke.

- Jtoby