The Ram's Eye - A Driver's Blog: Limited Slip Differentials - The Basics



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Saturday, 22 October 2016

Limited Slip Differentials - The Basics




I'm finishing up a comparison post (link to introduction: Intro: Focus RS vs Golf R vs WRX STI vs Evo X) and, throughout the post, I realized that I have to go off topic a lot to talk about how each type of differential changes the way the car drives. As a result, I thought I'd write a separate post to go into more detail before I post the comparison to keep it more focused on the cars and avoid veering off topic too much.

By saying "Limited Slip Differentials" in the title, I am including torque vectoring diffs because, although current conventional terminology treats them differently, a torque vectoring differential is, in essence, a very sophisticated limited slip diff (LSD) that can be manipulated to actively help the car handle better. And while none of the cars in the comparison use open (without help from the brakes) or non-gear mechanical LSD’s, I’ll briefly discuss them so that the post is more inclusive. I’ll only focus on using power to help the handling or how a diff can handicap that, since the reason I started to write this post is to demonstrate how the differentials help each car. I won’t talk about other techniques that could help you manage a car’s weaknesses, such as changing turn in points, apexes, trailbraking, etc.

So how do traditional LSD's and torque vectoring diffs (TVD) help the car? Let's first start with open differentials.


Open Differentials

These are the most common differentials and they are the best at being differentials. The differential's job is to allow two wheels on the same axle to spin at different speeds so a car could smoothly go around a corner since each wheel has to travel a different path and, therefore, at a different speed - hence the name - to reach the end point of the turn at the same time. The video below has been used countless times to demonstrate how a diff works and, although made by GM almost 80 years ago, is still one of the best videos I've found that explains very simply and visually how a differential works (fast forward to about 2:00 in).





I don't want to get into the internals and workings of a differential, but I wanted to share that video because understanding the basics will help with understanding the impacts of various types of differentials. As you can see in the video, an open diff allows one wheel to spin endlessly, even if the other is completely stationary. The demonstration at 5:30 into the video shows that. If one wheel has a lot of traction, it's harder to spin, much like being held still in the video relative to the other one, (the road is "holding" the tire, in effect). If the other has little traction for some reason, the diff will spin it, since it is easier to spin. The diff transfers virtually equal amounts of torque to both wheels so the wheel with little traction will dictate how much torque the wheel with a lot of traction gets because if you give more torque than the low traction wheel can hold, it will spin, reducing your traction even more as well as lateral grip.

This is a double whammy if you have uneven available grip between two wheels on the same axle. When you have one wheel that has relatively little torque carrying capacity, but no way to unevenly distribute torque, you can more easily overpower it. Moreover, the wheel with a lot of traction and, therefore, good torque carrying/transfer capacity is underutilized. The result is limiting how much power you can use to move (accelerate) and increased likelihood of reducing your grip by spinning the low-grip wheel, which still contributes to the car's overall lateral and forward grip available. If that happens at the rear axle (RWD), that spinning low-traction wheel means less grip at the rear end and more likely to oversteer. On the front axle, it's understeer. This is assuming that, in either scenario, you're applying power.

How does this work on track? When you're going around a turn, the inside wheel is unloaded because weight is transferred to the outside wheel, which means the inside wheel has less grip. That means it can transfer less torque than the outside and if you exceed that, it will spin. If it starts to spin (excessively), it will have even less grip. Less grip means you'll be able to use even less power and your corner speed has to come down since one of the tires now has less grip. In short, an open diff works really well at allowing different speeds between the two wheels but under-utilizes available traction so it limits how much power you can put down and makes it easier to spin under power.

So what does that mean if you're pushing the car? When approaching a turn, as you start to turn in, you come off the power. Typically.. The reason I say typically is that with some of the other differentials, you can actually start using more than maintenance throttle as soon as you come off the brakes, but more on that later. For an open diff, you are off, aside from maintenance throttle. If you can add power and gain speed between turn in and apex (where you start to unwind), you lost more speed than you needed on the brakes. Assuming optimal entry, you shouldn’t be able to add speed without understeer, oversteer, or a neutral drift, depending on the balance of the car. The diff can’t help you here. Worse yet, on a FWD car, you can’t use the power to help the car rotate. Unlike RWD, where you could judiciously overpower the rear wheels, inducing slip and rotating the car that way, if you overpower the driven wheels in a FWD car, there’s no way to go but straight. And this is very easy to do in an open diff while going around a turn, with the inside wheel being unloaded.

Need more bad news? The vast majority of FWD cars have a transverse engine layout, placing the engine far outside the wheelbase of the car. The Dodge and Chrysler Intrepid come to mind as exceptions, with longitudinal engine, FWD layout. Audi A4s, too, if you don't get the AWD option. But even those still put the engine basically entirely in front of the front axle. This generates very nasty forces and moments that do their best at pulling the car straight when you want to turn. Then, of course, you have typical OEM suspension tuning that favours the front end letting go before the rear end for safe limit-understeer. The result is frustration and anger, perhaps some cursing, and eventually vowing against open differentials on the track and maybe even FWD all together (which can actually be made to work very well on a track).


Limited Slip Differentials



There are many types of limited slip differentials and, like I mentioned, I won't get into how they operate, just how they affect the car. I'm referring strictly to mechanical, non-gear type limited slip differentials here. These differentials are typically open differentials at heart with modifications or additions. Those modifications are designed to resist a speed variance across the differential. The result is a limit to how much faster a wheel can spin relative to the other, overcoming the limitations I mentioned for an open diff. This is achieved by locking the two axles together (to an extent). That extent depends on the design and spec of the differential - typically referred to in a percentage (%) number and occasionally as a Torque Bias Ratio (TBR). That % number is the difference in torque (in % of total) the diff can provide between the two axles. TBR is the ratio between the torque sent to the outside wheel to the inside wheel that the diff can deliver. The higher either number, the better the diff will be at putting power down as it allows more lock up. But higher isn't always better.

Limiting slip of a low traction wheel is great, as it can be the difference between accelerating and backing off the power when exiting a turn on a track. Trouble is, when under power, a limited slip diff of this type can't differentiate between turning and a slipping wheel. If you're going around a turn and starting to feed in power, the outside wheel is spinning faster than the inside wheel, which is normal. But the diff will start to lock up, in response to the speed differential, thereby transfering torque to the inside wheel. That means the unloaded wheel gets more torque, the opposite of what you want, and generates a steering moment in the opposite direction of the turn. Moreover, by locking up, there is resistance to the wheels spinning at different speeds, which is resistance to turning (i.e. understeer) since that requires each wheel travels a different arc at a different speed around a turn.

So how do these help, considering all that? You can go faster by using more power earlier in corner exit and, due to limiting inside wheel spin, you won't lose traction as easily which means you can better maintain your available grip. The downside is understeer on a RWD car. This is introduced by three factors:

- Locking up to any degree provides less speed differentiation than no lock up at all, which we've established is required for the car to turn.

- Putting more power down means more weight transfer to the rear end, which results in less grip at the front end; more understeer.

- You can maintain your grip for longer due to no inside wheel spin. If the rear axle can hold on for longer, you'll increase understeer.

- Torque transfer to inside rear wheel in a turn prior to it slipping generates negative steering moment (in opposite direction to the turn), resulting in understeer.

With that said, a car without a LSD will be slower than one with because, even if your corner speeds come down a little, you can get back on the power much sooner and more aggressively and that's where you make most of your time. Moreover, you can tune the suspension and chassis to reduce understeer so you typically only notice the understeer on a car that had a LSD added but is otherwise unchanged. And most good summer/track tires generate their highest grip with a very small amount of slip, meaning that if you're aggressive with the throttle, enough to just barely overpower the inside wheel where the diff is working as intended, that very small amount of slip is not hurting you and now the inside wheel is beginning to slip, causing lockup and torque transfer to the outside. As a result, you'll find that most good handling RWD cars actually have LSD's, such as modern Camaros and Mustangs, Corvettes, BMW's, Subaru BRZ/Toyota 86, etc. 

It gets even better on a FWD car, since you only have the first two factors against you. The other two are actually helping you; more grip at the front is less understeer and torque delivered by either front tire generates positive steering moment.  That means a LSD typically curbs understeer on a FWD car, even with all else being the same. The one caveat is that the axle locking can make it difficult to steer, if aggressive.


Torque sensing or gear type differentials




Torsen and Quaife are probably the most common of these types of differentials. They are very similar in function to more common LSDs discussed above, except rely on gears configured in a way to bind and provide locking. A gear type LSD is torque sensitive, hence the name Torsen (Tor for Torque and sen for Sensing). Torsen has two major designs T1 (first gen) and T2 (shown above). T2's are very similar to Quaife design (main picture above introduction). They all operate based on friction between the gears and the differential casing. Due to the inherent angle of the teeth on a helical gear, transmitting torque from gear to gear also generates thrust forces. These forces pushes the "pinion" helical gears against the differential case, providing lockup, instead of using a clutch pack to lock the axles to the case, for instance. The great thing about them is that they transfer torque even before slip occurs, since they progressively lock up as gear thrust forces increase and these forces are proportional to torque transferred by the diff and independent of speed differential across axles. In other words, as you apply more power, the diff progressively locks up and its capacity to carry torque increases, regardless of whether one of the wheels has begun to slip or not.

Both Torsen generations, T1 and T2, use the same basic principle but T1's are very rarely used now in new applications, if at all, and they rely on a different design that increases lock up. They utilize two different types of gears (helical and worm). Inherent to the design and arrangement of gears, the gears will progressively bind as speed difference between the wheels increases when there is excessive or uneven slip. Due to this nature, T1 LSD's typically have very high TBR's and provide a lot of lock-up.

The downside to gear type differentials is that they typically can't take as much abuse. They don't like to be launched hard and high hp, high grip cars seem to have issues with them since they operate on the principal of binding gears and diff cases. With that said, they are low maintenance and last longer in more forgiving cars. That's not necessarily slow, pedestrian cars - the list of high hp, high performance cars that includes them as OEM diffs includes 5th gen Camaro Z/28, the '12-13 Mustang Boss 302's, and the current Shelby GT350's, all of which utilize the T2 generation.

So how do these differ from the more conventional LSD's in operation? The main difference is how it locks. As discussed earlier, they lock because of the helical gears generating thrust forces that push the gears against the diff case, effectively binding and locking it up. Since the force generated is proportional to the force (torque) being transferred by the gears, lock up is proportional to input power (i.e. how much power you're applying). If you're off the gas, it's basically an open differential. As you roll into the power, it progressively and smoothly locks up. The benefit to that is, because lock up is smoother and the diff is more open off power, you can typically get away with higher torque bias ratios than non gear LSD's at maximum lockup without seeing as much of the side effects of higher locking. The higher TBR allows better traction performance.

Moreover, the fact that lock up is proportional to input power means the diff locks up as you send more power, without the need for slip. Non-gear LSD's need slip to work as intended. If you are going around a turn with no inside wheel slip at all, the outside wheel is traveling faster and the traditional LSD is locking up, slowing it down and speeding up the inside wheel, therefore, transferring more torque to the inside wheel. As you increase power, the inside wheel begins to slip and only as its speed passes the outside does the diff begin to slow it down. In other words, the inside wheel must slip first and then be limited. The diff will go through the sequence of little lock up (outside wheel faster than inside), then no lock up (inside wheel beginning to get over powered, spin, and accelerate to match outside, which from the diffs perspective is like the car going straight), then lock up again as the inside wheel speed starts to exceed outside. In a Torsen, the inside wheel is limited before it slips, since lock up happens before slip. Subtle differences, but can change how the car feels, plus the higher TBR means cars can better put power down, accelerate faster out of turns, and generally perform better on track.


Brake-based Differential Lock

A car that uses brake-based limit slip action utilizes an open differential just like described above but attempts to solve the shortcomings by applying the brakes to individual wheels. If you go on the power and one wheel spins, the car realizes that and applies the brakes at the spinning wheel. From the differential's perspective, that wheel now is harder to turn and more torque will get transferred to it. Fortunately, just as much torque will get transferred to the wheel with grip, giving better traction performance.

In high performance driving, this solves the two shortcomings of an open differential, loss of grip due to a spinning wheel and under utilizing good grip at the loaded, outside tire. As we've established, an open diff transfers equal torque to both wheels. In order to distribute torque where you want it (unevenly), the brakes are engaged to slow down the one wheel spinning excessively. It is artificially creating resistance at the low traction wheel (i.e. the brakes "grip" the wheel instead of the road through the tire). This increases the torque holding capacity of that wheel, and the diff as a whole, thereby allowing the diff to transfer more torque overall, half of which goes to the outside wheel where it can all be used. The downside is wasting some power simply spinning the low traction wheel against the brakes. The second problem is, as a result of trying to power the low traction wheel against the brakes, the brakes can over heat and prematurely wear.

What's it like to drive? The tech is extremely flexible because it provides complete uncoupling and independence between the two wheels when no lock up is needed and infinitely variable and adjustable bias when you do. You have non of the shortcomings of mechanical LSD's. But you'll hear a lot of owners and reviewers complain about their effectiveness, or lack thereof. The problem is the application, not the tech. In a Focus ST or a Golf GTI (non PP), you don't have liberally sized brakes, brake cooling, brake system capacity, etc. In reality, an optimized brake based set up can work very well. McLaren uses them, for example. You won't hear too many people complain about their performance.

When you already have massive braking thermal capacity, cooling air flow, braking power, etc, you could rely on this system and avoid a similarly flexible torque vectoring system. That would not only save cost and complexity since all you're adding is the programming to control the brakes the car already has, it also saves weight since a torque vectoring differential can be heavy. The one Lexus uses on the RC F and GS F, for instance, adds almost 70 lbs compared to the standard Torsen differential offered, itself a heavier system than open differentials. But brake-based lockup does have issues, otherwise, on non optimal cars - think non mid-engine, cost constrained, limited in space, or just about every other car that us mere mortals can buy.. And you waste the engine's power spinning the inside wheel.

To put that into perspective, my car has a Torsen diff with a bias ratio of 2.7 - meaning it can allow the outside wheel to get 2.7 times the amount of torque the inside wheel has while remaining locked up (which is equivalent to a 46% clutch type LSD, if you're curios). My car has 380 lb-ft of torque. That means, in an ideal traction scenario, at peak torque and lockup, going WOT, the engine is sending 380 lb-ft of torque to the diff and the diff is transferring all of it - 103 lb-ft will go to the inside wheel and 277 lb-ft will go to the outside - a difference of 174 lb-ft. To achieve the same bias with brake lock, each axle has to get the same amount of torque - the difference is that some will be used to spin the brakes. How much? 50% of the difference goes to the brakes or 87 lb-ft.  That translates to 75 hp (at 4,500 rpm where peak torque occurs), in effect turning my car down from a 444 hp car to a 369 hp car. Bad.. very bad. Moreover, those 75 hp have to be transferred into heat by the brakes and once those brakes overheat, they back off and you approach an open differential. This extent of power loss would be rare and if it were to happen, wouldn't last long, but it demonstrates how bad it can be. In a mid-engine car like a McLaren, where you have gobs of traction due to rear weight and optimal suspension tuning, you may not need as aggressive a torque bias and you have brakes the size of the moon that can handle the heat. But in every day cars, it doesn't work very well. Not yet anyway.


eLSD 

eLSD is typically used as short for electronic limited slip differentials. They basically combine the benefits of all the above without any of the downsides. It can take more abuse than a gear type. It can lock up smoothly like a gear type. It doesn't have the same resistance to speed differentiation (unless activated) so it can have a higher lock-up with no downside. It is electronically controlled so it can selectively lock and unlock as needed based on real time calculations and inputs from various sensors. It doesn't have to worry about brakes overheating. Its only downside, really, is complexity.

Unlike a mechanical LSD, it can distinguish between a faster spinning outside wheel as you turn (with no slip) and a faster spinning inside wheel due to slip. It won't lockup unless slip is happening, eliminating the negative moment due to torque sent to the inside rear wheel before slip occurs - what a mechanical LSD will do. It can give you high lock when you need, say, exiting a slow narrow turn, and low or no lock in corner entry, reducing understeer you'd get with a high lock. In summary, it gives you higher traction performance while reducing understeer when you don't need lockup.


Torque Vectoring Differential



A torque vectoring differential is very similar to an eLSD. The main difference is that eLSD's only transfer torque from slower to faster. An eLSD is a basically a typical LSD, say a clutch-type, where the clutches, and therefore amount of lockup, are electronically controlled instead of passively based on the difference in speed between the two wheels on an axle. That means that they can control when and how much to lock up but after that, the same principles apply and torque is biased from the faster spinning wheel to the slower wheel. However, a torque vectoring diff can transfer torque either way and can do so independently of a speed differential. The benefit is better control (from the car) and wider range of adjustability, allowing the car to correct and/or improve more frequently. Moreover, a torque vectoring differential typically doesn't transfer torque by locking up. Instead, it utilizes actuators (clutches and/or motors) and gear sets to overdrive or under-drive each wheel independently.

What does this mean? It means you have no resistance to speed differentiation (i.e. understeer) but as much torque transfer to either wheel (can be up to 100% of torque sent to the diff) as you want. The downside of lockup (understeer) is eliminated, a huge plus to start with. Then you get the best torque bias (basically infinite if designed to allow 100%) you could get, allowing you to utilize every last bit of traction available, and to top it off, you can have individual wheel torque control to help the car handle. For example, if the back end is coming out, you could vector torque to the inside to bring it in. This has the same effect as a stability control system applying individual braking to a wheel or more to bring the car back in shape but braking means scrubbing off speed. Torque vectoring doesn't. You could also transfer torque to the outside wheel to help the car rotate if the car is understeering, without forcing lock up. It's a technically wonderful system. The range of adjustments is huge. Opportunities to improve the handling are plentiful. It can make a huge difference in how the car handles. The only downsides, really, are even more complexity and a less "mechanical" feel.


Conclusion 

Which one is best? Well, brake-based systems are hugely variable, but because of the heat issue and power wasted, I'd only take one if I had to choose between one and an open diff. Otherwise, my preference is the gear type LSDs, even though they aren't as capable as electronic controlled ones. They provide the best performance without going to an electronically controlled system, in my opinion. Compared to electronically controlled ones, they're more natural feeling, simpler, and cheaper to maintain. They demand more of you, expect less of the car. But the same can be said for better tires, better shocks, stiffer chassis, etc. so I can see arguing both ways. I would imagine that someone learning on and sticking to torque vectoring tech on track would see it as natural and consider it a baseline, anything else is a compromise. That wasn't the case for me, so they will always seem like the deviation from norm - the cool tech that manipulates the car to your advantage, not the bare essentials.

With that said, in a FWD (never seen one) or FWD-based AWD car, I would absolutely and unquestionably give in and take torque vectoring and/or eLSD's. In a heart beat. The drivetrain layout is working very hard against you to prevent the car from doing what you want it to do. The tech does its best to mitigate the limitations. The way I see it: it almost undoes the crime that is FWD-based, transverse engine layout as opposed to improve the text book longitudinal front engine, RWD layout.


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