Limited-Slip Differential & Torque Vectoring Explained

Let's get stright into the topic.

Vehicle wheel & tire dynamics:
Vehicle on-rail driving experience is physically impossible because of the following factors
1. Tire elastic creep
With wheel torque, the wheelspeed is always higher(acceleration) or lower(brake) than the groundspeed(vehicle speed relative to the ground) because of this.

The higher the wheel torque, the less the "adhesion area" the more the "slip area" the faster the wheelspeed at a given ground speed.
2. Contact patch deflection
During cornering the slip angle is never zero because of the lateral G generated by the tires. The high the lateral G, the higher the slip angle


3. Non-linear tire friction
The maximum friction is load X friction coefficient. However, in automotive tires, the higher the load, the lower the friction coefficient. Thus, if a tire is 2X loaded, the max friction is slightly less than 2X.


Cornering dynamics.

1. Non-aggressive cornering
In low throttle and low G condition, the tire elastic creep and contact patch deflection is insignificant.
The larger the turning radius, the faster the wheel speed. So the actual wheelspeed are outer front > outer rear > inner front > inner rear



2.Aggressive cornering (important for understanding the following content)
In high throttle high G cornering, the outer wheels are "heavier" than the inner wheels. so the inner tires have higher creep than the outer tires, and because of the slip angle, the rear axle is spinning faster than the front axle.

This is, by far, the most important of understanding the role of limited-slip differential in terms of handling improvement.


Differentials
1.Open differential
Open front/rear differentials always transfer the same amount of torque regardless of the wheelspeed.
Some planetary center differentials can transfer an unequal amount of torque, such as 40%/60%, regardless of the wheelspeeds. Vehicles have open differentials typically have predictable handing if driven non-aggressively. However the vehicle traction is limited to the least tractive tire, results in a poor traction and handling in aggressive driving. Most econoboxes use this type of differential.

2. Limited-slip differential
Mechanical limited-slip differentials always transfer torque from the faster wheel to the slower wheel, regardless of type.

Clutch limited-slip differential
This type of LSD is mechanically similiar to the open diff. The main difference is the differential gears are pressed to a set of multi-plate clutches, and the higher the torque the more those clutches are compressed and the more the cross-axle torque. Maximum torque difference = torque bias ratio(TBR) X input torque + preload

One advantage of the clutch LSD is that the TBR can be different in either direction, so both the acceleration locking and engine braking locking torque can be individially tuned.

Disadvantages of the clutch LSD are low TBR(most of them less than 2:1) so preload is required, clutch can be worn out requiring an replacement.

Note: most of the clutch LSD are marked in "locking percentage". This is the maximum torque bias without preload. For example a 15% locking is 1.15:0.85 or 1.35:1 TBR. Increase preload to get (potentially) more TBR at a given % locking, but too much preload will cause driveline windup, worsening handling.

Geared limited-slip differential
All differentials have gears, the "geared" differential refers to both the speed differential and the slip limitation are done by the gears inside the diff, in other words, "two in one" differential.
Geared LSDs are based on the worm drive.

In a worm drive, the worm gear can drive the spur gear, but the spur gear cannot drive the worm gear. This is called self-locking. Thus, a geared LSD has a high TBR (3:1 or more) and no preload is required.


Helical/crown gear limited-slip differential
Helical LSD is somewhat between clutch LSD and geared LSD, the gear itself has a very high angle, which pushing it against the housing, where the cluch packs are loaded.
They have lower TBR than geared LSDs but higher TBR than clutch LSDs.


Viscous limited-slip differential
Viscous LSD doesn't have a TBR rating, instead it has a viscous coefficient. The torque bias is viscous coefficient X wheelspeed difference.

All mechanical LSD can be interpreted like this

LSD in action


3. Locking differential & Driveline windup

A locking differential binds the axle solidly so they rotate at the same speed, regardless of throttle position or surface traction. Make sure to disengage the locker before entering tarmac or driveline windup will occur(poor handling, stress drivetrain)

All wheel drive & Active systems
1. Transfercase/Splitshaft
A transfer case transfer power form the engine to the front and/or rear wheels. A transfer case can be made by a center differential or a split shaft.
Both a center diff and a split shaft have one imput and two output. In the center diff, the input RPM is always equals to the average speed of the two output shaft. In the split shaft, the input RPM is always equals to ONE of the output shaft, the other output shaft can be slower, equal to, or faster than the input shaft.

The 3 diff configuration(front, center and rear) is a full time AWD configuation. Examples are HMMWV (front and rear geared LSD, center locking), Mercedes 4-Matic (3 open center 40/60 torque distribution), Gavril D15/Roamer V8 Sport(front open, center 40/60 clutch LSD, rear clutch LSD), Hirochi Sunburst Sport RS AWD ( front viscous LSD, center 60/40 viscous LSD, rear clutch LSD), ETK 2400tix TTSport Evolution (front and rear clutch LSD, center 40/60 clutch LSD)
The front/rear biased is according the default torque distribution of the center diff (slip-limiting mechanism not in action)

Part time AWDs have two types, front biased and rear biased.

Front biased AWD is an FWD without significant wheelslip or tire creep. In the viscous AWD trasfercase, the faster the front wheels spin relative to the rear wheel, the more the rear wheel torque. Examples are Hirochi Sunburst Sport S AWD and Ibishu Pessima GTz.
In a computer controlled multi-plate clutch AWD. This can be tuned close to full-time performance. Since during non-aggressive driving, the front axle is never slower than the rear axle. Thus, if the computer is tuned to increase the clutch force on a stright line, and decrease the clutch force on curves. However in aggressive driving where the rear axle is faster than the front axle, this system cannot sent more torque to the rear and it'll power understeer like an FWD vehicle. Examples are Audi Quattro Ultra (default 70/30, 100/0 on cruising, up to 0/100 if both of the front wheel are spinning due to loss of traction), and Subaru ACT-4 (default 60/40, 90/10 on cruising, up to 50/50 on aggressive driving, up to 0/100 if both of the front wheel are spinning due to loss of traction).

Rear biased AWD is an RWD without significant wheelslip or tire creep. In the viscous AWD trasfercase, the faster the rear wheels spin relative to the front wheel, the more the front wheel torque. Example ETKI 3000ix
In a computer controlled multi-plate clutch AWD. During non-aggressive driving, the front axle is never slower than the rear axle. Thus, if any clutch force is applied on curves, it'll trasfer torque from front to rear, causing a "negative/more than 100%" torque distribution, this is driveline windup. Thus the vehicle is always RWD on non-aggressive cornering. However in aggressive driving where the rear axle is faster than the front axle, this system can send more torque to the either rear or the front, depending on the clutch force. Thus, both understeer and oversteer can be corrected. Examples are BMW xDrive and Jaguar F-Type/F-Pace.

Note: The computer controlled multi-plate clutch transfercase should not to be confused with computer controlled multi-plate clutch center LSD, when the clutch is disengaged the former is 2WD but the latter is still AWD.

2. Active differential & Torque Vectoring
An active differential is an LSD with computer-controlled slip-limiting mechanism (mostly multi-plate clutch)

An active diff can adjust the TBR and preload on the fly, actually it could theoretically applies a clutch torque perportional to the throttle to mimic a mechanical LSD, but not actually did that. In fact, it can inprove traction and handling at the same time. It disengage the clutch when the outer wheel is faster (non-aggressive driving, see above Cornering Dynamics section), and engage the clutch when the inner wheel is faster (aggressive driving). It can also create understeer or oversteer to counteract mechanical under/oversteer caused by suspension tuning. Disengage the clutch with zero throttle to cause a lift-off oversteer, engage the clutch with zero throttle to cause an understeer, disengage the clutch with high throttle to cause an understeer, and engage the clutch with high throttle to cause a power oversteer.
The limitation of active differential is that like a mechanical LSD, it cannot send more torque to the faster wheel. Examples are Mitsubishi Active Front Differential (Outlander), Active Center Differential (Lancer Evolution), BMW Active M Differential, Range Rover Sport e-Diff.

Torque Vectoring is the ability to send more torque to the faster wheels, making them even faster.
This can be done in several ways.

Open diff + planetary gearboxes

This system includes an open diff and planetary gearbox on one or two axles, the working is as shown.
The planetry gearbox can be set to step-up or step-down, since the wheelspeeds are "controlled" by surface traction, the step-up is actually decreased the speed of the differential side, and vise versa.

It can apply more torque to the desired wheel regardless of the wheel speed, but is less powerful due to it's open differantial lacks of limited-slip.

Active torque transfer from the differential casing to each axle

It has a differential which is useful when the torque vectoring is not in use. This type of torque vectoring use two step-up gears, one in each axle, which can be connected to the differential casing (i.e the final drive) via electronically-controlled multi-plate clutch.

The step-up gears spin at 10% faster than the differential speeds, thus when the clutch is engaged, up to 10% faster can be achieved to the outer wheel.

Step-up/step down gears + multiplate clutches

This type of torque vectoring consists two gearing and two clutches, one for step-up, the other for step-down. It can generate lateral torque regardless of the throttle position, thus brake vectoring can be minimized.



Spool + multi clutches
This usually appears in a part-time AWD drivetrain.
Acura Super Handling AWD

The "Acceleration" device is located in the drive shaft, when activated, will accelerate the rear spool up to 5.7% faster than the front differential. The rear spool is not a differential(effectively a permanently locked "differential"), torque vectoring is achieved by adjusting the engagement forces of the rear clutches, note the planetry gearbox on the rear clutch is solely for clutch force multiplication (reducing clutch wear).
FWD when not in use, RWD-ish (rear biased torque) when the acceleration device is activated and both of the rear clutches are more than 50% engaged.


Ford "Drift Mode" torque vectoring

In this drivetrain, the front differential, the rear spool and the transmission are connected together solidly.
When both of the rear clutches are disengaged, the vehicle is FWD. When the rear clutches are engaged, torque is transferred to the rear wheels. The rear spool cannot spin faster than the front differential, so the problem is the same as the front-biased part-time AWD discussed above. Since the rear spool is active and the front differential is open, the inner front wheel will lose traction first (spinning). Then the front differential will spin faster than the outer front (gripping) wheel, hence the rear spool. Torque vectoring is then applied to improve turning, as shown below.


3. Traction control & brake vectoring
Traction control is effectively the opposite of the anti-lock brakes. It applies brake to the spinning(loss of traction) wheel to improve traction. It can be used in conjuction with open, limited-slip, active or torque-vectoring differentials, but most of them use open diff to minimize cost. An open diff always apply the same torque to the two output wheels, if a wheel lose traction, the wheel has traction lose torque too. Braking is applied to the spinning wheel to make sure the gripping wheel's torque doesn't lose (but not gaining more torque), and the maximun effectiveness is up to 50%, compared to a mechanical locking differential, traction control is enough for everyday commuting or casual off-roading but not capable of serious off-roading.
Traction control only brake the spinning wheel if the wheelspeed is significantly higher than the gripping wheel.
Brake vectoring, on the other hand. Apply brake to the less traction wheel before wheelslip occurs and slows down the inner wheel to reduce understeer, which effectively prevents wheelspinning. Examples are BMW Selective deceleration and Audi Wheel-selective torque control. Not to be confused with torque vectoring

Brake vectoring is better than just open diffs, because if the wheelspin is left uncontrolled, the engine will eventually over-rev, reducing torque to the high traction wheel, but the efficiency of brake vectoring is lower than torque vectoring.


4. Individual wheel drive (IWD)
IWD drivetrains can do torque vectoring and regenerative brake vectoring at the same time.

 

Dude, how did I miss this thread, this is amazing!

 

I don't think its exactly safe to say brake traction control is not capable of serious off roading. Toyota relies on it entirely for the Land Cruiser, which only has a locking center diff and open front and rear axles. Both Jeep and Land Rover rely on it heavily too. Sure an open diff can only send 50% of the torque to each wheel by braking the one slipping wheel your increasing the total amount of torque being generated. Meaning that your increasing the amount of torque going to the wheel with traction. When tuned properly brake traction can be almost as effective as a locked diff and can be way more effective than most limited slip diffs.

 

the hummer h1 works like that. Open diffs, but when you press the gas and brake, it stops the freely rotating wheels and the open diffs send power to the other wheels too. you loose like half of the torque and power, but each wheel spins equally

 

Although in the H1's case, that's a geared limited-slip diff (as mentioned above). It senses torque rather than speed. An open diff can only transmit as much torque to either wheel as the one with the least load. If you apply brakes to both wheels, both have a significant load, so both get more torque. If it's an open diff, nothing much happens. If it's a torque-sensing LSD, though, the wheel with more load gets more torque. With a 3:1 TBR, if you apply 1000 N*m of braking torque to both wheels, the higher-loaded one gets up to 3000 N*m. This means you have up to 2000 N*m of usable tractive effort on that wheel, which might be enough to move the vehicle. This is the locking action we see on the Hummer and other vehicles with geared LSDs.