I feel that it’s time that I give back to the community in the form of a proper FAQ. As such, I present to you: the LSD and eLSD FAQ! So, let’s first discuss the purpose of a differential.
What is a differential?
When a car is driving in a straight line, wheels on both sides of the car are turning at a constant rate. However, when a car enters a turn, the inside wheel covers a shorter distance from the outside of the wheel. As such, the outside wheel turns faster than the inside wheel. If the inside and outside wheels are connected by a single shaft, this differential between the wheel velocities results in a dangerous condition that can stall the inner wheel, changes the toe on the inner or outer wheel, and puts excess stress on the drivetrain. Enter the differential. The purpose of the differential is to allow a speed differential between the inner and outer wheel while being driven by the input shaft. In its most common form, the differential consists of a Pinion and Ring and Planetary bevel gears to connect the output shafts. Here is an example of a typical [open type] differential:
In a standard [open type] differential, the rotational velocity of the input shaft is the average of the rotational velocity of the output shafts under normal traction conditions. Therefore, increasing the speed of one output shaft will decrease the speed of the other output shaft. As conservation of momentum is considered, this means that 50% of the torque transferred to the ground will always remain on each output shift in a standard open differential. As such, we are now presented with a problem: what happens during loss of traction? To investigate, let’s do some basic maths.
Input shaft velocity is ‘V’
Radius of the turn is ‘r’
Track of rear wheels is ‘T’
So the inside wheel is traveling on an arc that has a radius of r-0.5T while the outside wheel is traveling on an arc with a radius of r+0.5T. Therefore, the differential in velocity of output shafts is V*(r+0.5T)/(r-0.5T). So, as you can see, any increase in input shaft velocity is met in the middle by the average of the velocity of the output shafts. During a loss of traction, one output shaft is allowed to spin freely. As a result, a large percentage of the input shaft velocity (V) is diverted to the free-spinning wheel. This is then countered by a reduction in speed (but equivalent torque) for the gripping wheel to meet the requirements of the math above. If 10 lb-ft of torque is enough to cause a loss of traction on one output shaft, 10 lb-ft of torque will be applied to the output shaft with traction. When this loss of traction is present in inclement conditions the car may not be able to accelerate. More critical are the conditions that occur in spirited driving from the loss of traction. When navigating a turn, the car preloads the outside tire of the corner in a process called “loading.” Effectively this increases the traction on the outside tire while simultaneously decreasing the traction on the inside tire. The larger the rotational velocity, the greater this effect. The car may lose traction on the inner tire at the limit of grip and, in the worst case, be presented with a loss of control. To circumnavigate these issues, many manufacturers of performance vehicles install Limited Slip Differentials (LSDs) across axles.
What is a Limited Slip Differential?
In the most basic sense, a Limited Slip Differential (LSD) equalizes the difference in either speed between output shafts or applied torque between output shafts to maintain traction in adverse or performance conditions. The benefits of installing an LSD are
1. Enhanced traction in snow, gravel, and sand
2. More predictable handling at the limits of grip
Among LSDs, different types are utilized. From a top-down perspective, LSDs are classified into the following major categories:
1. Torque Sensitive – Provides varying limiting torque depending on least output shaft traction.
2. Speed Sensitive – Provides varying limiting torque depending on speed difference between output shafts
3. Electromechanical – Utilizes electronically controlled continually variable transfer clutches to vary limiting torque.
4. Fixed Torque – Provides constant limiting torque regardless of speed differential or traction.
5. eLSD or Virtual – Utilizes brake system to limit provide limiting torque.
Furthermore, LSDs in each of these categories may be further subcategorized using the following technologies:
1. Clutch-type or plate-type LSD
2. Geared LSD
3. Electromechanical clutch LSD
4. Viscous LSD
5. Brake Vectoring LSD
The purpose of each technology is maximize traction by transferring applied torque from the shaft with the last traction to the shaft with the most traction.
Clutch-type or Plate-type LSD
Clutch based mechanical LSDs fall into the torque sensing or fixed torque category. A common LSD thanks to the low cost and simplicity, clutch type LSDs fall under a very broad category of mechanical design. In the simplest arrangement, a spring will press a clutch between the bevels of the output shafts with fixed mechanical pressure. This results in a fixed amount of torque application between the output shafts (Fixed Torque). In more complex arrangements, the clutches will act on plates and cones kinematically with varying force depending on input torque.
Since the clutches will provide limiting torque before wheel slip occurs, this type of LSD has the virtue of being “predictive” and not waiting until the wheel loses traction to apply limiting torque. This is an advantage in performance applications when wheel slip may result in a loss of control of the vehicle. An additional advantage include easy tune-ability: the TBR or preload can be adjusted quite easily without complex differential swaps. The disadvantage of clutch-LSDs is quite evident: clutches wear over time.
Geared LSDs are considered a wholly mechanical version of torque sensitive LSD technology. In a common implementation, a worm gear within the differential housing reacts to differential in output traction, expanding to induce friction between the worm gear and the differential housing.
As the traction differential increases, the limiting torque between the two output shafts increases. This occurs up to a quantity known as the “Torque Bias Ratio.” This quantity is usually represented as a ratio: 2:1, 3:1, 4:1 etc. The torque bias ratio represents the maximum amount of total torque that can be transferred from the axle with the least traction to the axle with the most traction. For example, if the axle with the least traction allows 30 lb-ft of torque to cause slippage, 60 lb-ft of torque can be applied to the axle with greater traction in the case of a 2:1 TBR and 90 lb-ft in the case of 3:1 TBR. Since the mechanism for binding the output shafts is dependent on traction differetntial and not shaft speed differential, the geared LSD has the virtue of being “predictive” and not waiting until the wheel loses traction to apply limiting torque. This is an advantage in performance applications when wheel slip may result in a loss of control of the vehicle. On the other hand, geared LSDs assume the presence of traction to accomplish torque transfer. In the case when one wheel is spinning freely, little torque transferred by the output shaft and even a 5:1 geared LSD cannot equalize the rotation between the output shafts. Remember, 5 x 0 is still 0, so no torque is applied to the wheel with traction. Common geared LSDs are Torsen (which actually stands for TOrqueSENsing), Quaife, and Eaton. The 2005+ USDM WRX STi employs a Torsen LSD in the rear differential, as does the 2000-2001 JDM WRX.