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 condition known as “wheel hop.” Wheel hop is a dangerous condition that stall the inner wheel, changes the toe on the outer or outer wheel, and puts excess stress on the drivetrain. Enter the differential. The purpose of the differential is to allow different speeds 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 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 the 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 weight on the outside tire while simultaneously decreasing the weight 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) in vehicles.
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 torque input
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 torque input.
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 to apply friction to one output shaft in order to equalize the momentum to the other output shaft. Each particular technology has distinctive pros and cons with no “perfect system” available.
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. 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 this LSD implementation, a worm gear within the differential housing reacts to the torque, expanding to induce friction between the output shafts.
As the input torque rises, the limiting torque between the two output shafts increases. This occurs up to a point known as the “maximum torque bias.” This number, as is usually represented as 2:1, 3:1, 4:1 etc. The maximum torque bias represents the upper limit on how much torque will be allocated to equalizing the rotation of the two output shafts. Since the mechanism for binding the output shafts is input torque 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 torque to equalize the rotation of the output shafts. In the case when one wheel is spinning freely, little torque is required by the input 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.