Limited Slip Differential and eLSD FAQ!
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This is a discussion on Limited Slip Differential and eLSD FAQ! within the Transmission & AWD forums, part of the Tech & Modifying & General Repairs category; I feel that it’s time that I give back to the community in the form of a proper FAQ. As ...

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    zax
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    Limited Slip Differential and eLSD FAQ!

    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 LSD
    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.
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    zax
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    Electromechanical clutch LSD
    An emergent technology, electromechanical LSD systems have become increasingly prevalent in AWD and performance applications over the last decade. What once was available at high-dollar in Rally and circuit racing is now commonplace in streetcar applications especially in AWD systems. Electromechanical LSD systems commonly use a planetary or bevel gearset with electronically-activated continually variable transfer clutches.

    This type of LSD system incorporates the benefit of being partially torque-sensitive and partially speed-sensitive. Like torque-sensing LSDs, Electromechanical clutch arrangements are predictive and do not require wheel slip to provide limiting torque. Conversely, unlike torque-sensing LSDs, these systems do not fully lose traction when a wheel is allowed to rotate freely. Since the limiting torque is controlled fully by a computer, various chassis sensors can be referenced to vary limiting torque. While this is considered the most complete system, it is also the most expensive and complex. Like other clutch-based systems, Electromechanical clutch LSDs will wear the clutches over time.

    Uses: Porsche 959, Subaru DCCD system, BMW X-Drive,

    Alternatively, Electrohydraulic clutch systems use a gerorator pump to produce hydraulic pressure, which can be diverted to a hydraulic locking mechanism. This hydraulic clutch can be computer controlled to very the split of power to each axle. Like the Electromechanical systems, the hydraulic systems CAN use a clutch, or uses a friction fluid like what is found in the typically torque converter of an Automatic.

    Uses: Haldex AWD systems, on demand AWD, MazdaSpeed6, and Subaru 4EAT/5EAT/CVT

    Viscous LSD
    Viscous LSDs or vLSDs are a speed-sensing LSD utilizing the mechanical force of a viscous fluid to equalize the speed difference between output shafts. Most commonly vLSDs implement a silicone fluid within a housing containing stacked “disks” between the output shafts.

    As one output shaft begins to spin faster than the other, the disks begin spinning within the silicone medium. Taking advantage of the properties of adhesion and cohesion, the silicone fluid transfers energy from one output shaft to the other to equalize the speed difference. This type of LSD has obvious advantages. Firstly, the vLSD is low-cost compared to geared LSDs. Second, vLSDs are very low maintenance and perform surprisingly well. Like all speed-sensing LSDs, the Viscous LSD must experience wheelslip before the device can equalize the output shafts. As such, the vLSD is considered a “reactive system” and is less effective in performance applications. At the limit, this type of differential can cause sudden loss in traction before regaining traction ultimately resulting in a loss of control. Furthermore, repeated operation of this type of differential can heat the silicone fluid resulting in a permanent loss of the binding properties of the fluid. Luckily vLSDs fail as open differentials.
    vLSDs have been used within center and axle differentials for street and rally cars in AWD applications over the years. A once common LSD in the 1980s and 1990s, vLSDs have been systematically replaced by electromechanical systems of similar cost. This is the type of LSD utilized by Subaru in its “Symmetrical AWD” implementation on manual transmissions and within the rear differential in USDM WRXs between 2002 and 2007. Many iconic Rally cars in the early 1990s utilized vLSDs such as the Celica GT-Four, Lancia Delta Integrale, Subaru Liberty WRC, Mitsubishi Gallant VR4, Ford Escort RS Cosworth and many more. Later vehicles such as the DSM variant of the Eclipse and 3000GT used vLSDs.

    eLSD
    eLSDs or Virtual LSDs are becoming increasingly more common thanks to advances in computer control and software. With an eLSD, the differential is physically an open type differential. Instead of applying friction within the differential housing to equalize the rotation of the output shafts, the eLSD system uses onboard speed sensors to monitor each wheel and modulate the brakes to shift the speed bias. For example, during hard cornering, the computer will modulate the brakes on the inside wheels shift the speed bias between the inside and outside wheels. The advantages of such a system is the exceptional low cost and the low maintenance required. eLSDs perform a very similar job to other speed-sensing LSDs (especially the clutch-type) at a fraction of the cost. However, this system also has significant disadvantages compared to a traditional LSD. Firstly, since the eLSD uses the braking system, during track events a car equipped with an eLSD may experience brake fade quicker than a car without an eLSD. Perhaps even more unappealing is the unpredictability of the system compared to a traditional LSD. To investigate this second point, one must consider the more complex mechanics of the system. With a traditional LSD, the equalizing friction is contained within the differential housing implying that the suspension and wheel hubs do not see a moment of force as the LSD shifts the bias within the housing. By applying friction at the brakes, as the eLSD shifts the bias from inner to outer wheel the half-shafts and suspension will experience a moment of force that can alter the handling characteristics of the vehicle. Some eLSD system can anticipate the change in handling utilizing onboard yaw and roll sensors, but this increases the cost and complexity of the overall system. In general, a traditional LSD is considered superior in conditions when speed and torque differences between inner and outer wheels are common. As an added effect, traditional LSDs separate the duty of equalizing output shaft speed without compromising the braking system.
    Cars that use Brake Vectoring: 2015+ Subaru WRX, Ford Focus ST, Volkswagen Golf R and GTi, BMW F-Body among many others

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    Last edited by zax; 04-09-2014 at 06:30 PM.
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    Dimensional Drifter Rambo's Avatar
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    Nice writeup! Here's a great old-timey video explaining the basics of a simple differential:

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    Dimensional Drifter Rambo's Avatar
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    Although not specifically related, I've seen some questions on here about how the viscous coupled center differential in the WRX works. Here's another excellent video explaining viscous couplings:

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    Registered User Big_Ben's Avatar
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    Nice write-up!

    and nice Videos Isaac

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