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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    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 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. 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 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.
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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 accomplish torque transfer 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 in an attempt 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 transfer torque between 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-homologated roadgoing 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 facilitate torque transfer, 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 thus transferring torque. 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

    NEXT UP: 2-Way, 1.5-way, and 1-way L
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    Nice writeup! Here's a great old-timey video explaining the basics of a simple differential:

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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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    Nice write-up!

    and nice Videos Isaac

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    AWD Configurations in Common Performance applications:

    ATESSA-ETS in the 2009+ Nissan GT-R

    The ATESSA-ETS system is primarily a RWD application. In the GT-R configuration, the engine transmits power via cardan shaft to the transmission in the rear of the car. The transmission, which houses the rear and center differentials, transfers torque (if necessary) to the front of the car via an electronic transfer clutch. Under normal operation the car sends 2% of the power to the front saving 98% of the power for the rear. If necessary, the clutch engages sending up to 50% of the power to the front wheels. The GT-R AWD consists of an electronic torque-vectoring rear transaxle, an electronic center transfer clutch, and an open front differential.

    S-AWC in the JDM Lancer Evolution IX and [all markets] Lancer Evolution X:

    The S-AWC system maintains a 50/50 torque split via an active center differential termed the "ACD." The ACD system employs a hydraulic transfer clutch which can vary the level of differential locking via gerotor pump pressure. While the center differential in the Evolution does not have the quick response of the torsen differential in the Subaru DCCD or the Audi Quattro, the car makes up for this deficiency by incorporating an advanced active rear differential. Using a hydraulic transfer clutch, the rear differential in the S-AWC system can actually send more power to the outside wheel in a corner. The rear differential in the Evolution is a component in Mitsubishi's successful Active Yaw Control (AYC) system. By varying the level of center differential lock, individual brake-force distribution, and vectoring power to the rear differential, Mitsubishi can greatly control the behavior of the car through the corners. While the torque vectoring system in the Evo X controls the power transfer, the differentials themselves are technically open. The configuration in the Evo X is an open center differential, an open rear differential, and a Helical front LSD.


    Audi Quattro in the B7 S4/RS4:

    There are many "flavors" of Audi's Quattro AWD system. With the exception of the Audi TT and R/S3 (Haldex AWD) and Audi R8 (Viscous Center Coupling), all Quattro systems between 1987 and 2010 have employed a Torsen center LSD. While the Torque Bias ratio is contingent on the model, the performance Audis have always employed center LSDs with greater torque transfer capability (4:1 for the B7 RS4, 2:1 for the B7+ S4). Torque split is set at a constant 40% front and 60% rear. The B7 Audi RS4 employs a torque vectoring rear differential that consists of two super-imposed hydraulic transfer clutches. Audi calls this system the "Active Sport Differential" (ASD). Under normal operation, the rear sport differential splits power evenly between left and right half-shafts. Under hard cornering, the stability program can intelligently induce a speed difference between the half-shafts to aid in cornering stability and neutrality. Sound familiar? Yes it is very similar to the AYC system in the Lancer Evolution X. The B7 RS4 and S4 employ an open front differential while the B7 S4 receives an open rear differential. Both cars are augmented with a stability program that can brake individual wheels for improved traction.

    Audi Quattro in the B8 S4/RS4:

    A significant departure from prior Quattro systems, the B8 Quattro system tosses aside the Torsen center differential in favor of a Crown-type center differential. While still purely mechanical, the Crown differential transfers power front-to-rear on wheel slip. Unlike the Torsen differential, the Crown differential employs a mechanical locking mechanism that can physically lock the front and rear wheels at the permanent 40% front 60% rear torque split. Both the B8 S4 and RS4 utilize an open front differential. The B8 RS4 carries over the ASD from the B7 generation, while the S4 gains this differential as an option. An explanation of the ASD system: https://www.youtube.com/watch?v=tYCr36DVOVY

    Symmetrical AWD with DCCD in the 2008+ STi:

    Few manufacturers utilize as many mechanical LSDs as Subaru in the STi. For the top level Symmetrical AWD, Subaru has incorporated a total of three limited slip differentials. The motor sends power to the transmission which integrates the transfer case: front and center differentials are contained within the transmission. Subaru uses a Torsen limited slip center differential to limit front to rear traction loss and maintains a nominal 41:59 F:R torque split. Different to other manufacturers, Subaru has chosen to augment the Torsen center differential with an electromagnetic clutch that can very the force of lockup from completely open to completely locked. This electromagnetic clutch is termed the "DCCD" or Driver-Controlled Center Differential. It is important to note a common misconception: the DCCD does not actually vary the torque split. Rather, it varies the amount of force contributing to the torque transfer from front:rear under wheelslip conditions. The DCCD system will only step in when the Torsen differential has exceeded the torque bias ratio (2.7:1 TBR) or has lost traction entirely. The rear differential is a passive Torsen LSD differential augmented by the VDC (electronic torque vectoring) under wheelslip conditions. The front differential is a Helical type LSD which has been enhanced with Subaru's ATV (Active Torque Vectoring) system for the MY2015. ATV, which is evolution of the VDC system used in prior generations, applies the inner brake in a corner to facilitate torque transfer and provide more neutral cornering.

    EDIT:
    The Torsen center differential was added in the 2006+ STi. 2004-2005 USDM STi used an open center differential with a 35:65 F:R torque split at full traction. The 2004 STi used an AP Suretrac front mechanical LSD while the 2005+ use a Helical geared LSD at the front axle. It appears that the Torsen differentials at center and rear have a TBR of 2.7:1.

    Symmetrical AWD in Subaru Manual Transmissions (1988+ non-DCCD applications)
    Subaru made the switch to full-time AWD in 1988 by implementing a viscous center coupling mechanism. In the majority of implementations, the viscous center coupling limits slip between front and rear axles set to a standard 50:50 front:rear torque split (at full traction). Some implementations such as the non-RA JDM STi used a planetary gearset for a nominal torque split of 35:65 F:R while still retaining a center viscous coupler to allocate torque front to rear in the event of traction loss. The standard viscous coupler has a maximum binding force of 4kg between the front and rear axles (speed differential dependent). Unlike the DCCD system, the viscous coupler cannot vary lockup force (except with increased speed-differential). To achieve greater torque-transfer capabilities, VCUs with increased binding force are available: a 20kg center differential is available for use in cars intended for gravel and snow rally stages (where increased torque transfer is in demand).

    The 2002-2007 USDM WRX received a VCU rear LSD, while the JDM WRX received a Torsen rear LSD until 2001, when the Torsen was removed in favor of a VCU. In 2008, the rear LSD was removed in favor of Subaru's advanced stability program termed VDC. Up until 2008, most Subarus employed open differentials on the rear axle, with the WRX/STi, Legacy GT (spec B), Forester XT, Outback, and 2.5RS as exceptions to the rule.

    Symmetrical AWD in Subaru Automatic Transmissions (1988+)
    The E4AT, E5AT, and CVT have employed similar AWD systems, albeit with different overall operating specifications. Subaru's automatic systems forgo the VCU in favor of a more complex (and effective) Active center coupling OR Variable Torque Distribution (VTD) center differential. Most E4AT applications with the exception of the WRX use the active center coupling. This hydraulic multiplate transfer clutch mechanism normally transfers only 10% of the engine torque to the rear axle, but can transfer up to 50% of the engine torque to the rear axle if slippage occurs. The E4AT in the WRX and the E5AT/CVT employ a more advanced VTD system. The VTD incorporates a planetary center differential (similar to DCCD) with a nominal 45:55 F:R torque split. If the need arises, the TCU (transmission control unit) can allocate up to 100% of the torque to be sent to the rear or front axle by manipulation of a hydraulic multiplate transfer clutch. This system is technically superior to the VCU found in the Manual WRX for the following reasons: 1. Faster reaction 2. Variable torque transfer 3. greater lockup force. While similar in operation to the DCCD system, the mechanical components are vastly different. Front and rear axles are open differentials, with the exception of the WRX, Legacy GT (spec B), Forester XT, Outback, and 2.5RS.
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    Expanded the FAQ to include some common AWD configurations!

    If you have any questions, wish me to clarify, or have any suggestions on another AWD system, please feel free to PM me and I will make changes!

    To clarify a common misconception:

    Limited slip differentials do not actually vary the torque split between axles. The Limited slip differential can only send more torque to one axle if wheelslip is detected OR (in the case of Torsen LSDs) one side of the differential is perceived to have a lower limit of traction. Once wheelslip or traction differential is mitigated, the system returns to the designed torque split. Torque split is a mechanical configuration that is set by the design of the planetary gearset. I've seen this written often: "XXXX manufacturer with a center differential that varies torque split from 100% rear to 50% front and 50% rear. This statement is false. The torque transfer occurs due to traction differences between front and rear. Given equal traction at all four corners, the torque split is a mechanical configuration. Electronic Torque Vectoring applications do not abide by the same rules, but technically torque vectoring is not considered a "Limited Slip Differential."

    Interesting Adendum:

    With the 2015 STi, Subaru has managed to approach the cornering prowess of the Evo X, reducing the understeer commonplace in prior generations. How was this done? Interestingly, both manufacturers take nearly opposite approaches.

    Mitsubishi has chosen to incorporate a torque vectoring rear axle that can actually speed up the outside rear tire. The slight speed difference mitigates the understeering nature of an AWD vehicle facilitating neutral cornering and serving to rotate the car into the corner.

    Subaru has chosen to incorporate "Active Torque Vectoring" on the front axle. The ATV system brakes the front inside tire serving to rotate the car into the corner.

    An initial concept of operation can be found in the following quote:

    Quote Originally Posted by zax View Post
    In a corner, the outer wheel is loaded by the component centripetal force acting into the suspension. As such, the outer tire typically has greater traction compared to the inner tire. At this point, the Helical front LSD is actually applying torque to the outside wheel up to the TBR (I think this is 2.7:1 from what I've read). The TBR represents the MAXIMUM amount of torque that can be transferred from the inner tire to the outer tire dependent on inner tire traction. At the limit of traction, the inner tire cannot transfer any torque to the outer tire (at the extreme limit, the inner tire is now slipping, so no torque can be sent to the outer tire!). This is where the ATV steps in, applying the brake to the inner tire and sending more torque to the outer tire. Remember, the helical differential is already sending the maximum amount of torque (according to the TBR), from the inner tire to the outer tire, so as long as the outer tire has more traction, the ATV will be effective at transferring torque to the outer tire.


    In both cases, the rotation is induced by a slight speed difference between the inside front tire and the outside rear tire. Only Mitsubishi has chosen to speed up the outside rear tire while Subaru focused on slowing the inside front tire. So which is superior? Technically, though the outcome of both system is similar, Mitsubishi's system is the more elegant solution. Torque transfer systems will always have heat loss as will braking. However, by using a separate torque-vectoring system, Mitsubishi frees up the brakes to be used exclusively for braking. At the highly technical level, Subaru's system will contribute to brake-fade while Mitsubishi's will not. Furthermore, brake-torque apportioning is less energy efficient and places a moment arm on the suspension. The downsides to Mitsubishis AYC: weight, cost, and complexity.
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    Crown LSD:
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    Torsen LSD:
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    2015 CWP WRX STi ... But how did I get roped back into an EJ motor?!
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    Zach | Moderator -- Mid-Atlantic States, Tech & Modifying & General Repairs
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  13. #12
    Registered User tirerob's Avatar
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    great read! thank you zax! love the new stuff
    when my friends come up, i hear, "you sold the camarrrroooh.....HOLY BLEEP A WRX!"
    Ya has that effect on me too.
    Rob

  14. #13
    zax
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    I do recommend that anyone who had read through this FAQ, read through it one more time. I found a lot of errors in my original text. I'm sure there are still more technical errors to be corrected.
    2015 CWP WRX STi ... But how did I get roped back into an EJ motor?!
    Zax's utterly unimaginably stock 2015 STi build thread
    Zax's Shaggin' Wagon Build Thread Now tuned for 99% pure Unicorn Jizz!

    Zach | Moderator -- Mid-Atlantic States, Tech & Modifying & General Repairs
    Rollin' with the Bugeye Mafia #302 | N.E.R.D. Subject Zero
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