Limited-Slip Differential

The problem the open differential creates

Every car with two driven wheels needs a differential. When you turn a corner the outer wheel traces a longer arc than the inner wheel and must rotate faster; without a differential the axle would be a rigid bar forcing both wheels to the same speed, scrubbing the tyres and fighting the steering on every turn. The open differential solves this elegantly with a set of bevel spider gears that let the two wheels turn at different speeds while the ring-gear input drives the carrier between them.

But the open differential has a property that is fine on dry pavement and catastrophic anywhere else: it always delivers exactly equal torque to both wheels. That follows directly from the geometry — the spider gears act like a balance beam, pressing both side gears with the same force. Equal torque sounds fair, but torque at a wheel is capped by grip. A wheel on ice can transmit only a tiny torque before the tyre breaks loose and spins. And because the open diff insists both wheels get the same torque, the gripping wheel is held down to that same tiny value. One wheel spins furiously, the other sits dead, and the car does not move. This is the single defining failure of the open differential, and it is exactly what the limited-slip differential — the LSD — exists to fix.

An LSD does not change the basic differential action. The wheels can still turn at different speeds for cornering. What it adds is internal resistance to that speed difference. Once a resistance exists between the two side gears, the two wheels are no longer forced to equal torque: the gripping wheel can receive substantially more torque than the slipping one, with the gap set by the differential's torque-bias ratio.

The torque-bias ratio — the one number that matters

The torque-bias ratio (TBR) is the maximum ratio of torque the LSD can deliver to the high-grip wheel divided by the torque at the low-grip wheel before it gives up and lets them spin freely:

TBR = T_high / T_low   (maximum, before relative slip)

Open differential:        TBR = 1.0   (always equal torque)
Street clutch-pack LSD:    TBR ≈ 1.5–2.5
Sport clutch-pack LSD:     TBR ≈ 2.5–3.5
Torsen / Quaife helical:   TBR ≈ 2.5–5.0
Fully locked spool:        TBR → ∞   (wheels can never differ in speed)

The crucial — and frequently misunderstood — consequence is that the low-grip wheel sets the floor. The total torque the axle can deliver is the slipping wheel's capacity multiplied by (1 + TBR). Work an example:

One rear wheel on ice; it can hold T_low = 20 Nm before spinning.
Other wheel on dry tarmac; plenty of grip available.

Open diff (TBR 1.0):   T_high = 20 Nm,  total = 40 Nm   → stuck on most grades
Torsen   (TBR 3.0):    T_high = 60 Nm,  total = 80 Nm   → drives away
Spool    (TBR ∞):      T_high = whatever grip allows     → maximum traction

So an LSD multiplies the useful torque, but it cannot conjure grip from nothing. If both wheels are on ice, every wheel torque is small and a TBR of 5 still leaves you stuck — bias 5× a tiny number and you still have a tiny number. This is why an LSD helps enormously in the common case (one wheel slick, one gripping) and not at all in the symmetric case (both wheels equally slick).

The clutch-pack LSD — friction you can tune

The most common mechanical LSD is the plate-type, or clutch-pack, design. Behind each of the two side gears sits a stack of alternating friction plates and steel plates — much like the clutch pack in an automatic transmission. Friction plates are splined to the side gear; steel plates are splined to the differential case. Squeeze the stack and the side gear is partially coupled to the case, resisting any speed difference between that wheel and the carrier.

The clamping force comes from two sources working together:

• Preload. A stack of Belleville (coned-disc) springs holds a baseline clamp on the plates even at zero torque. This is the static breakaway resistance — the reason a clutch LSD provides some bias even with one wheel completely off the ground, unlike a Torsen. Typical street preload is 30–80 Nm of breakaway torque.
• Ramp loading. The cross-shaft (spider pin) sits in V-shaped ramps cut into pressure rings. As input torque rises, the wedge action of the ramps drives the pressure rings outward against the clutch packs. Steeper ramp angles produce more clamp per Nm of drive torque — and designers usually cut different ramp angles for the drive (acceleration) and coast (deceleration) faces, so the diff can lock hard on power and stay loose off-throttle. A common configuration is a 45° drive ramp and a 60° coast ramp, giving roughly a 2-to-1 split between on-power and off-power lock.

Plate-type LSDs are favoured in motorsport because every parameter is adjustable: number of plates, preload spring stack, and the two ramp angles. The penalties are wear — the friction surfaces degrade and the diff loses lock over tens of thousands of kilometres — and the requirement for a specific friction-modified gear oil. Run the wrong oil and the plates either grab and chatter on slow turns or never lock at all. The classic symptom of a tired or wrong-oiled clutch LSD is a shudder felt through the seat when parking-lot manoeuvring.

The Torsen and Quaife — gears that lock themselves

The Torsen (a contraction of Torque-Sensing, a Gleason trademark) and the very similar Quaife use no clutches and no wear surfaces. They bias torque through pure gear geometry. The two side gears are cut as worm gears (Torsen Type 1) or helical gears (Torsen Type 2, Quaife), and they mesh with sets of floating planet pinions carried in pockets in the differential case.

The trick is that worm and steep-helical gear meshes are partially self-locking. When torque flows through the mesh, the gear-tooth contact generates a large axial and radial separating force that jams the planet gears against the walls of their pockets and against thrust washers. That jamming friction is what resists differentiation — and, critically, it is proportional to the torque being transmitted. Push hard on the throttle and the diff locks hard; lift off and it frees up. This is the defining virtue of the Torsen family: it is torque-sensitive rather than speed-sensitive, so it reacts instantly and progressively, with essentially zero maintenance and no plates to wear out. It is the differential in the Audi quattro centre drive, many Toyota and Mazda sports cars, and the HMMWV.

The Torsen's weakness is the mirror image of the clutch pack's strength. With no preload spring, its bias depends entirely on there being torque to react against. Lift one wheel fully off the ground and that wheel's torque capacity is zero; multiply zero by any TBR and you still get zero, so the airborne wheel spins and the Torsen delivers almost nothing to the grounded wheel. Designers patch this by adding a small preload (a light Belleville stack) so the unit behaves as a hybrid, or by relying on the car's brake-based traction control to pinch the spinning wheel and create the artificial reaction torque the Torsen then multiplies.

The viscous coupling — silicone that thickens when sheared

A third family avoids gears and clutches entirely. A viscous limited-slip differential — really a viscous coupling pressed into the differential role — packs dozens of thin, closely spaced perforated plates into a sealed drum filled with high-viscosity silicone fluid. Alternate plates are keyed to each output. When both outputs spin together the fluid simply circulates harmlessly. When a speed difference develops, the plates shear the fluid; the silicone heats, expands, and undergoes shear-thickening, sharply raising the torque it transmits across the gap — sometimes to the point of near-lockup, the so-called hump mode.

Viscous units are silent, smooth, and maintenance-free, which made them the heart of 1980s–1990s all-wheel-drive: the centre coupling in early Subaru and Volkswagen Syncro systems, and many rear axles. Their flaw is that they are speed-sensitive: they only react once a real speed difference already exists, so the response lags the event, and the fluid degrades with thermal cycling, gradually losing its bite over the life of the car. They have largely given way to electronically controlled multi-plate clutches that a controller can pre-load proactively, but the viscous coupling remains a clean illustration of using a fluid's rheology to do a mechanical job.

LSD versus the alternatives

Property	Open differential	Clutch-pack LSD	Torsen / Quaife	Locker / spool
Torque-bias ratio	1.0 (none)	1.5–3.5	2.5–5.0	∞
Senses	—	Preload + torque (ramps)	Torque	Always fully locked
Works with one wheel airborne	No	Yes (from preload)	Poorly (no torque to react)	Yes
Cornering smoothness	Excellent	Good (some drag)	Excellent (frees off-throttle)	Poor — scrubs, crow-hops
Maintenance / wear	None	Friction oil + plate wear	Essentially none	None
Typical use	Economy cars	Sports cars, motorsport	AWD, performance road cars	Off-road, drag racing

Electronic and active variants

• Brake-based traction control (eDiff / "electronic LSD"). Not a real differential at all — an open diff plus software. Wheel-speed sensors detect a spinning wheel and the ABS pump pinches that wheel's brake, raising its reaction torque so the open diff feeds the gripping side. Cheap, no extra hardware, but it wastes energy as brake heat and cannot sustain high torque transfer for long.
• Electronically controlled multi-plate clutch. A clutch-pack LSD whose clamp force is applied by a hydraulic or electromechanical actuator under computer control rather than purely by ramp geometry. The controller can lock the diff before a slip occurs, using throttle, steering angle, and yaw data. This is the modern performance-car solution — examples include the Subaru DCCD centre diff and many torque-vectoring rear units.
• Torque-vectoring differential. Goes beyond limiting slip to actively overdrive one wheel relative to the other through a planetary step-up and a clutch, steering the car by sending more torque to the outer wheel in a corner. Found on the Mitsubishi Evo's AYC, the Acura SH-AWD, and high-end AWD sports cars.
• Selectable locker. A driver-engaged full lock (air-, electric-, or cable-actuated, e.g. ARB Air Locker, Eaton ELocker) that behaves as an open diff until commanded, then becomes a spool. The off-road answer: open and civilised on the road, fully locked when the trail demands it.

Failure modes and trade-offs

• Clutch-plate wear. Friction surfaces glaze and thin over time, dropping the breakaway preload and the effective TBR. A street clutch LSD may lose meaningful lock after 60,000–120,000 km of hard use. Cure: rebuild with new plates and fresh Belleville springs.
• Wrong gear oil. Clutch LSDs need a friction modifier; the wrong oil causes either chatter (stick-slip on slow turns) or a complete loss of lock. Always match the oil spec, including the LSD additive.
• Understeer on power. A diff that locks too aggressively pushes the front end wide on corner exit, because both rear wheels are forced toward the same speed. Motorsport tuning of ramp angles and preload is largely about balancing this against the traction benefit.
• Torsen lift-off. A Torsen delivers almost nothing when one wheel is fully airborne — a real limitation off-road and on bumpy circuits. Hybrid preload or brake-based traction control is the standard patch.
• Viscous fade and "hump" lockup. The silicone degrades thermally, and repeated abuse (e.g. towing a car with mismatched tyre sizes) can drive a viscous centre coupling into permanent hump-mode lockup, binding the driveline.
• Driveline windup with too-tight a setup. An over-locked LSD on dry pavement loads the half-shafts and tyres in tight manoeuvres, accelerating tyre and CV-joint wear and producing the tell-tale low-speed shudder.

Design notes and rules of thumb

• Match the bias to the surface. A high TBR is a liability on a low-grip road, where it provokes snap oversteer; a track car on slicks can use far more lock than a road car on all-seasons.
• Asymmetric ramps for feel. Different drive and coast ramp angles let the diff lock under power for traction while staying free on a trailing throttle for predictable turn-in. This is the single most-tuned parameter in racing LSDs.
• Preload is your one-wheel insurance. If the application must drive with a wheel lifted (off-road, autocross kerbs), choose a clutch design with healthy preload or add preload to a helical unit — a pure Torsen will let you down.
• Pair mechanical LSD with electronics, don't fight them. Modern stability systems can interfere with an aggressive mechanical LSD; the best results come from tuning the two together rather than maximising either alone.
• Watch the heat. All friction-based LSDs convert slip into heat; sustained slip (deep mud, long climbs) can cook the oil and the plates. Differential coolers exist for exactly this reason on heavy-duty and competition vehicles.