Every time a car goes through a corner, its wheels follow paths of different radius. The outer wheel describes a longer arc than the inner one and, in order to cover it in the same amount of time, it necessarily has to turn faster. If the two wheels on the same axle were joined by a single rigid shaft they would be forced to rotate at the same speed: one of the two would have to scrub across the tarmac, with abnormal tyre wear, high stresses on the transmission components and a loss of grip at the very moment when it is needed most. The differential is the mechanism that solves this problem: it splits the drive coming from the engine between the two half-shafts, allowing them to rotate at different speeds without interrupting the transmission of torque.
The classic differential is an epicyclic gear train built with bevel gears. Drive travels from the propeller shaft to the pinion, which meshes with a large-diameter crown wheel fixed to the differential housing, also known as the carrier or cage. Two or four bevel gears are mounted inside the cage, the spider gears, free to rotate around their own pin; these in turn mesh with two further bevel gears, the side gears, each splined to a half-shaft. In a straight line the two wheels turn at the same speed: the spider gears do not rotate about their own axis and simply drag the side gears along, so that the whole assembly behaves as a single body. In a corner the inner wheel slows down and the outer one speeds up: the spider gears start turning on themselves, giving back to the outer side gear exactly the revolutions taken away from the inner one. The sum of the speeds of the two half-shafts remains equal to twice the rotational speed of the housing.
There is, however, an important consequence, which is also the limitation of this architecture. Precisely because of the geometry of the gears, the differential always splits torque equally between the two half-shafts, regardless of how much grip each wheel actually has available. This is where the various solutions adopted by manufacturers come from:
- Open differential
- Limited-slip differential (mechanical self-locking)
- Locking and electronically controlled differential
Open differential
This is the most widespread solution on production cars, because it is simple, cheap, light and free of any specific maintenance. It performs its main task perfectly, namely allowing a difference in speed through a corner, but it pays for the fact that it splits torque equally. Since a wheel can only transmit to the ground the torque its grip allows, the torque that can actually be exploited is at most twice that which the worst-placed wheel can handle. The extreme case is a driven wheel on ice or lifted off the ground: its grip is close to zero, so the wheel that does have grip also receives a torque close to zero. The slipping wheel spins wildly and the car stays where it is. The same phenomenon appears in milder form on corner exit in a powerful front-wheel-drive car, when load transfer unloads the inner wheel and the torque that can be transmitted falls.
Limited-slip differential
To overcome that limitation, a controlled friction is introduced inside the mechanism, opposing the difference in speed between the two half-shafts and transferring part of the torque towards the wheel turning more slowly, that is the one with more grip. The degree of intervention is measured by the locking ratio, or bias ratio: a value of 3:1 means that the differential is able to send the gripping wheel three times the torque reaching the slipping wheel. There are two widespread mechanical designs.
Clutch-pack type. Discs splined alternately to the side gears and to the housing are stacked between them. A preload, obtained with Belleville springs, already keeps them partially engaged; the axial thrust generated by the bevel teeth under load then increases the compression of the pack in proportion to the torque transmitted. It is a solution that can be tuned and is widely used in motorsport preparation, but it is subject to wear of the discs and tied to the use of lubricants with specific additives.
Helical gear type (Torsen). Here the spider and side gears are replaced by helical gears coupled according to the worm drive principle, which transmits motion easily in one direction and with difficulty in the other. The internal friction that results is proportional to the torque transmitted: locking is nil on a trailing throttle and grows under acceleration, which makes the intervention progressive and barely noticeable. Its limitation is that it is sensitive to torque and not to speed: if one wheel loses grip completely, the reference torque collapses and the differential no longer has anything to multiply.
Locking and electronically controlled differential
On off-roaders a full lock is often used: a dog clutch, operated mechanically, pneumatically or electrically, locks the housing and the half-shaft together, forcing the two wheels to the same speed. Traction becomes maximum, but the differential stops performing its own function, which is why the lock should only be engaged at low speed on loose surfaces and disengaged on tarmac.
On modern road cars an electronically controlled limited-slip differential is preferred instead. The mechanical principle is still that of the clutch pack, but its compression no longer depends on preload alone: an electromechanical or hydraulic actuator, commanded by the control unit, modulates it in real time. The control unit cross-references the data from the wheel speed sensors, the steering angle, the accelerometer and the throttle pedal, and decides moment by moment how much to lock the differential, going as far as deliberately favouring the outer wheel in a corner in order to reduce understeer. Finally, this family should be distinguished from the so-called simulated electronic differential, found on many mass-produced cars: in that case the differential remains open and it is the traction control system that brakes the slipping wheel, indirectly obtaining a torque transfer towards the one with grip.