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  1. Operating principles
  2. Drive axle differentials
    1. Limited-slip
    2. Torsen
    3. Electronic self-locking
    4. Manual locking
  3. Central differential
    1. Ferguson
    2. Epicycloidal

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Immagine di copertina

JUNE 1st, 2018


When driving around a corner, the outside wheel travels more meters than the inside wheel. The rotation speeds of the two wheels will necessarily be different. The function of the differential is to allow this difference in rotation between two wheels on the same axle.

If a car had no differential (imagine for example a go-kart), the two wheels of the same axle would be forced to rotate at the same speed. As a result, one of the two wheels will have to lose grip, sliding on the asphalt.

Strada percorsa


Operating principle       top

The differential consists of 3 elements:

  • Ring gear
  • Sun gears
  • Planet gears

Motion is transmitted to the ring gear through the drive shaft, which is connected to the sun gears that transmit motion to the wheels through the planet gears.

Lifting the drive axle of a car, and rotating by hand (with the engine off) one of the two wheels, the opposite wheel will rotate in the other direction. Let's take an example: if we make one wheel rotate at 5 km/h, the opposite wheel will rotate at the same speed, but in the opposite direction. Now, imagine that this happens while the car is moving forward at, let's say, 50 km/h. One of the two wheels accelerates, and thus goes to 55 km/h, while the other one slows down in equal measure, rotating altogether at 45 km/h. This difference in speed allows the cornering. Of course, the relative speeds depend on the radius of curvature and the car's forward speed.

Let's imagine now a stationary car, with one wheel resting on the ground and the other raised. In this case the lifted wheel is free to rotate, so all the torque coming from the transmission shaft is discharged on that axle, blocking the car. This condition can also be found while driving. In case of loss of grip, this type of differential always transmits more torque to the axle with less grip, i.e. the axle that offers less resistance.

Because of its low cost, this differential is widely used on medium/low range cars, while sports cars (which therefore must always have maximum traction during acceleration) or off-road vehicles generally use different types of differentials.


Drive axle differential       top

We now describe the types of differential usually used in the drive axle, to control the internal and external wheel speeds.


Limited-slip       top

The LSD (Limited Slip Differential), differs from the "classic" differential for the presence of a clutch or viscous coupling between the two sun gears. If the speed difference between the two sun gears (and therefore between the two wheels) is low, the viscous coupling or clutch offers little resistance, allowing rotation. The greater the speed difference, the more resistance they offer, braking the motion between the two gears. This ensures that if a wheel lifts off (or loses grip), the resistance it opposes is never zero, but is always at least equal to the friction of the clutch or viscous coupling. Part of the torque is therefore always transmitted to the wheel with the most grip.

The locking level of this differential is generally between 20 and 40%. In advanced cars, the clutch discs can be controlled by a control unit, which then allows the most suitable locking level to be selected according to conditions.


Torsen       top

The Torsen (Torque Sensitive) is mechanically more complicated, larger and heavier than traditional differentials. Instead of using friction to implement locking, it uses the principle of the involute screw (or worm screw).

If the shaft ("wormshaft") is rotated, the crown ("worm wheel") rotates easily. On the contrary, if I rotate the wormshaft, the shaft will be blocked. In the case of the torsen differential, the shaft is the gear keyed to the axle shaft, while the crown wheel is the satellite gear. Consider now the cutaway of the torsen differential (picture above).

The torque coming from the engine is applied to the crown gear, not visible in the picture, which rotates the whole box containing the gears. The satellites are connected to the box, coupled to the axle shaft through a helical gear. Finally, the satellite coupled to the right half shaft and the satellite coupled to the left half shaft are connected to each other through a normal spur gear. Note that the two driveshafts have the helical gear in the same direction, not mirrored.

Vite senza fine Differenziale Torsen
Endless Screw Torsen differential

Imagine now to "break" the differential in half (separating the right from the left part) and apply a driving torque. The right satellite will start to rotate around the axis of the axle shaft. Let's imagine this motion from the satellite point of view. We will see the semi-axis (i.e. the shaft, in the involute screw) rotating, which will then induce in rotation the satellite that will rotate around its axis. The same is true for the left satellite. Right and left satellite will rotate in the same direction, being the helix of the semi-axis not specular.

This motion (if we join the two halves of the differential) is not allowed, as the two satellites are connected by a gear. Therefore they cannot rotate, the whole system is blocked and torque is transmitted to the wheels. If a curve is taken, the outer wheel accelerates while the inner one brakes. The differential will see one wheel turn clockwise and the other counterclockwise. The previous case is repeated, with the difference that now the two satellites will rotate one in the opposite direction to the other. This motion is allowed by the gear that connects the two satellites, so the turn can take place without problems.

If under acceleration a wheel loses grip, it would begin to rotate faster dragging its satellite gear. The satellite would drag the one of the other axle. However, we know that in an involute screw, rotating the crown gear would not be able to rotate the shaft. Therefore, the satellite of the other semi-axis will be blocked. In the instant in which a wheel loses grip, the differential locks transmitting all the torque towards the wheel that in that moment has more grip. Compared to the clutch or viscous joint LSD differential, which allows a certain amount of slip, the torsen does not allow this by locking instantly. This is a big point in favor of traction.


Electronic self-locking       top

From a mechanical point of view, it is a normal open type differential. Any loss of grip of a wheel is detected by the control unit, which brakes it. The big advantage of this system is the cost, as mechanically nothing changes compared to a car not equipped with a self-locking differential.

On the other hand, in heavy use, the components of the brake system overheat and wear out prematurely. This is why this system is mainly used in small cars, where it only plays an active safety role.


Manual locking       top

Used almost exclusively on 4x4 cars intended for intensive off-road use. The mechanical structure is the one just described, with the addition of a manual block that has the purpose of rigidly locking the axle, thus excluding the differential function. It is used in all those cases in which the car is unable to proceed because of the skidding of a wheel, the differential is blocked and the drive can continue. It should never be used on tarmac, to avoid premature wear of the transmission components.


Central differential       top

In the case of cars with permanent 4x4 traction, the engine torque is applied to a differential that distributes it on the front and rear axles, to allow speed differences between the two axles. The differential used will always be of the self-locking type or manually lockable. If an open (classic) differential were used, the slippage of a single wheel would be enough to lock the entire vehicle. For this purpose could be used one of the differentials described above, or specially designed differentials. Generally, there is no central differential in cars with insertable 4x4, but the two axles will be locked.


Ferguson       top

With the use of this system, the torque from the engine is not applied to the center differential and then divided between the two axles, but is applied to one axle, which is then connected to the second through the interposition of this differential, or "viscous coupling". For this reason, it is a differential widely used in cars originally with 2-wheel drive, later converted to 4x4.

Inside this differential is a series of discs. Some of them are drilled and are keyed to the, let's say, output shaft, while the others are shovel shaped, and are connected to the input shaft. The whole is filled with a non-Newtonian fluid, i.e., a fluid capable of changing its viscosity as the rate of stress changes. In this case, it is a dilatant fluid, i.e., one that increases its viscosity as the speed of stress increases.

When the front and rear axles rotate at the same speed, the discs inside the differential also rotate at the same speed, there is no fluid displacement, and the two shafts are decoupled. The moment there is a speed difference between the two axles, the shovel-shaped discs push fluid through the holes, causing an increase in its viscosity and thus an increase in resistance. Some of the torque begins to be transferred to the second axis.



Epicycloidal       top

A " epicycloidal gear" is a gear system consisting of a central gear (pinion or "sun"), outermost gears (satellites) held together by a satellite holder, and an outer gear.

When connecting two shafts, the planetary gear can be used in various configurations:

  • Lock the sun, apply an input torque to the crown and get an output torque on the satellite holder, or vice versa;
  • Lock the satellite holder, apply an input torque to the sun and get an output torque to the crown, or vice versa;
  • Lock the crown, apply an input torque to the sun and get an output torque on the satellite holder, or vice versa.


If none of the 3 components is locked, the system is free and cannot transmit torque. In the case of using it as a center differential, I have a torque transmission on each of the 3 components: typically, the torque coming from the engine is applied to the crown wheel (in red in the picture), the rear axle is connected to the planetary carrier (in blue) and the front axle to the sun (in yellow). If I have the car lifted up, I lock the front axle and apply torque to the crown (in simple words, I accelerate), only the rear axle will rotate, case 1 seen above occurs again.

If instead I lock the rear axle, only the front one will rotate (case 2, above). The planetary gear behaves as if it were an open differential, and in case of loss of grip of an axle the whole car would lock. For this reason, a ferguson viscous joint is usually placed between sun and planetary carrier, to lock the axles in case of loss of grip.

With the planetary, you can get different gear ratios between crown-axle and crown-sun. So if you lifted the car, as seen before, and locked first one axle and then the other, the two axles would rotate at different speeds respectively.

While driving, both axles are free, as long as there is no loss of grip they will rotate at the same speed. However, the torque that is applied to the axles will be different, and will depend on the transmission ratio. Thanks to the planetary gear, it is therefore possible to obtain a 4-wheel drive car with a different torque distribution between the front and rear axles, which can be chosen on the basis of the weight distribution of the vehicle and the type of road behavior desired.


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