Differential

In an automobile and other wheeled vehicles, a differential is a device, usually consisting of gears, that allows each of the driving wheels to rotate at different speeds, while supplying equal torque to each of them. In automotive applications, the differential and its housing are sometimes collectively called a "pumpkin" (because the housing resembles a pumpkin).

Purpose

A vehicle's wheels rotate at different speeds, especially when turning corners. The differential is designed to drive a pair of wheels with equal force, while allowing them to rotate at different speeds. In vehicles without a differential, such as karts, both driving wheels are forced to rotate at the same speed, usually on a common axle driven by a simple chain-drive mechanism. When cornering, the inner wheel travels a shorter distance than the outer wheel, resulting in the inner wheel spinning and/or the outer wheel dragging. This results in difficult and unpredictable handling, damage to tires and roads, and strain on (or possible failure of) the entire drive train.

Functional Description

The following description of a differential applies to a "traditional" rear or front-wheel-drive car or truck: Power is supplied from the engine, via the gearbox, to a driveshaft (British term: propeller shaft), which runs to the drive axle. A pinion gear at the end of the propeller shaft is encased within the differential itself, and it engages with the large ring gear (British term: crownwheel), shown in the diagrams. The ring gear is attached to a carrier, which holds a set of three small planetary gears. The three planetary gears are set up in such a way that the two outer gears (the side gears) can rotate in opposite directions relative to each other. The pair of side gears drive the axle shafts to each of the wheels. The entire carrier rotates in the same direction as the ring gear, but within that motion, the side gears can counter-rotate relative to each other.

Thus, for example, if the car is making a turn to the right, the main ring gear may make 10 full revolutions, and during that time, the left wheel will travel more revolutions because it has further to travel, and the right wheel will travel fewer revolutions correspondingly, as it has less distance to travel. The side gears will turn in opposite directions relative to each other by, say, 2 full turns each (4 full turns with regard to each other), resulting in the left wheel making 12 revolutions, and the right wheel making 8 revolutions.

When the vehicle is traveling in a straight line, there will be no differential movement of the planetary system of gears other than the minute movements necessary to compensate for slight differences in wheel diameter, undulations in the road (which make for a longer or shorter wheel path), etc.

Loss of Traction

One undesirable side effect of a differential is that it can reduce overall torque - the rotational force which propels the vehicle. The amount of torque required to propel the vehicle at any given moment depends on the load at that instant - how heavy the vehicle is, how much drag and friction there is, the gradient of the road, the vehicle's momentum and so on. For the purpose of this article, we will refer to this amount of torque as the "threshold torque".

The torque on each wheel is a result of the engine and transmission applying torsion, a twisting force, against the resistance of the traction at that wheel. Unless the load is exceptionally high, the engine and transmission can usually supply as much torque as necessary, so the limiting factor is usually the traction under each wheel. It is therefore convenient to define traction as the amount of torque that can be generated between the tire and the ground before the wheel starts to slip. If the total traction under all the driven wheels exceeds the threshold torque, the vehicle will be driven forward; if not, then one or more wheels will simply spin.

To illustrate how a differential can limit overall torque, imagine a simple rear-wheel-drive vehicle, with one rear wheel on asphalt with good grip, and the other on a patch of slippery ice. With the load, gradient, etc., the vehicle requires, say, 2000 Nm of torque to move forward (i.e. the threshold torque). Let us further assume that the non-spinning traction on the ice equates to 400 Nm, and the asphalt to 3000 Nm.

If the two wheels were driven without a differential, each wheel would push against the ground as hard as possible. The wheel on ice would quickly reach the limit of traction (400 Nm), but would be unable to spin because the other wheel has good traction. The traction of the asphalt plus the small extra traction from the ice exceeds the threshold requirement, so the vehicle will be propelled forward.

With a differential, however, as soon as the "ice wheel" reaches 400 Nm, it will start to spin, and then develop less traction ~300Nm. The planetary gears inside the differential carrier will start to rotate because the "asphalt wheel" encounters greater resistance. Instead of driving the asphalt wheel with more force, the differential will allow the ice wheel to spin faster, and the asphalt wheel to remain stationary, compensating for the stopped wheel by extra speed of the spinning ice wheel. The torque on both wheels will be the same - limited to the lesser traction of 300 Nm each. Since 600 Nm is less than the required threshold torque of 2000 Nm, the vehicle will not be able to move.

An observer will simply see one stationary wheel and one spinning wheel. It will not be obvious that both wheels are generating the same torque (i.e. both wheels are in fact pushing equally, despite the difference in rotational speed). This has led to a widely held misconception that a vehicle with a differential is really only "one-wheel-drive". In fact, a normal differential always provides equal torque to both driven wheels (unless it is a locking, torque-biasing, or limited slip type).

Traction-Adding Devices

There are various devices for getting more usable traction from vehicles with differentials.
 
·    One solution is the limited slip differential (LSD), the most well-known of which is the clutch-type LSD. With this differential, the side gears are coupled to the carrier via a stack of clutch plates which limits the speed difference between the two wheels.
·    A locking differential employs a mechanism for allowing the planetary gears to be locked relative to each other, causing both wheels to turn at the same speed regardless of which has more traction; this is equivalent to removing the differential entirely.
·    The torsion differential keeps sending some torque to the wheel with more resistance
·    Electronic traction control systems usually use the ABS system to detect a spinning wheel and apply the brake to that wheel. This progressively raises the reaction torque at that wheel, and the differential compensates by transmitting more torque through the other wheel - the one with better traction.
·    A viscous coupling unit can replace a center differential entirely or be used to limit slip in a normal differential. It works on the principle of allowing the two output shafts to counter-rotate relative to each other within a viscous fluid. The fluid allows slow relative movements of the shafts, such as those caused by cornering, but will strongly resist high-speed movements, such as those caused by a single wheel spinning.

A four-wheel-drive vehicle will have at least two differentials (one for each pair of wheels) and possibly a center differential to apportion power between the front and rear axles. In many cases (eg. Lancia Delta Integrale, Porsche 964 Carrera 4 of 1989 [2]) the center differential is an epicyclic differential to divide the torque asymmetrically between the front and rear axle. Vehicles without a center differential should not be driven on dry, paved roads in four wheel drive mode, as small differences in rotational speed between the front and rear wheels cause a torque to be applied across the transmission. This phenomenon is known as "wind-up" and can cause damage to the transmission or drive train. On loose surfaces these differences are absorbed by the tire slippage on the road surface.

A transfer case may also incorporate a center differential, allowing the drive shafts to spin at different speeds. This permits the four-wheel-drive vehicle to drive on paved surfaces without experiencing "wind-up".

Epicyclic Differential

An epicyclic differential uses epicyclic gears to split torque asymmetrically between the front and rear axles.

Epicyclic gearing is used here to split torque asymmetrically.The input shaft is the green hollow one, the yellow is the low torque output and the pink is the high torque output. The force applied in the yellow and the pink gears is the same, but since the arm of the pink one is 2x-3x bigger the torque will be 2x-3x higher.