In mathematics a differential is the expression which appears inside an integral, or on the top or bottom of a derivative, in calculus. Outside these contexts, they can be formalized as elements of cotangent spaces, and the like.
In this differential, input torque is applied to the ring gear (blue). The pinion gear (green) applies power to both side gears (red and yellow), which in turn may drive the left and right wheels. If both wheels turn at the same rate, the pinion gear does not rotate.
If the left side gear (red) encounters resistance or is immobile, the pinion gear (green) rotates about the left side gear, in turn applying extra rotation to the right side gear (yellow).
In an automobile and other wheeled vehicles, a differential is a device for supplying equal torque to the driving wheels, even as they rotate at different speeds.
In some vehicles such as karts, torque is simply applied evenly to all driving wheels using a simple driveshaft. This works well enough when travelling in a straight line, but when changing direction the outer wheel actually needs to travel further than the inner wheel. Hence, the simple solution results in the inner wheel spinning. For general road use, such a method would result in too much damage to both the tire and road surface.
Differentials are typically comprised of a gear mechanism in which a ring gear receives input power, which is transferred to two side gears by means of a central pinion gear. The pinion gear or gears are mounted to a cage which is affixed to the ring gear. When the ring gear and cage rotate, the pinion gears drive the side gears; the pinion gears are free to rotate about their own axis when either of the side gears meets resistance.
In a motor vehicle, the two side gears may be used to transfer power to the left and right wheels. When the vehicle turns a corner, or one of the wheels encounters resistance, the pinion gears rotate around the side with the most resistance; this rotation drives the other side gear with additional speed.
The most basic differential described above, known as an open differential, suffers from one important problem, however. In an automobile, if one wheel begins to slip while the other maintains traction, the slipping wheel will receive most of the power. This means that if one wheel is spinning on ice while the other is still in contact with the pavement, acceleration of the driveshaft will only cause the slipping wheel to spin faster and very little power will reach the wheel with good traction. Similarly, if one wheel is lifted off the ground, nearly all the power will go to the wheel that is off the ground; not a hopeful prospect for off-road vehicles. Such a loss of traction is sometimes called "diffing out."
One solution to this problem is the limited-slip differential (LSD), one of the most common of which is the clutch-type LSD. With this differential, each of the side gears has a clutch which limits the speed difference between the two wheels. Another solution is the locking differential, which employs a mechanism for allowing the pinion gear to be locked, causing both wheels to turn at the same speed regardless of which has more traction; this is equivalent to removing the differential entirely.
A four-wheel-drive vehicle will have at least two differentials (one for each pair of wheels) and possibly a centre differential to apportion power between the front and rear wheels. Vehicles without a centre differential should not be driven on dry bitumen roads in four wheel drive.
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