A differential gear is an arrangement of beveled gears in such a manner such that the input torsion is taken up by a ring gear and distributed equally through two planetary gears to the side gears which drive the shafts on either side.
One of the common applications of differential gears is in automobiles. Consider a vehicle following a curved path. As one can easily imagine, the inner wheel covers a shorter distance than the outer wheel. In case the system consists of only a single shaft connecting the inner and outer wheel, both the wheels are forced to turn at the same angular momentum and hence makes turning difficult leading to slippage and binding of tires. In addition to this, the strain on the inner wheels is passed on to the outer wheels through the axle putting undue strain on it.
This problem is solved by using the differential gear system. In this, the power of the engine is transferred through a drive shaft and pinion arrangement to the ring gear and the torque is further split by the differential gears into two components such that the outer wheel spins at greater angular momentum than the inner wheel. This eliminates slippage of the wheels and strain on the axle.
However simple differential gears have one major disadvantage. If the inner and outer wheels are on surfaces of unequal roughness, the wheel on the smoother surface spins with a higher angular momentum. Since the differential splits the torque equally, the wheel on rougher surface will decrease in angular momentum and hence the vehicle will move at a very low speed or may not move at all. In case the difference in traction is too large i.e. when one of the wheels is off road, torque from the wheel on the road will be transferred to the wheel that is off the surface and it will spin at double angular momentum. Hence the vehicle will remain stationary.
In order to solve this problem, we need to transfer more of the torque to the stationary wheels. LSD, viscous coupling and torsen(R) are some of the technique used for the transfer of torque.
LSD Limited Slip Differential consists of a series of coupled clutches which limit the difference in the rotation of the inner and outer wheels to a specific limit.
Viscous Coupling In this system, a liquid whose viscosity increases on agitation is coupled with perforated metal discs which help in limiting the differential action above a particular ratio.
TORSEN(R) It is a proprietary system designed by Zexel Torsen Inc. When one of the wheel losses traction the difference in torque causes the gears to bind together thus reducing the differential action.