02-02-2013, 04:28 PM
Differential (mechanical device)
Differential.rtf (Size: 36.07 KB / Downloads: 33)
INTRODUCTION
A differential is a device, usually, but not necessarily, employing gears, which is connected to the outside world by three shafts, through which it transmits torque and rotation. The gears or other components make the three shafts rotate in such a way that \scriptstyle a=pb+qc, where \scriptstyle a, \scriptstyle b, and \scriptstyle c are the angular velocities of the three shafts, and \scriptstyle p and \scriptstyle q are constants. Often, but not always, \scriptstyle p and \scriptstyle q are equal, so \scriptstyle a is proportional to the sum (or average) of \scriptstyle b and \scriptstyle c. Except in some special-purpose differentials, there are no other limitations on the rotational speeds of the shafts, apart from the usual mechanical/engineering limits. Any of the shafts can be used to input rotation, and the other(s) to output it. See animation here of a simple differential in which \scriptstyle p and \scriptstyle q are equal. The shaft rotating at speed \scriptstyle a is at the bottom-right of the image.
In automobiles and other wheeled vehicles, a differential allows the driving roadwheels to rotate at different speeds. This is necessary when the vehicle turns, making the wheel that is travelling around the outside of the turning curve roll farther and faster than the other. The engine is connected to the shaft rotating at angular velocity \scriptstyle a. The driving wheels are connected to the other two shafts, and \scriptstyle p and \scriptstyle q are equal. If the engine is running at a constant speed, the rotational speed of each driving wheel can vary, but the sum (or average) of the two wheels' speeds can not change. An increase in the speed of one wheel must be balanced by an equal decrease in the speed of the other. (If one wheel is rotating backward, which is possible in very tight turns, its speed should be counted as negative.)
Purpose
A vehicle's wheels rotate at different speeds, mainly when turning corners. The differential is designed to drive a pair of wheels 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 needs to travel a shorter distance than the outer wheel, so with no differential, the result is the inner wheel spinning and/or the outer wheel dragging, and this results in difficult and unpredictable handling, damage to tires and roads, and strain on (or possible failure of) the entire drivetrain.
Functional description
Input torque is applied to the ring gear (blue), which turns the entire carrier (blue). The carrier is connected to both sun gears (red and yellow) only through the planet gear (green). Torque is transmitted to the sun gears through the planet gear. The planet gear revolves around the axis of the carrier, driving the sun gears. If the resistance at both wheels is equal, the planet gear revolves without spinning about its own axis, and both wheels turn at the same rate.
If the left sun gear (red) encounters resistance, the planet gear (green) spins as well as revolving, allowing the left sun gear to slow down, with an equal speeding up of the right sun gear (yellow).