Differential (mechanical device)

Called The differential (or differential gear ), also differential gear or short differential (or differential ), is a planetary gear system with a drive and two output drives ( transfer gearbox ).

• 5.1 kinematics

History

In coming from the ancient Antikythera mechanism, the basic type is included epicyclic gearbox, which was used before as a summing. The differential is a distribution epicyclic gear train and first detected at Leonardo da Vinci. As differential gear for vehicles it was invented by Frenchman Onésiphore Pecqueur (1792-1852) in 1827.

Application

Most often, the differential is used as axle differential in automobiles. There, its purpose is two wheels to drive so that they can rotate at different speeds but with the same driving force in curves.

The same purpose, the central differential in four-wheel drive vehicles in which the power to two or more driven axles is to be distributed.

Design and operation

The differential gear has as its basic type with an internally toothed ring gear ( first image below) three coaxial shafts. Its special feature is that the level translation the value i0 = -1 usually has. As a prior translation, the gear ratio between the two central shafts is called when the Umlaufradträger ( web, cage or basket ) is held. The transmission then is no different from the so-called stationary gear that has no rotating shafts. With i0 = -1 the gear distributed in the three- wave operation, the output power from the jetty on the two central shafts, each with the same high torque. Because the two driven wheels are the same size, the transmission structure symmetrical ( two to five photos, below).

Bevel differential gear, operating status: same speeds of the driven shafts

Bevel differential gear, operating status: a shaft not the other doubly fast rotation

Not shown spur gear differential gear, driving the Umlaufradträgers

Helical gear differential gear

The bevel gear differential gear (second and third picture ) comes with four wheels and is most commonly used. Inside the Umlaufradträgers (also referred to as a cage or basket ) the bevel gear is symmetrical: Right and left is each one connected to the driven shafts bevel gear. About the scope of the basket carries several, meshing with the driven bevel gears, bevel gears (usually two). A rare variant contains the bevel gears related crown wheels.

Designs with larger wheels number are helical differential gear (fourth picture) and helical differential gear (fifth image ), in which the planet gears each have two inter- meshing gears.

In all types of Umlaufradträger is designed ring-or box-shaped. Mostly it is a further gear stage, the one wheel is attached to it, driven. But it can also be driven via a hollow shaft.

Differential gear in the car

Axle differential

Is used in the differential gear of a driven axle of a motor vehicle, it is referred to as axle differential. It provides for the equalization of the rotational speeds between the two wheels. His status translation is i0 = -1. If you hold the Umlaufradträger (eg by engaging a gear with the engine off ), the wheels raises and turns on one of the wheels, then the other rotates at the same speed but in the opposite direction.

Central or longitudinal differential

For vehicles in which all wheels are driven ( four wheel drive ), another transfer case are required: first, an axle differential per each additional driven shaft, also central or longitudinal differentials for the distribution of the motor drive on several axes. A four wheel drive vehicle having two axle differentials and a central differential.

Central differentials as axle differentials can have a stationary ratio of i0 = -1. Their torque distribution between the axles is 1:1 or 50% to 50 %. However, there are also built central differentials of 1:1 differing state translation. The rear axle often receives a higher torque than the front, which is an advantage when accelerating and on inclines. The distribution is for example 65% to 35%. Such asymmetrically acting differential is unbalanced built such as the epicyclic gearbox with ring gear ( picture above series: first image; driven is the bridge).

Axle differentials in motor vehicles

The differential mechanism is located generally between the wheels. The Umlaufradträger is almost always fixed to a wheel of a driving gear stage. This is a spur gear with a transverse engine, with a longitudinally installed engine a bevel gear and drive through a propeller shaft is almost always a hypoid gear. In the latter case, the axes of pinion and crown cutting equipment, the cardan shaft is slightly lower. Before asserted itself the hypoid gearing, there were worm gearbox ( Peugeot).

The driven shafts lead to the wheels. Both wheels are driven with the same high torque, even if they do - turn at different rates - such as when cornering. At the same quick turning the wheels of the differential gear no power loss and no wear cause as they questioned among themselves do not move. If one of the wheels are quite so turns the other twice as fast as the Umlaufradträger (third picture). This occurs at the start-up, namely, when one of the two wheels loses the static friction with the ground, such as on mud, snow, and the like. This wheel spins then "through" and both wheels forward driving torque transmitted no more. Even in fast cornering, the inner wheel can be relieved to the extent that it is spinning. A limited slip differential can prevent this: The balancing effect is rigidly connecting the two drive shafts is prohibited ( full lock) or reduced by specific friction. In the latter case, a part of the power to the driving wheel is output, and implement transmission of the rest of the heat. Full lock there is almost only in off-road vehicles. With activated lock the wheels turn at the same speed, the torque is distributed to the wheels depending on traction. If they are used on the road or other good ground, the drivetrain can tense up and take damage, since the different path lengths can be taken only by the slip of the tire when cornering.

The popular in action movies stunt to balance a car while riding on two wheels does not work with a normal differential. The spa located in the air driving wheel makes the other the same effect as it would on a smooth floor.

Kinematics

The speed basic equation ( Willis equation)

The planetary gear is simplified with the stationary gear to

This means that in any operating condition, the sum of the speeds of the two driven wheels (index 1 and 2 ) is equal to twice the speed of the Umlaufradträgers ( subscript S ), or that the speed of Umlaufradträgers is the arithmetic mean of the wheel speeds.