Differential (Mechanical Device)
Differential (Mechanical Device)
ZF Dierential. The drive shaft enters from the front and the
driven axles run left and right.
1 Overview
Car dierential of a koda 422
1
2 2 HISTORY
3 Epicyclic dierential displaced axially, such that they mesh only for the part of
their length between the two spur gears, and rotate in op-
posite directions. The remaining length of a given pinion
meshes with the nearer spur gear on its axle. Therefore,
each pinion couples that spur gear to the other pinion, and
in turn, the other spur gear, so that when the drive shaft
rotates the carrier, its relationship to the gears for the in-
dividual wheel axles is the same as that in a bevel-gear
dierential.
A spur gear dierential is constructed from two identical
coaxial epicyclic gear trains assembled with a single car-
rier such that their planet gears are engaged. This forms
a planetary gear train with a xed carrier train ratio R =
Epicyclic gearing is used here to apportion torque asymmetrically. 1.
The input shaft is the green hollow one, the yellow is the low
In this case, the fundamental formula for the planetary
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
gear train yields,
arm of the pink one is 2 to 3 as big, the torque will be 2 to
3 as high.
s c
= 1,
An epicyclic dierential can use epicyclic gearing to split a c
and apportion torque asymmetrically between the front or
and rear axles. An epicyclic dierential is at the heart
of the Toyota Prius automotive drive train, where it in-
terconnects the engine, motor-generators, and the drive 1
c = (s + a ).
wheels (which have a second dierential for splitting 2
torque as usual). It has the advantage of being relatively Thus, the angular velocity of the carrier of a spur gear
compact along the length of its axis (that is, the sun gear dierential is the average of the angular velocities of the
shaft). sun and annular gears.[6]
Epicyclic gears are also called planetary gears because the In discussing the spur gear dierential, the use of the term
axes of the planet gears revolve around the common axis annular gear is a convenient way to distinguish the sun
of the sun and ring gears that they mesh with and roll gears of the two epicyclic gear trains. The second sun gear
between. In the image, the yellow shaft carries the sun serves the same purpose as the annular gear of a simple
gear which is almost hidden. The blue gears are called planetary gear train, but clearly does not have the internal
planet gears and the pink gear is the ring gear or annulus. gear mate that is typical of an annular gear.
Ring gears are also used in starter motors.
5 Non-automotive applications
4 Spur-gear dierential
Chinese south-pointing chariots may also have been very
early applications of dierentials. The chariot had a
This is another type of dierential that was used in some pointer which constantly pointed to the south, no mat-
early automobiles, more recently the Oldsmobile Toron-
ter how the chariot turned as it travelled. It could there-
ado, as well as other non-automotive applications. It con- fore be used as a type of compass. It is widely thought
sists of spur gears only. that a dierential mechanism responded to any dierence
A spur-gear dierential has two equal-sized spur gears, between the speeds of rotation of the two wheels of the
one for each half-shaft, with a space between them. In- chariot, and turned the pointer appropriately. However,
stead of the Bevel gear, also known as a miter gear, as- the mechanism was not precise enough, and, after a few
sembly (the spider) at the centre of the dierential, miles of travel, the dial could have very well been pointing
there is a rotating carrier on the same axis as the two in the complete opposite direction.
shafts. Torque from a prime mover or transmission, such The earliest denitely veried use of a dierential was in
as the drive shaft of a car, rotates this carrier. a clock made by Joseph Williamson in 1720. It employed
Mounted in this carrier are one or more pairs of iden- a dierential to add the equation of time to local mean
tical pinions, generally longer than their diameters, and time, as determined by the clock mechanism, to produce
typically smaller than the spur gears on the individual solar time, which would have been the same as the reading
half-shafts. Each pinion pair rotates freely on pins sup- of a sundial. During the 18th Century, sundials were con-
ported by the carrier. Furthermore, the pinion pairs are sidered to show the correct time, so an ordinary clock
4 6 APPLICATION TO VEHICLES
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 (yel-
Hypoid gear pair that connects an automotive drive shaft to a low).
dierential.
right wheel making 8 rotations.
7 Functional description The rotation of the ring gear is always the average of the
rotations of the side sun gears. This is why if the driven
roadwheels are lifted clear of the ground with the engine
o, and the drive shaft is held (say, leaving the transmis-
sion in gear preventing the ring gear from turning inside
the dierential), manually rotating one driven roadwheel
causes the opposite roadwheel to rotate in the opposite
direction by the same amount.
When the vehicle is traveling in a straight line there will
be no dierential movement of the planetary system of
gears other than the minute movements necessary to com-
pensate for slight dierences in wheel diameter, undula-
tions in the road which make for a longer or shorter wheel
path, etc.
Input torque is applied to the ring gear (blue), which turns the
entire carrier (blue). The carrier is connected to both sun gears 8 Loss of traction
(red and yellow) only through the planet gear (green). Torque is
transmitted to the sun gears through the planet gear. The planet
One undesirable side eect of an open dierential is that
gear revolves around the axis of the carrier, driving the sun gears.
it can limit traction under less than ideal conditions. The
If the resistance at both wheels is equal, the planet gear revolves
amount of traction required to propel the vehicle at any
without spinning about its own axis, and both wheels turn at the
same rate. given moment depends on the load at that instanthow
heavy the vehicle is, how much drag and friction there is,
The following description of a dierential applies to a tra- the gradient of the road, the vehicles momentum, and so
ditional rear-wheel-drive car or truck with an open or lim- on.
ited slip dierential combined with a reduction gearset The torque applied to each driving wheel is the result of
using bevel gears (these are not strictly necessary see the engine, transmission, and drive axle applying a twist-
spur-gear dierential): ing force against the resistance of the traction at that road-
Thus, for example, if the car is making a turn to the right, wheel. In lower gears, and thus at lower speeds, and un-
the main ring gear may make 10 full rotations. During less the load is exceptionally high, the drivetrain can sup-
that time, the left wheel will make more rotations because ply as much torque as necessary, so the limiting factor
it has farther to travel, and the right wheel will make fewer becomes the traction under each wheel. It is therefore
rotations as it has less distance to travel. The sun gears convenient to dene traction as the amount of force that
(which drive the axle half-shafts) will rotate at dierent can be transmitted between the tire and the road surface
speeds relative to the ring gear (one faster, one slower) by, before the wheel starts to slip. If the torque applied to
say, 2 full turns each (4 full turns relative to each other), one of the drive wheels exceeds the threshold of traction,
resulting in the left wheel making 12 rotations, and the then that wheel will spin, and thus provide torque only
6 9 ACTIVE DIFFERENTIALS
tires (caused by turns or bumpy ground) drives the sec- by its freewheel. Thus, while turning, the vehicle
ond degree of freedom, (overcoming the torque of inner had only one driving wheel. Driving in reverse is im-
friction) to equalise the driving torque on the tires. The possible as is engine braking due to the freewheels.
sensitivity of the dierential depends on the inner friction
through the second degree of freedom. All of the dier- Vehicles with two continuously variable transmis-
entials (so called active and passive) use clutches and sions, such as the DAF Daodil. The Daodil,
brakes for restricting the second degree of freedom, so all and other similar vehicles which were made until
suer from the same disadvantagedecreased sensitivity the 1970s by the Dutch company DAF, had a type
to a dynamically changing environment. The sensitivity of transmission that used an arrangement of belts
of the ECU controlled dierential is also limited by the and pulleys to provide an innite number of gear ra-
time delay caused by sensors and the response time of the tios. The engine drove two separate transmissions
actuators. which ran the two driving wheels. When the vehi-
cle turned, the two wheels could rotate at dierent
speeds, making the two transmissions shift to dif-
ferent gear ratios, thus functionally substituting for
10 Automobiles without dieren- a dierential. The slower moving wheel received
tials more driving torque than the faster one, so the sys-
tem had limited-slip characteristics. The duplica-
Although most automobiles in the developed world use tion also provided redundancy. If one belt broke,
dierentials there are a few that do not. Several dierent the vehicle could still be driven.
types exist: Light vehicles with closely spaced rear wheels, such
as the Isetta and Opperman Unicar, or very low mass
Race cars and trucks in certain classes. Drag racing vehicles.
is done in a straight line (and often on a prepared
surface), which obviates the need for a dierential. Vehicles with separate motors for the driving
A spool is used to make a solid connection between wheels. Electric cars can have a separate motor
both drive wheels, which is simpler and less likely for each driving wheel, eliminating the need for a
to break under very heavy acceleration. Racing on dierential, but usually with some form of gearing
dirt or mud tracks also allows the use of spools, be- at each motor to get the large wheel torques nec-
cause the loose surface gives way while cornering. essary. A multi-motor electric vehicle such as the
NASCAR mandates the use of spools in their cars, Dual Motor Tesla Model S can electronically con-
which does cause axle wind-up, and degrades han- trol the power distribution between the motors on a
dling in turns. Other forms of racing without dif- millisecond scale, in this case acting as a centre dif-
ferentials include tractor pulling, mud bogging, and ferential where open dierentials are still employed
other 4x4 motorsports where dierential action is left-to-right.[13]
not needed.
Vehicles with a single driving wheel. Besides mo- 11 See also
torcycles, which are generally not classied as au-
tomobiles, this group includes most three-wheeled Ball dierential
cars. These were quite common in Europe in the
mid-20th Century, but have now become rare there. Equation clock
They are still common in some areas of the develop-
Hermann Aron#Electricity meters
ing world, such as India. Some early four-wheeled
cars also had only one driving wheel to avoid the Limited slip dierential
need for a dierential. However, this arrangement
led to many problems. The system was unbalanced, Locking dierential
the driving wheel would easily spin, etc.. Because Torque vectoring
of these problems, few such vehicles were made.
Whippletree (mechanism)
Vehicles using two freewheels. A freewheel, as used
on a pedal bicycle for example, allows a road wheel Tests on rollers
to rotate faster than the mechanism that drives it, al-
lowing a cyclist to stop pedalling while going down-
hill. Some early automobiles had the engine driv- 12 References
ing two freewheels, one for each driving road wheel.
When the vehicle turned, the engine would continue [1] Wright, M. T. (2007). The Antikythera Mechanism re-
to drive the wheel on the inside of the curve, but the considered (PDF). Interdisciplinary science reviews. 32
wheel on the outside was permitted to rotate faster (1). Retrieved 20 May 2014.
8 13 EXTERNAL LINKS
13 External links
A video of a 3D model of an open dierential
An article explaining dierentials with illustrations
and video
Around the Corner (1937), a Jam Handy lm
made for Chevrolet explaining very clearly how an
open dierential works.
14.2 Images
File:13-04-05-Skoda_Museum_Mlad_Boleslav_by_RalfR-009.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/2f/
13-04-05-Skoda_Museum_Mlad%C3%A1_Boleslav_by_RalfR-009.jpg License: CC BY 3.0 Contributors: Own work Original artist:
Dieses Foto ist von Ralf Roletschek
File:20-TallyTakeupDrive.JPG Source: https://upload.wikimedia.org/wikipedia/commons/4/4f/20-TallyTakeupDrive.JPG License:
CC0 Contributors: Own work Original artist: Douglas W. Jones
File:ARB_Air_Locking_Differential_(RLH).JPG Source: https://upload.wikimedia.org/wikipedia/commons/c/c9/ARB_Air_
Locking_Differential_%28RLH%29.JPG License: CC BY-SA 3.0 Contributors: Own work Original artist: Richard Harvey
File:Around_the_Corner_(1937)_24fps_selection.webm Source: https://upload.wikimedia.org/wikipedia/commons/3/3e/Around_
the_Corner_%281937%29_24fps_selection.webm License: Public domain Contributors: http://archive.org/details/Aroundth1937 Origi-
nal artist: Handy (Jam) Organization
File:BAUMA_2004_ZF_Differentialgetriebe.jpg Source: https://upload.wikimedia.org/wikipedia/commons/a/ad/BAUMA_2004_
ZF_Differentialgetriebe.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Aconcagua (<a href='//commons.wikimedia.
org/wiki/User_talk:Aconcagua' title='User talk:Aconcagua'>talk</a>)
File:ChartDriveDetail.JPG Source: https://upload.wikimedia.org/wikipedia/commons/b/ba/ChartDriveDetail.JPG License: CC0 Con-
tributors: Own work Original artist: Douglas W. Jones
File:Commons-logo.svg Source: https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg License: PD Contributors: ? Origi-
nal artist: ?
File:Differential_(Manual_of_Driving_and_Maintenance).jpg Source: https://upload.wikimedia.org/wikipedia/commons/3/3b/
Differential_%28Manual_of_Driving_and_Maintenance%29.jpg License: Public domain Contributors: Scan from (1937) Manual of
Driving and Maintenance for Mechanical Vehicles (Wheeled), HMSO Original artist: Andy Dingley (scanner)
File:Differential_free.png Source: https://upload.wikimedia.org/wikipedia/commons/6/61/Differential_free.png License: CC-BY-SA-
3.0 Contributors: en:Image:Differential_free.png. This image was originally uploaded on en.wikipedia.org by user: Wapcaplet. Original
artist: Wapcaplet
File:Differential_locked-2.png Source: https://upload.wikimedia.org/wikipedia/commons/5/5a/Differential_locked-2.png License:
CC-BY-SA-3.0 Contributors:
Dierential_locked.png Original artist: Dierential_locked.png: Wapcaplet
File:Differentialgetriebe2.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/fe/Differentialgetriebe2.jpg License: CC-
BY-SA-3.0 Contributors: Own work Original artist: DrJunge
File:Epicyclic_gear_ratios.png Source: https://upload.wikimedia.org/wikipedia/commons/d/d5/Epicyclic_gear_ratios.png License: CC-
BY-SA-3.0 Contributors: ? Original artist: ?
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sa-3.0 Contributors: ? Original artist: ?
File:Portal-puzzle.svg Source: https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg License: Public domain Contributors: ?
Original artist: ?
10 14 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES