A cutaway view of a car final drive
unit which contains the differential
A
differential is a device, usually but not
necessarily employing gears, capable of transmitting
torque and rotation through three shafts, almost
always used in one of two ways. In one way, it receives one input
and provides two outputs; this is found in most automobiles. In the
other way, it combines two inputs to create an output that is the
sum, difference, or average, of the inputs.
In
automobiles and other wheeled
vehicles, the differential allows each of the driving
roadwheels to rotate at different speeds, while for
most vehicles supplying equal torque to each of them. In automotive
applications, the differential housing is sometimes colloquially
called a "pumpkin" as the differential housing typically resembles
a
pumpkin.
Purpose
A vehicle's wheels rotate at different speeds, mainly when turning
corners. The differential is designed to drive a pair of wheels
with equal force, whilst allowing them to rotate at different
speeds. In vehicles without a differential, such as
kart, 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.
History
There are many claims to the invention of the differential gear,
but it is likely that it was known, at least in some places, in
ancient times. Here are some of the milestones in the history of
this device.
- 1050 BC-771 BC:
The Book of Song claimed the
South Pointing Chariot, which
uses a differential gear, was invented during the Western Zhou Dynasty in China.
- 200-100 BC - The antikythera Mechanism: The device is
remarkable for the level of miniaturization and for the complexity
of its parts, which is comparable to that of 18th century clocks.
It has over 30 gears, although Michael Wright (see below) has
suggested as many as 72 gears, with teeth formed through
equilateral triangles, In Greece
- 227 -
239 AD - Despite doubts from fellow ministers at court, Ma Jun from the Kingdom of
Wei in China invents the
first historically verifiable South Pointing Chariot, which
provided cardinal direction as a
non-magnetic, mechanized compass.
- 658, 666 AD - two Chinese Buddhist monks and engineers create
South Pointing Chariots for Emperor
Tenji of Japan.
- 1027, 1107 AD - Documented Chinese reproductions of the South
Pointing Chariot by Yan Su and then Wu Deren, which described in
detail the mechanical functions and gear ratios of the device much
more so than earlier Chinese records.
- 1720 - Joseph Williamson uses a differential gear in a
clock.
- 1810 - Rudolph Ackermann of
Germany invents a four-wheel steering system for carriages, which
some later writers mistakenly report as a differential.
- 1827 -
modern automotive differential patented by watchmaker Onésiphore Pecqueur (1792-1852) of
the Conservatoire des Arts et
Métiers in France for use on a
steam cart. (Sources: Britannica
Online and [29697])
- 1832 - Richard
Roberts of England patents 'gear of compensation', a
differential for road
locomotives.
- 1876 -
James Starley of Coventry invents
chain-drive differential for use on bicycles; invention later used on automobiles by
Karl Benz.
- 1897 - first use of differential on an Australian steam car by David Shearer.
- 1913 - Packard introduces the
spiral-gear differential, which cuts gear noise.
- 1926 - Packard introduces the hypoid
differential, which enables the propeller shaft and its hump in the
interior of the car to be lowered.
- 1958 - Vernon Gleasman patents
the Torsen Dual-Drive Differential, a type of
limited slip differential
that relies solely on the action of gearing instead of a
combination of clutches and gears.
Note:
The Antikythera mechanism
(150 BC - 100 BC),
discovered on an ancient shipwreck near the Greek island of
Antikythera, was once suggested to have employed a differential
gear. This has since been disproved.
Functional description
The following description of a differential applies to a
"traditional" rear-wheel-drive car or truck:
Torque is supplied from the engine, via the
transmission, to a
drive shaft (British term: 'propeller shaft',
commonly and informally abbreviated to 'prop-shaft'), which runs to
the
final drive unit and contains
the differential. A
spiral bevel
pinion gear takes its drive from the end of
the propeller shaft, and is encased within the housing of the final
drive unit. This meshes with the large spiral bevel
ring
gear, known as the
crown wheel. The
crown wheel and pinion may mesh in
hypoid
orientation, not shown. The crown wheel gear is attached to the
differential
carrier or cage, which contains the 'sun' and
'planet' wheels or gears, which are a cluster of four opposed bevel
gears in perpendicular plane, so each bevel gear meshes with two
neighbours, and rotates counter to the third, that it faces and
does not mesh with. The two sun wheel gears are aligned on the same
axis as the crown wheel gear, and drive the axle
half shafts connected to the vehicle's
driven wheels. The other two planet gears are
aligned on a perpendicular axis which changes orientation with the
ring gear's rotation. In the two figures shown above, only one
planet gear (green) is illustrated, however, most automotive
applications contain two opposing planet gears. Other differential
designs employ different numbers of planet gears, depending on
durability requirements. As the differential carrier rotates, the
changing axis orientation of the planet gears imparts the motion of
the ring gear to the motion of the sun gears by pushing on them
rather than turning against them (that is, the same teeth stay in
the same mesh or contact position), but because the planet gears
are not restricted from turning against each other,
within
that motion, the sun gears can counter-rotate relative to the ring
gear and to each other under the same force (in which case the same
teeth do not stay in contact).
Thus, for example, if the car is making a turn to the right, the
main crown wheel may make 10 full rotations. During that time, the
left wheel will make more rotations because it has further to
travel, and the right wheel will make fewer rotations as it has
less distance to travel. The sun gears (which drive the axle
half-shafts) will rotate in opposite directions relative to the
ring gear by, say, 2 full turns each (4 full turns relative to each
other), resulting in the left wheel making 12 rotations, and the
right wheel making 8 rotations.
The rotation of the crown wheel 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 off, and
the drive shaft is held (say leaving the transmission 'in gear',
preventing the ring gear from turning inside the differential),
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
differential movement of the planetary system of gears other than
the minute movements necessary to compensate for slight differences
in wheel diameter, undulations in the road (which make for a longer
or shorter wheel path), etc.
Loss of traction
One undesirable side effect of a conventional differential is that
it can reduce overall
torque - the rotational
force which propels the vehicle. The amount of torque required to
propel the vehicle at any given moment depends on the load at that
instant - how heavy the vehicle is, how much drag and friction
there is, the gradient of the road, the vehicle's momentum, and so
on. For the purpose of this article, we will refer to this amount
of torque as the "threshold torque".
The torque applied to each driving
roadwheel
is a result of the
engine and
transmission applying a twisting
force against the resistance of the
traction at that roadwheel. Unless
the load is exceptionally high, the engine and transmission can
usually
supply as much torque as necessary, so the
limiting factor is usually the traction under each wheel. It is
therefore convenient to define traction as the amount of torque
that can be generated between the
tire and the
road surface, before the wheel starts to slip. If the total
traction under all the driven wheels exceeds the threshold torque,
the vehicle will be driven forward; if not, then one or more wheels
will simply spin.
To illustrate how a differential can limit overall torque, imagine
a simple
rear-wheel drive vehicle,
with one rear roadwheel on asphalt with good grip, and the other on
a patch of slippery ice. With the load, gradient, etc., the vehicle
requires, say, of torque to move forward (i.e. the threshold
torque). Let us further assume that the non-spinning traction on
the ice equates to , and the asphalt to .
If the two roadwheels were driven without a differential, each
roadwheel would be supplied with an equal amount of torque, and
would push against the road surface as hard as possible. The
roadwheel on ice would quickly reach the limit of traction
(400 N·m), but would be unable to spin because the other
roadwheel has good traction. The traction of the asphalt plus the
small extra traction from the ice exceeds the threshold
requirement, so the vehicle will be propelled forward.
With a differential, however, as soon as the "ice wheel" reaches
400 N·m, it will start to spin, and then develop less traction
~300 N·m. The planetary gears inside the differential carrier
will start to rotate because the "asphalt wheel" encounters greater
resistance. Instead of driving the asphalt wheel with more force,
the differential will still symmetrically split the total amount of
available torque equally. ~300 N·m is sufficient to make the
ice wheel to spin, but the equal amount of ~300 N·m is not
enough to turn the asphalt wheel. Since the asphalt wheel remains
stationary, the spinning ice wheel will rotate twice as fast as
before. As the
actual torque on
both roadwheels
is the same - the amount is determined by the
lesser
traction of the ice wheel. So both wheels will get 300 N·m
each. Since 600 N·m is less than the required threshold torque
of 2000 N·m, the vehicle will not be able to utilise the
output from the engine, and will not move.
An observer will simply see one stationary roadwheel on one side of
the vehicle, and one spinning roadwheel on the opposite side. It
will not be obvious that both wheels are generating the same torque
(i.e. both wheels are in fact pushing equally, despite the
difference in rotational speed). This has led to a widely held
misconception that a vehicle with a differential is really only
"one-wheel-drive". In fact, a normal differential always allows the
transmission of equal torque to both driven roadwheels; unless it
is a specific type of differential, such as locking,
torque-biasing, or limited slip type.
A proposed way to distribute the power to the wheels, is to use the
concept of
gearless differential, of which a
review has been reported by Provatidis , but the various
configurations seem to correspond either to the "sliding pins and
cams" type, such as the ZF B-70 available for early VWs, or are a
variation of the
ball
differential.
Traction-aiding devices
ARB, Air Locking Differential
There are various devices for getting more usable traction from
vehicles with differentials.
- One solution is the limited slip differential (LSD),
the most well-known of which is the clutch-type LSD. With this
differential, the side gears are coupled to the carrier via a
multi-disc clutch which allows extra torque to be sent to the wheel
with high resistance than available at the other driven roadwheel
when the limit of friction is reached at that other wheel. Below
the limit of friction more torque goes to the slower (inside)
wheel. If there is no load on one wheel then no torque goes to the
other so the LSD provides no torque except for spring loading, but
some extra effect can be obtained by partially applying the
vehicle's parking brake when one
roadwheel is spinning, as this can provide some resistance there to
increase the overall torque, and allow the
other driven roadwheel to move the vehicle. This only works where
the handbrake acts on the driven wheels, as in the traditional
rear-wheel drive layout. Naturally,
the handbrake should be released as soon as the vehicle is moving
again.
- A locking differential,
such as ones using differential gears in normal use but using air
or electrically controlled mechanical system, which when locked
allow no difference in speed between the two wheels on the axle.
They employ a mechanism for allowing the planetary gears to be
locked relative to each other, causing both wheels to turn at the
same speed regardless of which has more traction; this is
equivalent to effectively bypassing the differential gears
entirely. Other locking systems may not even use differential gears
but instead drive one wheel or both depending on torque value and
direction.
- A high-friction 'Automatic Torque Biasing' (ATB) differential,
such as the Torsen differential, where the
friction is between the gear teeth rather than at added clutches.
This applies more torque to the driven roadwheel with highest
resistance (grip or traction) than is available at the other driven
roadwheel when the limit of friction is reached at that other
wheel. When tested with the wheels off the ground, if one wheel is
rotated with the differential case held, the other wheel will still
rotate in the opposite direction as for an open differential but
there with be some frictional losses and the torque will be
distributed at other than 50/50. Although marketed as being
"torque-sensing", it functions the same as a limited slip
differential.
- A very high-friction differential, such as the ZF "sliding pins
and cams" type, so that there is locking from very high internal
friction. When tested with the wheels off the ground with torque
applied to one wheel it will lock, but it is still possible for the
differential action to occur in use, albeit with considerable
frictional losses, and with the road loads at each wheel in
opposite directions rather than the same (acting with a "locking
and releasing" action rather than a distributed torque).
- An additional function of the conventional electronic traction control systems usually use
the anti-lock braking
system (ABS) roadwheel speed sensors to detect a spinning
roadwheel, and apply the brake to that wheel.
This progressively raises the reaction torque at that roadwheel,
and the differential compensates by transmitting more torque
through the other roadwheel - the one with better traction. In
Volkswagen Group vehicles, this
specific function is called 'Electronic Differential Lock'
(EDL).
- In a four-wheel drive vehicle,
a viscous coupling unit can
replace a centre differential entirely, or be used to limit slip in
a conventional 'open' differential. It works on the principle of
allowing the two output shafts to counter-rotate relative to each
other, by way of a system of slotted plates that operate within a
viscous fluid, often silicone. The fluid
allows slow relative movements of the shafts, such as those caused
by cornering, but will strongly resist high-speed movements, such
as those caused by a single wheel spinning. This system is similar
to a limited slip differential.
A four-wheel drive (4WD) vehicle will have at least two
differentials (one in each
axle for each pair
of driven roadwheels), and possibly a centre differential to
apportion torque between the front and rear axles. In some cases
(eg.
Lancia Delta Integrale,
Porsche 964 Carrera 4 of 1989
[29698]) the centre differential is an
epicyclic differential (see below) to
divide the torque asymmetrically, but at a fixed rate between the
front and rear axle. Other methods utilise an 'Automatic Torque
Biasing' (ATB) centre differential, such as a
Torsen - which is what
Audi use
in their
quattro
cars (with
longitudinal
engines).
4WD vehicles without a centre differential should not be driven on
dry, paved roads in four-wheel drive mode, as small differences in
rotational speed between the front and rear wheels cause a torque
to be applied across the
transmission. This phenomenon is
known as "wind-up", and can cause considerable damage to the
transmission or drive train. On loose surfaces these differences
are absorbed by the tire slippage on the road surface.
A
transfer case may also incorporate a
centre differential, allowing the drive shafts to spin at different
speeds. This permits the four-wheel drive vehicle to drive on paved
surfaces without experiencing "wind-up".
Epicyclic differential
An epicyclic differential uses
epicyclic gearing to split and apportion
torque asymmetrically between the front and
rear axles. An epicyclic differential is at the heart of the
Toyota Prius automotive drive train,
where it interconnects the engine, motor-generators, and the drive
wheels (which have a second differential for splitting torque as
usual). It has the advantage of being relatively compact along the
length of its axis (that is, the sun gear shaft).
Epicyclic gears are also called planetary gears because the axes of
the planet gears revolve around the common axis of the sun and ring
gears that they mesh with and roll between. In the image, the
yellow shaft carries the sun gear which is almost hidden. The blue
gears are called planet gears and the pink gear is the ring gear or
annulus.
Spur-gear differential
This is another type of differential that was used in some early
automobiles, more recently the
Oldsmobile Toronado, as well as other
non-automotive applications. It consists of
spur gears only.
A spur-gear differential has two equal-sized spur gears, one for
each half-shaft, with a space between them. Instead of the
Bevel gear, also known as a miter gear, assembly
(the "spider") at the centre of the differential, there is a
rotating carrier on the same axis as the two shafts. Torque from a
prime mover or
transmission, such as the drive
shaft of a car, rotates this carrier.
Mounted in this carrier are one or more pairs of identical pinions,
generally longer than their diameters, and typically smaller than
the spur gears on the individual half-shafts. Each pinion pair
rotates freely on pins supported by the carrier. Furthermore, the
pinions pairs are displaced axially, such that they mesh only for
the part of their length between the two spur gears, and rotate in
opposite 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 individual wheel axles is the
same as that in a miter-gear differential.
Non-automotive applications
A differential gear train can also be used to allow a difference
between two input axles.
Mills often used such
gears to apply torque in the required axis. It's also used in fine
mechanical watches with a hand to show the amount of reserve power
in the mainspring.
The oldest known example of a differential was once thought to be
in the
Antikythera mechanism.
It was supposed to have used such a train to produce the difference
between two inputs, one input related to the position of the
sun on the
zodiac, and the
other input related to the position of the
moon
on the zodiac; the output of the differential gave a quantity
related to the moon's
phase. It has now
been proven that the assumption of the existence of a differential
gearing arrangement was incorrect.
In the first half of the twentieth century, mechanical
analog computers, called
differential analyzers, were
constructed that used differential gear trains to perform
addition and
subtraction. The U.S. Navy Mk.1 gun fire control
computer used about 160 differentials of the miter gear type.
Active differentials
A relatively new technology is the electronically-controlled
'active differential'. An
electronic control unit (ECU) uses
inputs from multiple sensors, including
yaw rate, steering input angle, and lateral
acceleration - and adjusts the distribution of
torque to compensate for undesirable handling
behaviours like
understeer. Active
differentials used to play a large role in the
World Rally Championship, but in
the 2006 season the
FIA has limited the use of
active differentials only to those drivers who have not competed in
the
World Rally
Championship in the last five years.
Fully integrated active differentials are used on the
Ferrari F430,
Mitsubishi Lancer Evolution, and
on the rear wheels in the
Acura RL. A
version manufactured by
ZF is
also being offered on the latest
Audi S4
and
Audi A4.
The second constraint of the differential is passive – it is
actuated by the friction kinematics chain through the ground. The
difference in torque on the roadwheels and tires (caused by turns
or bumpy ground) drives the second
degree of freedom,
(overcoming the torque of inner friction) to equalise the driving
torque on the tires. The sensitivity of the differential depends on
the inner friction through the second degree of freedom. All of the
differentials (so called “active” and “passive”) use clutches and
brakes for restricting the second degree of freedom, so all suffer
from the same disadvantage – decreased sensitivity to a dynamically
changing environment. The sensitivity of the ECU controlled
differential is also limited by the time delay caused by sensors
and the response time of the actuators.
See also
References
- Provatidis, Christopher, G. (2003). "A critical presentation of
Tsiriggakis’ gearless differential". Mobility & Vehicles
Mechanics 29 (4): 25-46; also at
http://www.tsiriggakis.com/gd.html
- "ZF Press release"
External links