chainless cycle.docx

8/19/2019 Chainless cycle.docx

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ABSTRACT

This project making of the shaft driven chainless bicycle instead

of simple chain drive bicycle.7 This idea is consistence

performance. Stress analysis on gear and simulation. A shaft-

driven bicycle is a chainless bicycle that uses a drive shaft

instead of a chain to transmit power from the pedals to the

wheel. Shaft drives were introduced over a century ago, but

were mostly supplanted by chain-driven bicycles due to the

gear ranges possible with sprockets and derailleur. ecently,

due to advancements in internal gear technology, a small

number of modern shaft-driven bicycles have been introduced.

http://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Bicycle_chainhttp://en.wikipedia.org/wiki/Derailleurhttp://en.wikipedia.org/wiki/Bicycle_chainhttp://en.wikipedia.org/wiki/Derailleurhttp://en.wikipedia.org/wiki/Drive_shaft


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INTRODUCTION

A shaft-driven bicycle is a bicycle that uses a drive

shaft instead of a chain to transmit power from the pedals to

the wheel. Shaft drives were introduced over a century ago, but

were mostly supplanted by chain-driven bicycles due to the

gear ranges possible with sprockets and derailleur. ecently,



Shaft-driven bikes have a large bevel gear where a

conventional bike would have its chain ring. This meshes with

another bevel gear mounted on the drive shaft. The use of

bevel gears allows the a!is of the drive tor"ue from the pedals

to be turned through #$ degrees. The drive shaft then has

another bevel gear near the rear wheel hub which meshes with

a bevel gear on the hub where the rear sprocket would be on a

conventional bike, and cancelling out the %rst drive tor"ue

change of a!is.

An automotive drive shaft transmits power from the engine tothe di&erential gear of a rear wheel drive vehicle. The driveshaft is usually manufactured in two pieces to increase thefundamental bending natural fre"uency because the bendingnatural fre"uency of a shaft is inversely proportional to thes"uare of beam length and proportional to the s"uare root of

speci%c modulus which increases the total weight of anautomotive vehicle and decreases fuel e'ciency. So, a singlepiece drive shaft is preferred here and the material of it isconsidered to be Titanium alloy because of its high strengthand low density. (rive shafts are carriers of tor"ue and aresubject to torsion and shear stress, e"uivalent to the di&erencebetween the input tor"ue and the load. They must therefore bestrong enough to bear the stress, whilst avoiding too muchadditional weight as that would in turn increase their inertia.

)arker *anni%n is a motion and control technologiescorporation+ in $$ they started the hainless hallenge, it is

http://en.wikipedia.org/wiki/Bicyclehttp://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Bicycle_chainhttp://en.wikipedia.org/wiki/Bevel_gearhttp://en.wikipedia.org/wiki/Chainringhttp://en.wikipedia.org/wiki/Gearhttp://en.wikipedia.org/wiki/Bicyclehttp://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Bicycle_chainhttp://en.wikipedia.org/wiki/Bevel_gearhttp://en.wikipedia.org/wiki/Chainringhttp://en.wikipedia.org/wiki/Gear


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a competition that was inspired by the cycling community.Since a large portion of )arker/s business focuses on hydraulicsthey decided to merge the two ideas into a competition. Thiscompetition rules are fairly simple develop a 0$$1 human

powered bicycle without using any chains to transfer power. This competition was primarily aimed towards students of universities as a senior design project. 2ach university chosento compete selects a group of -3 seniors to participate. Thesestudents start from scratch and design either a hydraulically orpneumatically powered bike to compete in several di&erentraces. There was an endurance race, an e'ciency race, and asprint race. The endurance race was an 3 mile course. Thee'ciency race deals with utili4ing an accumulator to store

energy for a later use. The sprint race was 0$$ meter dash tothe %nish. 2ach team needs to work together to create a bikethat works the best in each race in order to win the hainlesshallenge.

This year/s team had four members on it, so the bikedevelopment was split into three sections+ hris lark and5a!ton 6own were working the hydraulic power train, randonandal was assigned on the braking system, and 8ick 5acaluso

was assigned to the bike frame.

Components

1. Bicycle Chassis2. Drive shaft. Bevel !ear".


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#istory

The %rst shaft drives for cycles appear to have been invented

independently in 03#$ in the 9nited States and 2ngland. A.:ear head, of ;< aledonian oad, 8orth 6ondon developed

one in 03#$ and received a patent in =ctober 03#0.*is

prototype shaft was enclosed within a tube running along the

top of the chain stay+ later models were enclosed within the

actual chain stay. >n the 9nited States, $alter Stillman %led

for a patent on a shaft-driven bicycle on (ec. 0$, 03#$ whichwas granted on ?uly 0, 03#0.

The shaft drive was not well accepted in 2ngland, so in 03#<

:earn head took it to the 9SA where olonel )ope of the

olumbia %rm bought the e!clusive American rights. elatedly,the 2nglish makers took it up, with *umber in particular

plunging heavily on the deal. uriously enough, the greatest of

all the @ictorian cycle engineers, )rofessor Archibald Sharp, was

against shaft drive+ in his classic 03# book Bicycles and

TricyclesB, he writes BThe :earn head Cear.... if bevel-wheels

could be accurately and cheaply cut by machinery, it is possible


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that gears of this description might supplant, to a great e!tent,

the chain-drive gear+ but the fact that the teeth of the bevel-

wheels cannot be accurately milled is a serious obstacle to their

practical successB.

>n the 9SA, they had been made by the 6eague ycle ompany

as early as 03#;. Soon after, the :rench company 5etropole

marketed their Acatane. y 03#7 olumbia began aggressively

to market the chainless bicycle it had ac"uired from the 6eague

ycle ompany. hainless bicycles were moderately popular in

03#3 and 03##, although sales were still much smaller than

regular bicycles, primarily due to the high cost. The bikes were

also somewhat less e'cient than regular bicyclesD there was

roughly an 3 percent loss in the gearing, in part due to limited

manufacturing technology at the time. The rear wheel was also

more di'cult to remove to change Eats. 5any of these

de%ciencies have been overcome in the past century.

>n 0#$, The *ill-limber icycle 5fg. ompany sold a three-

speed shaft-driven bicycle in which the shifting was

implemented with three sets of bevel gears.F Ghile a small

number of chainless bicycles were available, for the most part,

shaft-driven bicycles disappeared from view for most of the

$th century. There is, however, still a niche market

for chainless bikes, especially for commuters, and there are a

number of manufacturers who o&er them either as part of a


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larger range or as a primary speciali4ation. A notable e!ample

is io mega in (enmark.

%&rpose of the Drive Shaft

The tor"ue that is produced from the engine and transmission

must be transferred to the rear wheels to push the vehicle

forward and reverse. The drive shaft must provide a smooth,

uninterrupted Eow of power to the a!les. The drive shaft and

di&erential are used to transfer this tor"ue.

'&nctions of the Drive Shaft

aH :irst, it must transmit tor"ue from the transmission to the

di&erential gear bo!.

bH (uring the operation, it is necessary to transmit ma!imum

low-gear tor"ue developed by the engine.

cH The drive shafts must also be capable of rotating at the

very fast speeds re"uired by the vehicle.

dH The drive shaft must also operate through constantly

changing angles between the transmission, the di&erential

and the a!les. As the rear wheels roll over bumps in the

road, the di&erential and a!les move up and down. This

movement changes the angle between the transmission

and the di&erential.

http://en.wikipedia.org/wiki/Biomega_(bicycles)http://en.wikipedia.org/wiki/Biomega_(bicycles)


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eH The length of the drive shaft must also be capable of

changing while transmitting tor"ue. 6ength changes are

caused by a!le movement due to tor"ue reaction, road

deEections, braking loads and so on. A slip joint is used to

compensate for this motion. The slip joint is usually made

of an internal and e!ternal spline. >t is located on the front

end of the drive shaft and is connected to the

transmission.

8ow days all automobiles Iwhich are having front engine rearwheel driveH have the transmission shaft as shown in %gure. A

pair of short drive shafts is commonly used to send power from

a central di&erential, transmission, or transa!le to the wheels.

Two piece drive shaft increases the weight of drive shaft which

is not desirable in today/s market. 5any methods are available

at present for the design optimi4ation of structural systems and

these methods based on mathematical programming

techni"ues involving gradient search and direct search.

The reduction in weight of the drive system is advantageous in

overall weight reduction of automobiles which is a highly

desirable goal of design engineer.


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Fig.1.2(a) 3D model of a drive shaft Fig.1.2(b) Position of

Drive Shaft

(IT)RATUR) R)*I)$

Intro+&ction

(rive shafts are carriers of tor"ue+ they are subject to torsion

and shear stress, which represents the di&erence between the

input force and the load. They thus need to be strong enough to

bear the stress, without imposing too great an additional inertia

by virtue of the weight of the shaft. 5ost automobiles today use

rigid driveshaft to deliver power from a transmission to the

wheels. A pair of short driveshaft is commonly used to send

power from a central di&erential, transmission, or transa!ie to

the wheels. There are di&erent types of drive shafts in

Automotive >ndustryD

aH 0 piece driveshaft

bH piece driveshaft

cH Slip in Tube driveshaft

The Slip in Tube (riveshaft is the new type which also helps in

rash 2nergy 5anagement. >t can be compressed in case of

crash. >t is also known as a collapsible drive shaft. :ront-wheel

drive is the most common form of engineJtransmission layout

used in modern passenger cars, where the engine drives the

front wheels. 5ost front wheel drive vehicles today feature


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transverse engine mounting, where as in past decades engines

were mostly positioned longitudinally instead. ear-wheel drive

was the traditional standard and is still widely used in lu!ury

cars and most sport cars.

Di,erent Types of Shafts

0. Transmission shaft- These shafts transmit power

between the source and the machines absorbing power. The counter shafts, line shafts, overhead shafts and all

factory shafts are transmission shafts. Since these shafts

carry machine parts such as pulleys, gears etc., therefore

they are subjected to bending moments in addition to

twisting.

. achine Shaft- These shafts form an integral part of the

machine itself. :or e!ample, the crankshaft is an integral

part of >..engines slider-crank mechanism.

;. A/le- A shaft is called Kan a!leL, if it is a stationary

machine element and is used for the transmission of

bending moment only. >t simply acts as a support forrotating bodies.

Application- To support hoisting drum, a car wheel or

a rope sheave.


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:ig 0.;

Demerits of a Conventional Drive Shaft

0. They have less speci%c modulus and strength.

. >ncreased weight.

;. onventional steel drive shafts are usually manufactured in

two pieces to increase the fundamental bending natural

fre"uency because the bending natural fre"uency of a shaft is

inversely proportional to the s"uare of beam length and

proportional to the s"uare root of speci%c modulus. Therefore

the steel drive shaft is made in two sections connected by a

support structure, bearings and 9-joints and hence over all

weight of assembly will be more.

ts corrosion resistance is less as compared with composite

materials.


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. Steel drive shafts have less damping capacity.

erits of Composite Drive Shaft

0. They have high speci%c modulus and strength.

. educed weight.

;. The fundamental natural fre"uency of the carbon %ber

composite drive shaft can be twice as high as that of steel

or aluminum because the carbon %ber composite material

has more than < times the speci%c sti&ness of steel or

aluminum, which makes it possible to manufacture the

drive shaft of passenger cars in one piece. A one-piece

composite shaft can be manufactured so as to satisfy the

vibration re"uirements. This eliminates all the assembly,

connecting the two piece steel shafts and thus minimi4es

the overall weight, vibrations and the total cost


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Drive Shaft *i0ration

@ibration is the most common drive shaft problem. Small cars

and short vans and trucks I65@H are able to use a single driveshaft with a slip joint at the front end without e!periencing any

undue vibration. *owever, with vehicles of longer wheel base,

the longer drive shaft re"uired would tend to sag and under

certain operating conditions would tend to whirl and then setup

resonant vibrations in the body of the vehicle, which will cause

the body to vibrate as the shaft whirls.

@ibration can be either transverse or torsional. Transverse

vibration is the result of unbalanced condition acting on the

shaft. This condition is usually by dirt or foreign material on the

shaft, and it can cause a rather noticeable vibration in the

vehicle. Torsional vibration occurs from the power impulses of

the engine or from improper universal join angles. >t causes a

noticeable sound disturbance and can cause a mechanical

shaking. >n e!cess, both types of vibration can cause damage

to the universal joints and bearings. Ghirling of a rotating shaft

happens when the centre of gravity of the shaft mass is

eccentric and so is acted upon by a centrifugal force which

tends to bend or bow the shaft so that it orbits about the shaft

longitudinal a!is like a rotating skipping rope. As the speed

rises, the eccentric deEection of the shaft increases, with the

result that the centrifugal force also will increase. The e&ect is

therefore cumulative and will continue until the whirling

become critical, at which point the shaft will vibrate violently.


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:rom the theory of whirling, it has been found that the critical

whirling speed of the shaft is inversely proportional to the

s"uare of the shaft length. >f, therefore, a shaft having, for

e!ample, a critical whirling speed of $$$ revJmin is doubled in

length, the critical whirling of the new shaft will be reduced to a

"uarter of this, i.e. the shaft will now begin to rotate at 0$$

revJmin. The vibration problem could solve by increasing the

diameter of the shaft, but this would increase its strength

beyond its tor"ue carrying re"uirements and at the same time

increase its inertia, which would oppose the vehicle/s

acceleration and deceleration. Another alternative solution

fre"uently adopted by car, van, and commercial vehicle

manufacturers is the use of two-piece drive shafts supported by

intermediate or centre bearings. ut this will increase the cost

considerably.

DRI*) )C#ANIS

Intro+&ction

:or the gear-like device used to drive a roller chain,

see Sprocket. This article is about mechanical gears. :or other

uses, see Cear IdisambiguationH Two meshing gearstransmitting rotational motion. 8ote that the smaller gear is

rotating faster. Although the larger gear is rotating less "uickly,

its tor"ue is proportionally greater. =ne subtlety of this

particular arrangement is that the linear speed at the pitch

diameter is the same on both gears.

http://en.wikipedia.org/wiki/Sprockethttp://en.wikipedia.org/wiki/Gear_(disambiguation)http://en.wikipedia.org/wiki/Sprockethttp://en.wikipedia.org/wiki/Gear_(disambiguation)


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A !ear or co!heel is a rotating machine part having

cut teeth, or cogs, which mesh with another toothed part in

order to transmit tor"ue, in most cases with teeth on the one

gear being of identical shape, and often also with that shape on

the other gear. Two or more gears working in tandem are called

a transmission and can produce a mechanical

advantage through a gear ratio and thus may be considered

a simple machine. Ceared devices can change the speed,

tor"ue, and direction of a power source. The most common

situation is for a gear to mesh with another gear+ however, a

gear can also mesh with a non-rotating toothed part, called a

rack, thereby producing translation instead of rotation.

The gears in a transmission are analogous to the wheels in a

crossed belt pulley system. An advantage of gears is that the

teeth of a gear prevent slippage. Ghen two gears mesh, and

one gear is bigger than the other Ieven though the si4e of the

teeth must matchH, a mechanical advantage is produced, with

the rotational speeds and the tor"ues of the two gears di&ering

in an inverse relationship.

>n transmissions which o&er multiple gear ratios, such as

bicycles, motorcycles, and cars, the term !ear, as in frst gear ,

refers to a gear ratio rather than an actual physical gear. The

term is used to describe similar devices even when the gear

ratio is continuous rather than discrete, or when the device

does not actually contain any gears, as in a continuously

variable transmission. The earliest known reference to gears

was circa A.(. $ by *ero of Ale!andria, but they can be traced

http://en.wikipedia.org/wiki/Rotatinghttp://en.wikipedia.org/wiki/Machine_(mechanical)http://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Transmission_(mechanics)http://en.wikipedia.org/wiki/Rotatinghttp://en.wikipedia.org/wiki/Machine_(mechanical)http://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Transmission_(mechanics)


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back to the Creek mechanics of the Ale!andrian school in the

;rd century .. and were greatly developed by the

Creek polymath Archimedes I37M0 ..H. The Antikythera

mechanism is an e!ample of a very early and intricate geared

device, designed to calculate astronomical positions. >ts time of

construction is now estimated between 0$ and 0$$ .

The de%nite velocity ratio which results from having teeth gives

gears an advantage over other drives Isuch as traction drives

and @-beltsH in precision machines such as watches that dependupon an e!act velocity ratio. >n cases where driver and follower

are pro!imal, gears also have an advantage over other drives in

the reduced number of parts re"uired+ the downside is that

gears are more e!pensive to manufacture and their lubrication

re"uirements may impose a higher operating cost.

Types

0. )/ternal !ear- An e!ternal gear is one with the teeth

formed on the outer surface of a cylinder or cone.

onversely,. Internal !earD an internal gear is one with the teeth

formed on the inner surface of a cylinder or cone.

:or bevel gears, an internal gear is one with

the pitch angle e!ceeding #$ degrees. >nternal gears do

not cause output shaft direction reversal.

(ist of !ears

Sp&r !ear

Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder or disk with the teeth projecting


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radials, and although they are not straight-sided in form Ithey

are usually of special form to achieve constant drive ratio,

mainly involuteH, the edge of each tooth is straight and aligned

parallel to the a!is of rotation. These gears can be meshed

together correctly only if they are %tted to parallel shafts.

#elical !ears

*elical or Bdry %!edB gears o&er a re%nement over spur gears.

The leading edges of the teeth are not parallel to the a!is of

rotation, but are set at an angle. Since the gear is curved, this

angling causes the tooth shape to be a segment of a heli!.

*elical gears can be meshed unparallel or crossed orientations.

The former refers to when the shafts are parallel to each other+

this is the most common orientation. >n the latter, the shafts

are non-parallel, and in this con%guration the gears are

sometimes known as Bskew gearsB.

The angled teeth engage more gradually than do spur gear

teeth, causing them to run more smoothly and "uietly. Gith

parallel helical gears, each pair of teeth %rst make contact at a

single point at one side of the gear wheel+ a moving curve of

contact then grows gradually across the tooth face to a

ma!imum then recedes until the teeth break contact at a single

point on the opposite side. >n skew gears, teeth suddenly meet

at a line contact across their entire width causing stress and

noise. Skew gears make a characteristic whine at high speeds.

Ghereas spur gears are used for low speed applications and

those situations where noise control is not a problem, the use of

helical gears is indicated when the application involves high

speeds, large power transmission, or where noise abatement is

important. The speed is considered to be high when the pitch

line velocity e!ceeds mJs.

A disadvantage of helical gears is a resultant thrust along the

a!is of the gear, which needs to be accommodated by

appropriate thrust bearings, and a greater degree of sliding

friction between the meshing teeth, often addressed with

additives in the lubricant.


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Se !ears

:or a NcrossedN or NskewN con%guration, the gears must have the

same pressure angle and normal pitch+ however, the heli!

angle and handedness can be di&erent. The relationship

between the two shafts is actually de%ned by the heli! angleIsH

of the two shafts and the handedness, as de%nedD

Ghere is the heli! angle for the gearO The crossed con%guration

is less mechanically sound because there is only a point contact

between the gears, whereas in the parallel con%guration there

is a line contact.

Puite commonly, helical gears are used with the heli! angle of

one having the negative of the heli! angle of the other+ such a

pair might also be referred to as having a right-handed heli!

and a left-handed heli! of e"ual angles. The two e"ual but

opposite angles add to 4eroD the angle between shafts is 4ero M

that is, the shafts are parallel. Ghere the sum or the di&erence

Ias described in the e"uations aboveH is not 4ero the shafts

are crossed. :or shafts crossed at right angles, the heli! angles

are of the same hand because they must add to #$ degrees.

Do&0le helical !ears

(ouble helical gears, or herringbone gears, overcome the

problem of a!ial thrust presented by BsingleB helical gears, by

having two sets of teeth that are set in a @ shape. A double

helical gear can be thought of as two mirrored helical gears

joined together. This arrangement cancels out the net a!ial

thrust, since each half of the gear thrusts in the opposite

direction resulting in a net a!ial force of 4ero. This arrangement

can remove the need for thrust bearings. *owever, double

helical gears are more di'cult to manufacture due to their

more complicated shape.

:or both possible rotational directions, there e!ist two possible

arrangements for the oppositely-oriented helical gears or gear

faces. =ne arrangement is stable, and the other is unstable. >n

a stable orientation, the helical gear faces are oriented so that


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each a!ial force is directed toward the center of the gear. >n an

unstable orientation, both a!ial forces are directed away from

the center of the gear. >n both arrangements, the total Ior netH

a!ial force on each gear is 4ero when the gears are aligned

correctly. >f the gears become misaligned in the a!ial direction,

the unstable arrangement will generate a net force that may

lead to disassembly of the gear train, while the stable

arrangement generates a net corrective force. >f the direction of

rotation is reversed, the direction of the a!ial thrusts is also

reversed, so a stable con%guration becomes unstable, and vice

versa.

Stable double helical gears can be directly interchanged with

spur gears without any need for di&erent bearings.

Bevel !ear

A bevel gear is shaped like a right circular cone with most of its

tip cut o&. Ghen two bevel gears mesh, their imaginary

vertices must occupy the same point. Their shaft a!es also

intersect at this point, forming an arbitrary non-straight angle

between the shafts. The angle between the shafts can be

anything e!cept 4ero or 03$ degrees. evel gears with e"ual

numbers of teeth and shaft a!es at #$ degrees are called miter

gears.

Spiral 0evels

Spiral bevel gears can be manufactured as Cleason types

Icircular arc with non-constant tooth depthH, =erlikon and

urve! types Icircular arc with constant tooth depthH,

Qlingelnbergyclo-)alloid I2picycloids with constant tooth

depthH or Qlingelnberg)alloid. Spiral bevel gears have the same

advantages and disadvantages relative to their straight-cut

cousins as helical gears do to spur gears. Straight bevel gears

are generally used only at speeds below mJs I0$$$ ftJminH, or,

for small gears, 0$$$ rpm.

8oteD The cylindrical gear tooth pro%le corresponds to an

involute, but the bevel gear tooth pro%le to an octoid. All

traditional bevel gear generators Ilike Cleason, Qlingelnberg,


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*eidenreichR*arbeck, and G5G5oduleH manufacture bevel

gears with an octoidal tooth pro%le. >5)=TA8TD :or -a!is

milled bevel gear sets it is important to choose the same

calculation J layout like the conventional manufacturing

method. Simpli%ed calculated bevel gears on the basis of an

e"uivalent cylindrical gear in normal section with an involute

tooth form show a deviant tooth form with reduced tooth

strength by 0$-31 without o&set and


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just the phenomenon it causes+ thus, one could speak of a pair

of gears as having, for e!ample, B$.0 mm of backlash.B A pair of

gears could be designed to have 4ero backlash, but this would

presuppose perfection in manufacturing, uniform thermal

e!pansion characteristics throughout the system, and no

lubricant. Therefore, gear pairs are designed to have some

backlash. >t is usually provided by reducing the tooth thickness

of each gear by half the desired gap distance. >n the case of a

large gear and a small pinion, however, the backlash is usually

taken entirely o& the gear and the pinion is given full si4ed

teeth. acklash can also be provided by moving the gears

further apart. The backlash of a gear train e"uals the sum of

the backlash of each pair of gears, so in long trains backlash

can become a problem.

:or situations in which precision is important, such as

instrumentation and control, backlash can be minimi4ed

through one of several techni"ues. :or instance, the gear can

be split along a plane perpendicular to the a!is, one half %!ed

to the shaft in the usual manner, the other half placed

alongside it, free to rotate about the shaft, but with springs

between the two halves providing relative tor"ue between

them, so that one achieves, in e&ect, a single gear with

e!panding teeth. Another method involves tapering the teeth in

the a!ial direction and providing for the gear to be slid in the

a!ial direction to take up slack.

Shiftin! of !ears

>n some machines IautomobilesH it is necessary to alter the

gear ratio to suit the task, a process known as gear shifting or

changing gear. There are several outcomes of gear shifting in

motor vehicles. >n the case of vehicle noise emissions, there are

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higher sound levels emitted when the vehicle is engaged in

lower gears. The design life of the lower ratio gears is shorter,

so cheaper gears may be used Ii.e. spur for 0st and reverseH

which tends to generate more noise due to smaller overlap

ratio and a lower mesh sti&ness etc. than the helical gears used

for the high ratios. This fact has been utili4ed in analy4ing

vehicle generated sound since the late 0#$s, and has been

incorporated into the simulation of urban roadway noise and

corresponding design of urban noise barriers along roadways.

Tooth pro3le

A pro%le is one side of a tooth in a cross section between the

outside circle and the root circle. 9sually a pro%le is the curve

of intersection of a tooth surface and a plane or surface normal

to the pitch surface, such as the transverse, normal, or a!ial

plane. The %llet curve Iroot %lletH is the concave portion of the

tooth pro%le where it joins the bottom of the tooth space. The

velocity ratio is dependent on the pro%le of the teeth. :riction

and wear between two gears is also dependent on the tooth

pro%le. There are a great many tooth pro%les that will give a

constant velocity ratio, and in many cases, given an arbitrary

tooth shape, it is possible to develop a tooth pro%le for the

mating gear that will give a constant velocity ratio. *owever,

two constant velocity tooth pro%les have been by far the most

commonly used in modern times. They are the cycloid and the

involute. The cycloid was more common until the late 03$$s+

since then the involute has largely superseded it, particularly in

drive train applications. The cycloid is in some ways the more

http://en.wikipedia.org/wiki/Sound_levelhttp://en.wikipedia.org/wiki/Noise_barrierhttp://en.wikipedia.org/wiki/Frictionhttp://en.wikipedia.org/wiki/Cycloid_gearhttp://en.wikipedia.org/wiki/Involute_gearhttp://en.wikipedia.org/wiki/Sound_levelhttp://en.wikipedia.org/wiki/Noise_barrierhttp://en.wikipedia.org/wiki/Frictionhttp://en.wikipedia.org/wiki/Cycloid_gearhttp://en.wikipedia.org/wiki/Involute_gear


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interesting and Ee!ible shape+ however the involute has two

advantagesD it is easier to manufacture, and it permits the

center to center spacing of the gears to vary over some range

without ruining the constancy of the velocity ratio. ycloidal

gears only work properly if the center spacing is e!actly right.

4ear materials

8umerous nonferrous alloys, cast irons, powder-metallurgy and

plastics are used in the manufacture of gears. *owever, steels

are most commonly used because of their high strength-to-

weight ratio and low cost. )lastic is commonly used where cost

or weight is a concern. A properly designed plastic gear can

replace steel in many cases because it has many desirable

properties, including dirt tolerance, low speed meshing, the

ability to BskipB "uite well and the ability to be made with

materials not needing additional lubrication. 5anufacturers

have employed plastic gears to reduce costs in consumer items

including copy machines, optical storage devices, cheap

dynamos, consumer audio e"uipment, servo motors, and

printers.

The mo+&le system

As a result, the term module is usually understood to mean the

pitch diameter in millimeters divided by the number of teeth.

Ghen the module is based upon inch measurements, it is

known as the 2nglish module to avoid confusion with the metric

module. 5odule is a direct dimension, whereas diametral pitch

is an inverse dimension Ilike Bthreads per inchBH.


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D)SI4N O' CAST IRON DRI*) S#A'T

Intro+&ction

A shaft5+riven 0icycle is a bicycle that uses a drive

shaft instead of a chain to transmit power from the pedals to

the wheel through contact of gears and a shaft rod to smoothly

and e'cient. Shaft drives were introduced over a century ago,

but were mostly supplanted by chain-driven bicycles due to thegear ranges possible with sprockets and derailleurs. ecently,



%&rpose of the Drive Shaft

The tor"ue that is produced from the engine and transmissionmust be transferred to the rear wheels to push the vehicle

forward moment. The drive shaft must provide a smooth,

uninterrupted Eow of power to the a!les. The drive shaft and

di&erential are used to transfer this tor"ue.

'&nctions of the Drive Shaft

0. >t must transmit tor"ue from the transmission to the pedal

. (uring the operation, it is necessary to transmit ma!imum

low-gear tor"ue

;. The drive shafts must also be capable of rotating at the

very fast speeds re"uired by the vehicle.

http://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Bicycle_chainhttp://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Drive_shafthttp://en.wikipedia.org/wiki/Bicycle_chain


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t is located on the front end of the drive shaft and

is connected to the transmission.

2 Constr&ction an+ orin! principle

The term (rive shaft is used to refer to a shaft, which is used

for the transfer of motion from one point to another. Ghereas

the shafts, which propel Ipush the object aheadH are referred to

as the propeller shafts. *owever the drive shaft of the

automobile is also referred to as the propeller shaft because

apart from transmitting the rotary motion from the front end to

the rear end of the vehicle, these shafts also propel the vehicle

forward. The shaft is the primary connection between the front

and the rear end Iengine and di&erentialH, which performs both

the jobs of transmitting the motion and propelling the front end.

Thus the terms (rive Shaft and )ropeller Shafts are used

interchangeably. >n other words, a drive shaft is a longitudinal

power transmitting, used in vehicle where the pedal is situated

at the human feet. A drive shaft is an assembly of one or more

tubular shafts connected by universal, constant velocity or


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Ee!ible joints. The number of tubular pieces and joints depends

on the distance between the two wheels.

The job involved is the design for suitable propeller shaft and

replacement of chain drive smoothly to transmit power from

the engine to the wheel without slip. >t needs only a less

maintenance. >t is cost e&ective. )ropeller shaft strength is

more and also propeller shaft diameter is less. it absorbs the

shock. ecause the propeller shaft center is %tted with the

universal joint is a Ee!ible joint. >t turns into any angular

position. The both end of the shaft are %tted with the bevel

pinion, the bevel pinion engaged with the crown and power is

transmitted to the rear wheel through the propeller shaft and

gear bo!. . Gith our shaft drive bikes, there is no more grease

on your hands or your clothes+ and no more chain and

derailleur maintenance.

Shaft-driven bikes have a large bevel gear where a

conventional bike would have its chain ring. This meshes with

another bevel gear mounted on the drive shaft. The use of

bevel gears allows the a!is of the drive tor"ue from the pedalsto be turned through #$ degrees. The drive shaft then has

another bevel gear near the rear wheel hub which meshes with

a bevel gear on the hub where the rear sprocket would be on a

conventional bike, and canceling out the %rst drive tor"ue

change of a!is.

http://en.wikipedia.org/wiki/Bevel_gearhttp://en.wikipedia.org/wiki/Chainringhttp://en.wikipedia.org/wiki/Gearhttp://en.wikipedia.org/wiki/Bevel_gearhttp://en.wikipedia.org/wiki/Chainringhttp://en.wikipedia.org/wiki/Gear


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The #$-degree change of the drive plane that occurs at

the bottom bracket and again at the rear hub uses bevel gears

for the most e'cient performance, though other mechanisms

could be used, e.g. *obson/s joints, worm gears or crossed

helical gears. The drive shaft is often mated to a hub

gear which is an internal gear system housed inside the rear

hub.

:ig


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optimally for following speci%ed design re"uirements as shown

in Table.

Ta0le- Desi!n re6&irements an+ speci3cations

S.

No

Name Notation Unit *al&e

0. 9ltimate

Tor"ue

Tma! 8m

. 5a!. Speedof shaft

8ma! rpm

;. 6ength of

Shaft

6 mm

Steel IS5


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. )oisson atio v 555555

". (ensity V QgJm;

8. Uield Strength Sy 5)a

:. Shear Strength Ss 5)a

Bevel 4ear

Bevel !ears are gears where the a!es of the two shafts

intersect and the tooth-bearing faces of the gears themselves

are conically shaped. evel gears are most often mounted on

shafts that are #$ degrees apart, but can be designed to work

at other angles as well. The pitch surface of bevel gears is a

cone.

)O)TR; AND T)RINO(O4;

Ghen intersecting

shafts are connected by

gears, the pitch cones

https://en.wikipedia.org/wiki/Gearshttps://en.wikipedia.org/wiki/Cone_(geometry)https://en.wikipedia.org/wiki/Gearshttps://en.wikipedia.org/wiki/Cone_(geometry)


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Ianalogous to the pitch cylinders of spur and helical gearsH are

tangent along an element, with their ape!es at the intersection

of the shafts as in :ig. where two bevel gears are in mesh.

The si4e and shape of the teeth are de%ned at the large end,

where they intersect the back cones. )itch cone and back cone

elements are perpendicular to each other. The tooth pro%les

resemble those of spur gears having pitch radii rbg and rbp and

are shown in :ig. 0;.;. which e!plains the nomenclatures of a

bevel gear.


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where Wv is called the virtual number of teeth, p is the circular

pitch of both the imaginary spur gears and the bevel gears. W0

and W are the number of teeth on the pinion and gear, X0 and

X are the pitch cone angles of pinion and gears. >t is a practice

to characteri4e the si4e and shape of bevel gear teeth as those

of an imaginary spur gear appearing on the developed back

cone corresponding to Tredgold/s appro!imation.

aH evel gear teeth are inherently non - interchangeable.

bH The working depth of the teeth is usually

m, the same as for standard spur and

helical gears, but the bevel pinion is

designed with the larger addendum I $.7

working depthH.

cH This avoids interference and results in

stronger pinion teeth. >t also increases the

contact ratio.

dH The gear addendum varies from 0m for a gear ratio of0, to $.< m for ratios of

6.8 and greater.

The gear ratio can be determined from the number of teeth, the

pitch diameters or the pitch cone angles as,


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Ill&stration of spiral an!le

The :ig.0;.< illustrates the measurement of the spiral angle

of a spiral bevel gear. evel gears most commonly have a

pressure angle of $o, and spiral bevels usually have a spiral

angle of ; o.

'i!.


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omparison of intersecting and o&set shaft bevel type gearings

'orce Analysis


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4ear an+ shaft forces


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4ear an+ shaft forces

'i!. 1.1= Bevel !ear 5 'orce analysis

>n :ig. 0;.0$, :n is normal to the pitch cone and the resolutionof resultant tooth force :n into its tangential Itor"ue producingH,


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radial IseparatingH and a!ial IthrustH components is

designated :t, :r and :a respectively. An au!iliary view is

needed to show the true length of the vector representing

resultant force :n Iwhich is normal to the tooth pro%leH.

esultant force :n is shown applied to tooth at the pitch cone

surface and midway along tooth width b. >t is also assumed that

load is uniformly distributed along the tooth width despite the

fact that the tooth width is larger at the outer end Ghere @av is

in meters per second, dav is in meters, n is in revolutions per

minute, :t is in 8 and G is power in kG.

dav = d-bsin

Fn

= Ft/cosφ

Fr= F

ncosγ = F

ttanφ c

Fa

= Fnsinγ = F

ttanφ sin


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Transmission of Torque

Action and reaction my friend. >f a person does not turn the

pedal then he will stand on it and so the ma!imum tor"ue willY Ibody mass of the rider ! gH ! the length of the pedal lever.

emember to consider the gearing of the bike though. The

average, %t, adult rider can produce only 7 watts or 0J0$hp

when cycling at a continuous 0mph I0#.;kphH.B This usually

happens with a pedaling speed of $-3$ rpm though many rider

pedal faster. Ghen > cycle, > usually spin at between 0$$-0$rpm, but > have been riding for years and have found that the

higher speed works better for me.

Spiral 0evel !ear

A spiral 0evel !ear is a bevel gear with helical teeth. The

main application of this is in a vehicle di&erential, where the

direction of drive from the drive shaft must be turned #$

degrees to drive the wheels. The helical design produces less

vibration and noise than conventional straight-cut or spur-cut

gear with straight teeth.

https://en.wikipedia.org/wiki/Bevel_gearhttps://en.wikipedia.org/wiki/Helical_gearhttps://en.wikipedia.org/wiki/Differential_(mechanical_device)https://en.wikipedia.org/wiki/Drive_shafthttps://en.wikipedia.org/wiki/Bevel_gearhttps://en.wikipedia.org/wiki/Helical_gearhttps://en.wikipedia.org/wiki/Differential_(mechanical_device)https://en.wikipedia.org/wiki/Drive_shaft


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A spiral bevel gear set should always be replaced in pairs i.e.

both the left hand and right hand gears should be replaced

together since the gears are manufactured and lapped in pairs.

#an+e+ness

A ri!ht han+ spiral bevel gear is one in which the outer half of

a tooth is inclined in the clockwise direction from the a!ial

plane through the midpoint of the tooth as viewed by an

observer looking at the face of the gear.

A left han+ spiral bevel gear is one in which the outer half of a

tooth is inclined in the counter clockwise direction from the

a!ial plane through the midpoint of the tooth as viewed by an

observer looking at the face of the gear.

8ote that a spiral bevel gear and pinion are always of opposite

hand, including the case when the gear is internal.

Also note that the designations right hand and left hand are

applied similarly to other types of bevel gear, hypoid gears, and

obli"ue tooth face gears.

#ypoi+ !ears

A hypoi+ is a type of spiral bevel gear whose a!is does not

intersect with the a!is of the meshing gear. The shape of a

hypoid gear is a revolved hyperboloid Ithat is, the pitch surface

of the hypoid gear is a hyperbolic surfaceH, whereas the shape

of a spiral bevel gear is normally conical. The hypoid gear

places the pinion o&-a!is to the crown wheel Iring gearH which

https://en.wikipedia.org/wiki/Bevel_gear#Introductionhttps://en.wikipedia.org/wiki/Hypoidhttps://en.wikipedia.org/wiki/Hyperboloidhttps://en.wikipedia.org/wiki/Pinionhttps://en.wikipedia.org/wiki/Differential_(mechanical_device)https://en.wikipedia.org/wiki/Bevel_gear#Introductionhttps://en.wikipedia.org/wiki/Hypoidhttps://en.wikipedia.org/wiki/Hyperboloidhttps://en.wikipedia.org/wiki/Pinionhttps://en.wikipedia.org/wiki/Differential_(mechanical_device)


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• >nner spiral angle is the spiral angle of a bevel gear at the

inner cone distance.

Comparison of spiral 0evel !ears to hypoi+ !ears

*ypoid gears are stronger, operate more "uietly and can beused for higher reduction ratios, however they also have somesliding action along the teeth, which reduces mechanicale'ciency, the energy losses being in the form of heat producedin the gear surfaces and the lubricating Euid.

>n older automotive designs, hypoid gears were typically usedin rear-drive automobile drive trains, but modern designs havetended to substitute spiral bevel gears to increase drivinge'ciency.

*ypoid gears are still common in larger trucks because theycan transmit higher tor"ue. A higher hypoid o&set allows thegear to transmit higher tor"ue. *owever increasing the hypoido&set results in reduction of mechanical e'ciency and aconse"uent reduction in fuel economy. :or practical purposes,it is often impossible to replace low e'ciency hypoid gears withmore e'cient spiral bevel gears in automotive use because the

spiral bevel gear would need a much larger diameter totransmit the same tor"ue. >ncreasing the si4e of the drive a!legear would re"uire an increase of the si4e of the gear housingand a reduction in the ground clearance.

Another advantage of hypoid gear is that the ring gear of thedi&erential and the input pinion gear are both hypoid. >n mostpassenger cars this allows the pinion to be o&set to the bottomof the crown wheel. This provides for longer tooth contact and

allows the shaft that drives the pinion to be lowered, reducingthe BhumpB intrusion in the passenger compartment Eoor.*owever, the greater the displacement of the input shaft a!isfrom the crown wheel a!is, the lower the mechanical e'ciency.

$orm +rive

A worm drive is a gear arrangement in which a worm Iwhich isa gear in the form of a screwH meshes with a worm gear Iwhichis similar in appearance to a spur gearH. The two elements arealso called the worm screw and worm wheel. The terminology is

https://en.wikipedia.org/wiki/Automobilehttps://en.wikipedia.org/wiki/Powertrainhttps://en.wikipedia.org/wiki/Efficient_energy_usehttps://en.wikipedia.org/wiki/Truckhttps://en.wikipedia.org/wiki/Torquehttps://en.wikipedia.org/wiki/Fuel_economy_in_automobileshttps://en.wikipedia.org/wiki/Gear_housinghttps://en.wikipedia.org/wiki/Gear_trainhttps://en.wikipedia.org/wiki/Screw_threadhttps://en.wikipedia.org/wiki/Gear#Spurhttps://en.wikipedia.org/wiki/Machine_elementhttps://en.wikipedia.org/wiki/Automobilehttps://en.wikipedia.org/wiki/Powertrainhttps://en.wikipedia.org/wiki/Efficient_energy_usehttps://en.wikipedia.org/wiki/Truckhttps://en.wikipedia.org/wiki/Torquehttps://en.wikipedia.org/wiki/Fuel_economy_in_automobileshttps://en.wikipedia.org/wiki/Gear_housinghttps://en.wikipedia.org/wiki/Gear_trainhttps://en.wikipedia.org/wiki/Screw_threadhttps://en.wikipedia.org/wiki/Gear#Spurhttps://en.wikipedia.org/wiki/Machine_element


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often confused by imprecise use of the term worm gear to referto the worm, the worm gear, or the worm drive as a unit.

6ike other gear arrangements, a worm drive can reduce

rotational speed or transmit higher tor"ue. The image shows asection of a gear bo! with a worm gear driven by a worm. Aworm is an e!ample of a screw, one of the si! simple machines.

)/planation

A gearbo! designed using a worm and worm-wheel is

considerably smaller than one made from plain spur gears, and

has its drive a!es at #$Z to each other. Gith a single start

worm, for each ;$Z turn of the worm, the worm-gear advances

only one tooth of the gear. Therefore, regardless of the wormNs

si4e Isensible engineering limits notwithstandingH, the gear

ratio is the "size o the worm gear - to - 1". Civen a single start

worm, a $ tooth worm gear reduces the speed by the ratio of

$D0. Gith spur gears, a gear of

0 teeth Ithe smallest si4e if

designed to good engineering

practicesH must match with a


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>n the era of sailing ships, the introduction of a worm drive to

control the rudder was a signi%cant advance. )rior to its

introduction, a rope drum drive controlled the rudder. ough

seas could apply substantial force the rudder, often re"uiring

several men to steer the vessel[some drives had two large-

diameter wheels so up to four crewmen could operate the

rudder.

Gorm drives have been used in a few automotive rear-a!le %nal

drives Ithough not the di&erential itselfH. They took advantageof the location of the gear being at either the very top or very

bottom of the di&erential crown wheel. >n the 0#0$s they were

common on trucks+ to gain the most clearance on muddy roads

the worm gear was placed on top. >n the 0#$s the Stut4 %rm

used them on its cars+ to have a lower Eoor than its

competitors, the gear was located on the bottom. An e!ample

from around 0#$ was the )eugeot


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e'cient as a hypoid gear, and such trucks invariably have a

very large di&erential housing, with a correspondingly large

volume of gear oil, to absorb and dissipate the heat created.

Gorm drives are used as the tuning mechanism for many

musical instruments, including guitars, double-basses,

mandolins, bou4oukis, and many banjos Ialthough most high-

end banjos use planetary gears or friction pegsH. A worm drive

tuning device is called a machine head.

)lastic worm drives are often used on small battery-operated

electric motors, to provide an output with a lower angular

velocity Ifewer revolutions per minuteH than that of the motor,

which operates best at a fairly high speed. This motor-worm-

gear drive system is often used in toys and other small

electrical devices.

https://en.wikipedia.org/wiki/Hypoidhttps://en.wikipedia.org/wiki/Gear_oilhttps://en.wikipedia.org/wiki/Guitarhttps://en.wikipedia.org/wiki/Double-basshttps://en.wikipedia.org/wiki/Mandolinhttps://en.wikipedia.org/wiki/Bouzoukihttps://en.wikipedia.org/wiki/Banjohttps://en.wikipedia.org/wiki/Banjohttps://en.wikipedia.org/wiki/Planetary_gearshttps://en.wikipedia.org/wiki/Machine_headhttps://en.wikipedia.org/wiki/Hypoidhttps://en.wikipedia.org/wiki/Gear_oilhttps://en.wikipedia.org/wiki/Guitarhttps://en.wikipedia.org/wiki/Double-basshttps://en.wikipedia.org/wiki/Mandolinhttps://en.wikipedia.org/wiki/Bouzoukihttps://en.wikipedia.org/wiki/Banjohttps://en.wikipedia.org/wiki/Banjohttps://en.wikipedia.org/wiki/Planetary_gearshttps://en.wikipedia.org/wiki/Machine_head


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A worm drive is used on jubilee-type hose clamps or jubilee

clamps. The tightening screwNs worm thread engages with the

slots on the clamp band.

=ccasionally a worm gear is designed to run in reverse,

resulting in the output shaft turning much faster than the input.

2!amples of this may be seen in some hand-cranked

centrifuges or the wind governor in a musical bo!.

>ong the a!is.

Di,erential

A di&erential is a particular type of simple planetary gear train

that has the property that the angular velocity of its carrier is

the average of the angular velocities of its sun and annular

gears. This is accomplished by packaging the gear train so it

has a %!ed carrier train ratio R = -1, which means the gears

corresponding to the sun and annular gears are the same si4e. This can be done by engaging the planet gears of two identical

https://en.wikipedia.org/wiki/Hose_clamphttps://en.wikipedia.org/wiki/Centrifugehttps://en.wikipedia.org/wiki/Governor_(device)https://en.wikipedia.org/wiki/Musical_boxhttps://en.wikipedia.org/wiki/Planetary_gear_trainhttps://en.wikipedia.org/wiki/Epicyclic_gearing#Fixed_Carrier_Train_Ratiohttps://en.wikipedia.org/wiki/Hose_clamphttps://en.wikipedia.org/wiki/Centrifugehttps://en.wikipedia.org/wiki/Governor_(device)https://en.wikipedia.org/wiki/Musical_boxhttps://en.wikipedia.org/wiki/Planetary_gear_trainhttps://en.wikipedia.org/wiki/Epicyclic_gearing#Fixed_Carrier_Train_Ratio


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and coa!ial epicyclic gear trains to form a spur gear

dierential. Another approach is to use bevel gears for the sun

and annular gears and a bevel gear as the planet, which is

known as a bevel gear dierential.

)picyclic +i,erential

An epicyclic di&erential can use epicyclic gearing to split and

apportion tor"ue asymmetrically between the front and rear

a!les. An epicyclic di&erential is at the heart of the Toyota )rius

automotive drive train, where it interconnects the engine,

motor-generators, and the drive wheels Iwhich have a second

di&erential for splitting tor"ue as usualH. >t has the advantage of

being relatively compact along the length of its a!is Ithat is, the

sun gear shaftH.

2picyclic gears are also called planetary gears because thea!es of the planet gears revolve around the common a!is of the

sun and ring gears that they mesh with and roll between. >n 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.

https://en.wikipedia.org/wiki/Epicyclic_gearinghttps://en.wikipedia.org/wiki/Bevel_gearhttps://en.wikipedia.org/wiki/Epicyclic_gearinghttps://en.wikipedia.org/wiki/Torquehttps://en.wikipedia.org/wiki/Toyota_Priushttps://en.wikipedia.org/wiki/Epicyclic_gearinghttps://en.wikipedia.org/wiki/Bevel_gearhttps://en.wikipedia.org/wiki/Epicyclic_gearinghttps://en.wikipedia.org/wiki/Torquehttps://en.wikipedia.org/wiki/Toyota_Prius


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Sp&r5!ear +i,erential

This is another type of di&erential that was used in some early

automobiles, more recently the =ldsmobile Tornado, as well as

other non-automotive applications. >t consists of spur gears

only.

A spur-gear di&erential has two e"ual-si4ed spur gears, one for

each half-shaft, with a space between them. >nstead of the

evel gear, also known as a miter gear, assembly Ithe BspiderBH

at the centre of the di&erential, there is a rotating carrier on the

same a!is as the two shafts. Tor"ue from a prime mover or

transmission, such as the drive shaft of a car, rotates this

carrier.

5ounted 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. 2ach

pinion pair rotates freely on pins supported by the carrier.

:urthermore, the pinion pairs are displaced a!ially, such thatthey 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 a!le. 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

https://en.wikipedia.org/wiki/Oldsmobile_Toronadohttps://en.wikipedia.org/wiki/Spur_gearhttps://en.wikipedia.org/wiki/Bevel_gearhttps://en.wiktionary.org/wiki/prime_moverhttps://en.wikipedia.org/wiki/Transmission_(mechanics)https://en.wikipedia.org/wiki/Oldsmobile_Toronadohttps://en.wikipedia.org/wiki/Spur_gearhttps://en.wikipedia.org/wiki/Bevel_gearhttps://en.wiktionary.org/wiki/prime_moverhttps://en.wikipedia.org/wiki/Transmission_(mechanics)


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the individual wheel a!les is the same as that in a bevel-gear

di&erential.

Application to vehicles

A vehicle with two drive wheels has the problem that when it

turns a corner the drive wheels must rotate at di&erent speeds

to maintain traction. The automotive di&erential is designed to

drive a pair of wheels while allowing them to rotate at di&erent

speeds. >n vehicles without a di&erential, such as karts, both

driving wheels are forced to rotate at the same speed, usually

on a common a!le driven by a simple chain-drive mechanism.

Ghen cornering the inner wheel travels a shorter distance than

the outer wheel, so without a di&erential either the inner wheel

rotates too fast or the outer wheel drags, which results in

di'cult and unpredictable handling, damage to tires and roads,and strain on Ior possible failure ofH the entire drive train.

>n rear-wheel drive automobiles the central drive shaft Ior prop

shaftH engages the di&erential through a hypoid gear Icrown-

wheel and pinionH the crown-wheel is mounted on the carrier of

the planetary chain that forms the di&erential. This hypoid gear

is a bevel gear that changes the direction of the drive rotation.

(oss of traction

=ne undesirable side e&ect of a conventional di&erential is that

it can limit traction under less than ideal conditions. The

amount of traction re"uired to propel the vehicle at any given

moment depends on the load at that instant[how heavy the

https://en.wikipedia.org/wiki/Kart_racinghttps://en.wikipedia.org/wiki/Axlehttps://en.wikipedia.org/wiki/Tirehttps://en.wikipedia.org/wiki/Powertrainhttps://en.wikipedia.org/wiki/Hypoid_gearhttps://en.wikipedia.org/wiki/Kart_racinghttps://en.wikipedia.org/wiki/Axlehttps://en.wikipedia.org/wiki/Tirehttps://en.wikipedia.org/wiki/Powertrainhttps://en.wikipedia.org/wiki/Hypoid_gear


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vehicle is, how much drag and friction there is, the gradient of

the road, the vehicleNs momentum, and so on.

The tor"ue applied to each driving wheel is a result of theengine, transmission and drive a!les applying a twisting force

against the resistance of the traction at that roadwheel. >n

lower gears and thus at lower speeds, and unless the load is

e!ceptionally high, the drivetrain can supply as much tor"ue as

necessary, so the limiting factor becomes the traction under

each wheel. >t is therefore convenient to de%ne traction as theamount of tor"ue that can be generated between the tire and

the road surface, before the wheel starts to slip. >f the tor"ue

applied to one of the drive wheels e!ceeds the threshold of

traction, then that wheel will spin, and thus only provide tor"ue

at each other driven wheel limited by the sliding friction at the

slipping wheel. The reduced net traction may still be enough to

propel the vehicle.

A conventional BopenB Inon-locked or otherwise traction-aidedH

di&erential always supplies close to e"ual Ibecause of limited

internal frictionH tor"ue to each side. To illustrate how this can

limit tor"ue applied to the driving wheels, imagine a simple

rear-wheel drive vehicle, with one rear road wheel on asphalt

with good grip, and the other on a patch of slippery ice. >t takes

very little tor"ue to spin the side on slippery ice, and because a

di&erential splits tor"ue e"ually to each side, the tor"ue that is

applied to the side that is on asphalt is limited to this amount.

ased on the load, gradient, et cetera, the vehicle re"uires a

certain amount of tor"ue applied to the drive wheels to move

https://en.wikipedia.org/wiki/Wheelhttps://en.wikipedia.org/wiki/Enginehttps://en.wikipedia.org/wiki/Transmission_(mechanics)https://en.wikipedia.org/wiki/Traction_(engineering)https://en.wikipedia.org/wiki/Tirehttps://en.wikipedia.org/wiki/Rear-wheel_drivehttps://en.wikipedia.org/wiki/Wheelhttps://en.wikipedia.org/wiki/Enginehttps://en.wikipedia.org/wiki/Transmission_(mechanics)https://en.wikipedia.org/wiki/Traction_(engineering)https://en.wikipedia.org/wiki/Tirehttps://en.wikipedia.org/wiki/Rear-wheel_drive


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forward. Since an open di&erential limits total tor"ue applied to

both drive wheels to the amount used by the lower traction

wheel multiplied by a factor of , when one wheel is on a

slippery surface, the total tor"ue applied to the driving wheels

may be lower than the minimum tor"ue re"uired for vehicle

propulsion.

5any newer vehicles feature traction control, which partially

mitigates the poor traction characteristics of an open

di&erential by using the anti-lock braking system to limit orstop the slippage of the low traction wheel, increasing the

tor"ue that can be applied to both wheels. Ghile not as

e&ective in propelling a vehicle under poor traction conditions

as a traction-aided di&erential, it is better than a simple

mechanical open di&erential with no electronic traction

assistance.

https://en.wikipedia.org/wiki/Traction_control_systemhttps://en.wikipedia.org/wiki/Anti-lock_braking_systemhttps://en.wikipedia.org/wiki/Traction_control_systemhttps://en.wikipedia.org/wiki/Anti-lock_braking_system


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