ABSTRACT
This project making of the shaft driven chainless bicycle instead of simpl ple e chai hain drive bicy icycle. le.7 This id ide ea is consist istence performance. Stress analysis on gear and simulation. A shaftdriv driven en bi bicy cycl cle e is a chai chainl nles ess s bi bicy cycl cle e that that us uses es a dri drive ve sha shaft ft inst in stea ead d of a chain chain to transmit power from the pedals to the wheel. Shaft drives were introduced over a century ago, but wer were most mostly ly suppl supplant anted ed by chain chain-dr -driv iven en bi bicyc cycle les s due to the the gear gear range ranges s poss possibl ible e with with sp sprrocket ockets s and and derailleur derailleur.. ecently, due due to adva advanc ncem emen ents ts in in inte terrnal nal gear gear tech techno nolo logy gy,, a smal smalll number of modern shaft-driven bicycles have been introduced.
INTRODUCTION
A shaft-driven bicycle is a bicycle that uses a drive shaft instead shaft instead of a chain chain to to transmit power from the pedals to the wheel. Shaft drives were introduced over a century ago, but wer were most mostly ly suppl supplant anted ed by chain chain-dr -driv iven en bi bicyc cycle les s due to the the gear ranges ranges possibl possible e with with sprock sprockets ets and deraill derailleur eur.. ecently ecently,, due due to adva advanc ncem emen ents ts in in inte terrnal nal gear gear tech techno nolo logy gy,, a smal smalll number of modern shaft-driven bicycles have been introduced. Shaft-driven bikes have a large bevel gear where a conventional bike would have its chain ring. ring. This meshes with anothe anotherr bevel bevel gear moun mounte ted d on the the driv drive e sh shaf aft. t. The The us use e of bevel gears allows the a!is of the drive tor"ue from the pedals to be tur turned ned thr through ough #$ degr degree ees. s. The The driv drive e sh shaf aftt then 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 conve convent ntio iona nall bi bik ke, and and cance cancelli lling ng out the the %rst %rst drive drive tor tor"ue change of a!is. An automotive drive shaft transmits power from the engine to the di&erential gear of a rear wheel drive vehicle. The drive shaft shaft is us usua ually lly manuf manufac actu turred in two two piece pieces s to incr increase ease the the fundamental bending natural fre"uency because the bending natu natura rall fre"u fre"uenc ency y of a sh shaf aftt is in inve vers rsely ely propo proport rtion ional al to the the s"uare of beam length and proportional to the s"uare root of spec sp eci% i%c c modul odulus us whic which h in incr crea ease ses s the tot total weig weight ht of an automotive vehicle and decreases fuel e'ciency. So, a single piece piece driv drive e sh shaf aftt is prefe preferr rred ed here here and and the the mate materia riall of it is considered to be Titanium alloy because of its high strength and and low low densit density y. (riv (rive e sh shaf afts ts are are carr carrie iers rs of tor" tor"ue ue and are are subject to torsion and shear stress, e"uivalent to the di&erence between the input tor"ue and the load. They must therefore be strong enough to bear the stress, whilst avoiding too much additional weight as that would in turn increase their inertia. )arker *anni%n is a motion and control technologies corporation+ in $$ they started the hainless hallenge, it is
a comp compet etit itio ion n that that was was inspir inspired ed by the the cycli cycling ng comm commun unit ity y. Since a large portion of )arker/s business focuses on hydraulics they decided to merge the two ideas into a competition. This comp compet etiti ition on rules rules are are fair fairly ly simp simple le develo develop p a 0$ 0$$1 $1 human 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 chosen to compete selects a group of -3 seniors to participate. These students students start from scratch scratch and design either a hydraulically hydraulically or pneumat pneumatical ically ly power powered ed bike bike to compet compete e in severa severall di&ere di&erent nt races. There was an endurance race, an e'ciency race, and a sprint race. The endurance race was an 3 mile course. The e'cie e'ciency ncy race race deals deals with with utili utili4i 4ing ng an accu accumu mula lato torr to st stor ore e energy for a later use. The sprint race was 0$$ meter dash to the %nish. 2ach team needs to work together to create a bike that works the best in each race in order to win the hainless hallenge. This year/s team had four members on it, so the bike develo developm pmen entt was was spl split it in into to thr three sect sectio ions+ ns+ hri hris s lar lark k and and 5a!ton 6own were working the hydraulic power train, randon andal was assigned on the braking system, and 8ick 5acaluso was assigned to the bike frame.
Components 1. Bicycle Bicycle Chassis Chassis 2. Drive Drive shaft shaft . Bevel Bevel !ear !ear ".
#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 receiv ceived ed a patent in =cto 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. stay. >n the 9nited States, $alter Stillman %led for a patent on a shaft-driven bicycle on (ec. 0$, 03#$ which was granted on ?uly 0, 03#0.
The shaft drive was not well accepted in 2ngland, so in 03#< :ear earn head head took ook it to the the 9SA 9SA wher here olo olone nell )ope ope of the olumbia %rm bought the e!clusive American rights. elatedly, the the 2ngli nglish sh maker akers s took took it up, up, with ith *umbe umberr in par particu ticula larr plunging heavily on the deal. uriously uriously enough, enough, the greatest of all the @ictorian cycle engineers, )rofessor Archibald Sharp, was agai agains nstt sh shaf aftt driv drive+ e+ in hi his s clas classi sic c 03 03# # book book Bic Bicyc ycle les s and and TricyclesB, TricyclesB, he writes BThe :earn head Cear.... Cear.... if bevel-wheels could be accurately and cheaply cut by machinery, it is possible
that gears of this description might supplant, to a great e!tent, the chain-drive gear+ but the fact that the teeth of the bevelwheels 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 regular bicycles, primarily due to the high cost. The bikes bikes were 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' i'c cul ultt to remove to chan hange Eats. 5any of thes hese de%ciencies have been overcome in the past century. century.
>n 0#$, The *ill-limber icycle 5fg. ompany sold a threespeed
shaft-driven
bicycle
in
which
the
shifting
was
impl implem ement ented ed with with thr three sets sets of beve bevell gears gears..F Ghil Ghile e a smal smalll number of chainless chainless bicycles bicycles were were available, available, for the most part, shaft-d shaft-drive riven n bicycles bicycles dis disappe appear ared ed from from view view for most most of the $th
century.
There
is,
however,
still
a
niche
market
for chainless bikes, chainless bikes, especially for commuters, and there are a number of manufacturers who o&er them either as part of a
larger range or as a primary speciali4ation. A notable e!ample is io mega in mega in (enmark.
%&rpose of the Drive Shaft The tor"ue that is produced from the engine and transmission must must be tran transfe sferr rred ed to the the rear ear whee wheels ls to push push the the vehic vehicle le 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 transmit tor"ue from from the transmission transmission to the di&erential gear bo!. bH (uring the operation, operation, it is necessary necessary to transmit transmit ma!imum ma!imum low-gear tor"ue developed by the engine. cH The The driv drive e shaft shafts s must must also be capab capable le of rotat otatin ing g at the very fast speeds re"uired by the vehicle. dH The The driv drive e sh shaf aftt must must also also oper operat ate e thr through ough cons consta tant ntly ly 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.
eH The The leng length th of the the driv drive e sh shaf aftt must must also also be capa capabl ble e of changing while transmitting tor"ue. 6ength changes are caused by a!le movement due to tor"ue reaction, road deEections, 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 en d
of
the
drive
shaft
an d
is
connected
to
the
transmission. 8ow days all automobiles Iwhich are having front engine rear wheel 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 Two piece drive shaft increases i ncreases the weight of drive shaft which is not desirable in today/s today/s market. 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 i s advantageous in over overal alll weig weight ht reduc educti tion on of auto automo mobi bile les s whic which h is a hi high ghly ly desirable goal of design engineer eng ineer..
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 rigi rigid d drive drivesh shaf aftt to deliv deliver er powe powerr from from a tran transm smis issio sion n to the 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. ls. There are di&e i&erent types pes of drive shafts in Automotive >ndustryD aH 0 piece piece drives driveshaf haftt bH piece piece drivesh driveshaf aftt cH Slip in Tube Tube driveshaf driveshaftt
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 fron frontt whee wheels. ls. 5ost 5ost front front whee wheell driv drive e vehic vehicle les s toda today y featu featurre
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
ransmissi ssion on 0. Transmi
shaftshaft-
Thes hese
shaft afts
trans nsm mit
pow 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 they are are subjec subjecte ted d to bendi bending ng mome moment nts s in addit additio ion n to twisting. . achine Shaft- These shafts shafts form an integral part of the machine itself. :or e!ample, the crankshaft is an integral part of >..engines slider-crank slider-crank mechanism. ;. A/le- A sh shaf aftt is calle alled d Kan Kan a!le a!leL L, if it is a st stat atio ion nary ary mach machin ine e elem elemen entt and and is us used ed for for the the tran transm smis issi sion on of bend bendin ing g mome moment nt only only.. >t simp simply ly acts acts as a su supp ppor ortt for for rotating bodies.
Application- To support hoisting drum, a car wheel or a rope sheave.
<. Spin+le- A shaft is called Ka spindleL, if it is a short shaft that imparts imparts
motion motion either either to to a cutting cutting tool tool or to a workwork-
piece.
Applications0. (rill press spindles-impart motion to cutting tool Ii.e.H drill. . 6athe spindles-impart motion to work-piece. Apart from, an a!le and a spindle, shafts are used at so many places and almost almost everywher everywhere e wherever wherever power transmission transmission is re"uired. :ew of them areD 0. A&tomo0ile Drive Shaft- Transmits power from main gearbo! to di&erential gear bo!. . Ship %ropeller Shaft- Transmits power from gearbo! to propeller
attached
on it. ;. #elicopter Tail Rotor Shaft- Transmits power to rail rotor fan.
Part of Drive Shaft
: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 two pi piec eces es to in incr crea ease se the the fund fundam amen enta tall bend bendin ing g nat natural ural fre"uency because the bending natural fre"uency of a shaft is inve in verrsely sely prop propor orti tion onal al to the s" s"ua uarre of beam beam leng length th and and proportional to the s"uare root of speci%c modulus. Therefore the steel drive shaft is made in two sections connected by a suppo support rt st stru ruct ctur ure, e, bear bearing ings s and 9-joi 9-joint nts s and and henc hence e over over all all weight of assembly will be more. <. >ts corrosion resistance is less as compared with composite materials.
. Steel drive shafts have less damping capacity. capacity.
erits of Composite Drive Shaft 0. They have have high speci%c speci%c modulus modulus and streng strength. th. . educed educed weigh weight. t. ;. The The funda fundame ment ntal al natur natural al fre" fre"uen uency cy of the the carb carbon on %ber %ber composite drive shaft can be twice as high as that of steel or aluminum because the carbon %ber composite material material has more than < times the speci%c sti&ness of steel or aluminum aluminum,, which which makes makes it possibl possible e to manufa manufactur cture e 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 <. (ue (ue to the the weig weight ht reduc educti tion on,, fuel fuel cons consum umpt ptio ion n will will be reduced. . They have high high damping capacity capacity hence they they produce produce less vibration and noise. . They have have good corros corrosion ion resistance resistance.. 7. Creater Creater tor"ue tor"ue capacity capacity than steel or aluminum aluminum shaft. shaft. 3. 6onger 6onger fatigue life life than steel or or aluminum shaft shaft.. #. 6ower rotating rotating weight transmits more of available power. power.
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 drive shaft with a slip joint at the front front end without without e!periencing 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. @ibrat ibratio ion n can can be eithe eitherr tran transv sver erse se or tors torsio ional nal.. Transv ransver erse se vibration is the result of unbalanced condition acting on the shaft. This condition is usually by dirt or foreign material on the shaft shaft,, and and it can can caus cause e a rath rather er noti notice ceabl able e vibra vibrati tion on in the the vehicle. Torsional vibration occurs from the power impulses of the engine or from improper universal join angles. >t causes a notic noticea eable ble sound sound dis distu turb rban ance ce and and can caus cause e a mecha mechanic nical al shaking. >n e!cess, both types of vibration can cause damage to the universal joints and bearings. Ghirling of a rotating shaft happ happen ens s when hen the cent centrre of gra gravit vity of the the sh shaf aftt mass ass 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 longit longitudi udina nall a!is a!is like like a rotat otating ing skipp skipping ing rope. ope. As the the speed speed rises, the eccentric deEection of the shaft increases, with the result that the centrifugal force also will increase. The e&ect is ther theref efor ore e cumu cumula lati tive ve and and will will cont contin inue ue unti untill the the whir whirli ling ng become critical, at which whi ch point the shaft will vibrate violently. violently.
:rom the theory of whirling, it has been found that the critical whir whirlin ling g speed speed of the the shaft shaft is inver inversel sely y propo proport rtio iona nall to the the s"uar s"uare e of the the shaft shaft lengt length. h. >f, >f, ther theref efor ore, e, a shaft shaft havi having ng,, 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 diame diamete terr of the the sh shaf aft, t, but but this this woul would d in incr crea ease se its st strrengt ength h beyond its tor"ue carrying re"uirements and at the same time inc in crease
its
iner nertia,
which ich
woul uld d
oppose ose
the
vehicle icle//s
accel acceler erat atio ion n and and decele decelera rati tion on.. An Anot othe herr alter alternat native ive solu solutio tion n fre" fre"ue uent ntly ly adop adoptted by car car, van, van, and and com commer mercial cial vehi vehicl cle e 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 Sprocket.. This article is about mechanical gears. :or other uses,
see Ce Cear ar
Idis Id isam ambi bigu guat atio ionH nH Two Two
meshing
gears
transmitting rotational motion. 8ote that the smaller gear is rotating faster. Although the larger gear is rotating less "uickly, its its tor"u or"ue e is prop propor orttiona ionall lly y grea greate terr. =ne subtl ubtlet ety y of thi his s particular arrangement is that the linear speed at the pitch diameter is the same on both gears.
A !ear or co!heel is
a rotating machine part
having
cut teeth, teeth, or cogs, cogs, which which mesh with with anot another her toot toothed hed part part in order to transmit tor"ue 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. gear. Two Two or more gears working in tandem are called a transmission and
can
produce
a mechanical
advant advantage age through through a gear gear ratio ratio and thus may be conside considere red d a simp simple le mach machin ine. e. Cear Ceared ed devi device ces s can can chan change ge the the sp spee eed, d, tor tor"ue, "ue, and di dire rect ctio ion n of a powe powerr sour source ce.. The The most most commo common n 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 tran transm smis issi sion ons s whic which h o&er o&er mult multip iple le gear gear rati ratios os,, su such ch 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 rati ratio o is conti continuo nuous us rath rather er than than di disc scre rete te,, or when when the the device device does does not not actu actual ally ly cont contai ain n any any gear gears, s, as in a cont contin inuo uous usly ly variable transmission. The earliest known reference to gears was circa A.(. $ by *ero of Ale!andria, but they can be traced
back to the Creek mechanics of the Ale!andrian school in the ;rd
century
..
and
were
greatly
Creek Creek polymat polymath h Archim Archimedes edes I37M I37M0 0
developed
by
the
..H. ..H. The Antik Antikyt ythera hera
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 depend upon 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 more e!pensive e!pensive to manufactur manufacture e and their lubrication lubrication re"uirements may impose a higher operating cost. Types
)/te tern rnal al !ear !ear-- An e!te 0. )/ e!tern rnal al gear gear is one one with with the the teet teeth h formed on the outer surfac face of a cylinde nder or cone cone.. onversely, Internal !earD an in . Internal inte tern rnal al gear gear is one one with with the the teet teeth h formed on the inner ner surface of a cylin ind der 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 di rection 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
radials, and although they are not straight-sided in form Ithey are ar e us usua ually lly of sp speci ecial al for form m to ac achie hieve ve co const nstan antt dr driv ive e ra rati tio, o, mainly involut involuteH, eH, the edge of each tooth is straig straight ht 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 parall el to each other+ this is the most common orientation. >n the latter, the shafts are ar e no nonn-pa para rall llel el,, an and d in thi his s con on% %gu gura rati tion on th the e ge gear ars s ar are e 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 parallell helical gears, each pair of teeth %rst make paralle make contact at a single point at one side of the gear wheel+ a moving curve of cont co ntac actt the hen n gr grow ows s gr grad adua uall lly y ac acrros oss s th the e too ootth fa face ce to a ma!imum then recedes until the teeth break contact at a single point on the opposite side. >n sk skew ew 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, whi hic ch needs to be acc cco ommodated by appropr appr opriate iate thr thrust ust bear bearings ings,, and a gr great eater er degr degree ee of slid sliding ing fric fr icti tion on be betw twee een n th the e me mesh shin ing g te teet eth, h, of ofte ten n ad addr dres esse sed d wi with th additives in the lubricant.
Se !ears :or a NcrossedN or NskewN con%guration, the gears must have the same sa me pr pres essur sure e ang angle le an and d no norm rmal al pi pitc tch+ h+ ho howe weve ver, r, th the e he heli! li! angl an gle e an and d ha hand nded edne ness ss ca can n be di di&e &erren entt. The rel elat atio ions nshi hip p 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 opposit e angles add to 4eroD the angle between shafts shafts is 4er 4ero oM that is, the shaft shafts s are parallel. parallel. Ghere the sum or the di&erence 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 (oub le he heli lica call ge gear ars, s, or he herrri ring ngbo bone ne ge gear ars, s, ov over erco come me th the e 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 together.. This arrangement cancels out the net a!ial thru th rust st,, si sinc nce e ea each ch ha half lf of th the e ge gear ar th thru rust sts s in th the e op oppo posi site te direction resulting in a net a!ial force of 4ero. This arrangement can ca n re remo move ve th the e ne need ed fo forr th thru rust st bea beari rings ngs.. *o *owe weve ver, r, do doubl uble e helica hel icall gea gears rs ar are e mo morre di' di'cul cultt to ma manu nufa fact ctur ure e due to th their eir more complicated shape. :or both possible rot :or rotationa ationall dire directions ctions,, ther there e e!is e!istt 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
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 lea le ad to disass sse embly of the ge gea ar train, while the stab ablle arrangement generates a net corrective force. >f the direction of rotation is reversed, the direction of the a!ial thrusts is also reversed, rev ersed, so a stable con%guration 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 ti p cu cutt o& o&.. Gh Ghen en tw two o be beve vell ge gear ars s mes esh, h, th thei eirr im imag agin inar ary y vert ve rtice ices s mu must st oc occup cupy y th the e sa same me po point int.. Th Their eir sh shaf aftt a! a!es es al also so intersect at this point, forming an arbitrary non-straight angle betw be twee een n th the e sh shaf afts ts.. Th The e an angl gle e be betw twee een n the sh shaf afts ts ca can n 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 Spir al be beve vell ge gear ars s ca can n be ma manu nufa fact ctur ured ed as Cl Clea easo son n ty type pes s Icirrcul Ici cular ar ar arc c wi with th no non-c n-con onst stan antt to toot oth h de dept pthH hH,, =e =erl rlik ikon on and urve! types Ic Iciircu cullar arc with co con nstant tooth dept pth hH, Qling Ql ingel elnbe nberg rgy yclo clo-) -)al alloi loid d I2p I2picy icyclo cloid ids s wi with th co cons nsta tant nt to toot oth h depthH or Qlingelnberg)alloid. Spiral bevel gears have the same advant adv antage ages s and disa disadva dvanta ntages ges re relati lative ve to thei theirr str straigh aight-c t-cut ut 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. 8ote 8o teDD Th The e cy cyli lind ndri rica call ge gear ar to toot oth h pr pro% o%le le co corrres espo pond nds s to an invo in volu lute te,, bu butt th the e be beve vell ge gear ar to toot oth h pr pro% o%le le to an oc octo toid id.. Al Alll tradit tra ditiona ionall bev bevel el gea gearr gen genera erator tors s Ilik Ilike e Cle Cleason ason,, Qli Qlingel ngelnber nberg, g,
*eidenreich *eidenr eichR*a R*arbe rbeck, ck, and G5G G5G5od 5oduleH uleH man manufac ufactur ture e bev bevel el gears gear s wit with h an oct octoid oidal al too tooth th pr pro%l o%le. e. >5) >5)= =T TA8T A8TDD :or -a -a!is !is mill mi lled ed be beve vell ge gear ar se sets ts it is im impo port rtan antt to ch choo oose se th the e sa same me calc ca lcul ula ati tion on J la lay you outt li lik ke the co conv nve ent ntio iona nall man anuf ufac acttur urin ing g method. Simpli%ed calculated bevel gears on the basis of an e"uivalent cylindrical gear in normal section with an involute toot to oth h fo forrm sh show ow a de devi vian antt to toot oth h fo forrm wi with th red educ uced ed to toot oth h strength by 0$-31 without o&set and <1 with o&set F(iss. *necke, T9 (resden. :urthermore those Binvolute bevel gear setsB causes more noise. #ypoi+ !ear *ypoid gears resemble spiral bevel gears e!cept the shaft a!es do no nott in inte ters rsec ect. t. Th The e pi pitc tch h su surf rfac aces es ap appe pear ar co coni nica call bu but, t, to comp co mpen ensat sate e for th the e o& o&set set sha shaft ft,, ar are e in fac factt hy hype perb rbolo oloids ids of revolution. *ypoid gears are almost always designed to operate with shafts at #$ degrees. (epending on which side the shaft is o&set to, relative to the angling of the teeth, contact between hypoid gear teeth may be even smoother and more gradual than with spiral bevel gear teeth, but also have a sliding action action along alo ng th the e me meshi shing ng te teet eth h as it rot otat ates es an and d th ther erefo eforre us usua ually lly re"uire some of the most viscous types of gear oil to avoid it being e!truded e!truded from the mating tooth faces, the oil is normally designated *) Ifor hypoidH followed by a number denoting the viscosity. Also, the pinion can be designed with fewer teeth than a spiral bevel pinion, with the result that gear ratios of $D0 and higher are feasible using a single set of hypoid gears. This style of gear is most commonly found driving mechanical di&erentials+ which are normally straight cut bevel gears+ in motor vehicle a!les. Baclash acklash is acklash is the error in motion that occurs when gears change direction. >t e!ists because there is always some gap between the trailing face of the driving driving tooth and the leading face of the tooth behind it on the driven gear, and that gap must be closed before force can be transferred in the new direction. The term BbacklashB can also be used to refer to the si4e of the gap, not
just the phenomenon it causes+ cau ses+ thus, one could speak of a pair of gears as having, for e!ample, B$.0 mm of backlash.B A pair of gears could be designed to have 4ero backlash, but this would pres presup uppo pose se perf perfec ecti tion on in manu manufa fact ctur urin ing, g, unif unifor orm m ther therma mall e!pan !pansi sion on char charac acte teri rist stic ics s thr through oughou outt the the sy syst stem em,, and and no lubri lubrica cant nt.. Ther Therefo eforre, gear gear pair pairs s are are desig designed ned to have have some some backlash. backlash. >t is usually provided provided by reducing reducing the tooth thickness 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 teet teeth. h. ack acklas lash h can can also also be prov provide ided d by movi moving ng the the gear gears s furthe furtherr apart. apart. The backlash backlash of a gear train e"uals 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 whi hic ch preci ecisio sion is important, su suc ch as inst in stru rume ment ntat atio ion n and and cont contrrol, ol, back backla lash sh can can be mini minimi mi4e 4ed d 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 ual manner, er, the other half pl pla aced alongside it, free to rotate about the shaft, but with springs betwe between en the the two two halve halves s prov providi iding ng relati elative ve tor tor"ue betwee between n them them,, so that hat one one achie chiev ves, es, in e&ec e&ect, t, a sing single le gear gear wit 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, emissions, there are
high hi ghe er sound levels 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 which tends tends to gener generat ate e mor more nois noise e due to small smaller er over overla lap p ratio and a lower mesh sti&ness etc. than the helical gears used for for the the hi high gh rati ratios os.. This This fact fact has been been utili utili4e 4ed d in analy analy4i 4ing ng 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 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 velocit velocity y ratio ratio is depende dependent nt on the pro%le pro%le of the teeth. 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 cycloid and and the involute.. The cycloid was more common until the late 03$$s+ involute since then the involute has largely superseded it, particularly in drive train applications. The cycloid is in some ways the more
interesting and Ee!ible shape+ however the involute has two adva advant ntag ages esDD it is easie easierr to manu manufac factu turre, and and it perm permit its s the 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 are most most common commonly ly used because because of their their high high strengt strength-t h-tooweight ratio and low cost. )lastic is commonly used where cost or weight is a concern. A properly designed plastic gear can replac eplace e st stee eell in many many cases cases becau because se it has has many many desir desirabl able e proper propertie ties, s, includi including ng dirt dirt tolera tolerance nce,, low speed speed meshing meshing,, the abili ability ty to Bskip BskipBB "uite "uite well
and and the abilit ability y to be made made with
materi materials als not needing needing additi additional onal lubrica lubricatio tion. n. 5anufa 5anufactu cture rers rs have employed plastic gears to reduce costs in consumer items incl in clud udin ing g copy copy mach machin ines es,, opti optica call st stor orag age e
devi device ces, s, chea cheap p
dyna dynamo mos, s, cons consum umer er audi audio o e"ui e"uipm pmen ent, t, serv servo o moto motors rs,, and 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 Ghen the the modu module le is base based d upon upon in inch ch meas measur urem emen ents ts,, 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.
D)SI4N O' CAST IRON DRI*) S#A'T
Intro+&ction shaft5 t5+r +riv iven en A shaf
0icy 0icycl cle e is
a bicycle that
uses
a drive
shaft instead shaft instead of a chain chain to 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 the gear ranges possible with sprockets and derailleurs. ecently, due due to adva advanc ncem emen ents ts in in inte terrnal nal gear gear tech techno nolo logy gy,, a smal smalll number of modern shaft-driven bicycles have been introduced.
%&rpose of the Drive Shaft The tor"ue that is produced from the engine and transmission must must be tran transfe sferr rred ed to the the rear ear whee wheels ls to push push the the vehic vehicle le forw forwar ard d mome moment nt.. The The driv drive e sh shaf aftt must must prov provid ide e a smoo smooth th,, 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 transmit tor"ue tor"ue from from the transmission transmission to the pedal . (uring the operati operation, on, it is necessary necessary to transmit transmit ma!imum ma!imum low-gear tor"ue ;. The The driv drive e shaft shafts s must must also be capab capable le of rotat otatin ing g at the very fast speeds re"uired by the vehicle.
<. The The driv drive e sh shaf aftt must must also also oper operat ate e thr through ough cons consta tant ntly ly changing gear velocity ratio . . The The leng length th of the the driv drive e sh shaf aftt must must also also be capa capabl ble e of changing while transmitting tor"ue. 6ength changes are caused by a!le movement due to tor"ue reaction, road deEections, deEections, braking loads and so on. A slip joint is used to compensate for this motion. . The slip joint joint is usually usually made of an inter internal nal and e!tern e!ternal al spline. >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 propell pelle er shaf hafts. *owever ever the dri drive shaf haft 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. forward. The shaft shaft is the primary primary connection between the front 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, transmitting, used in vehicle where where the pedal is situated situated at the human feet. A drive shaft is an assembly of one or more tubu tubular lar shaft shafts s conne connect cted ed by unive univers rsal al,, const constan antt velo velocit city y or
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 the engi engine ne to the whee wheell with ithout out slip slip.. >t need needs s only only a less less maint mainten enanc ance. e. >t is cost cost e&ect e&ective ive.. )rope ropelle llerr sh shaf aftt st strrength ength is more and also propeller shaft diameter is less. it absorbs the shock shock.. eca ecause use the the prop propell eller er sh shaf aftt cent center er is %tte %tted d with with the the univ univer ersa sall join jointt is a Ee!i Ee!ibl ble e join joint. t. >t tur turns in into to any any angu angula larr 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 clot lothes+ and no more chai hain and derailleur maintenance. Shaft-driven
bikes
have
a
large bevel
gear where
a
conventional bike would have its chain ring. ring. This meshes with anothe anotherr bevel bevel gear 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 tur turned ned thr through ough #$ degr degree ees. s. The The driv drive e sh shaf aftt then 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 conve convent ntio iona nall bike, bike, and and cance cancelin ling g out out the the %rst %rst driv drive e tor tor"ue change of a!is.
The #$-degree change of the drive plane that occurs at the bottom bracket and bracket and again at the rear hub uses hub uses bevel gears for the most e'cient performance, though other mechanisms coul uld d be used, ed, e.g. *ob *obson son/s /s joi joints nts,, wo worm rm gea gears rs or or crossed helica hel icall
gears gea rs.. The drive shaft is often mated to a hub
gear which is an internal gear system housed inside the rear hub.
:ig <.0.evel Cear 5echanism
Speci3cation of +rive shaft The
speci%cations
of
the
composite
drive
shaft
of
an
automotive transmission are same as that of the steel drive shaft shaft for for opti optima mall desig design. n. The funda fundame ment ntal al natu natura rall bendin bending g fre"uency for passenger cars, small trucks, and vans of the prop propel elle lerr sh shaf aftt sh shou ould ld be hi high gher er than than , ,$ $$ $ rpm rpm to avoi avoid d whirling whirling vibration vibration and the tor"ue tor"ue transmission transmission capability capability of the drive shaft should be larger than ;,$$ 8m. The drive shaft oute outerr di diam amet eter er sh shou ould ld not not e!ceed ceed 0$$ mm due to sp spac ace e limitations. *ere outer diameter of the shaft is taken as #$ mm. The drive shaft of transmission system is to be designed
optimally optimally for following speci%ed speci%ed design re"uirement re"uirements s as shown in Table.
Ta0le- Desi!n re6&irements an+ speci3cations
S.
Name
Notation
Unit
*al&e
No 0.
9ltimate Tor"ue Tor"ue
Tma!
. 5a!. Speed of shaft
8ma!
;. 6ength of Shaft
6
8m
rpm
mm
Steel IS5<H used for automotive drive shaft applications. The material properties of the steel IS5<H are given in Table. The steel drive shaft should satisfy three design speci%cations such as tor"ue tor"ue transm transmissi ission on capabili capability, ty, buckling buckling tor"ue tor"ue capabil capability ity and bending natural fre"uency.
Ta0le- echanical properties of Cast iron 7S"8C9
S.N o
ech.%ropertie Sym0ol s
Units
1.
Uoungs Uoungs 5odulus
2
C)a
2.
Shear 5odulus
C
C)a
Cast Iron
.
)oisson atio
v
555555
".
(ensity
V
QgJm;
Sy
5)a 5)a
Ss
5)a 5)a
8.
Uield Strength Strength
:.
Shear Strength
Bevel 4ear Bevel Bevel !ears !ears ar are gears wher where e the the a!es a!es of the two two sh shaf aftts 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.. cone
)O)TR; AND T)RINO(O4;
Ghen shafts
intersecting are
gears, the pitch
connected cones
by
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 i n :ig. :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 shown in :ig. :ig. 0;.;. 0;.;. which e!plains e!plains the nomenclatur nomenclatures es of a bevel gear.
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 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 gear teeth are are inherently inherently non non - interchangea interchangeable. ble. bH The The work workin ing g dept depth h of the the teet teeth h is us usua uall lly y m, m, the the same same as for for stan standa darrd sp spur ur and and helical
gears,
but
the
bevel
pinion
is
desi design gned ed with with the the larg larger er adde addend ndum um I $.7 $.7 working depthH. cH This
avoids
interference
and
results
in
stronger pinion teeth. >t also increases the contact ratio. dH The gear gear addendum addendum varies varies from from 0m for a gear gear ratio of of 0, to $.< m for ratios of 6.8 and greater.
The gear ratio can be determined from from the number of teeth, the pitch diameters or the pitch cone angles as,
Ill&stration of spiral an!le The :ig.0;.< illustrates the measurement of the spiral angle
of a spi spira rall bevel bevel gear gear. eve evell gear gears s most most comm commonl only y have have a pressure angle of $o, and spiral bevels usually have a spiral angle of ; o.
'i!.
omparison of intersecting and o&set shaft bevel type gearings
'orce 'orce Analysis
4ear an+ shaft forces
4ear an+ shaft forces
'i!. 1.1= Bevel !ear 5 'orce analysis
>n :ig. 0;.0$, :n is normal to the pitch cone and the resolution of resultant tooth force :n into its i ts tangential Itor"ue producingH,
radial
Ise Isepar paratingH
and and
a!i a!ial
Ith IthrustH
component ents
is
design designat ated ed :t, :t, :r and and :a respe espect ctive ively ly.. An au!i au!ilia liary ry view view is neede needed d to sh show ow the the true true lengt length h of the the vect vector or repr epresent esenting ing 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, minute , :t is in 8 and G is power in kG. kG. dav = d-bsin
Fn = Ft /cosφ Fr = Fn cosγ = Ft tanφ c Fa = Fn sinγ = Ft tanφ sin
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 will Y Ibody mass of the rider ! gH ! the length of the pedal lever. emem emember ber to consi conside derr the the geari gearing ng of the the bike bike thou though gh.. The 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 i s a bevel gear gear wi with helical helical teeth. The main main appli applica cati tion on of this this is in a vehic vehicle le di&erential di&erential,, where the dirrecti di ection on of driv drive e from from the the dri drive ve sha shaft ft must must be tur turned ned #$ degrees to drive the wheels. The helical design produces less vibration and noise than conventional straight-cut or spur-cut gear with straight teeth.
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 toot tooth h is inclin inclined ed in the the cloc clockw kwise ise direc directi tion on from from the the a!ia a!iall plan pl ane e throu hrough gh the the mid idpo poin intt of the the tooth ooth as view viewed ed by an observer looking at the face of the gear. 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. gear. 8ote that a spiral bevel gear and pinion are always of opposite hand, including the case when the gear is internal internal.. Also note that the designations right hand and left hand are applied similarly to other types of bevel gear, hypoid hypoid gears, 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 revolved hyperboloid hyperboloid Ithat Ithat is, the pitch surface of the hypoid gear is a hyperbolic surfaceH, whereas the shape of a sp spir iral al beve bevell gear gear is nor normall mally y coni conica cal. l. The The hypo hypoid id gear gear places the pinion pinion o&-a!is o&-a!is to the crown wheel Iring wheel Iring gearH which
allo allows ws the the pi pini nion on to be lar larger ger in di diam amet eter er and and have have mor more contact area. >n hypoid gear design, the pinion and gear are practically always of opposite hand, and the spiral angle of the pinion is usually larger than that of the gear. The hypoid pinion is then larger in diameter than an e"uivalent bevel pinion. A hypoid gear incorporates some sliding and can be considered halfway between a straight-cut gear and a worm gear. gear. Special gearr oi gea oils ls are are re"uir e"uired ed for for hypo hypoid id gear gears s beca becaus use e the the slidi sliding ng acti action on re"uir e"uires es e&ect e&ective ive lu lubr brica icati tion on under under e!t e!trem reme e pre pressure ssure betw etween the teeth. *ypoid gear earings ngs are used in power transmission products that are more e'cient than conventional worm gearing. They are considerably stronger in that any load is conveyed through multiple teeth simultaneously. y contrast, bev bevel gear gears s are are load loaded ed thr throug ough one one toot tooth h at a time. ime. The The multiple contacts of hypoid gearing, with proper lubrication, can be nearly silent, as well.
Spiral an!le The spiral sp iral angle angl e in a spiral bevel gear is the angle between the tooth trace and an element of the pitch cone, and corresponds to the heli! angle in helical teeth. 9nless otherwise speci%ed, the term spiral angle is understood to be the mean mean spiral spiral angle. •
•
5ean spiral angle is the speci%c designation for the spiral angle at the mean cone distance in a bevel gear. gear. =uter spiral angle is the spiral angle of a bevel gear at the outer cone distance.
•
>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 be used for higher reduction ratios, however they also have some slid slidin ing g acti action on alon along g the the teet teeth, h, whic which h reduc educes es mech mechan anic ical al e'ciency, the energy losses being in the form of heat produced in the gear surfaces and the lubricating Euid. >n older automotive designs, hypoid gears were typically used in rear-drive rear-drive automobile drive trains, trains, but modern designs have tende tended d to su subs bsti titu tute te sp spir iral al beve bevell gear gears s to incr increase ease driv drivin ing g e'ciency.. e'ciency *ypoi *ypoid d gear gears s are are st still ill common common in lar larger trucks trucks because they can transm transmit it higher tor"ue tor"ue.. A higher hypoid o&set allows the gear to transmit higher tor"ue. *owever increasing the hypoid o&se o&sett resul esults ts in reduc educti tion on of mech mechan anic ical al e'ci e'cien ency cy and and a conse"uent reduction in fuel economy. economy. :or practical purposes, it is often impossible to replace low e'ciency hypoid gears with more e'cient spiral bevel gears in automotive use because the spir sp iral al beve bevell gear gear woul would d need need a much uch lar larger ger di diam amet eter er to transmit the same tor"ue. >ncreasing the si4e of the drive a!le gear would re"uire an increase of the si4e of the gear housing and a reduction in the ground clearance. Another advantage of hypoid gear is that the ring gear of the di&erential and the input pinion gear are both hypoid. >n most passenger cars this allows the pinion to be o&set to the bottom of the crown wheel. This provides for longer tooth contact and allows the shaft that drives the pinion to be lowered, reducing the the Bhum BhumpB pB in intr trus usio ion n in the the passe passeng nger er comp compar artm tment ent Eoor Eoor.. *owever, the greater the displacement of the input shaft a!is from the crown wheel a!is, the lower the mechanical e'ciency. e'ciency.
$orm +rive A worm drive is a gear arrangement in arrangement in which a worm Iwhich is a gear in the form of a screw screwHH meshes with a worm gear Iwhich is similar in appearance to a spur gearH. gearH. The two elements are also called the worm screw and worm wheel. The terminology is
often confused by imprecise use of the term worm gear to to refer to the worm, the worm gear, or the worm drive as a unit. 6ik 6ike othe otherr gear gear arra arrang ngem emen entts, a wor worm driv drive e can reduc educe e rotational speed or speed or transmit higher tor"ue tor"ue.. The image shows a section of a gear bo! with a worm gear driven by a worm. A worm is an e!ample of a screw screw,, one of the si! simple machines. machines.
)/planation A
gearbo!
designed
using
a
worm
and
worm-wheel
is
considerably smaller than one made from plain spur gears, gears, and has has its its driv drive e a!es a!es at #$ #$Z Z to each each othe otherr. Gith ith a single single start start worm, for each ;$Z turn of the worm, the worm-gear advances only one tooth of the gear. Therefore, regardless of the wormNs si4e si4e Is Isens ensibl ible e engi enginee neeri ring ng limit limits s notw notwit iths hsta tand nding ingH, H, the the gear gear ratio is the "size o the worm gear - to - 1". 1". Civen a single start worm, a $ tooth worm gear reduces the speed by the ratio of $D0. Gith spur
gears, a gear of
0
smallest
te teeth
It Ithe
si4e
if
designed to good
engineering
practicesH
match with a <$
tooth
must to
achieve the same
ratio.
Therefore, if the
diametrical pitch
I()H of each gear
$D0
gear
is the same, then, in terms of the physical si4e of the <$ tooth gear to that of the $ tooth gear, the worm arrangement is considerably smaller in volume.
Direction of transmission 9nlike with ordinary gear trains, the direction of transmission Iinput shaft vs output shaftH is not reversible when using large reduction ratios, due to the greater friction involved between the worm and worm-wheel, when usually a single start Ione spiralH worm is used. This can be an advantage when it is desired to eliminate any possibility of the output driving the input. >f a multistart worm Imultiple spiralsH is used then the ratio reduces accordingly and the braking eect of of a worm and worm-gear may need to be discounted, as the gear may be able to drive the worm. Gorm gear con%gurations in which the gear cannot drive the worm are called sel-locking. sel-locking. Ghether a worm and gear is selflocking depends depends on the lead angle, the pressure pressure angle, and the coe'cient of friction+ however, it is roughly correct to say that
a worm and gear are self-locking if the tangent of the lead angle is less than the coe'cient of friction.
Applications >n early $th century automobiles prior to the introduction of power steering, the e&ect of a Eat or blowout on one of the front wheels tended to pull the steering mechanism toward the side with the Eat tire. The use of a worm screw reduced this e&ect. :urther worm drive development led to recirculating ball bearings to reduce reduce frictio frictional nal forces, forces, which which transm transmitt itted ed some some stee st eeri ring ng for force to the the wheel wheel.. This This aide aides s vehic vehicle le cont contrrol and and reduces wear that could cause di'culties in steering precisely. precisely. Gorm drives are a compact means of substantially decreasing speed
an d
increasing
tor"ue.
Small ele elect ctri ric c
moto mo tors rs are
generally high-speed and low-tor"ue+ the addition of a worm drive increases the range of applications that it may be suitable for,
especially
when
the
worm
driveNs
compactness
is
considered.
Gorm drives are used in presses presses,, ro rollin lling g mil mills ls,, conveying engineering,, mining industry machines, on rudders engineering rudders,, and and worm drive dri ve saw saws s. >n addi dittion, on, milling head eads and and rot rotary ary tables are posi posittione ioned d
usin us ing g
high hi gh-p -prrecis ecisio ion n du dupl ple e!
worrm wo
driv dr ives es with
adjustable backlash backlash.. Gorm gears are used on many liftJelevator and escalator-drive applications due to their compact si4e and the non-reversibility of the gear. gear.
>n the era of sailing ships, the introduction of a worm drive to cont contrrol the rudde udderr was was a sign signi% i%ca cant nt adva advanc nce. e. )rio rior to its 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 largediam di amet eter er whee wheels ls so up to four four crew crewme men n coul could d oper operat ate e the the rudder. Gorm drives have been used u sed in a few automotive rear-a!le rear-a!le %nal drives drives Ithough Ithough not the di&erential di&erential itselfH. itselfH. They took advantage of 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 <$<. <$<. The worm gear carries the the di di&er &eren enti tial al gear gearin ing, g, whic which h prot protect ects s the the vehic vehicle le agai against nst rollback. This ability has largely fallen from favour due to the higher-than-necessary higher-than-necessary reduction ratios. A more recent e!ception e!ception to this is the T the Torsen orsen di&erential di&erential,, which uses worms and planetary worm gears in place of the bevel gearing of conventional open di&erentials. Torsen di&erentials are most pro prominen nently feature ured in the *55G@ and and some some commer commercial cial *ummer *ummer vehicles, and as a center di&erential in some al alll wh whee eell dr drive ive sy syst stem ems, s, suc such as Audi AudiNs Ns "uattro "uattro.. @ery heavy trucks, such as those used to carry aggregates aggregates,, often use a worm gear di&erential for strength. The worm drive is not as
e'ci e'cien entt as a hypoid hypoid gear, and such trucks invariably have a very very large large di&er di&erent ential ial housing housing,, with with a corre correspon sponding dingly ly large large volume of gear oil, oil, to absorb and dissipate the heat created.
Gorm orm driv drives es are are us used ed as the the tuni tuning ng mech mechan anis ism m for for many many musical
instruments,
including
guitars,, guitars
double-basses,, double-basses
mandolins,, bou4oukis mandolins bou4oukis,, and many many banjos banjos Ialthough most highend banjos banjos use use planetary gears or gears or friction pegsH. A worm drive tuning device is called a machine head. head. )lastic worm drives are often used on small battery-operated elect electri ric c moto motors rs,, to prov provide ide an outp output ut with with a lowe lowerr angula angularr velocity Ifewer revolutions per minuteH than that of the motor, which operates best at a fairly high speed. This motor-wormgear gear driv drive e sy syst stem em is ofte often n us used ed in toys oys and and othe otherr smal smalll electrical devices.
A worm worm drive drive is used used on ju jubil bilee ee-t -typ ype e hose clamps clamps or jubilee clamps. The tightening screwNs worm thread engages with the slots on the clamp band. =ccas ccasio ion nally ally a worm orm gear gear is desi design gned ed to run in rever everse se,, resulting in the output shaft turning much faster than the input. 2!amples
of
this
may
be
seen
in
some
hand-cranked
centrifuges or centrifuges or the wind governor governor in in a musical bo!. 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, -1, which means the gears corresponding to the sun and annular gears are the same si4e. This can be done by b y engaging eng aging the planet p lanet gears gea rs of two identical identi cal
an d
coa!ial
epic ep icyc ycli lic c
gear ge ar tr trai ains ns to fo f orm a
spu sp ur
gear gear
dierential. dierential. Another approach is to use bevel gears for gears for the sun and annular gears and a bevel gear as the planet, which is known as a bevel gear dierential. dierential.
)picyclic +i,erential An epicyclic epicyclic di&er di&erential ential can use epicyclic gearing gearing to split and appo apport rtio ion n tor"ue asymme asymmetri trical cally ly betwee between n the front front and rear rear a!les. An epicyclic di&erential is at the heart of the T the Toyota oyota )rius auto automo moti tive ve drive drive trai train, n, wher where e it inter intercon connec nects ts the the engin engine, e, 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. 2picy 2picycl clic ic gear gears s are are also also calle called d planet planetar ary y gear gears s becau because se the the a!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.
Sp&r5!ear +i,erential This is another type of di&erential that was used in some early automobiles, more recently the =ldsmobile Tornado, Tornado, as well as othe otherr non-a non-aut utom omot otiv ive e appli applicat cation ions. s. >t cons consist ists s of spur gea gears rs only. A spur-gear spur-gear di&erential di&erential has two e"ual-si4ed spur gears, one for each each half half-s -sha haft ft,, with with a space space betw betwee een n them them.. >nst >nstea ead d of the the evel gear, 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 same a!is a!is as the the two two shaft shafts. s. Tor"u or"ue e from from a prime mover or transmission,, su transmission such ch as the driv drive e sh shaf aftt of a car, ar, rotat otates es this this carrier. 5oun 5ounte ted d in this this car carrier rier are are one one or mor more pair pairs s of id iden enti tica call pinions, pinions, genera generally lly longer longer than than their their diamete diameters, rs, and typical typically ly smaller than the spur gears on the individual half-shafts. 2ach pinio pinion n pair pair rotat otates es freel freely y on pins pins su suppo pport rted ed by the the carr carrier ier.. :urthermore, the pinion pairs are displaced a!ially, such that they mesh only for the part of their length between the two spur spur gears, gears, and rotat rotate e in opposit opposite e direct directions ions.. The remai remaining ning 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, 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 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 turns a corner corner the drive wheels must rotate at di&erent di&erent speeds to maintain traction. The automotive automotive di&erential di&erential is designed to drive a pair of wheels while allowing them to rotate rotate at di&erent di&erent speeds. speeds. >n vehicle vehicles s without without a di&er di&erent ential ial,, such as karts karts,, both driving wheels are forced to rotate at the same speed, usually on a common a!le a!le driven 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 rotat otates es too too fast fast or the the oute outerr whee wheell drag drags, s, whic which h resul esults ts in di'cult and unpredictable handling, damage to tires tires and and roads, and strain on Ior possible failure ofH the entire drive train. train. >n rear-wheel drive automobiles the central drive shaft Ior prop shaftH shaftH engages engages the di&erenti di&erential al throug through h a hypoid gear gear Icrownwheel 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 can limi limitt trac tracti tion on unde underr less less than than id idea eall cond condit itio ions ns.. The The amount of traction re"uired 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 vehicleNs momentum, and so on. The tor"ue applied to each driving wheel wheel is a result of the engine,, transmission engine transmission and and drive a!les applying a twisting force agai agains nstt the the resis esista tanc nce e of the the traction at that that roadw oadwhee heel. l. >n lower gears and thus at lower speeds, and unless the load is e!ceptionally high, the drivetrain can supply as 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 the amount 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 conventional BopenB Inon-lock Inon-locked ed or otherwise otherwise traction-aide traction-aidedH dH 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, 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
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 5any newe newerr vehic vehicles les featu featurre traction control, control, which partially mitig itiga ates
the
poor
tractio ction n
char haracterist stic ics s
of
an
open
di&er di&erent entia iall by using using the the anti-lo anti-lock ck brakin braking g system system to limit or stop st op the the slipp slippag age e of the the low low tract tractio ion n wheel wheel,, incr increasin easing g the the tor tor"ue "ue that hat can can be appli pplied ed to both both whee wheels ls.. Ghil Ghile e not not as e&ective in propelling a vehicle under poor traction conditions as a trac tracti tion on-a -aid ided ed di di&e &errenti ential al,, it is bett better er than than a simp simple le mecha echani nica call assistance.
open open
di&e di &errenti ential al
wit with
no
elec electtronic onic
trac tracti tion on
