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MACHINE ELEMENTS INMECHANICAL DESIGN

Chapter 1:

Kinematics of Gears

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http://en.wikipedia.org/wiki/Image:Gears_animation.gif

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Objectives

Recognize and describe the main features of spur gears,

helical gears, bevel gearsand worm/wormgear sets.

Describe the important operating characteristics of these

various types of gears with regards to the similarities and

differences among them and their general advantages and

disadvantages.

Describe the involute-toothform and discuss its relationshipto the law of gearing.

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Define velocity ratio as it pertains to two gears operatingtogether.

Specify appropriate numbers of teeth for a mating pair ofgears to produce a given velocity ratio

Define train valueas it is pertains to the overall speed ratiobetween the input and output shafts of a gear-type speed

reducer (or speed increaser) that uses more than two gears.

Objectives (Concluded)

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INTRODUCTION

A gear is a component within a transmission device that transmits rotational force toanother gear or device.

A gear is different from a pulley in that a gear is a round wheel which has linkages("teeth" or "cogs") that mesh with other gear teeth, allowing force to be fully

transferred without slippage.

Depending on their construction and arrangement, geared devices can transmitforces at different speeds, torques, or in a different direction, from the power source.ears are a very useful simple machine.

ears are used to reverse rotational direction, increase or decrease speed of rotation,transfer rotation to a different a!is, or to synchronie rotation across two or more a!isin a machine or engine

#he smaller gear in a pair is often called thepinion$ the larger, either the gear, or thewheel.

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INTRODUCTION

Gears may be classified according to the relative

position of the axes of revolution. The axes may be parallel,

intersecting,

neither parallel nor intersecting.

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Gears for connecting parallel

shafts:

Spur gear

pair of gears makes ete!n"l

cont"ctpair of gears makes inte!n"l

cont"ct

#

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arallel helical gears$

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!ac" and pinion%

Rack and pinion gears are usedto conert rotation into linear

motion!

"#ample: $

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Ge"!s &o! connectin'

inte!sectin' s"&ts

Straight bevel gears

&'piral (eel gears

#

$

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Neite! "!"llel no!

inte!sectin' s"&ts

Crossed#helical gears

&&)orm and *orm gear$

#

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*+ Use Ge"!s,,

!educe speed

$ncrease tor%ue

&ove po'er from one point to another Change direction of po'er

Generally this functionality is accomplished by many

gears mounted in a gear box

12

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#- Su! 'e"!s

Gears that have teeth that are straight and arranged

parallel to the axis of the shaft that carries the gear.

Spur gears are the most common type of gears. They

have straight teeth, and are mounted on parallel shafts!

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(bove: the involute

tooth form (bove: diagram

illustrating the la' of

gearing.

+eeth hae inolutes cures to maintain a constant angular elocit, ratio

*hen t*o *orking gears mate!

-ngular elocit, can (e achieed *hen a line dra*n perpendicular to the

surfaces of t*o rotating (odies at their point of contact al*a,s crosses

the center.line (et*een the t*o (odies at the same place!+he a(oe statement is also kno*n as the law of gearing!

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Te!.inolo'+ &o! Su! Ge"!s

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Spur gear teeth features: Circular pitch:

)iametral itch

*teeth+in:

&odule *mm:

where N - number of teeth and the

D -pitch diameters of the gears.

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Ge"! Toot /e"tu!es

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Pitch surface: The surface of the imaginary rolling cylinder *cone, etc. that the toothed gearmay be considered to replace.

Pitch circle: ( right section of the pitch surface. Addendum circle: ( circle bounding the ends of the teeth, in a right section of the gear. Root (or dedendum) circle: The circle bounding the spaces bet'een the teeth, in a right section

of the gear. Addendum: The radial distance bet'een the pitch circle and the addendum circle. Dedendum: The radial distance bet'een the pitch circle and the root circle.

Clearance: The difference bet'een the dedendum of one gear and the addendum of the matinggear. Face of a tooth: That part of the tooth surface lying outside the pitch surface. Flank of a tooth: The part of the tooth surface lying inside the pitch surface. Circular thickness*also called the tooth thickness : The thic"ness of the tooth measured on the

pitch circle. $t is the length of an arc and not the length of a straight line. Tooth space: The distance bet'een ad-acent teeth measured on the pitch circle.

Backlash: The difference bet'een the circle thic"ness of one gear and the tooth space of themating gear. Circular pitchp: The 'idth of a tooth and a space, measured on the pitch circle. Diametral pitch: The number of teeth of a gear per inch of its pitch diameter. ( toothed gear

must have an integral number of teeth. Thecircular pitch, therefore, e%uals the pitchcircumference divided by the number of teeth. Thediametral pitchis, by definition, the numberof teeth divided by thepitch diameter.

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Modulem: itch diameter divided by number of teeth. The pitch diameter isusually specified in inches or millimeters in the former case the module is the

inverse of diametral pitch. Fillet : The small radius that connects the profile of a tooth to the root circle. Pinion: The smaller of any pair of mating gears. The larger of the pair is called

simply the gear. Velocity ratio: The ratio of the number of revolutions of the driving *or input gear

to the number of revolutions of the driven *or output gear, in a unit of time.

Pitch point: The point of tangency of the pitch circles of a pair of mating gears. Common tanent: The line tangent to the pitch circle at the pitch point. !ine of action: ( line normal to a pair of mating tooth profiles at their point of

contact. Pressure anle : The angle bet'een the common normal at the point of tooth

contact and the common tangent to the pitch circles. $t is also the angle bet'een theline of action and the common tangent.

Base circle:(n imaginary circle used in involute gearing to generate the involutesthat form the tooth profiles.

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2%

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3%

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ressure angle The pressure angle is the angle bet'een the tangent to the

pitch circles and the line dra'n normal to the surfaces of the

gear tooth.

cosDDb =

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Su.."!+ o& Ge"! No.encl"tu!e0

/0 0itch diameter of pinion

/G 0itch diameter of gear

0 o! teeth t for pinion

G o! teeth t or gear

0d diametral pitch / constant for meshing gears

p circular pitch / constant for meshing gears

n0 speed of pinion rpm

nG speed of gear rpm

R elocit, ratio n0nG G00o*er constant across mating gears or series s,stem:

0in 0out0o*er in (ranched s,stem is consered:

0in 0- 0 !!

+orue *ill change;;rpm

hpinlbTorque

=

///,0* 0 +elix angle *? typically range from 1

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%- 1evel Ge"!s

Gear teeth arranged in a cone shape manner.

Types:

Straight bevel gears

Spiral bevel gears >ypoid gears

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1evel Ge"!s

Gear axis at @/;, based on

rolling cones

(dvantages

!ight angle drives )isadvantages

Get axial loading 'hich

complicates bearings and

housings

G i l f f i h b l

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Geometrical features of straight bevel gears

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2- *o!. Ge"!s

Ased to transmit motion and po'er bet'een t'o

nonintersecting shafts, usually @/; to each other.

>ave threads rather than teeth as li"e most gears.

Can achieve higher speed reduction, but lo'er mechanicalefficiency.

Worms and Worm gears

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*o!. Ge"!s $ears that are -./ to each other Ad0antaes

Buiet + smooth drive

Can transmit tor%ue at right angles

2o bac" driving Good for positioning systems

Disad0antae

&ost inefficient due to excessive

friction *sliding 2eeds maintenance

Slo'er speed applications

*orm

*orm gear

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3- Ge"! T!"ins

$ear trainsconsist of t'o or more gears for the purpose of

transmitting motion from one axis to another. 1rdinary ear trains

have axes, relative to the frame, for all gears comprising the train.

5elocity ratio:

)efined as the ratio of the rotational speed of the input gear to thatof the output gear for a single pair of gears.

P

G

G

P

P

G

P

G

P

G

G

P

G

P

size

size

speed

speed

N

N

D

D

R

R

n

nVR =======

where subscripts P and G represents the pinion and

the driven gear respectively

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Ge"! t!"insare a group of gears that *ork together toproduce large gear ratios

- 'e"! t!"inis a set or s,stem of gears arranged totransfer rotational torue from one part of a

mechanical s,stem to another

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Gear trains consists of:

Dri0in ears# attached to the input shaft

Dri0en ears# attached to the output shaft

2dler ears# interposed bet'een the driving anddriven gear in order to maintain the direction of theoutput shaft the same as the input shaft or to increasethe distance bet'een the drive and driven gears. (

compound gear train refers to t'o or more gears usedto transmit motion.

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34amples of $ear Trains

Types of gear trains

1. Simple gear train4. Compound gear train

. picyclic gear train

9. !everted gear train

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Gear Train !ule 7 itch of t'o gears in mesh must be

identical

G(!

P2"21"D$

"$#P

DP

"P#

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Train value:

!efers to the ratio of the input speed *for the first

gear in the train to the output speed *for the last gearin the train.

$t is the product of the values of 5! of each gear pair

in the train.

gear teethdrivingofproduct

gear teethdrivenofproduct=TV

ninnout

#TV

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4- Te AGMA

The (merican Gear &anufacturers (ssociation

*(G&( Standardi=es terms and symbols use, gear design and

applications. &ore information can be obtained from their 'ebsite:

http!""wwwagmaorg

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5UI6 /OR TODA7

)>-+ +?0" @A +>B' G"-R$

http://en.wikipedia.org/wiki/Image:Gears_animation.gifhttp://en.wikipedia.org/wiki/Image:Rack_and_pinion_animation.gif

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-/ A@R +>B' +@@

http://en.wikipedia.org/wiki/Image:Rack_and_pinion_animation.gif

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