1 Chapter 4 Spur Gears Intro Classif Terminology Law of Gearing

7/25/2019 1 Chapter 4 Spur Gears Intro Classif Terminology Law of Gearing

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Chapter 4: Spur Gears

Gears: Gears are

machine elements that

transmit motion by meansof successively engaging

teeth. The gear teeth act

like small levers.


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Belt!ope "rives # $arge center %istance of the shafts

Chain "rives # &e%ium center %istance of the shafts

Gear "rives # Small center %istance of the shafts


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ConveyorCounting Gear train

Gear *ump+atch gear ,heels
http://www.animationlibrary.com/animation/24371/3D/


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Printing machinery parts

Rotary die cutting machines

Blow molding machinery

Agricultural equipment

Boat out drives

Hoists and Cranes

Automotive prototype and reproduction

Diesel engine builders


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ewspaper !ndustry Plastics machinery

"otorcycle #ransmissions Polymer pumps

Automotive applications

Commercial and "ilitary operations

$pecial gear bo% builders


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Heavy earth moving vehicles

Canning and bottling machinery builders

$pecial machine tool builders

Boo& binding machines "arine applications

!n'ection molding machinery

"ilitary o(()road vehicles $tamping presses


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Gears may be classifie% accor%ing to the relative

position of the aes of revolution. The aes may be

parallel intersecting an% neither parallel nor intersecting.

1. Gears for

connecting

parallel shafts

Spur Gears: External contact Internal contact


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Parallel Helical gears Heringbone gears


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2. Gears for connecting

intersecting shafts 3 Bevel Gears


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Spiral bevel gearsStraight bevel gears


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Crossed-helical gears Worm +orm +heel


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


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http:,,,.%rgears.comgearanims.htm
http://www.drgears.com/gearanims.htmhttp://www.drgears.com/gearanims.htm


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http://www.mech.uwa.edu.au/DANotes/gears/intro/gearboxBIG.jpeg


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Addendum: The ra%ial %istance bet,een the *itch

Circle an% the top of the teeth.

Arc o( Action: 5s the arc of the *itch Circle bet,een

the beginning an% the en% of the engagement of a

given pair of teeth.Arc o( Approach: 5s the arc of the *itch Circle

bet,een the first point of contact of the gear teeth

an% the *itch *oint.

Arc o( Recession: That arc of the *itch Circle

bet,een the *itch *oint an% the last point of contact

of the gear teeth.

Bac&lash:*lay bet,een mating teeth.


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Base Circle: The circle from ,hich is generate% the

involute curve upon ,hich the tooth profile is base%.

Center Distance:The %istance bet,een centers of t,o

gears.

Chordal Addendum: The %istance bet,een a chor%passing through the points ,here the *itch Circle

crosses the tooth profile an% the tooth top.

Chordal #hic&ness: The thickness of the tooth

measure% along a chor% passing through the points,here the *itch Circle crosses the tooth profile.

Circular Pitch:&illimeter of *itch Circle circumference

per tooth.


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Circular #hic&ness: The thickness of the tooth

measure% along an arc follo,ing the *itch Circle

Clearance:The %istance bet,een the top of a tooth an%

the bottom of the space into ,hich it fits on the meshing

gear.

Contact Ratio: The ratio of the length of the 6rc of

6ction to the Circular *itch.

Dedendum:The ra%ial %istance bet,een the bottom ofthe tooth to pitch circle.

Diametral Pitch: Teeth per mm of %iameter.


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*ace: The ,orking surface of a gear tooth locate%

bet,een the pitch %iameter an% the top of the tooth.

*ace +idth:The ,i%th of the tooth measure% parallel

to the gear ais.

*lan&: The ,orking surface of a gear tooth locate%

bet,een the pitch %iameter an% the bottom of the teeth

Gear: The larger of t,o meshe% gears. 5f both gears

are the same si7e they are both calle% 8gears8.

,and:The top surface of the tooth.


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,ine o( Action:That line along ,hich the point of contact

bet,een gear teeth travels bet,een the first point of

contact an% the last.

"odule:&illimeter of *itch "iameter to Teeth.

Pinion:The smaller of t,o meshe% gears.

Pitch Circle: The circle the ra%ius of ,hich is e9ual to the

%istance from the center of the gear to the pitch point.

Diametral pitch: Teeth per millimeter of pitch %iameter.Pitch Point: The point of tangency of the pitch circles of

t,o meshing gears ,here the $ine of Centers crosses the

pitch circles.


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Pressure Angle:6ngle bet,een the $ine of 6ction an%

a line perpen%icular to the $ine of Centers.

Pro(ile $hi(t: 6n increase in the uter "iameter an%

!oot "iameter of a gear intro%uce% to lo,er the

practical tooth number or acheive a non#stan%ar%Center "istance.

Ratio:!atio of the numbers of teeth on mating gears.

Root Circle:The circle that passes through the bottom

of the tooth spaces.Root Diameter:The %iameter of the !oot Circle.

+or&ing Depth: The %epth to ,hich a tooth eten%s

into the space bet,een teeth on the mating gear.


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pitchCircularXTeeth

pitchDiametral

TeethdiameterPitch

=

=

T

D

pitchDiametralppitchCircular c

===

c

dpD

TpitchCircular

ppitchDiametral ====


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2/

( )

pitchDiametral

GearonTeethpiniononTeeth

pitchCircular

GearonTeeth

piniononTeeth

cedisCenter

+=

+=

2

2tan

CosDiameterPitchDiameterCircleBase =


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Addendum ; 1 < "iametral *itch

; 0.'1' = Circular *itch

Dedendum ; 1.1(- < "iametral *itch; 0.')' = Circular *itch

+or&ing Depth ; 2 < "iametral *itch

; 0.)')) = Circular *itch

+hole Depth ; 2.1(- < "iametral *itch

; 0.))) = Circular *itch


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Clearance ; 0.1(- < "iametral *itch

; 0.0( = Circular *itch

-utside Diameter ; >Teeth ? 2@ < "iametral *itch

; >Teeth ? 2@ = Circular *itch < A

Diametral Pitch ; >Teeth ? 2@ < utsi%e "iameter


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N2 is the foot of the perpendicular

from O2to N1N2.

Tooth profile 1 %rives tooth profile 2

by acting at the instantaneous

contact point K.

N1N2is the common normal ofthe t,o profiles.

N1is the foot of the perpen%icular

from O1to N1N2


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6lthough the t,o profiles have

%ifferent velocities V1an% V2at

point K their velocities along

N1N2 are e9ual in bothmagnitu%e an% %irection.

ther,ise the t,o tooth

profiles ,oul% separate from

each other. Therefore ,e have

( )1.4222111

NONO =


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( )2.411

22

2

1

NO

NO=

+e notice that the intersectionof the tangency N1N2 an% the

line of center O1O2 is point P

an% from the similar triangles

( )3.42211 PNOPNO =


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Therefore. velocity ratio

( )4.41

2

2

1

PO

PO=

*oint P is very important to thevelocity ratio an% it is calle% the

pitch point. *itch point %ivi%esthe line bet,een the line of

centers an% its position %eci%es

the velocity ratio of the t,o teeth.The above epression is the

(undamental law o( gear)

tooth action


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rom the e9uations 4.2 an% 4.4

,e can ,rite

( )5.411

22

1

2

2

1

NO

NO

PO

PO==

#ratio of the ra%ii of the t,o base

circles an% also given by

( )6.4coscos

222

111

PONOandPONO

=

=


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#centre %istance bet,een the base

circles

( ).4cos

coscos

2211

2211

2121

NONO

NONO

POPOOO

+=

+=

+=

; pressure angle or the angle ofobli9uity. 5t is angle bet,een the common

normal to the base circles an% the

common tangent to the pitch circles.


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6 common normal >the line of action@to the tooth profiles at their point of

contact must in all positions of the

contacting teeth pass through a

fie% point on the line#of#centerscalle% the pitch point

6ny t,o curves or profiles engaging

each other an% satisfying the la, of

gearing are con'ugate curves. an%

the relative rotation spee% of the

gears ,ill be constant >constant

velocity ratio@.


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To obtain the epecte% velocity ratioof t,o tooth profiles the normal line

of their profiles must pass through

the correspon%ing pitch point ,hich

is %eci%e% by the velocity ratio. Thet,o profiles ,hich satisfy this

re9uirement are calle% con'ugate

pro(iles.


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5t is essential for correctly

meshing gears the si7e of the

teeth > the mo%ule @ must be

the same for both the gears.

6nother re9uirement # the

shape of teeth necessary for

the spee% ratio to remain

constant %uring an increment

of rotation this behaviour ofthe contacting surfaces >ie.

the teeth flanks@ is kno,n as

conjugate action.

1 Chapter 4 Spur Gears Intro Classif Terminology Law of Gearing

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Transcript of 1 Chapter 4 Spur Gears Intro Classif Terminology Law of Gearing