Kinematics of machine (Tooth Profiles of Gears)

Detailed introduction on tooth profile of gears. Advantages and disadvantages of each type of profile.

1. Tooth Profiles.
Presented by:-
Prakhersingh
2011058 (10)
Kinematics of machine.

2. Gear Terminology.
1.Pitch:-
Itisthetheoreticalcircleonwhichall
calculationsarebased,thediameterof
pitchcircleiscalledtheeffectivediameter
orpitchdiameter.
2.Tooththickness:-
itisthethicknessofthetoothmeasured
alongthepitchsurface.
3.Pressureangle:-
Pressureangleinrelationtogearteeth,it
istheanglebetweenthetoothfaceandthe
gearwheeltangent.

3. 4.Flank:-
Itisthesidesurfaceofgearlyingbelow
pitchsurface.
5.Dedendum:-
Itistheradialdepthoftoothfromthe
pitchcircletotherootofthetooth.
6.Adendum:-
Itistheradialheightofthetoothfrom
pitchcircletotopofthetooth.
7.Adendumcircle:-
Thecirclewhichlimitsthtopofthegear
toothisknownasaddendumcircle.
8.Dedendumcircle:-
Thecirclewhichlimitsthebottomofthe
geartoothiscalleddedendumcircle.

4. Tooth Profile.
Aprofileisonesideofatoothina
crosssectionbetweentheoutside
circleandtherootcircle(dedendum
circle).
Or
Usuallyatoothprofileisthecurveof
intersectionofatoothsurfaceanda
planesurfacenormaltothepitch
surface.

5. Conjugate profile.
Ifthetoothprofileofapairofgearsare
sodesignedthataconstantangular
velocityratioisproducedand
maintainedduringtheoperation,than
thegearsaresaidtohaveconjugate
action.
“Hencethetoothofsuchgearswhich
performtheconjugateaction,aresaid
tohavetheconjugateprofile”.
Thegearsinwhichtoothprofileis
conjugate,thetoothofsuchgearsare
thickeratbaseformaximummoment.

6. ▪Gearsaremostlydesignedtohavetheconjugateactiontotransmitthe
desiredmotion.Formakingatoothwiththeconjugateprofile“firstlyan
arbitraryprofileforonetoothisselectedandthenaprofileofmeshing
toothisfoundwhichwillgivetheconjugateaction”.
▪Conjugateprofilehavesomedisadvantagesas;
1.DifficulttoManufacture.
2.Higherproductioncost.
3.Standardizationisdifficult
Someotherprofiles:-
1.Cycloidalprofile.
2.Involuteprofile.

7. Cycloidalprofile.
Cycloid curve.
Cycloid:-
Acycloidisacurvetracedbyapointona
circlebeingrolledonstraightlinewithout
slipping.
Acycloidisacurvetracedbyapointonthe
circumferenceofthecirclewhichrolls
withoutslipping.
Thegeartoothwhichtracecycloidcurveon
itsparinggearissaidtohaveacycloidal
profile.
Typesofcycloidalprofile:-
1.Epicycloidalprofile.
2.Hypocycloidalprofile.

8. 1. Elicycloidalprofile.
Ifthecirclerollswithoutslipping
outsidethebasecirclethecurve
tracedbypointonthe
circumference is called
“epicycloid”andprofileissaidas
“epicycloidalprofile”.
2. Hypocycloidal profile.
Ifthecirclerollswithoutslipping
insidethebasecirclethecurve
tracedbythepointonthe
circumferenceofthebasecircleis
knownas“hypocycloid”and
profileissaidas“hypocycloidal
profile”.

9. Cycloidaltooth profile.
Thegearsinwhichtoothprofile
iscycloidal,thetoothofsuch
gearsarethickerattipand
thinneratbase.
Cycloidalgearingrequirestwo
differentcurvestoobtain
conjugateaction.
NOTE:-

10. Involute profile.
Thegearswhosetoothtracean
involutecurveduringrevolutionor
duringtheprocessofmeshingand
unmeshingwithitsparinggearthe
profileoftoothofsuchgearsisknown
asinvoluteprofile.
Involutecurve:-
Aninvolutecurveisobtainedfrom
anothergivencurve,byattachingan
imaginarytautstringtothegiven
curveandtracingitsfreeendasitis
unwoundfromthatgivencurve.
Involute curve.

11. Difference between involute and cycloidal
gear.
Cycloidalgear.
1.Incycloidalprofile,pressureangle
variesfrommaximumatthe
beginningofengagement,
reducestozeroatthepitchpoint
andagainincreasestomaximum
attheendofengagement
resultinginimproperrunningof
gears.
2.Duetocomplexmanufacturing,
cycloidalgearsarecostlier.
Involute gear.
Whileininvoluteprofile,pressureangle
remainsconstantthroughoutthe
engagementperiod.Thisresultsin
smoothrunningofgears.
Whileinvolutegearsaresimpleto
manufactureandthusarecheaper.

12. Thank you.