Planetary Gear Ratio Calculations
-
Upload
leonex30078127 -
Category
Documents
-
view
58 -
download
10
description
Transcript of Planetary Gear Ratio Calculations
-
5/29/2015 Planetarygearratiocalculations
https://woodgears.ca/gear/planetary.html 1/5
PlanetarygearratiocalculationsThisarticlealsoavailableinSpanish
AquestionthatIoftengetishowtoworkoutplanetarygearsusingthegeartemplategenerator
Workingoutthetoothcountsforplanetarygearsisactuallynotthatcomplicated,soIinitiallyneglectedtomentionhowtodoit.Buthavingreceivedthequestionanumberoftimes,I'llelaborate.
Forconvenience,let'sdenoteR,S,andPasthenumberofteethonthegears.
R Numberofteethinringgear
SNumberofteethinsun(middle)gear
P NumberofteethinplanetgearsThefirstconstraintforaplanetarygeartoworkoutisthatallteethhavethesamepitch,ortoothspacing.Thisensuresthattheteethmesh.
Thesecondconstraintis:R=2P+S
Thatistosay,thenumberofteethintheringgearisequaltothenumberofteethinthemiddlesungearplustwicethenumberofteethintheplanetgears.
Inthegearatleft,thiswouldbe30=29+12
Thiscanbemademoreclearbyimagining"gears"thatjustroll(noteeth),andimagineanevennumberofplanetgears.Fromtheillustrationatleft,youcanseethatthediametersofthesungear,plustwoplanetgearsbemustequaltotheringgearsize.
Nowimaginewetakeoutoneofthegreenplanetwheels,andrearrangetheremainingonestobeevenlyspaced.Stillthesamesizegear.
Nowimaginethewheelshaveteeth.Theteethwouldstickoutbeyondthelineofthewheelasmuchastheyindent,sothatthepitchlineofthegearswouldbethelinearoundthegears.Thegeometrystillworksthesame.Ifyougointothegeargeneratorandselect"show
-
5/29/2015 Planetarygearratiocalculations
https://woodgears.ca/gear/planetary.html 2/5
pitchdiameter",youcanseehowthepitchdiameterisjustacirclethattheteetharecenteredover.
Thepitchdiameterofagearisjustthenumberofteethdividedbydiametricalpitch(largervaluesof"diametricalpitch"meansmallerteeth).Thegeargeneratorprogramtendstorefertotoothspacing.Pitchdiametercanalsobecalculatedastoothspacing*numberofteeth/(2*),where2*=6.283
Here'sanotherplanetarygearset.Themiddlearrangementisremoved...
...andhereitisinserted.
Gear Worm1 Million+ Prequalified
Suppliers. Contact Directly& Start Trading!
-
5/29/2015 Planetarygearratiocalculations
https://woodgears.ca/gear/planetary.html 3/5
Inthiscase,theplanetgearshave12teeth,thesungearhas18andtheringgearhas42teeth.
So,applying
R=2P+S
Weget
42=212+18
Thesepicturesarepartofafasincatinglycomplicatedplanetarygear
drivebyRonaldWalters.
Workingoutplanetarygearturnsratios
Workingoutthegearratioofaplanetarygeartraincanbetricky.Let'sdenotethefollowing:Tr TurnsoftheringgearTs TurnsofthesungearTy Turnsoftheplanetarygearcarrier(theYshapedthinginthepreviousphoto)R RinggearteethS SungearteethP PlanetgearteethTheturnsratioisasfollows:
(R+S)Ty=RTr+TsS
Example:
Now,usuallyinaplanetarygear,oneofthegearsisheldfixed.Forexample,ifweholdtheringgearinafixedposition,Trwillalwaysbezero.Sowecanremovethosetermsfromtheaboveformula,andweget:
(R+S)Ty=TsS
Now,ifwedrivethesungear,wecanrearrangetheformulatosolveforturnsoftheYcarrier:
Ty=TsS
R+SSothegearratiois
S/(R+S)
-
5/29/2015 Planetarygearratiocalculations
https://woodgears.ca/gear/planetary.html 4/5
Constraintsonnumberofteethandplanets
Ifyouwanttheplanetarygearstobeevenlyspaced,andallbeengagingthenexttoothatthesametime,thenbothyoursunandyourringgearneedstobeevenlydivisiblebythenumberofplanets.
Ifyouwantthemtobeevenlyspaced,butdon'tneedthemtoallbeinthesamephasewithrespecttotheirteeth,thenthenthesumoftheringgear'steethandthesungear'steethmustbeevenlydivisiblebythenumberofplanets.Thatis:
(R+S)isevenlydividesbythenumberofplanets.
Ifhoweveryouarewillingtospacetheplanetsunevenly,thisconstraintdoesnotapply.Theanglebetweentheplanetgearsaboutthesungearishoweverstillconstrainedby:
Anglep2p=360
N WhereNisawholenumberR+S
Thatistosay,theanglebetweenplanetgearsisamultipleof360/(R+S).
Finally,here'sanothercoolarrangementofgears,thoughnotreallya"planetary"gearset.
Ifyouplaceagearinsideanothergear,withtheinternalgearhavingatoothcountofhalftheringgear'stoothcount,anypointonthepitchdiameteroftheinsidegearwillmovebackandforthinastraightline.
Thebrassrodinthisphotowillmovestrictlylefttorightintheslot,whilethegearitisattachedtorollsaroundinsidetheringgear.Thatgearisactuallyattachedtoacrankwhichkeepsitrollingaroundtheedge,althoughonlythecenterpartofthatcrankisvisible,soitdoesn'treallylooklikeacrankinthephoto.
Photocredits:Ihaven'tactuallyhadaneedtobuildaplanetarygearsetmyself,soIusedsomephotosthatweresenttomebyreaders.ThefirstandlastphotosweretakenbyBrianKerrThesecondandthirdphotosweresenttomebyRonaldWalters
Seealso:
-
5/29/2015 Planetarygearratiocalculations
https://woodgears.ca/gear/planetary.html 5/5
Geartemplategenerator Cuttingplywoodgears Howtomakewoodengears
Workingoutcompoundgearratios
RonWalters'splanetarygeardrive
Penshakingcontraption
Makingrightanglegears