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3．BasicGeometricandKinematicPrinciplesofSpiralBevelandHypoidGears
Spiralbevelgearswerefirstmentionedin1820asaninventionofJamesWhitedatingbackto1788／4,Nearlyacenturywouldpass,however．beforethefirstmachinetoolwasbuiltformanufacturingspiralbevelgear(Chapter2).In1899theFrenchmanMonneretreceived
apatentforageneratingmethodand,aboutthesametimePaulBottcherfromHamburg．Germany，becameinterestedinthistechnology. In1910，Bottcherpublishedanumberofpatentswithintheframeworkofthistheme／1／.Theworkhecreatedwasvoluminousandbroadlybased.Hisworkonbevelgearsdealtnotonlywithcontinuous(facehobbing)butalsosingleindexing(facemilling}manufacturingmethods.Sincepinionandgearwerecutbythesamegeneratinggear,bothmethodsresultedinuniformtoothdepthandconjugatedflanks(Figure1).Atthattime，themeaningofcrowningwasnotyetknown Bottcherbuiltafunctioninglaboratoryprototypeinordertodemonstratetheprinciplesofhismethod，andwiththisprototypehemanufacturedsamplegearsetsthatwerecapableofoperationIn1919，theGleasonWorksintheUSAacquiredtherightstoallBottcherpatents.Infact,Gleasonexploitedonlythosemethodsthatworkedwithsingleindexing(facemilling)and，accordingtoBottcher,haduniformtoothdepth.Duringthe1930sand40s,longaftertheexpirationofthepatents,continuousspiralhobbing(thefacehobbingmethod)wastakenupbyMammanoFiat,Oerlikon-Buhrle,andKlingelnberg-Sons.ThesemethodsalsohadBottchertypeuniformtoothdepth,whichwouldberetainedunchangedbyOerlikonandKlingelnberg untiltoday.
Figurel：Generatingtheworkwheelonafictitiousplanegeneratinggearor“crowngear”accordingtoBottcher
Figure2:Classicalcharacteristics,left,Gleasonandright,Oerlikonmethods
ThefacemillingmethodsincommonusetodayarestillbasedontheinventionsofPaulBottcher.Characteristically
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