May/June 2001 Gear Technology

liNCD-ROM BUtSEE IP 141~

Revolultionary EllectlronicGuide System ellmlnatescostllY meehanleal chlangeover~Small-lot helical gear production winnever be the same not for users of theGleason Pfauter GP 300 IESGearShapero Imagine adding hundreds ofhours a year in valuablechip-making time to youroperation simply by

eliminating the time and effortyou now require for changingmechanical or hydrostatic guidefor every new workpiece lead

The GP 300 ES does this andmore In addition to its normalCNC axes the GP 300 ES uses a cutterhead with a backlash-free direct drive for

controlling the cutter spindle rotation(Esaxis) through a torque motor andsoftware Almost any helix anglewithin a wide range of stroking ratesand face widths can be createdsimply by changing the CNCprogram

E-Axls and softwaJfI forcontrolling cuttefspindle

rotation enable the GP 300 ESto produce helicaJgears

without a mechanical guae

End resultYou can handle newworkpiece leads -and shorten leadtimes -like never before

For more inpoundormationcontact

Tlhe Gleason WOlrksWOOUniversity Ave PO Box 22970

Rochester NY 14692-2970 USAPhone 716473~WOO Fax 716461~4348

Web site wwwgleasoncomE~Mail salesgleasoncom

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MAYJUNE 2001

FEATURES

The Journal of Gear Manufacturing

FOCUS ON GEAR DESIGN

211

DEPARTMENTS

11

56

Talking On Nature Three IGearCompanies And Their End-ProductsA look at several gear manufacturers with special products on the side 18

IGearbox ~ieldl Pedormance from a IRebuUders PerspectivelTips on gearbox design from someone whos seen gearbox failures 22

Gealr Design Speciall Section 27

Design Formulas for Evaluating Contact Stress in Generalized IGearPairsDetermining contact stress no matter the gear type 3

alA CalcullatingllDynamic Loads Sizingl Worm Gearsand figuringl Geometry factorsTechnical editor Robert Errichello answers your design-related questions 39

load IDistribution lin IPIanetaryGearsPredicting the dynamic behavior of planetary gear systems 41

Publishers PageFinding your core competency 7

IRevolutionsA new planetary gear system and microgears 11

Industry NewsWhats happening in the gear industry 15

Adveniser IindexGet information from advertisers by using the response card or going online l1

Technical CalendarDont mi s these important upcoming events 46

CD~ROMBuyers Guiide FormsFREE USTlNGS for gear-industry companies 41

Product NewsThe latest products for gear design manufacturing and testing 150

literalllre MartFree brochures and catalogs from our advertisers 52

IClassifiedsServices Help Wanted and more 54

AddendumGear Fashion 56

VOL 18 NO3I GEAR TECHNOLOGV Tn Jourtllll or GolOr

Manu[aclurlllg (lSSN 01-13-6858) pubUhed bunonth-Iy by RaJdnJI Publishing Inc bull 1421 I~u Avenue POBox 1426 Elk Greve Village IL 600071amp471437-6604Cove price S~OO US rioltlJoaI postage paid alArlington HeIghtamp ILbull and 31 eddmonnl mailing offieeRandall Publishing makes eety ffort 10 ensure lhallhltprocesses descnbed in GEAR TECHNOLOltiY conformto soond engmecringpraaioe Neilher the authors IlOI thepublisher can be hed responsible for IJIjuri~s sustainedtill foil tho procedllrtS desenbed PostmasterSend address change to GEAR TECHNOLOGY Jcurnal of Gear Manufacturing 142~ Lum Avonue POBo 1426 Elk Grov ViUogelL 60007 OConlents copy-righted hy RANDALL PUB[JSHlNG TNC 2001 Nopart of this publication may be reproduced or uansmluedin any r or by any means olccllDic or 1llOclJanioaIincfudmg pOOllymg ncordioB or by any informationstorage and relrieval system withOUJEpermission in wrtt-Log ampom be publisber Cootents 0( ads IOIljecl 10

CIRC(E136 LPo_b_lilhr_middot_ _pprDi__Ill JI

4 MAYJUNE 2001 bull GEAR TECHNOLOGY bull ww~98rt9chngycom wwwpowertransmlssloncom

OLS

EDITORIALPublisher amp Editor-in-CDief

Michael Goldstein

Managjng Editor WilIiam R Stott

Associate Editor Joseph L Hazelton

Editorial Consultant Paul R Goldstein

TeChnical EditorsRobert Errichello

Don McVittieRobert E Smith

Dan Thurman

ARTArt Dirtttor Jean Bartz

ADVERTISINGAdvertising Manager Patricia Flam

Advertising Coordinator Susan Brandl

CIRCULATIONICirculation Coordinator Dina Krauss

INTERNETInternet Editor Dan Mackenzie

Gear industry Home PagelMSalesPatricia Flam

powerrransmissUJ1MomTill SalesRobert Poll

RANDALL PUBLISHING STAFFPmident Michael Goldstein

Vice Presldent Richard GoldsteinAccounting Mary Lou Napadow

Phone 847-437-6604E-mailpeoplegeartechnologycom

Web wwwgeartechnologycomwwwpowertransmi~sioncom

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_-----------IIPUBUSHERS IPAGiE 1 _

Co CoConcentrating on the CllAdal Components

Co Keep Yow CompanyCompe+i+ive

Rodgers and Hammerstein producedorne of Americas most memorable and

lasting songs in musical theater lyricistOscar Hammerstein IIonce aid of com-poser Richard Rodgers I hand him alyric and get out of his way Hammer-stein knew what Rodgers was good atand vice versa and each trusted his part-ner Their partnership was 0 successfulthat you can scarcely think of one manwithout the other

Musical composers arent the onlyones who form uccessful partnership mntodays manufacturing world partner-ships arealmo t a necessity Originalequipment manefacturers have competi-Lion not only from other manufacturersof similarequipment but 3110 from man-ufacturers of the components that go intotheitrequipment and the service pro-viders who process some of those com-ponems along the way

Ron Davi of Caterpillar Tnc madethis point at the recent annual meetingof the American Gear ManufacturersAs ociation Davis works in Caterpil-lars busine s administration divisionwhich help decide when to manufac-ture components in-house and when tooutsource them

Caterpmarequipment require abroad range of gear products includingtransmission shafts straight and spiralbevel gears planet gears sun gears andfinal drive ring gears They use largequantities of both machined and powdermetal gears

But Caterpillar cant hope to staycompetitive by rnanufaciuri ng all of itscomponents when other companies spe-cialize in manufacturing some of thosecomponents Davis says

The challenge is to decide whichcomponents and manufacturing process-es give Caterpillar the greatest competi-tive advantage when manufactured in-house and which give them the greatestcompetitive advantage when outsourcedOf course the ccmpanyexamines factorssuch as cost quality and customer satis-faction when considering competitiveadvantage Another factor is whetherCaterpillar has special expertise in man-ufacturing a particular component Thecompany also examines various risk cri-teria whether a part requires proprietarytechnology whether its an aftermarket-critical component or whether its time-to-market is critical

Those components that give them thegreatest competitive advantage whenmanufactured in-house are part of Cat-erpillars core competency Outsourcingthose components could lower the quali-Iy of the end-product make it moreexpensive or otherwise worsen the com-panys position in the marketplaceComponent that are not a part ofCaterpillars core competency might bebetter manufactured by others special-ists who can lower the costs improve thequality or both Outsourcing those nOI1-

core components also affords Caterpillarthe opportunity to devote its ownresources to improving those processesand products that are part of its covecompetency

Many of Caterpillars less criticalhigh-volume components such as enginegears are generally outsourced Criticalcomponents such as large transmissionsor filial drive gears are generally manu-factured in-house Medium-duty compo-nents such as small axles and small

transmissions are mixed between in-house manufacturing and outsourcing

Some of the ontsoureed gears aremanufactured by Avon Gear Co a divi-sion of Okubo Gear Co Ltd inRochester Hill MI At the AGMA meet-ing ] had the chance to talk with AvonGears president Aaron Remsing

According to Rem ing there was alime not long ago when Avon Gear hada near-death experience Business wasdown the company had just moved intoa new expensive building and thefuture wa uncertain Avon Gear had todo some soul-searching about its busi-ness Management wa forced to thinkabout the companys capabilities andreinvent the way that it obtained newbusiness Rernsing says The answer layin examining the companys own corecompetencies

Avon Gear knew it had the technicalexpertise equipment and experience tomanufacture certain sizes Iypes andquantities of gears of excellcru qualityand at competitive prices Instead ofwaiting for orders to come in Remsing

wlO powertransmuoncom bull f1OfgllarrechnoJogycom bull GEAR TECHNOLOGY 11IYfJUNE 2001 7

PUBLISHERS PAGEsays the company began approachingthose customers who could best takeadvantage of Avon Gears core compe-tencies One of those companies wasCaterpillar

By making a commitment to special-ize in a certain type of gear for a certainmarket segment Avon Gear was able tocapture Caterpillars business That busi-ness in tum allowed the company anopportunity to invest in new equipment

and training to provide even greater com-petitive advantage

Today according to Davis AvonGear is one of the most important sup-pliers for Caterpillars transmissionbusiness unit Working together thecompanies are able to provide theworld-class manufacturing quality andpricing on gear components that helpkeep Caterpillars equipment competi-tive in the world market Furiliermore

bullIng

Remove nicks buns hest treat scaleand Improve gear tooth surface

Onr 30 J8IlI ago morllaar1lalll developed the gelDbilihlmidlddDglllllllilnnJllOC8llPat JOU trust In tbe people who Invented the process

MAatlNE FEATURESINCLUDEbull Fully automated systemsbull High speed machinesbull Patented Gerac

Oscillation Systembull Automatic spherical

position Ingbull Trl-varlable die designbull Horizontal or vertical axis

machinesbull Variety of gear types

For additional information on IhHuBurnishingandor Functional flfiu

Inectionvisit our website ottIVIIVw ilWgearscom

ITP1tl HeartlandWorkilll9 components 01 theHorizontal Bumisher

1205 36th Avenue WestAlexandria MN 56308 USA

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E-mail ItwgeaISOrea-alpoom

8 MAYJU NE 2001 GEAFi TECHNOLOGYmiddot www9Ilartllchnolo9ycom bull wWWpowllrtransmissioncom

~c~l(JoldsteinPublisher amp Editor-in-Chief

the processes machines and expertisedeveloped by Avon Gear have given thecompany the ability to sell gears ofworld-class quality and price to othercustomers with similar needs

In fact Davis saysthe partnershipbetween these two companies has devel-oped into one of mutua] trust and plan-ning Like most successful partnershipsits now in the best interest of each partythat the other doesnt fail

Like Caterpillar and Avon Gear eachof our own companies has core compe-tencies-things that are central to ourbusiness which years of working in cer-tain areas allow us to do better than othercompanies without the same focusFinding those things concentrating onthem and expanding on them can helpmake us more successful

Not finding and developing your corecompetency can have the opposite effectIts true that some companies will bemore focused than others But even themost generalist of companies has corecompetencies For example a general-purpose gear job shop with a broad rangeof equipment and tooling might not seemto have a specific niche Neverthelessthat same company might specialize infast turnaround design assistance orextremely high quality each of whichcould be developed for greater competi-tive advantage in certain marketplaces

You can learn more about your corecompetencies by choice or by necessityIf you do so by choice perhaps you II beable to make intelligent decisions aboutyour companys operations as Caterpil-lar did However if you wait you may beforced to learn about your core compe-tencies the hard way Perhaps youll beable to act quickly enough to save yourcompany as Avon Gear did But thenagain

For 96 years the Bodine name has symbollized quality in power transmissionand motlon control IBodine EIectric Company pioneered the concept ot fracticnalhorsepower motors with integrall gear reducers We calrefully guard our reputationfor producing the quietest smoothest Iiongest-life products in the industry

Now you can tnccrporate those same higlhstandards of qualityrellabtlltyand on-time deillivelry iinto your products that require filneand medium pitch open gears from hundreds to hundreds oftLo - - - ~ -d -nousancs

Bodine Gear Manufacturing employs state-of-the-art eNG gearmanufactuning and inspection technology with in-depthengineening support to service your most demandinQappucattons For skived gears we can be your most competitiivecompetent source

To learn more about Bodiine Gear Manufacturing and get your Free Bodiine Gears capvisit ww-wBodineGearscomFreeCaphtm or call toll flree 877-4GEARS9

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Dura-Bars continuous-cast gray and ductileiron performs like free-machining steel with anImportantadded bonus - quieter operation

Like steel Dura-Bar can he austemperedthrough-hardened flame-hardened or induction-hardened for added wear resistance Butthesuperior noise and vibration damping characteristicsof Dura-Bar make for quieter runninggears AndDura-Bar is 10Ughter than steel

Dura-Bar round bars are avatlable In diametersnnging from 58~ to 20 and lengths of 6-20 So youwont need to make major changes in your machining equipment And our extensive mventory means Dura-Bar is available now - when you need U

Wben Its quaUtymaterial quiet performance and quick deUverythatcount look to continuous-cast Dura-Bar for your gear production needs

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REVOLUTIONS -- _

Hlarmonic ConceptsJazz lp

Planetary DesiglnIn the world of planetary

servo drives precision iseverything Advertisementsabound fOJ ervo gear driveswith extremely low or evenzere backlash With that typeof drive in high demand man-ufacturers have done every-thing they can to tighten theirdesigns-thmugh more exact-ing tolerances tighter assem-bly and better materials

Instead of tightening onemanufacturer of planetaryservo drives has tried loosen-

mg in order [0 provide the lowbacklash that manufacturers ofrobotics and other precise posi-

tioning equipment requireThat loosening bas nothing

te do with the manufacturingtolerances or assembly Pre-cision manufacturing is stillrequired Ithas to do with atype of flexibility borrowedfrom a related technologyharmonic drive gearing

Harmonic drive gearinghas long been known for itslow backlash high precisionand compact design Har-monic drive systems use a cir-cular spline a flex spline and

Cut-away view of the HPG gear drive from HIl Systems

me HPG drive includes II 11111 lIear 10 cantro bacldash(defoRnltion 8xallllerated for mustrative purposes

wavegenera~or to createextremely high ratios in a sin-gle reduction One of theadvantages of the harmonicdrive system is that the flexspline deforms as it rotates tokeep its teeth fully loadedagainst the circular spline alaU times

Engineers at HD Systems ofHauppauge NY haveliguredout how to apply the deforma-tion concept of harmonic drivesystems to planetary gears aswell Instead of a flexible imlerspline bull the HPG harmonicplanetary gearheads use aflexible outer ring gear to pre-load the gearset

The flexible outer ringgear of the HPG gearheadcreates a continually adju l-ing backlash compensationmethod The ring gear is thin-ner in the radial directionthan a typical ring gear Thismakes it radjaUy flexible yettorsionally stiff says HDSystems marketing managerBrian St Denis As normal

Wecome to Revolu-

Iions th column tIItbrings you the Illtest

most up-to-dBtl ndeasY-Io-read informll-

tion bout the people

nd technology of thegell industry Revolu-

Uons welcomes OUsubmissions PleBSe

sefid them to Gear

Technologv PO Box1426 flk Grore VillageIt 60009 or fx (HI)

431-6618 If youd like

more infomllltion sbout

flY of the articles that

appellrpiliS cirelli theappropiate number on

the Reader Service Card

gear wear occurs any in-crease in space between the

jteeth is immediately compen- Isated by the preload in the ring gear The concept is as if Ithe ring gear is a spring in the Iradial direction

The system employed byHD Systems has a huge advan-tage over those commonlyemployed by other maaufac-turers says St Denis Thebackla h of the HPG drivewont deteriorate over time

One method commonlyemployed toprovide low orzero backlash ill planetarygear systems is to create atight fit between all of thegears However this methodis subject to gear tooth wearand over the life of the gear-box the backl3sll can increasesignificantly

Another method is to usepreloaded bevel gears as panof the mechanism Shimsforce the bevel gears togetheraxially which forces a raclialpreload in the planetary gearsBacklash in this type of sys-tem also increases over timebecause of gear tooth wear

Because of the flexibledefermation of the planetaryring gear the HPG gearheadautomaucally compensatesfor gear tooth wear 81 Dellisays This helps ensure con-sistent backlash throughoutthe rated life of the gearbox

The H~ Series planetarygearheads have standardbacklash of less than 3 arc-minutes and they can beordered with 1 arc-minute ofbacklash as an option Theyare available in ratios from51 to 331

Cirele3mwwwpow9rrsnsmlssloncom bull wwwge8rtechnQJoycom bull GEAR TECHNOLOGYmiddotmiddot MAYJUNE 2001

MicmgearsFor Use In Tlhe

IHuman MachineIn a Hungarian lab using a

microscopes laser research-ers are creating gears androtors thinner than a humanhair ADd willie hair growsout of the body the re-searchers want to put theirgears and rotors into the bodyin microsoopic machines forconducting experiments

Its like the movie innerSpace wilh Dennis Quaidsays researcher p~ OrmosThe machines could be builtso small that they would fitinto blood vessels for analyz-ing blood

To create the gears androtors Onnos uses hardenedliquid photopolymer Butunlike the micropans and their

pos ible lise the material isntnearly as exotic

Dentists use it a letann os says The material isthe same as whats II ed fortooth fillings hardened withultraviolet light

Ormes developed the tech-nique with Fewr Galajda in alittle more than a year--Just now weare perfectingit Ormes acids that hed likero use the technique in lessthan a year to build everaltypes of machine

Willi a doctorate ill phys-ics Ormos belongs to theHungarian Academy of Sci-ences and works at itsBiological Research Centrelocated in Szeged Ormos isdirector of the centres Insti-tnte of Biophy it Galajda istis doctoral snrdent

We study thephysics of

Created undBr II microscope threll rotan appear in front of the Dak-likeIJIIJ1Jc lif bullbullbull II 110mB n bairLivingsystems Ormes says Ormos and Galajdas gearsHe acids lliat theres a strong and rotors could be usedjndrive ill biology toward minia- that study as parts in micro-turizing which has a lot of scopic biochemical device promise in it The micromachines would be

bull accuracybull reliabilitybull maintolinCibilitybull Hexibilily performancebull and life cyde eest

AI Klingelnberg the point ofprecision is 10 help you controlyour gear manufocturing pro-cess and improve gearqudlitywith measuring systems thaIare benchmarks for

Klingelnberg measuringtechnology contaeLiebherr Gear Technology Co1465 Woodland DriveSaline MI4B 176-1259

_------------REVOLUTIONS------------_used ro investigate living sys-terns at a cellular level per-mitting the movement of indi-vidual ceIls-even individuallarge molecules Ormos says~ts a very precise tool thatcan be used in biology

With such machines scien-tists could introduce chemi-cals into cells manipulatetheir reactions and maintainthose cells environmentspumping different solutions todifferent regions They couldmeasure cell properties toselect certaia cells create achannel for transporting thosecells and transport the cellsindividually They could alsoremove compounds fromcells even destroy cells

The gears and rotors diam-eters can be as small as twomicrons A human hales diam-eter is about 100 microns At

two microns the parts canweigh as little as ]()LO grams

Ormos and GaIajda maketheir microparts by placingliquid photopolymer under amicroscope then moving acomputer-controlled laser fo-cus into the microscopeWhereverthe focus movesthe liquid becomes hardenedIf it moves in a gear shape thefocus makes a hardened gear

We can create a three-dimensionalobject that is ascomplicated as we wantOrmes says

DUI theres a wri nkle inthe technology that needs tobe ironed out

The micro gears are rotatedby the microrotors The micro-rotors are rotated by light

Its not easy to introducelight into the blood vesselsOmms says

But he adds there may be asolution to that problemOrmos explains that themachines in the body could bepowered by tightlfit wereintroduced effectively-via athin optic fiber for example

In similar research SandiaNational Laboratories in NewMexico has used chemicalmiddotelching to create microgearsand experimental micro-engines electric motors no

1 larger than a grain of sandOrmos started his research

j to understand how light causesI different trapped particles toj rotate But he later realizedi such light-induced rotationi could have useful applicationsI

1 It was not really the areaI

1 in which we were deliberately

II

moving he saysOnnos is unsure about the

techniques future-Whether

this can be commercialized ornot isnt clear Still he andOalajda are testing resins todecide which works best forcreating their gears and rotors

I think the possibilities arereally uolimited Ormes saysAnything that can be donewith larger machines can bedone with smaller ones too

Cirde302

Tbullbull V

If you found tIriI IfticfI ofinterest andor UIefuI

~

l1~~

Phone + 1-734-429-7225Fax 1-734-429-2294wwwpointofprecisioncominfopointofprecisioncom

bull 1INDUSTRV NEWS _

Regal-Beloit Buys Spiral Bevellune from Pbiladelphia GearRegal-Beloit corp has purchased the

piraJ bevel gear product line of thePhiladelphia Gear Co according taatarernent released earlier this year The

purchased assetsinclnded itnventmy andselected machinery equipment and tool-ing relating 10 the pLraI bevel gear line

OIfOlfOlfpoOlfOrnlmluoncom (I bullbull tlchnologycom GEAR TECHNOLOGY MAYJUNE 2001 15

AGMA IElects New OfficersThe American Gear Manufacturers

Assoeiation elected its 200]-2002officmiddotersat the associations annualmeeting in March The new officerswill help direct the organizationthrough March 2002

The newly elected officers are Chairman Arlin Peny president of

Comer Inc in Charlene NC Perry wasfonnerly pre id lit of Gear ProductsIncin Tul a OK

bull Vice Chai_rrrum Roger Pennycook vicepre ident of sales for Textron PowerTransmission North America in Trav-erse City Mm

bull Treasurer 1Cameron Drecoll presidentof Brad Foote Gear Works Inc inCicero [L

bull Cllainnan 01 the Administrative Divi-si(lfl Executive CommittEe Marlin Wood-nouse vice president of sales for StarCutter Co in Farmington Hills Ml

bull Chaimmn of the Technical Divi ion Ex-ecutive Committee David McCarthyvice president of engineering for DorrisCo Incm St Louis MO

Outgoing chairman Frederic MYoung president of Forest City Gear Coin Ro coe IL assumes the title of chair-man emerinu

IBn Shearingl Joins IMitsubishiIan Shearing has been

named vice president ofsale for the MitsubishiGear Technology Centerheadquartered in Wixom

11- ~ MI a Detroit uburbAccording to an announcement from

Thomas P Kelly the center presidentShearing will be responsible for all USand Canadiaa sale of tbecompanys tineof gear-cutting machine tool and cutters

The line with annual sales of about $4million includes design and manufactur-ing capabilitie for Klingelnberg bevelgearing The business will be moved toChicago to the fcote-Jonesllliecis Geardivision of Regal-Beloit

Derlan Acquires Wind orIGear amp D~ive

Derlan Industries Ltd a TomlllD-basedi

manufacturer ofproclucts for the 8J rospaceand pu_mp indusnies acquired ubstantiallyall the assets ofWmclsor Gear amp Drive Incof Windsor Ontario in March

Windsor Gear amp Drive manufacturegears and drive for aero pace and auto-motiveapplication The cquiitionhelps Derlan compete in tile com_modilysegment of the aerospace gear marketac-cording to a release issued by Derlan

THE PURDYCORPORATION

S86 HilliardStreet RO Box 1898 Manchester CT06045-1898 USATelephone 86() 1649-0000 bull Fax 860 645-629g

Home Page httpwwwpurdytransmissionscomf-Mail salespurrlytransmissonsfOffl

Gary L IForbes Appointed GM otUoM Power Products

UQM Technologies Inc (formerlyUnique Mobility lllc)a developer ofalternative energy technologies inGolden CO named Gary L Forbes asgeneral manager of its UQM PowerProducts unit in January The PowerProducts unir manufactures gears gear-boxes and brushless DC motors at the

Yesterdays ReliabilityTomorrouis Tedmologu

Fifty years or VARI-ROLL applications providebull Production Composite Inspectionbull Custom Design amp Build Part Gear Mounting Fixturesbull Standard Mounting Fixtures - Spurs Helicals Pinion Shafts

Worms Throated Worms Bevels Internals

When coupled with the VARI-PC Composite Gear AnalysisSystem will providebull Reduced Inspection Cost Improved Accuracy Historical Record Keepingbull Serialization of Partsbull Interface to SPC programsExperience the difference See why customers worldwide havechosen the VARI-ROLUVARImiddotPC For further informationplease contact us

Precision Gage ce Inc100 Shore Drive Burr Ridge IL 60521

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United Gear 81 Assembly AddsHleat1ireating Capacity

United Gear amp A embly Inc ofHudson WI has installed a large-capac-ity pusher furnace tocarburize quenchand temper gears and shafts The newfurnace has a capacity of 1000 lbshr

TIle system bas been integrated intoUnited Gear amp Assemblys manufactur-ing operations so high-volume compo-nents can move right from manufactur-ing cells to the furnace and directly intopress quenching accordiinglO a state-ment released bylhe oompany

United Gear amp Assembly manufae-rures gears shafts and assemblies for theautomotive agriculture construction andmarine markets

bull ~~~NDUSTRYNEWSII _

companys facility in Frederick COForbes joined UQM after more than

35 years with Hamilton Srllldslrandwller~ he was most recently plant man-ager of the companys Denver manufac-turing facility Prior to that Forbes wasmanaging director of Sundstrand PacificAerospace located in Singapore Ham-ilton Sundstrand is a subsidiary ofUnited Technologies Corp

CIRCLE 1Ji

ASME Codes and StandardsAvaHable Online

The ASME Digital Store whichopened in March allows engineers tobrowse and obtain electronic versions ofASMEs codes and standards via thesocietys Website at wwwasmeorg

The online store include electronicfiles of 400 ASME [publications includ-ing codes and standards for tools fasten-ers flow measurement pumps turbinesdimensioning and toleraneiag as well asother categories Visilors can search thestores database by keyword or categofY

fairfield IExpandstOI IndiaFairfield Manufacturing Co Inc ofLafayette IN acquired Atlas Gear Ltdin October

Located just outside Belgaum IndiaAtlas Gear is a major supplier of gearsfor agriculturaland off-road vehicles inhe Indian market The division win beknown as Fairfield Atlas Ltd 0

Will YoI TIIiIk bullbullIf you found 1his column of inbaIt lIIdIoruseful pIe

If did notcn forflll coIumn _

I

If you would like to mpond to this or anyother article In tltil adlllon of 60rTMhntw=faxvour ~totheIIlIfIdon If SIDU manqlnt edIIur ItIMJ437-1818 or I8ftd melII1D ~com

16 MAYJUNE 2001 bull GEAR TECHNOLOGY wgurhnolol1yrom bull 1I1I1IpOIIrlrllI~mlulollcom

S- Amcricllinc

Tool ink EngineeringT ran tllllltiC Connection IncUnited Tool Supply

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IIEAtIER PAGEAJlVER1lSER SERVICE NUMBER NUMBER

taycar Gear amp Machine Co 177

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Div of MIlgtubhi ll~mational CorpGle on CUlling Tools Corp

TIle Gleason WollksHolroyd

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ORPORATION

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made of a lightmetal alloy that

weigh up to70 less thana comparable

steel arborFeather lighthydraulicarbors can bemanufactured wilhrunout as low as2 microns The clampingsleeves are replaceabte Thistoolingl is suitable for measuringtesting balancinggear grindingand other applications

T_~O _--UIoIt--~-- ~~-~-~_ _ -1IIrIndIrit bull T-g bull LDbull OD ~-IumIn~

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An employ of ATA IGIIII Iltdworks on one of th eomplnylwlllr llltbiMl nil lurbinesL S1IJI11y_d tRlrgy-pro-dgcilfgl comlnill -_ priYIIICOlIIJlni Ihll own rivtrIIIpilh

Taking On NatureThree Gear Companies

And Their End- ProductsJoseph l Hazelton

Many gear companies male parts buildassemblies and stoptliere But some dontstop rJtey go a step further and createend-prod-uets Three gear companies have taken that stepand taken on nature with their creations

Ontario Drive amp Gear rides across land andwater with itsamphibious vehicles ATA Gearfunnels water through it turbines for electrici-ty Amarillo Gear raisestemperatures truoughits wind machines

Finding Theiir NichesAmarillo Gear Started in 1917 Amarillo

Gear Co of Amarillo TX manufactures spiral-bevel right-angle gear drives and fan drivesThe gear drives are used for agricultural pumpsbow thrusters for docking ships cooling towerfMS drilling rotary table gears fire contrclflood control sewage treatment plants andwater desalination plants

In 1934llle company started building andservicinggearboxes in agricultural applications

In [974 it turned its expertise to upper aJldlower gearboxes for wind machines

Years later Amarillo Gear used irs know-how to develop whole wind machines In 1989the company formed Amarillo Wind MachineCo

Located in Exeter CA Amarillo Wind man-ufacrures and services wiad machines used toprotect crops susceptible to ftost with a rela-tively high value per acre The crop includeavocados cherries flowers strawberries andcitrus fruits like grapefruits lemon andoranges

ATA Ge~lrS Started in 1937 ATA Gears Ltdof Tarnpere Finland manufactures spiral bevelgears and custom-made gearboxes The partsand assemblies are for machines thai handleheavy or shock loads and operate in extremetemperatures or dusty environments

ATA Gears spiral bevel gears are in its waterturbines Pentti Hallila general manager ofsales and technical services say the companystarted rna_king water turbisesto extend Lboegears to an end-product

The turbines are usually provided to energy-producing companies and private companiesthat own river rapids Hallila say 3 companybuys a turbine if it happens to be 011 a river andwants to make electricity from it He adds thatbu inesses may be in very remote place wherethey cant get electricity from a public network

Ontario Drive amp Gear Started in 1962Ontario Drive amp Gear Ltd (GOG) developedand manufactured a special transmission for asix-wheel-drive amphibious all-terrain vehicle

They were looking for a stable market fortheir products says Michael Eckardt ODGsvice president of finance

In 1967 the company entered the marketwith its own amplnbious vehlele bull called Argos

ocated in New Hamburg Ontario Canada18 MAYtJUNE 2001 bull GEAR TECHNOLOGY _gesrlechnoloflY cQm bull wp transmlssloneom

aDO manufactures sporvhelical internal andworm gears It also manufactures spur helicaland worm gearboxes Meanwhile its amphibi-ous vehicles use helicel and spur gears Theparts and assemblies are used in agricultureautomation material-handling mobile liftequipment municipal tractors and transporta-tion

The vehicles are used for disaster responseemergency medical service search and rescueresource exploration and recreation-like hunt-ing and fishing

And anything else where you have to be offthe beaten track Eckardt says

Tile Macbines In Their NichesAmarillo Gear Amarillo Gears spiral bevel

gears are in AmariUo Winds machinesAmarillo Wind receives the gears assembles theengines then creates their frames andthe windmachines towers

Each machine has two sets of spiral bevelgears one set in the lower gearbox one in theupper gearbox The lower box receives powerfrom the engine and sends it up the pipes driveline to the upper box which is connected to thefan blade

Also each machine has a set of worm-and-worm-whee] reduction gears allowing the uppergearbox-s-and the blade-to 1I0taW3600 aroundthe tower

As an example the standard machine fer cit-rus crops is about 3S feet tall from the ground tothe blades center-tall enough to clear treetopsThe blade is ]8 feet long

Tilted 60 down the blade draws warm airfrom above from the inversion layer and blowsit down on the trees raising the temperature atground level to protect the crops from frost

A machine is placed mthe center of every Wacres of citrus trees in an orchard To affect alll() acres the machine blows air at nearly 30mph

It stirs the air quite a lot says Roger HeinAmarillo Winds general manager

The wind machines cant hold nature at bayAs Hein says they dont prevent all frost buttheyaUow farmers to change Mother Nature bya few degrees

Those few degrees can make tile differencethough

For example Americas largest orchards foreating oranges are in southern California in theCentral Valley Despite its warm climateCalifornia can have freezing temperatures inNovember and December

The best temperatures for growing orangesrange from a high of 95deg to a low of about 30deg

I At about 27deg oranges can start to have prob-lems says farm manager Edward Lorenzi of SunPacific Located in Bakersfield CA Sun Pacificgrows citrus fruits in the Central Valley and usesmachines from Amarillo Wind

The oranges problems are dissipation oftheir juice and damage to their appearance

Oranges have small cells that hold their juiceIf the temperature is too [ow theoranges freezeand the frozen juice breaks through the cellsWhen the oranges later thaw their juice evapo-rates Also California eating oranges must lookappetizing-no wind scars no fungus

Once damaged the eating oranges would beused for any remaining juice Their value wouldbe limited to their juice value

The difference between a fresh marketorange and a juice orange in California is thedifference between making money and losingmoney Lorenzi says

He explains that depending on the marketeating oranges of export quality can sell for asmuch as $14 per carton As for a carton of eat-ing oranges used for juice You mighl be ableto gel $4

Each wind machine usuaUy rues about 100hour during winter and protects probably$20000--$30bull000 in citrus fruit As a farm man-ager Lorenzi himself is responsible for 3000acres of citrus fruits

AI Impkly of Oitlfio Orin ItGllr Udl Iblnd av-r I ArgoIIplliblaul nblel ani I IIIDmbly lillll DOG Impbibl-OUI YlIbJelll Irt Ibuilt In NlwH m u7g Ontario CI dl

J10seph L Hazeltonis associate editor ofGear Technology Trainedin journalism hI WQS areporter for two wtlkJy

newspapers in MichigO1before joining GearTechnologys slqff

pottlnsmiuiollcommiddot wwwg9I1rrechllolmiddotogycom bull GEAR TECHNOLOGY bull MAYJUNE2001 9

Made by Amarillo Wind IMachine Co a wind machine lor citrus crops can protect 10 acres of Iraes bylblowing higher warmer air down onlhem lIhemachines blow he air at almost 30 mph

Euch ala wind maehines gearbOIllS incld8l1 set olspi11 bevel gears as in this cress sectioD AmarilloWind gels hose gears rom its parenl complny Ama~ilIo GeM Co

A standard machine from Amarillo Windcosts $15000-$20000

ATA Gears ATA Gears water turbines createelectrical energy from flowing water The tur-bines power depends all the waters netheadand flow volume The turbine usually needwater with a head of 6-70 feet flowing at a rateof 30-] 800 cubic feet per second

Depending on those factors the turbinesusually generate 20-2500 kilowatts

To generate their power the turbines must bepart of a dam When the dam i opened waterflows through the turbine and rotates the runnerblades driving the shafts and spiral bevel gearthat power the generator

Hallila explains a water turbines costdepends on size and conditions but its roughly$1000 per rated kilowatt Also there may beadditional costs for other items like the dam

~Ontarjo Drive amp Gear The Argos are small

J-vehicles that look like rugged open automo-biles Depending om the model they have sixwheels and can carry four people or have eightwheels andcan carry six people They have 16-hp to 20-hp engines and bodies made of poly-ethylene a type of plastic Tneall-wheel-oriveArgos can travel at 20-22 mph

Weighing 765-1025 pounds the vehiclesmight not be expected to float but they do

They can go through any depth of waterEckardt says Theyre fully amphibious

In the water the six-wheelers can carry twopeople the eight-wheelers can carry four peo-ple With their wheels as propellers the Argoscan go 25 mph on water

We dont actually drive the vehicleEckardt adds we propel the vehicle throughthe water

An Argo typically costs $6000-$11000Gear Companies With End-ProductsAccording to Hallila its unusual for gear

companies to makeend-products Asheexplains gear companies dont want to competewith their own customers

Hallila knows of no other gear company thatmakes water turbines At 000 Eckardt saysthere is one other manufacturer of amphibiousvehicles but it isnt a gear company Also Heinisnt aware of any other gear companies withwind machine operations

The Machines MarkieampsHallila describes the water turbine market as

a relatively small market According to Heinthe domestic market for wind machines is prob-ably either shrinking or staying the same but

20 MAYJUNE 2001 GEAR TECHNOLOGY WWWgSllflsclmoiogycom wwwpowerltllnsmissioncom

the foreign market appears to be growingAs for amphibious vehicles Eckardt says the

markets size is difficult to determine Hede cribes it as wide but hallow explaining thereare many niche u e for ampbibious vehicles

But he adds the market has been growingrapidly during the past few years It mirrors-ina way-the ATV market for the four-wheelers

Niche in ProductionHaving gone a tep further the three gear

companies have made their end-products pari oftheir operation BUl Ole step hasnt had thesame effect on all of them

ATA Gears makes its small-scale water tur-bines only when customers specially order themAnd it designs them to suit ell iomers localconditions Amarillo Gears subsidiary makes itsend-product as part of its daily operationsAmarillo Wind makes 200-300 wind machineeach year Likewise anG makes its amphibiousvehicles in its daily operations-about 2000vehicles each year

Hallila says the water turbines are a special-ized part of ATA Gears not in the companysmain tream operations For example ATA Gearshas 170 employees but the number of employeesmaking water turbines varies depending onworkload

Hein also describes Amarillo Wind a a spe-cialized part of Amarillo Gear nol in its main-stream operations Amarillo Gear has more than130 employee Amarillo Wind has 21-andonly eight of them build wind machines

ButODG amphibious vehicles are its main-stream Out of I IO employees 30 work in alesand admini tration 34 in the gear divi ion and46 in the vehicle divi ion 0

Tell Ua WIIeIYDII T1IiK

If you found this article of interest andor usefulplease circle ~

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If you would like more information abouta-tllo Bear CO circle1fUATA Geelllld circ _00 Drive a Gear Ltd clrcl aU-If you would like to respond to this or any other articlein this edition of GeBr Technology please fax yourresponse to the attention of Randy Stott managingeditor at 847-437-6618

A waler lurbine rom AlA Gea~ includes IIset 0 its spiral blvel ijelf8 how in hI iIIltntld troISsettion Enlering theturbine water IIms themiddot rner blades (rigmiddotht) drivinglll ball md Ipinl bInilUfS hllt power the QelUlretof

ATA Gears middotturblnes generate power as part ofa dam as in tbis i1Luslrlltion To g lemla pOWlr middothmiddotturmiddotbines usually need waler with a head of IHOleel lowing IIIa ~al 0 3O-1i80(]cubic middotamp1 per nconll

wao erlrBnsmlssioncam QBarlechnologycom GEAR TECHNOLOGY MAYJUNE 2001 21

This paper was p~-

sented at hI 1999 Fall

Technical Muting of theAmerican Gear Manuat-

lurers AssociationPrinted with permis-

siO1of the copyright hold-er the American Gear

Manufacturus Association1500 Kill Street Suite201 Alttandria Virgin22314 Copies of the paper

are available from theAssociation

Statementlaquo presenfed

in this paper are those of

flu author and may no rep-resent the position or opin-ion ofhe Amertcaraquo GearManufacturers Associanafl

Figure J-Traditional in-spection cover

Figure 2-TlIleaded pipeplug inspectifJI porl

Gearbox FieldPerformance From a

Rebuilders PerspectiveCharles D Schultz

IntreducrionThe major focus of the American Gear

Manufacturers Association standards activity hasbeen the accurate determination of a gearboxs

ability to transmit a specified amount of powerfor a given amount of time The need for a levelplaying field in thai critical arena was one of the

reasons the association was formed in the firstplace Over the past 85 years AGMA committees

have spent countIes hours discussing the best

ways to calculate the rating of a gear set oftenarguing vigorously over factors that varied the

resulting answers by fractions of a percentagepoint WillIe all that science was being debatedin test labs and conference rooms an over the

country our industrys customers were conduct-ing their own experiments through the daily oper-ation of gear-driven equipment of all types

Unfortunately the results of those test pro-

grams are usually unavailable to the design engi-neer unless failure occurs during the relativelyshort warranty period offered on new equipmentMy employer the Pittsburgh Gear Co bas been

engaged in the repair rebuilding and field servic-

ing of gearboxes for many years The record ofthat activity provides some interesting insights

into what happens 10 gearboxes long after theirwarranties run 0111 (See Appendix A) While themajority of our customers are in the steel busi-

ness equipment from the chemical mining androck-quarrying industries has also been repaired

At one time or another products from mostdomestic and foreign suppliers have beenserv-iced The gearboxe cove much ofAGMAs his-tory and include most of the designs populartoday One of the drives Operated by a local cus-tomer was put on-line m 1921 and hasnt mis eda day of WOlK yet That type of performance isexceptional of course but it certainly inspiresrespect for the designers who labored in OUT tradelong before ihe advent of the computer

~t is 101 deference to those creative engineersthat] encourage todays gear designers to avail

themselves of any opportunity to study long-termperformance Having spent most of liIe last 2Syears engaged in gearbox design and develop-ment exposure to the far less glamorous ide ofthe business has been extremely beneficial to mydesign work In this paper Ill try to share some

of the things Ive learned and how theyve affect-

ed my design philosophyFailuR Definition

Our customers have their own definition of

gear failure and it has nothing to do with bend-ing tre or durability rating The average mil)

upenntendent care about ollly one thing Canthe equipment work today IT a little pitting or amall crack appears the user couldnt care less if

production can continue While some of the moresophisticated plants are rapidly moving towards apredictive maintenance environment the V3St

majority of mills react only [0 catastrophic break-downs Weve seen some incredible perform-

ances by gearboxes run completely without oilfor months or missl_ng sizable tooth fragments

due to bearing-related misabgnment We haveeen very few failures caused by overrating or

misapplication although overloads due toprocess line crashes and field modifications

remain a significant problem AGMAs standards

writers and the application engineers can be justi-fiably proud of their work

The arne pride cannot be shared by the plant

maintenance crews however The most commoncau es of failure recorded in OUl database are Iackof lubrication poor lubricant quality and debridamage Tooth breakage i rarely een unlessbearing damage extreme tooth wear or debris isinvolved Pined teeth are usually Iefl untreateduntil the drive becomes aoisyenough to attractattention or someone becomes alannedat themetal seen during an oil change While there arecertainly design deficiencies that contribute tothose problems mo t customers would enjoy

lower overall operating costs if they did a betterjob of monitoring the equipments oil quality For

22 MAYJUNE 2001 GEAR TECHNOLOGY wwwgsartschnorogycommiddot wwwpowsrtransmuoncom

ly reduced both their maintenance staffs and their

spares inventories Among the most distressingproblems we have to deal with on a regular basisis the housing bore damaged by II spun bearing(See Figure 6a) Repairing a damaged housing isvery time consuming and costlyespecially onspecialunits with multiple split lines ora dividedpower path The A[SE heavy-duty crane specifica-tion (see AISE Technical Repott 6 June 1996)requires that bearings be mounted in replaceable

cartridges (see Figure 6b) due to the difficulty inremoving the housings from their lofty perches for

re-machinlng Superintendents faced with expen-sive lin-place machining of gearbox housings

grouted into the floor quickly make sure futurepurcha e specifications follow the AISEs exam-

ple Except for bearings that must float axially bull itmight be worth studying the effects of tighter out-side diameter fits on most housings Where pas i-

ble anti-rotation pins (see Figures 7a and 7b)seem to be quite effective

Some ofthe lubricant loss experienced ill themin can be traced to worn eal diameters Manyoutput shafts are made of material that has notbeen heat treated Consequently those shaftshave soft seal diameters which wear out ratherquickly After-market wear sleeves have provento be quite effective in fixing tbat problemalthough the units have to be removed from theirmountings and stripped of their couplings to

the designer knowing that even the most state-of-

the-an gearbox will operate in an environment fullof soot sand water blunt instruments and

mechanics struggling to keep everything movingcan help reduce the anxiery of determming thecontact stress to the thjrd decimal place

Design Praetlee CbangesObserving the maintenance problems first-

hand has resulted ill sornechanges to my designphilosophy For example unless a customer

insists we no longer use the traditional bolt-oninspection covers (See Figure I) Weve found thethin plates almost impossible to seal against mois-

ture and have noticed that many time the debris

that inflicted the final damage to the gears was asmall cap screw used to attach the plate Our tech-nicians have found all incredible amount of stuff

inside gearboxes with large covers includingwrenches screwdrivers files and flashlights

Weve arlen joked that tile bigger the inspectioncover the bigger the debris While handy for gearinspection the covers ought to have a wantinglabel affixed reading No user serviceable parts

in here Weve switched to large threaded pipeplugs for inspection ports (See Figure 2) Theyseal tightly against water permit quick inspection

oftooth condition and are impossible to drop intothe Oil sump The pipe wrenches required toremove them are 100 big to drop though the hole

although the tiny flashlights favored by somemechanics do present a continuing hazard

Weve al a become believers in low oil

level sensors (See Figure 3) Originally wary ofputting delicate electrical device in the rough-

and-tumble mill environment observing a plantstart-up where the only gearboxes run dry werethe only ones without the sensors was convincing

evidence of their value Weve also been increas-ing the robustness of the external lubricationplumbing used on both new designs and rebuildsLube lines apparently make excellent ladders forclimbing serve as emergency crane hooks and areeasily snagged by passing loads One of our cus-tomers now has us fitung his more susceptiblegearboxe with guards made of O25-in plate toprotect them from dWIIage (See Figure 4) FOrmost pressure lines weVe switched to high-qual-ity bydraulic hose after discovering that even thebravest mechanic wont use them for a step or alift point (See Figure 5) So far the customershave been very accepting of that change especial-

Iy when they realize it is much cheaper to make anew hose than it is to repair a damaged pipe

Fast turnaround on repairs is increasinglyimportant to the mills many of which have great- FigulIe 5-ExIemQII14brbQliOlli system with hydnJUlic hose

Figure 4-Guardtd lllbrlcation system

Charles D Schultzis vice president of engi-neering al Pirulmrgh GearCo A registered profession-al engineer in flennryivaniaand Wisconsin he hasworked ill the geGr industryfor 30 years

w powetlransmlulonrom wwwgmiddotsIJrtechn0ollycom GEAR TECHNOLOGY bull MAYJUNE 2001 23

a) Conventionaltjmounted bearing

Housing bore urface prone10 damage if bearing spi ns

Housingbore surfaceunaffected bybearing spinInexpensivecarrier can bereplaced

b) Carrier orcartridgemounted bearing

Figure 6-Bturing mouJltingol exteruJed ervklaquo life

- Slot ground intobearing cup

a) Single-row taperroller installation

b) Double-row taperrolleror sphericalrollerinstallation

1- --- --

Figure 7-Commo ann-rouutoraquo pin designs

a) Conventionaldirect sealmounting

Bhn minimum

b) Severe-duty sealdesigngreasepurgedwith Ireplaceablesleeve andprovisionsfor splitouter seal

Figure S-Stlal de~igns01 er~fIdedserviclaquo lift

Figule 9-Example of miscellaneous damage

in tall them Coupling removal occasionaJlycauses enough additional damage to the shafts tonecessitate their replacement anyway We rec-ommend that seal diameters be at least 285 Bhnon all shafts unless wear leeves are lined (SeeFigures 8aand 8b) Chrome plaling or inductionhardening ispreferred by orne customersalthough those processes add to the turnaroundtime For severe-duty wash down environ-ments special seals such as packing glands arewell worth the extra expense

We are still trying to develop better ways tokeep water out of the sump Continuous castergearboxes are particularly prone to water contam-ination even when fitted with expansion cham-bers rather than breather A a result of that prob-lem the mills have reluctantly gone to trier pre-ventive malntenance programs all those criticaldrives Through careful attention to details suchas chrome plating seal diameters and regularlyrepainting the interior surfaces of the housing wehave been able to lengthen the time betweenrebuild by 50 The most amazing thing to meis how well the carburized bevel gears have heldupafter being lubricated with watered-down oilWn similar situationstmough-hardened helicalgears destroy themselves in a maner of weeks

Wear is a much more common gear failuremode than tooth breakage 011 the drives that werepair As noted earlier customers seldom react tothe appearance of pining even on carbunzedgears Severe wear frequently produces a notice-able change in how the gearbox sounds and drawsthe interest of the mechanics Carburized gearstypically outlast several sets of bearings unlessthe bearings are allowed to deteriorate so far thatmisalignment results in evere pining or toothbreakage In similar applications through-hard-ened gears do not seem to hold up as well and aremore frequently replaced at the same time as thebearings The Jongevityof through-hardened gearset i adversely affected by the high face-to-diameter ratios used ill some designs whichmake the sets prone to deflection-related loaddistribution problems In redesigning those gearsets we often use the additional capacity affordedby changing to carbusized gearing to reduce theface width thereby reducing jhe facediameterratio to more conservative levels

Basic design problem are relatively rare bUI

when poundheyoccur the customer has to live with theresults for years One installation we service has a49 1ratio doable-reduction gearbox Lfla very tightlocation The 7 I gear sets have face-to-diametermtios of over 20 and require replacement every J8

24 MAYJUNE 2001 bull GEAR TECHNOLOGY wwwgBsrI6chn0ogycom bull wwwpowBrlransmlssoncom

to 24 months Wellave other frequent visitors

with multiple input-multiple output configurations

that suffer from recirculating powerploblemsImproved part quality or increased hardness has

lengthened the time between rebuilds but the lackof redesign options prevents effective long-termre elution When designing our own specials we

try to give ourselves room for future upgrades bytaking a conservative approach to ratio selectionface-to-diameter proportions and internal housingclearance

DesigJI for Extended LifeWhile recognizing the commercial limitations

impo ed upon us by the global marketplace lbelieve that we can design for extended life byconsidering the problems likely to be encountered

during the 15- to 25-year operating life of the typi-

cal process line and addres sing them al the original

equipment level Not every gearbox needs car-tridge bearings but all deserve a water-free Slimp

Following the AISEs example of graduated serviceclasse to account for duty cycle reliability expec-

tations and life requirement would go a long waytowards improving customer satisfaction with ourindustry With~n the context of tho e service class-es it would be po sible to addre s detail de ignissue in a way that provide a consistent levelplaying field for all competitors without forcingcustomers to develop their own in-house specifica-

tions I realize the difficulty of changing from a cat-alog selection system based upon a list of applica-

tions and service factors to a system that includesnon-gear related factors uch as housing design Itwas just a few years ago however that we consid-

ered 10000000 cycles 10 be infinite life despiteknowi ng that that was less than I IX)hours of use for

the typical high-speed pinion A proposal for serviceclasse is shown ill A-ppendix B

AcknowledgmentsThe author would like to acknowledge the

assistance of Will Willman and Ed Besong ofPittsburgh Gear Co in preparing some of the pho-

tographs and illu tration used in this paper 0

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WWWpOwmiddot rtrsnemtestoncom WWWgflsrtBchllologycom GEAR TECHNOLOGY MAYJUNE 2001 251

AppendilAdause or repair summaryDescriUODI of IOrdersContaminatedloil 353

ID Toml1611205964905174

Cause of RepairInadequate lubricantlow Oil LevelBearingsMiscellaneousOverloadPreventive MaintenancePrecautionary Repairs

Totai

Insufficient oilWorn orfailed bearingsNon-Gear Searing lubeGear or bearing damage

44921111198381

5962188

272

IComments1 Bearings and seals were changed on all gearboxes unless the customerspeciflcallyrequested their re-use2 Worn or pitted gears were not changed unless authorized by the customer3 The Overload cBtegory includes all tooth breakage and indications of plastic flowFrequently the problem occurs when the process line crashes putting untcrasaanloads on the gears bearings and shafts -4 The ~Inadequate Lube category includes units with evidence of contamjnation andgeneral bearinggear wear The low Oil Level category was reserved lor cases of rol-atively sudden failure due to temporary lack at oil rather than long-term damage5 The Miscellaneous category includes physical damage to the gearbDx by externalsources leaks not related to seals handmiddotof-assemblv changes COlUplingchanges andmodification requests (See Figure 916 The Preventive Maintenance repairs are made based upon previous expenience thatfailure to do so on II regular basis will result in unplanned shutdowns

Class 2 3 4

Description IRegular Duty Heavy IDuty Severe IDuty Critical Duty

Abbreviation I AD liD SOl CD

Minimum Gear

Strength SF 125 175 250 300

Lube System Splash Splash Pressure Pressurewith filter with fiHer

Min Gear IDesign Life 110000hrs 150001hrs 20000 hrs 30000 hrs

Min Bearing L-l0 Life 10000 hrs 20000 hrs 40000 hrs 60000 hrs

Bearing Mounting Conventional Conventional Cartridge Cartridge

Seal Type Single Lip Single Lip Grease Plrged Grease Plrlledwith provlsons With prOVISIons

lor split fOr splilraplacemants replacements

Shaft Surface 220 Bhn min 285 Bhn min Replacea~le Replaceablesleeve reqUired sleeve requ ired

-----

Gea~boxesrepairedincluded

Alten Engineering Oivision Westerman CompaniesAmarillo Gear CDBr~wning a division 01 Emerson Power TransmissionCIucago GearmiddotDO James CorpCleveland Gear CoCone Drive a division of Textron Powar TransmissionDavid Brown a division ofTextron Power TransmissionDelroyd Worm Gear Products a division of Nuttall Gear LLrIDodgea division 01 Rockwell AutomationIDorns CoFalk CorpFessler Machine CoFiend er GorpFoote-JonesIllinois Gear a division of Regal-Beloit CorpHansen Corp a Minebea Group companyHarnischfeger Industries IncHitachi Zosen CorpHorsburgh amp Scott Co _ILohmann + Stolterfohl GmbHMorse a division of Emerson Power TransmissionNord GearNuttall Gear LLC bullPhila delphia GearPrager IncRenold picSantasalo Gears [now Metso Drives)SEW EurodriveSumitomo Machinery Corporation of Americ81Xteklnc

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Design Forrnulasfor Evalullting Contac1 Stress in Generalized Gear Pairs Page 31Q amp A Dynamic Loa~sWorm GeBrsamp Geometry Factors Page 39Load Distribution in PIanetary IGears w Page 41

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bull G~R DES~GNFOCUS ----_

Design Formulas forEvaluating Contact Stress in

Genelralilzedl Gelarl PairsIntroduction

A very important parameter when designing a gear pair isthe maximum surface contact stre s that exists between two gearteeth in mesh as it affects surface fatigue (namely pitting andwear) along with gear mesh losses A lot of attention has beentargeted to the determination of the maximum contact stressbetween gear teeth ill mesh resulting in many different for-mulas Moreover each of those formulas is applicable to a par-ticular class of gears (eg hypoid worm spiroid spiral bevelOf cylindrical-spur and helical) Morerecently FEM (the finiteelement method) has been introduced to evaluate the contactstre between gear teeth Pre ented below i a ingJe method-ology for evaluating the maximum contact stress that exists Fig1-Two pitch circles lncont8ctbetween gear teeth in mesh The approach is independent of llIe r----------------------- =r=t

gear [Oath geometry (involute or cycloid) and valid for any geartype (ie hypoid worm spiroid bevel and cylindrical)

Relative CurvatureThe contact stress between two gear teeth in mesh depends

on the relative gear tooth curvature material properties of thegear teeth and the transmitted load between the gear teethDetermination of the relative gear tooth curvature can be prob-lernanc for certain gear types The relative gear tooth curvaturebetween two gear teeth in mesh results in a contact that is eitherpoint-eentact or line-contact lit general the tran verse contactratio for two gears in mesh is greater than zero and line-contactexists between the two gear teeth in mesh Helical or spiral gearswith line-contact experience both axial andtransverse displace-ment during me h Such condirionsare inherent for any toothprofile type (namely involute or cycloid) Point-contact is the Fig 2-G88r nomenclature

David B Dooner

alternative cenario for two conjugate surface in me h Thatcondition occurs when the transverse contact ratioi zero Thattype of contact applies to circular-are type profiles (IlamelyNovikov-Wildhaber or BBC)

Determination of the relative gear Iooth curvature AI(between two planar involute gear teeth is demon trated prior topre enting he relative gear toolh curvature between two gener-alized gear teeth Depicted in Figure I are two involute gearteeth iII me h The radius of the input pitch circle is RibullwhereasR i the radius of the output pitch circle Pi and Po are the radiiof curvature for the input and outpur gear teeth respectivelyProjectimg the pitch radii R and R onto the contact normal

pitch surfaceof oulpu1llear

pitch circleL-----~~Uc----- langenl

bull Itooth

~ ccntaet nermalI

pilch surface of irrpulgear

gcnunlQr omiddotrhyperboloidalpitch surface

Iallis of rotation(output gear)

axis of roIalion (inpul gear)

David BDooneris an associate professor in thedepartmm ofmechanical engi-neering aI the Uni versify of PuertoRicomiddotMayagaez Ilis researchinvolves a universal approach forthe concurrent design and manumiddotfacture of gears That generalizedapproach can be used 10 producegears with any number of teethany face width and any spiralangle The approach applie 10helical bevel wonn spiroidhypoid ami nOli-circular gears

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CIRCLE

IIEHOlDPreclsiol1 Technologies

1 GEAR DESIGN FOCUS _

yields

Pi = Rsincentl (Ia)

Ob)

where cp is theangle between the pitch circle tangency and thetooth contact normal For planar curves tile curvature 1lt andradiu of curvature p are reciprocals (ie bull K lp) Thu bull rela-tive gear tooth curvature ~K can be expressed as follows

w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))

whereR radiu of input pitch circleRo radius of output pitch circlecentI pre sure angle

The above expre ion establishes a unique relation betweenthe pres ure angle centI the pitch radii R and R and the relativegear tooth curvature ~K Regardless of the radii of tooth curva-ture Pi and Po the relative gear tooth curvarure ax depends sole-ly onpitch radii R and Ro and pressure angle 41 The above rela-tion for relative gear tooth curvature ~sfor cylindrical gears withspur-type gear teeth Furthermore the relation is valid only forcontact at Ute pitch point

Prior to pre enting a generalized relation for the relative geartooth curvature it is necessary to establish some ncmenclanrre andintroduce certain expre ions Depicted in Figure 2 are two pitchsurfaces in mesh two axe of rotation ljElJldl~the perpendiculardistance E between the two axes Ii and 10and the included angle Lbetween the two axes Ii and 10 The piteh urfacesin Figure 2 arehyperboloids Notice in Figure 2 that each byperboloiclal pitch sur-face i determined by a series of straight lines Hyperboloids canbe envisioned the wface produced by rotating a line or gener-ator about a central axis For example rotaringjhe common gen-erator lilo between the illpul and OUtpllt body about the axis of rota-tion Ii produces the input hyperboloidal pitch surface The shape ofthe hyperboloidal pitch surface depends on an angle II and dis-tance u The angle 11 is the cone angle of the generator and u is theradiu of the hyperboloidal pitch urfaceat iliethroat Introducingup as he radius of the inpm hyperboloidal pitch surface and Upo asthe radius of the output hyperboloidal pitch surface then up+ Upo

= E for two hyperboloidal surfaces in mesh Similarly defining ~as the can angle foribe input hyperboloidal pitch surface and llpoas the cone ~e for the output hyperboloidal pitch surface thenOlp + ~ = L for two hyperboloidal pitch surfaces in mesh Alsoshown in Figure 2 is the distance wp between the throat and pointp As the twohyperboloids rotate they are always in contact alongthe common generator

Cylindrical gearing OCCllJS when die angle I between theinput axls of rotation and the output axis of rotation is zero (ie

32 MAYJUNE 2001 bull GEAR TECHNOLOGYmiddot wg6llmiddotrI6chnl1lrom bull ww po efIIsmssJoIIcom

_---- GEAR DESIGNI FDCUlS1 _l= o and hence me con angles crmd laquopo are al 0 zero) fugen-eral II gear type depends on hom the center distance E (offset) andangle 1 between the input and output axes of rotation When thedi tanee E between two axes of rotation is zero then the pitch sur-faces become cone and the throat radii uP and upltgtare zeroAlternately when neither E nor l is zero then the two pitch sur-faces are hyperboloids Equation 2b for relative curvature til( wasderived in terms of cylindrical pitch surface and consequently itil101 valid for conical or hyperboloidal pitch surface

All importam parameter for pecifying relative gear toothcurvature is the effective radius The effective radius is the dis-ranee between the point p on the pilCh surface and the axis ofrotation as shown in Figure 2 For generalized gear pair with acon tant inputoutput gear ratio g the effective radii Uel and Ueocan be expre ed

whereupi radius of the input pitch urface (atthe throat)uJXl radiu of the Olltput pitch urfaee (at the throat)E shaft center di tance between he two axes of rotation

(up + Upo= E)wpi axial position of tangent point on input pitch surfaceWpo axial position of tangent point on output pitch surface

(wp = -wpo)

Ilpi cone angle of input pitch surfaceClpo cone angle of oUlput pach surfaceL the included hafl angle between the I[WO axes of rota-

tion (01 + 00 = L)11is also convenient [a introduce the following relations

where

uposi notanYPo = ~~=~o====

uJXl2cOS2-a+ Wpo2sin2Clpo

to determine relative gear Loath curvature It is of ceatral impor-tance to know th at the gear ratio g is equal to the ratio of radiil Rand R (ie g = RlRo) C-one angles ~i and laquopo are zero fOJ

cylindrical gears and con equently Ypjand Ypo are also zero Forbevel gears the pitch radii up and upoare zero such that Ypi and

1110 reduce to zero For spur gears jI is zero In general the extreme relative curvature between two gear

teeth in mesh can be determined with the following expressions

(3a)

(3b)

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(4a)

(4b)

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_____________ GEAR DESIGNIFOCUS _

tooth profile with lip relief

Fig 3-Tootb profilemodification

ellipticalccntact

rMajor semi-axis of contact ellipse

Iiig 4-StniSI intensityfo ellipticill comet

HVpoid

Spiral bevel Splroid

Figi-Gear pairs

whered~ minimum relative curvature between gear teethdKmu maximum relative curvature between gear teethRi virtual radius of the input hyperboloidal pnch surfaceRo virtual radius of the output hyperboloidal pitch surfacelp instaruaneous piral angle of the input gear (pi == Ipo)centgtn normal pressure angle1 included sha uft angle

The above formulas for extreme relative gear tooth curva-ture are applicable forhypoid spiroid worm bevel and cylin-drical gear pairs Furthermore those formulas are independentohhe type of gear loath profile Recognize that when E = 0 (ie bullplanar gearing) and = 0 (ie spur gears) Equation 2band theabove relation for maximum relative gear tooth curvaturetlmax are identical The mathematical development of iheabove expression involves many mathematical relations andonly LIteresults are presented Additional insight into LItemath-ematical derivations is provided in Reference I_

Profile ModificationIdeally two gear teeth in mesh are in line-contact for gear

pairs with involute-type tooth profiles However gear designersintroduce both proftie relief and lead crown to accommodateerrors in tooth spacing runout misalignment and deflectionsGear teeth with profile or tip relief have a reduction in tooththickness in a particular transverse plane The magnitude of thetip relief is usually restricted to micrometers (IJlm)or a lew thou-sandths of an inch Crowned teeth have a reduction in tooth

thickness in the lengthwi e direction of the gear tooth The mag-nirade of crowning is restricted to a few micrometersacm s thetooth face Depicted in Figure 3 is a tooth profile with tipreliefand lead crown Such profile modification reduces theoreticalline-contact tc point-contact Consequently the above relationsfor extreme relative gear tooth curvature (ietlKmbullbulland tlrnm)must be modified to account for crown and profile relief

There is no established standard for specifying tooth profilemodificarion Here the deviation in ideal tooth profile is quadrat-icTip relief and leadcrown are specified here in a manner anal-ogous to the specification of addendum and dedendurn That isachieved by introducing a tip relief constant o and a lead crownconstant Bw Given the following tip relief con tant 011and leadcrown constant Gill the changes in CUIV8111reSxvandS~are

01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)

where~ lead crown constant0 tip relief constant

addendum constantdedendum constant

34 MAYJUNE 2001 bull GEAR TECHNOLOGY wwwgssrtechnoJogycom wwwpow)rtratlsmiss(oflcom

_-----------GEAIR DESIGNFOCUS _r r face width IPd normal diametrallitch

lland ll are the same for both the input and Olltput gear Ielements suchthat the modified curvature become

I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~

llIcmm change in minimum relative tooth curvamrei

OlCmu change in maximum relative toolil curvature jOK change in relative tooth curvature iII profile direction IEnc1IJ change in relative teeth curvature in lengthwise direction I

centIn normal pressure angle 1- __ --------------------I Fillmiddot amp-Mllximum contact ltrIu ICIIII 1lIfIll taco at C~Lllldnc I b-ypold b VIItVpl spiral angle I Ind _prald 111111Ipalr

F-or spur gears (ie bull tV 0) the face width Fi and Fo areidentical and equal to the distance between the heel and toe The Iabove change in relativegear looth curvature for modified gear I The tran mitted loadlletween two gear teeth is non-uni-Leeth mu t be added to the theoretical value Thu bull extreme gear formJy di tributed over the surtaee area of contact Depicted intooth curvature can be expre ed Figure 4 is an elliptical contact area with semi-axe r and rb

Kmin = bKmio (93) along with a parabolic Ire s intea ilY The sum of the pres ure I distribution over the area of contact results in th net force(9b) applied 10 the gear mesh interface Determination of the maxi-

II

OKp + ElK bull (sin2cent1n tan~pi)

~+ sin2lllo tan2ilj)Pi

500000

100000

400000

6K + ElKIl (sin2cj1o tanr1vp)I+ in2cent1n tan~pl

SpirDidBevelCy1indrinlHYpoid I

where

II IlOti

35 411 45 Ih 1

hia I position of contact in]

Contact Stress

_en technology10 sUlccess

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CIRCLE 125

_------------GEAR DESIIGN FOCUS _

That formula neglects common loading factors that instanta-neously increase the transmitted load POne such loading factor

that results in an instantaneous increase in transmitted load is

the dynamic load that results from transmission error A secondloading factor that increases the transmitted load is a distribu-

tion factor Shaft misalignment can result in a concentrated loadfor gears withl1igh contact ratios A third type of loading factorthat gives an instantaneous increase in transmitted load is anapplication factor Such factors are inherent in rough operat-ing machinery like internal combustion engines and crushing

(Lla) mechanisms Additional insight into those factors is provided by

AGMA Contact stress is further affected by tractive or shearforces that result from the relative sliding and friction at the

mesh and residual stresses in the tooth sub-surface The magni-(l 1b) tude of the shear load on the gear surface depends on the type of

lubricant and its thickness Simultaneously the gear designershould be aware that relative gear tooth sliding at the contact

mum contact stress is based 011 the following assumptions

gear tooth materials are elasticgear tooth materials are isotropicgear tooth materiall properties are homogeneouscontact area is frictionless andradii of curvature are very big compared with the semi-axes

contact ellipseThe maximum compressive stress is evaluated using a mat-

tress-based formula (see Reef 2) Hence it is advisable that the

elastic moduli of the foundations are similar in magnitude Itisrecommended that Hertzs formulas for predicting maximum

contact stress are used for gear elements with highlydissimilarelastic foundations Introducingthe constant

wbereP normal contact forceBi modulus of elasticity for input gearEo modulus of elasticity for output gearI Poissons ratio for input gear

110 Poissons ratio for output gearthe semi-axes of the contact ellipse become

ra= [c (~ t4 KJ W

_ [ ( Kmllgt ~14 ~1]13rb- C --- --Kmin Kmin

Table l-Gear Pair ParametersICylindrical Hy oid Bevel S iroid Cylindrical Hypoid Bevel Spiroid

2m 2m MQ 2JIQ E Eg (lbJin2Nm2) lID 3DIDD ~ BShaft center distance E [inJmm) 508 508 000 508 l1J1X10 207X10

M 9Il lK 00 JIi e Jlo (dimensionless) 0267 0287 0287 0287Included shaft angle 1 (degJrad) DD 1571 1571 1571 R(inJmml Q6m W Jill lllJl

315 l25 315 315 1695 3525 2914 300

Axial position oftoe WIO linJmm) 8255 8255 8255 8255 R (inJmm) L23i am 2ill ws3147 9634 lSM 6142

ill ill ill m 1 [degJrad) g L jIL IlAxjalposition of heel 111 (inJmmJ 12065 12065 12065 12065 0 1511 1511 1571

P[inJmmj 1049 54lI5 5Jll 8mNumber of teeth on input gear N integer) 14 15 12 2 Q Isectll ill

up Idegrad) 0 0461 0369 02341 Wli 0 ru

Number of teeth on output gear N (integer) 26 41 31 41 up) (degJrad) 0 llQ1 12111 13311 ~ I 15l1M1 ~ 3ill aLZl 1 (degJrad1 0 0099 0 1)021

Nominal spiral anglelj1p (degJradJ 03Il4 0620 0648 1411 II illli ~ ~3000 5U 65Jll illlI Yo(degJrad) 0 0373 0 0439

Nominal pressure angle (norman 41 (degrad) 0524 0976 1136 0834 lK 11in1mlIlm IllIW LlIZ5 IIIW0249 Osas US un

~ 00l OOQ 12Q()Km l1inJ1mJ IlJ3i1I 11M Mlffi MVli

I Input shaft torque T [ ) 1017 1017 WIJ 1436 S2S1 2118 11178 1)189

KmOinJlmJ Ilm DD22fI lll25II IIJJI1ll

Axial contact ratio mldimensionless) 15 15 15 4 om 01186 0984 4111

tom flinlmJ illli IlJill W il311U1 3412 3969 2525

Addendum constant (dimensionless) PjlbJN) lllZ illI Wli illBI03 ~51 8247 6~

Dedendum constant (dimensionless) C (in2mm2) UZ1l1~ UlWa 1mJ ~

0076 0Jl56 001III 0074

rlinmml lli1lI gm[ Q2lli JJmlip relief constant aldimensionlessl 001 001 0D1 001 11601 5419 6142 HilS

r~linmm) I2QIll ~ WIll ~0439 0866 0965 0412

Lead crown constant Iil (dimensionless) 002 002 002 002 (lI (ksVMPa) 1B ill ill m1018 823 100 2SZ5

36 MAYJUNE 2001 GEAR TECHNOLOGYmiddot wwwgesrtechn0oQycom bull wwwpowerfransmissoncom

wheremajor semi -axis of contact ellipseminor semi-axis of contactellipseconstantmaximum relative curvature with profile modification

Kmm minimum relative curvature with profile modification

The maximum contact stress Dc is obtained by integratingthe pressure distribution over the area of contact A aadequat-iag to the transmitted load P The maximum stress Oc is 3rrJ4times the average stress for an elliptical contact area and a pro-

portional stress intensity hence

3n P0=--- -----~----c 4 nrrb

(12)

Table L-Contact Stress Calculations

_----GEAR DESIGNFOCUSI _zone can cause a rise in temperature at the mesh resulting in a

temperature gradient in the gear tooth and thus further affecting

localized tooth contact stressExamples

Four examples are presented to illustrate the determination

of contact stress between gear teeth in mesh The first exampleis a helical cylindrical gear pair the second example is a hypoidgear pair with non-zero spiral angle the third example is a spi-ral bevel gear pair and the last example is a spiroid gear pair(ie a hypoid gear pair with high spiral angle) Each gear pair

has a L5-inch face width The nominal gear parameters for eachgear pair are provided in Table I Graphical illustrations of the

gear pairs are provided in Figure 5 Intermediate calculations

and final contact stress are presented in Table 2 for the face mid-point Values for maximum contact stress are based on a singleconcentrated load and neglect load sharing resulting from highcontact ratio tooth deflections or wheel body deflections A

computer program has been written and the variation in contactstress across the face of the gear pairs is depicted irnFigure 6

SummarySimplified design formulas for evaIuatinglbe maximum contact

middot tress between two gears in me h are presented The melbodologyIs summarized as followsbull demonstrated that relative tooth curvature for planar gearsdepends on pitch radii and pressure angle

presented a generalized formula for extreme relative curvaturebetween gear teeth in mesh that is valid for any tooth type (involuteor cycloid and any gear type (cylindrical bevel hypoid spiroid orworm)bull presented a generalized formula for relative gear tooth curvaturefor arbitral) tooth profile modification (tip relief and lead crown)

presented explicir expressions for semi-axes of e1liplical contactbased on mattress formulabull presented formula for maximum contact stress between gearteeth andbull presented four example to illustrate the use of formulas to deter-mine maximum contact stress

ReferencesI Dooner DB and A A Seireg The Kinematic Geometry ofGearing A Concurrent Engineering Approach John Wiley and SonsInc New York 19952 Dooner DB On jhe Generalized Contact Stress Thelntemational Conference 011 Mechanical Transmissions ChongqingPR China April 5-10 2001

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------ -- ----- IQMII _

Calculating Dynamic LoadsSizing Worm Gears and

Figuring Geometry FactorsAnswers submitted by Robert ErricheUoGear Consultant GEARTECHjbull Town-send MT and Technical Editor GearTechnology

Questions submitted by Mark H SwalleyUS Navy Pugel Sound Naval ShipyardBremerton WA

0 Wbat is tbe best metbod to measureer calculate dynamic loads in B Ilow-speed spur gear subject to Iloadl rever-sals

A cranes gear train issubject to sud-den load reversal when an emergencybrake suddenlly appUes on the hoistd~m As the drum comes eo a suddenstop thanks to large caliper Ibrakestheel~ectric-powered dfiive baiD colUinuesto rotate The backlash is taken up andthe pinion gear comacts the oppositeace of the drums bulillgear The piiniongear iis on the loutput shah of the speedreducer The limpact is so violent thepinion gear standi bolts snapthe headoff ricocheting around the machineryhouse

The gear train has about 10 times theinertisl of the hoist drum To complicatematters tbe electric motor has time toproduce regenerative Ibraking prior toimpact

A Strain gages are commonly used tomeasure dynamic loads They are a goodchoice because they are readily avail-able relativelyicexpensive and accu-rate for capturing transient loads such asyou describe Computer modeling onthe other hand is accurate only if massstiffness and damping are preciselyknown Damping is especially difficultto estimate and usually requires strain

IRobert Errichellomeasurement on the actual system todetermine accurate values Thereforestrain measurement is the best choice fordetermining dynamic loads in your Iapplication Additionally the mea~ure- I~ents c~ help determine ~ystem damp- Irag which you could use 1n a computer ~model to explore alternative design changes to reduce dynamic loads

0 How shoulld the strain gages be I

placed and how should the signal be I

transmined IIII am Icurrently working out II full j

Wheatstonu bridge arrangement Strain 11

gages win be placed on ~he ends of the19 geaJteetll one on eiither side of the gear tooth base Ithe high tensioneom

j

l

pression areaslThe 38 gages and twodead gages will be dMded into lour le~s o 10 gages iin series The signal Iwilli be transmiHedfrom Shel roSating ~shaft via one of the telemetry-type strain ItrBnsmittellS I

That Brrangement willl reduce the isignal I bout iveltimes ~ve~ the sing~e I

gage lin a 1f4 budge CircUit but Willransmit a constant signal The transmit- iCer sends 500 signalsa second and II j

believe that to be fast enoughtol catch Ithe dynamic event II can correlate the Iresults to strain gages reading from a 1steady state load

QampA is an interactive gar forumSend us your gear design mlnu-facturing inspection or atherrelated questions and we willpass them to our panll ofexperts Questions may bemailed to G Tchnology POBox 1426 Elk Groye Village IL6CDJ9 fixed to (8471 437fi618 orsent vial e-mail to p80plg-tchnoogycom An expandedversion of QampA is online It TIl

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For information on obtainingcopies of the AGMApublicationsmentioned in this column con-tact the association by tlle-phone It (703t 684-0211 by fo It

(703~ 684-0242 or by I-mlil It

techgm bull org

A Your transducer and method of trans- maximum stress However it is eldommitting signals are state-of-the-art To practical to mount gages atthe criticalcapture tooth bending stresses the gages point because of interference with theshould be placed on the root fillet at the matinggears tips You need to decidepoint of maximum bending stress That what it is you wantIsit maximum toothpoint can be found by painting the root bending stress or is it the maximumfillets with brittle lacquer and applying dynamic torque applied to the gears Itloads to the gears The first place to I may be sufficient to measure the torque

j

crack the brittle lacquer is the point of 1 and calculate tooth stresseswwwpoweJrlfliNlsminloncom bull wwwgsarlecllnQlogycom bull GEAR TECHNOLOGYmiddot MAYJUNE 2001 39

_-----------aampAII _

Fr ---i 0 C[ III I I

----+------+--- ----

bull

Fig 1 - Worm lieu basic dimensions Source A_NSIIAGMA602ZmiddotCQ

Question ubmitted by ChristianWilliamsTexasAampM University College Station TX

(1 How does the desired gear ratiiofor II

worm and worm gear relata tOIthe aelu-all size of the gears For example if Iwanl a gear ratio o 3Ot1Iwhat diameterconstraints are pJaeedi on the gears fortbat Irati01

A Worm wheel diameter is set byrequired load capacity ANSIIAGMA6034-B92 Practice for EnclosedCylindrical Wormgear Speed Reducersand Gearmotors relates worm wheeldiameter to tangential load as follows

Dm = [WII( Cs Cm ev Fe)JI-2i

Where

Dm = mean diameter of the worm wheelCs = materials factor (aceounts for the

worm wheel materials strength)Cm ratio correction factor (accounts

for the gearratio)ell velocity factor (accounts for slid-

ing velocity and vane with diam-eter lead and speed of the worm)

Fe = effective face width of the wormwhee1 (Fe FG or Fe = (23)dwhichever is less)

Wt = tangential loadThe diameter of the worm can vary

somewhat without significantly influenc-

Where

II C = center distance1 d = worm pitch diameter

I ANSlIAGMA 6022-C93 providesguideline that give a practical overview

of worm gear designYou should audit the gearset to ensure

lit meets the design guidelines of ANS]Ji AGMA 6022-C93 and rate the load

capacity in accordance with ANSIJii AGMA 6034-B92 to ensure it has an ade-

quate service factor for the applicationi

i

i Question s[~bmined by Richard Fried- II

man Nichols Aircraft Division Parker

i Hannifin Corp Ayer MA ~r--------------1 I0 Is there a Iclosed-form sOIUUOD for the

Lewis form factor

A No there is no known closed-form

iI

If you did not care for this articla solution However an efficient algorithmf all I bJ If you would like to respond to this or anyor numeric y sOJvmg me pro em JS 1 other article in trul edition of G8

given in AGMA 908-B89 (Ref 1) The1 Tchnologypaasefaxyourresponsatothealgorithm is readily programmed using attention of Randy Stott managingeditorlitthe flow chart given in AGMA 918-A93 i 847-437-8818 or sand a-ma~ messages to

peoptJOgllttechnologycom(Ref 2) Benchmark examples useful for I L JI

ing load capacity ANS1AGMA 6022-C93 Design Manual for CylindricalWormgearing recommends a wormdiameter in the following range

Cl815 S d S QI87S

30 16

lable 1-DellIlO11 of symbols

Worm and worm gear addendumWorm and worm gur dedendumCenter dlstence IClearanc a I

Worm gear mean diameter I

Worm gear outside diameter IWarm gear root diameterWorm gear throat diameterWorm pitch diameterWorm outside diametmiddoterWorm mot diameterWorm gear face widthWorm faca widthlfhread length 01worm)

Full depth of worm threadWorm axial pitch

Somce ANSIAGMA 16022-C9~

validating software are given in Ref-erence 2 and tables of J factor are givenin Reference 1 The algorithm derivesfrom References 3 and 4 0

References1 AGMA 908-B89 Ueomelry Factorsfor Determining the Pitting Re istance andBending Strength of Spur Helical andHerri ngbone Gear Teeth April 19892 AGMA 918-A93 A Summary ofNumerical Examples Demonstrating the

Procedures for Calculating Geometry Factorsfor Spur and Helical Gears Jan 19933 Errichello R ~ Efficient Algorithmfor Obtaining the Gear Strength Geome-try Factor on a Programmable CalculatorAGMA Paper No P 13903 Oct 19814 Errichello R Jn Efficient Algorithmfor Obtaining Ifle Gear Strength Geome-try Factor for Shaper Cut Gears AGMAPaper No P 13905 Oct 1983

hilUs WIllI V11IiIIk

If you found this article of interest andoruseful pI sa circle

MAYJUNE 2001 bull GiEAR TECHNQlQGY wWlIgurechlloloQycom bull wwwpowerlrslIsmluloncom

GEARDESiGINFOCUS _

LoadIIDistriblutionin Planetary Gears

fIrs pp was presentBd-1 me 4111 IWorld COOlfflSS onGfllITiag BDd POWIII lrsnsmis-sion in Pars AfLrch bull

IntroductionTwo- haft planetary gear

drives are power-branchingtransmissions which lead thepower from input to outputshaft on several parallel way iA part of the power is trans- I

ferred loss-free as clutchpower That re ults ill high

efficiency and high powerdensity Those advantages canbe used optimally only if aneven ditribution of load Oil

the individual branches of

Wolfgang Predki Friedrich JarchowandChristof Lamparski

possible today to predict the I

dynamic behavior of such Igears The result of those iinvestigations consolidate thapproximation equations forthe calculation of the load fac-tors KK and KHamp

Parameter Study on LoadFaeurotors

The calculation of the

power is ensured Static over-con~tr~inl manuf~cturi[lg Idevianens and the internal I considers the influence of medyaamies of those transmis- I mentioned disturbances on the

Iion gears obslruct the load masses dynamics The dy- i

balance With die help of COID- namic model underlying the jplex simulation programs it is program is shown in Figure ] i I

EnvirOnmIDtaIIconditiOns I Sizlandlgaomeby of Ute gearing II

Attached mass inertia Genter distanceStiffness of attachment Gear IratioLine load Number of planet gears ISpeed of sun wheel Sum of the addendum modification I

RelativBcircumferential Face widthfdiameter coefficients velocity Number ef teeth of sun i

BaSil helix angle

IGall tooth q1Illity OFP Gfp OfHII j

Pitdllolerame ohhe planet carrier

Bearing eccentricityBeariillg clearance of planat gears i

~ L-A_ng__I_e_Of_IP_O_S_jtj_O_n_Of_th_middot_e_PI_a_ne __t_g_e_ar_s~ I

operanonal dynamic behaviorof a planetary gear stage is done willi the 3-dimensionalirnulation program SIM-

PLEX which was developedin an earlier research project(Ref 2) The program is able

to describe all mas e within Ithe transmission with sixdegree of freedom each and i

Table 1 Parameters censidered on Ihe dynamiC snnulation

Tooth corractionGrowllinglip modificationtongl addendumteeth

I~illl~ynmic modelio1elpianelLIY- ar IIlge 11-lmIIY-nl elioa

Afterwards the masses are I Prot DrAnlllinked to the bearings and to ~olfgangIIPledki _th f d b di Ii the head 0 the chair 0 mechani--e _oulLallon -y arscrete cal components industrial andelastic sheck-absorbing ele- auromolive pltrwer rrl1JlfmLrsonaJments Table 1 quotes the the Ruhr University Bochum iocat-

ed in German) There QFe 16assls-lanlS employed allhe chairour 0whom perform research 011 planr-tary gear INJnsmissionr The

The single clementsare research focuses 011 load dislTibu-tton analysts gearing modific(llionlemperallLre calculalion and technt-cal design

parameters which were con-sidered on ihe dynamic simu-

IProf em DrAngIfriedrieb Jarctiowis Ihe former head oj tn chair 0mechanical components industrialand Q141omolivepower Iransmissionat the Ruhr Ulliversity Boehumlocated 11 GermQJl

lation

combined in nine differenttypes of planetary gears forwhich the parameter studygives th required load fac-tors The planetary gears arecategorized according to thedesignarions oflhefirst col-umn of Table 2 Thus forexample a transmission witha sun gear smiddotllaft and 8 hous-ing-fixed intemalgearreceives the de ignationSlHl That rransmi sion

Dr-InglChrismf Lamparskiiiis the head 0 th dqxmmelflorresearrh and developmen 0hydraulic components 0Schwaebische HuetriTrrwerke GmbHill Bad ScltuJJenried G nntm

This paper Is based on his dOCloraltransmissions provide the dissertation

version forms the basis for thparameter variation Ali other

_____________ IGiEARIDESIIGN FOCUS

Table 2-Collstrnctioll design 01 SlIl and ring

I

-

Var Description Scheme Var Description Scheme

SII Sun gearI 33 Hl Housing-fjxed ring gear Sm

I I

I

S2 Sun wheel with middotff]-middot H2I

Ringl gear with internall I rbnircurnfarential lengaging curved-toothengaging curveli-tooth gear couplinggear coupling

S3 Sun wheel with internalengaging curved-toothgear coupling ~

14

I i I II u ~ bullbull os

H3

S2HI1 S2Hi2 S2H3

S3H3

Ring gear witllflangeconnection rlh

11

100

Fig4--LOId fllctor KyK depedmg on tha Imllr of planel11e8B Iand onthe canler dlstan1 8 shown for me engagement aflun and plaoet gear

1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015

--VIIS1H1~5bull II iMwn~

011bill

11

S3H1 S3H2IFlgl-TyPlllof planetary gear IJInsmissionl

IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll

Fig 5-Loadl factors ~Kdepending DOtbe Iratio from face width b to diem-Ilerd of Ibe Slln wheelinfluences of the examined sented for a basic S1HI tran ~parameter field mission according to Figure

lnjluenceson the load 2 The indicated values of thejaetors KyK The following load factors apply to the trans-results were achieved by a mission specified in theparameter study with the pro- respective picture The loadgram SIMPLEX It shows the factors achieved by transmis-

sionsof other geometry ortype of constraction can bedetermined by approximatingequations contained inReference L The results applyto gears of DIN quality class 6

generally valid tendencies thaia modification of the singleparameter accordingto TableI has on the tooth load condi-lions as mentioned aboveFill 3-ilnfluncl of thlll lin load wand of Ibe clnllmferemjllli spoodl von

11111Iclol product KyIK in the engagement of Iun lIndl planet gau Those tendencies are repre-42 MAYJUNE 2001 bull GEAR TECHNOLOGY wwwgrsahflorogycom bull wwwpowerrlsmlssioncom

bullbullbullbullbull _IGEAR OESIIGN FOCUS II _All rolling bearings indicate a i from DIN quality class 4 Thebearing clearance of class eN housing-fixed ring gear of the

FiguJt 3 shows the mJlu- basic version S 1HI causes aence ~f the specific load w for I partial adjustment of the planetdifferent peripheral speeds v gear in reference to the ringon the dynamic behavior of gear which results in a morethe transmission favorable face width load dis-

The distribution of the I tribution Accordingly the val-load on several planet gears ilues of the factor KH~ of thepermits a higherthroughput of engagement planetring gearpower Figure 4 shows the i are lower than those of theinfluence of the associated Ii engagement of sunplanet gearincreasing static overcall- Figure 8 shows an increasestraint and the influence of the I of tl1e factor KH~ill the S IHIphase position of the engage- version which depends on thementsat the circumference of I number of the engagements ofthe coaxial gears dependent t sunplaner gearon the number of planet gears I Approximationequations

Figure Shows theeffect I 0 the actolroduct KyKvof a changed face width b on Dnd thefaclor KujI An irnpor-

the value of the load factors I tant result ofthis research proj-KyKv The basis of aJJ calcula- I ect is approximation equationslions is a constant line load w i for the determination of thewhicb corresponds to an I load factors ISKv and KHpincrease of the outside torque Detailed information is givenwith rising face width The I in Reference Iimprovement of the dynamic I Testingbehavior with an increasing A system of coupled inho-face width does not result mogeneous non-linear sec-from the modified geometry end-degree differential equa-but from the risen load level

The quality of gear pro-duction is crucial for the levelof the dynamic excitations inthe transmission Both thetotal pitch variation Fp and theindividual pitch variation Ipindicate a dear influence onthe load facto

Influences on the loadfactor KBIlA misalignment ofthe axles causes a system-dependent inclination of thegears For that reason anincrease of the effective toothtrace variation fH13 can gener-ally be expected Figure 7shows the dependence of thefactor KHP on the quality ofthe tooth trace angle variationfA13bull IDI both engagements of(he planet gear a significantrise of the factor KHI3is to beobserved already starting

tions describes the dynamicbehavior of an idealized plan-etary gear The solution of thatsystem of differential equa-tions provides the displace-ments of tile geometricalcen-ters of tile sunplanet gearsand of the planet caniersinthe plane of transverse sec-iOD Acomparisua of thecal-Ciliated andthe measured axisshift allows for the control ofthe simulation program

The measurements aretaken at the self-adjustingtransmission elements Theirmovements can be registeredwith contact-free working dis-placement transducers Twohorizontally and two verticallyattached displacement trans-ducers determine the mis-alignment of the transmissionelements The mounting

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_-----------_1 GEAROESIGNFOCUS _

121181UI

KKl1411211

111111081041(12

r- bull T-middot 300 NrnlI

Vr-- T-400INrn V-r- T -500Nm V

~ - - V~ -

I r -==--t

100

9

arrangement of the displace-mentiransducers can be eenill Figure 9

Reference I comparescalculation and measurementand discovers a good corre-spondence between tile re-speetive values

Notes for the Technica1Desgner

Based on recent findingsof projects concerning loaddistribution in planetary gearsthe following notes for designcan be recordedL With the rising extent of uul-ization of the transmis ionsthe dynamic effects lose orneof their importance Causedby a high Iine load the abilityof self-adjustment of the gearsimproves due to existingdegrees of freedom and due toelasticity The factors KKvand KH~decrease with risingload2 An increasing circumferen-tial velocity on the otherhand shows opposite tenden-cies regarding the load bal-ance High-speed transmis-sions usually show very high

load factors especially whenoperated on low load levels3 Gearing deviations such asFp r and fHIil if telerancedaccording to DIN quality class6 or better only exert a smallinfluence on the dynamicbehavior of the transmissionStarting from DIN qualityclas 6 it is advisable ItO pro--vide crowning orend relief4 Center distance deviationstolerated according to DIN3964 remain without influ-ence on the load factors aslong as there is still somebacklash existing However ifthe backlash is consumed theloads can achieve severaltimes the nominal values5 Large numbers of planetgear increase the degree of

2 e

44 MAYJUNE 2001 GEAR TECHNOLOGY WlfHUlechnologycom ww powerlrsnsmlssloncom

Figli--lioadl factors -tK dapunding on 1he production quality oftb [pitchvariations

14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e

Fig i-Load fact_orKJjpdapanden on till quality 01 tooth trIIC8 angle varia-lion IIHHIIshownl for the ling Bllemen a sllnlplanet gearalld plaDellii ng geu

30 110

bull [nwnll70

Fig B--Factar Ksp d~pending en lbe number of planl1 gean 111p11 and on tilecanter distance abullsltawnl forth engallm8n~ of sun nd Iplanef gell r

RIrIeoIItranav81M sectJon

Fig ~ection of the S2H2test tr nsmislIioll Thellloai1ion of lbe displilcement tnllllllucelS IS marllied by amIWl

static overconstraint of thetransmission Inorder [0 selectthe number of planet gears Iltegain at load carrying-capacityas a result of power branchinghas to be compared W the 10 -es resulting from increaseddynamic excitation6 The load factors KyKv ofspur gear transmissions can beup to 10 higher than withcomparable helical gearing

middot traasmissions

I ~~~een~~~~e~i size on the load distribution-

11 or more precisely on the loadfactoJS KyKv and KH~-could

middot be determined 0

~

I

bull ReferencesI Lamparski C Simple equa-I lions for determining the load

i

Imiddotincrease in light weight plane-tary gear transmissions FinaJ

i report on research projecti SIIIV Forschungsvereinigung

Antriebsteehnik FrankfurVMain 19942 Winkelmann L Load dis-tribution in helical planetarygear transmissions series ofinstitute for construction bull

issue 87~3 Ruhr UruversiUilj Bochum ]987

I1-----------I ~M~i If you did not care for thisI article cirde --

i If you would like to rtlJ)Ond

1 to this Dr any other article in1his edition of Gar TecIrJaqw

please fax your to thej atIBntion of Randy Stoa man-i aging adiIor It847-cJNI818 or

send amp-mill mtII8geamp toj ~com--1

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_-------------IPRODUCTNEWS-------------New Name for Gear Software

fromllHomel GmbHK1SSsoft gear software has been

renamed NORA Transmission Softwareand is being marketed by Hornet OmbHa German company

KlSSsoft was originaliy developedtOT internal use by Kissling amp Co aSwiss gear manufacturer In 1999 theprogram was combined with another

software package Himware Except forthe name NORA is identical to thatK1SSsoftHi17lware package

NORA Transmission Softwareincludes calculation modules for gearssprings tie rodstransmi sian elementsshafts and bearings The gearing can becalculated according 1[0 the most currentAGMA ISO or DIN standards fOf spurgears bullbevel gears worm gears and more

preci-ion through diaITIDnd

INTRODUCING PCD REINFORCINGFOR DIRECT PLATIED DRESSERS

For more infonnaliol1 contact HornetGmbH by mail at Seewiesenstr 90 D-73329Kuchen Germany bylelepbone at (49)7331-98-16-46 by fax at (49) 733198-16-47 or bye-mail at inollOmet-gmhhcmn

clnIe 327

Faik Inlroduces IDriva line wiUlIilexible Configurations

The Falk Corp of Milwaukee WIintroduced Drive One a line of medium-torque gear drives willi multiple mount-ing options and drive ccnfigorations

The new line of drives introduced inMarch can be mounted from any of thehousings six sides The drives can be COIl-

figured for use as general-purpose parallelhaft drives and as right-angle drives or

they can be used as shaft-mounted drivesmixer drives or alignment-free drives

Dri ve One gear drives come ill foursizes with torques ranging from 150000Jb-in to 5001)00 Ih-in (17000 Nm to

56000 Nm)For more information visit wwwfalk-

corpcom

We will design build and Quaranteefromvour gear summary charts gear dressers forReishauer SPA and Fassler IDSA Systems--Direct-Plated or Sintered-8ond Single- orDouble-Sided Dressers

WE also producegear dressers formealon CNC

81Phoenix-UebhenIUingelnbergl Pfauterbull Oerlikon-Opalbull Hoefler Kurthbull Kapil Nilesbull Sampu1ensiJiI- Mikron Maagbull Csepell

We oHer OUI customers Highest Accuracy- Fastest Delivery

- Competitive Prices-Relap amp Replating Service

cirde328

New SmsIII-FootprintInduction Machine

Welductlon Corp of Novi MJ intro-duced its Flexscan induction hardeningmachine a compact heat treating systemcomplete with controls and tooling forless than $]00000

The new model can induction hardenandtemper parts up to 13 long

The Flexscan comes with a built-inolid- tale power supply in II variel) of

power and frequency combinations Italso includes II quench cooling system

511 MAYJUNE 2001 bull GEAR TECHNOLOGY bull wflllurtlChnologycom bull wWlpOlsrjransmluIOncom

Call or fax us your gear dresser requirementsYou will quickly discover what leading US gear producers have learned

DistribvIH by~

DRIKAISERgear dressers are the best value available

SLMunsonamp Company

401 Huger St Columbia SC 29201PIlon 1-8110-115-1390middot Fax 1--81J392HI507E-RJlliI infatitslmuMoRcom

---------------- --------

- - -------------------

and heat potentiometerFor more information contact

Welduction by telephone at (800) 798-3042 by fax at (248) 735-282] bye-mailat weldnwelductioncom or 00 theInternet at wwwwelduclioTlmm

drde329

New Wind Turbine Unit fromICinciinnali Gear

The Cincinnati Gear Co ofCincinnati introduced a 15 megawattwind turbine gear unit for use in windpower generation applications

The new unit is rated at 166megawatts power and has a calculateddesign life of 20 years Features includeart integrated oil sump an electric motor-driven lubrication pump high capacityfiltration and visual inspection ports forall gear me hes

The geartlot bas an input speed of 20rpm an output speed of 1440 rpm and a ratioof 721 AU gearing meets AGMAlAWEA921-A97 and GerrnanisCher Uoyd standardsfor wind blrbine geaibolles

For more information contact TheCincinnati Gear Co by mail at 5657Wooster Pike Cincinnati bullOH 45227 bytelephone at (5[3) 27]-7700 by fax at

(513) 27[-0049 or bye-mail at industri-alsalescintigearcom The companysWebsite is at wwwcinligearcom

drele330

TIl MIl v1IIiIIl If you found this c~ of interest andorutefuI plea ~

If you lid not care for this column ~

If you would like to respond to thil or anyother articla in this edition of 6eTechnology plelse fax your response to theatl8ntion of Randy Stott managing editor at847-437-6818 or send e-mail messages to~Nrtechnologycom

Avoid Gear Failure and Save Thousandsof Dollars in Repair Costs

Analysisand lroWIlen gears fail unless the root cause offailure is identified they are likely to failrpnand again and again Br~ak this wastaruI circleof faJlureattend this seminarand - howto eliminategear failures at yorfllilities

Hands-On TraininJwi ampiled Gearsf

For more il1fortnationI 00-597-5460

WANTEDMORE ACCURACYMORE EXPANSIONMORE VERSATILITYLONGER LIFEAND LESS COST

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wwwpowrlmiddotrilnsmissioncom bull Wwwgearlechlologycom EAR TECHNOLOGY MAYJUNE 200 51

COMPONENT GEARMANUFACTURING

Literature available from TheCincinnati Gear Company pro-vides informal ion covering itsfacilities and expertise in com-ponent gear manufacturingincluding bobbing and cuttinggrinding turning boringmilling and inspection Thebrochure includes product pho-los and specifications as wella manufacturing capabiliue

CIRCLE READER SERVICE 1

INACHIIMACHININGTECHNOLOGY CO

Global EJ(pet1isfJFor AllApplications

OUf new Corporate Profilebrochure showcases he ma-chines tools and applicationsthat achis Trademark RedRingmiddot products offer inBroaching Gear Making RollForming and Hobbing

Centaet our sales departmentfor more lDformation

(810) 263-0loo orsalesnachimlccom

CIRCLE READER SERVICE 1M

GLEASON IINTRODUCESTIHE-IELIECTRONIC

IGUIDE SIHAPiERSmall-lot helical gear produc-lion will never be the same withthe New GP300 ES Revolu-tionary Electronic GuideSystem Users of the GP300 ESGear Shaper can increase theirehipmaking time by eliminatingthe need 10 change guides fornew workpiece leadsFor more information contactThe Gleason Worksi 16-473-1000 rCIRCLE REAJ)ER SERVICE iN4

gllDl ~ UUllrHIIlIlUU All loDfURIiD

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GUASON CUnlNGTOOLS ICORPORATIION

A full color catalog showing beproduct capabilities of our world-wide and Loves fark Illinoisfacilities We manufacture high-speed teel and carbide bobsshaper cuners shaving cuttersbevel blades form cutters CBNwheels and lhinlilm coatingsHeat-treat resharpeningandrecoating services are availableGleason CuttingToots CorporatioDTelephone 815-877-8900E-mail gctcglelJsoncomCIRCLe 1IIEADERSERVICE fI~

GROUND GEAIRSPECIAUSTS

Crown Power Train a leadingmanufacturer of gears and trans-mission parts with 20 ReishauerCNC gear grinding machines andremarkable experience in geardesign and production can satisfyall yOW gear requirements at areasonable cost and on limeCrown Power Train SJi1Tel 0039 ()30 7156530Fax 0039 030 7069035E-mailcrowncrownitWebsite wwwcrownitCIRCLE READERSERVICEllf7

HIGH SPEIEOGIEARIINGfaidield Manufacwrings 6-pagefull-color brochure highlightsour capacitie and machinerydedicated 10 producing premi-um quality gears for your highspeed gear application Teethand form grinding peeifica-tions as well as product listingFairfield competitive advan-tages also li ted

Fairfield Mllnufacturing(765) 772-4000

salesfalrlieldmfgcomwwwfhlriieldimfgcom

CIRCLE READER SERVICEII252 MAYJUNE 2001 bull GEAR TECHNOLOGY bull WWwl1uflechnologycomww powerlransmluioncom

AUSTEMPERINGIMIPROViES MATERIAL

TOUGHNIESSOur S-page brochure is an infor-mation-packed guide to theAustempering process bull a highperformance heat lreatment forductile iron gray iron and steelfor improved toughness wearresistance and fal~gue snengthLearn how to boost product per-formance and reduce costsCaliJ Applied hoce s Iac734-464middot2030 01 vi itbttplwwwapplledplOCfSScomCIRCLE RElaquoII)ERSERVICE 1169

NEAR~NET GEARSPresntes 8-pageoolor brochuredjscu=[Jle companys fGifgillgcapabilities equipment and forgingplants The Iiterarure also high-ligltts Presrite Bessemer divisiona near-net gear manufacturingfucility and identifies industriesserved and ru~tomerbenefitsPresrite Corporation366S East 78111 StreetCleveland 0844105middot2048Phone (216) 441-5990Fax (216) 441middot2644[middotMaill infQpmriteiomWeb Site wwwpresrUecomCIRCIEREADERSERV1CE ~

LITERATURE

INDUCTIONI FIXTURESThe LR-PAK data heet de-scribes induction lift rota te fix-tures useful for heat treatingparts such as transmission ODraces 1D CltlIlIS hubs spindlescv joint and gears LR-PAKsare completely assembled andinterconnectedAjax Mllgnethennrc Corp1745 Overland AvenueWarren 08 44482800-547-1527middot Fax 330-372-8608E-maD ajaxsalesajaxmagcomw-II~II1aj(UmQgbullromCIRCLE READER SERlICEIItI

ICALL fOR PAPERSGear Technology is looking forgood technical material for ourupcoming issues We need arti-cles on gear gri~ding powdermetal gears gear workholdingplant automationenvironmen-tal i uesand quality standardsOf course we are alway on thelookout for gear design manu-facturing and inspection arti-cles no matter what the subjectSend for our free writers guide-lines or visit our Websi~e atwwwgeartechnologycom todownload a copyOIRCUE READER SERVICE 12118

11M HEARTLANDITW Heartland Model 3500Gear Analyzer is designed foruse in the gear Iaboratory or onthe factory floor It is suitablefor either process inspection orfinal inspection Measures com-posite run out size nicks toothaction lead and taper Measure-ment accuracy in microns

C[RClE READERSERV1CEn~

SELLOEARS ONUNEThe POWBT Transmission HomePagelM i the Webs leadingdirectory of power transmis-sion manufacturers and suppli-ers Hundreds of buyers visitwWIVpowertronsmssioncomeach day to find the right manu-facturers for their jobs Call(847) 431-6604 to find out howinexpensive and effective Inter-net marketing can be Mentionthis ad and receive a FREBbonus page of advertising withyour orderl

CIRCLE READER SERVICE ~1

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SERVICE

HOIB SHAiRIPiENllNGIINDEX TECHNOLOGIES

c -AGMA ~lll~ ~Ia~sAAIndex~~o-Helical- - - 11 - Skivillg

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IIEIJ WANTED

RollsmiddotRoyce Gear Systems a Isader In the aero$pece power gena ration industy currently has anopeningi lor a skilled Gear Grinder 11 our scenicmountain site in Park CityUtah

Ideal applicant will have both 100 D and geargrinding and clitting experiance and willbe abletoperform own sst-u ps Must have 4+ years prioruperience wilh Gleason machines and witll I

shapers and hobbers AeroSJIlce or sLmUafcloseIolera nee work is B plus i

Rolls-Royce offers en excellent medical denIalvision and401[kl plans and 91 positive open-dooratmosphere thaI supports contin uous learning andimprovement To begin your rewarding career withour team send your lesume to

HROrollsmiddot ravcegscomor fax to (4351amp47middot2728RolI$-Roy~e is an Eqal Opportunity Emplover andvBlues dive~sity in ths workplace

Rael-Line Classified I minimum $310 Additionallines 145 per line (II line per inchj Display ClassifiedJ minimum IX-S700 31--$650 per msenion6X-$6IS per insertion Addilional per inch IX-S2lOlX-$225 per insertion middot6X-$215per insertionGear T~cIutology will SCI Itype 10 advertisers layout ordesigna classified ad al no extra charge hyment FullJraquooymenl IIW5I middotIICOOIIlp8IIY classified ads Send checkdrawn in US funds 00 a US bank orVisalMasteCardlAmcrkllll Express number and expira-ioo doe 10G~ar Technolagy PO Box J426 Elk GroveVill eo IL 60009 igmcy Comntis5Ioo No agencyoommissioo on classified ads rbleriab IlQdIlne Adltmusl be reeeived by 1M 20di of ib monlh two IIOOIhsprior 10 pubfication AaIptance Publi~her reserves theright to accept or reject advertisements at his discretion

SERVICE

Hilrth ColUlplingsStandalldland Custom

Fast DeUvery - Great IPricesVisit our website for data sheets

httpwwwtae-Inccom

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CIRCLE1~

GIEAR TOOTH IGRINDINGSpur bull IHelical

bull Heningbone Iwitb groove)Capacity up to 63 00

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AGMA ICertUication InspectionlDelivery 101 Mee~toDr Requiremants

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Direct your inquiries toRon lfIumphrerGeneral Manage

ronlmwgearcomOIRCUE 1iP-

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CUSTOM ENGINEERED ampMANUFACTURED CU1T1NG TOOLS

ESTABLISHED 1960

FORM REliEVED PIIOIUE GIIIlIJNDMIWNG CU1TEiRS

IGEARSHAPER 5HAVING ItUTiERSAll CLASSES OF IHOBS

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WHETHER YOU NEED NEW TOOLSMODIFICATIONS RESHARPENINGREPAlRS lOR MampM INSPECTIONS

ICIINTACT US FOR IIQIJOTE TiIlDAYI

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GEAR TOOTHGRINDING SERV~CES

bull Cost effective gear tooth grindinglspecialists

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PRECISION GROUND GEARSbull Spur Helicalland Pump ~

Gears to AGMA Class 15IFealuringlhelalest grindingand CNC technology includingbull Relshauer RZ300E Electronic

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bull High Performance CNG Hobbingbull Conttnuous Process ~

Utilizing SPC and Quality Planningbull JIT Delivery using Innovative

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23 Dick Road lI)epew NY 14043loll Free 877middot684-3810middot Fax 716-684middot77117

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HOB SHARPENINGSERVICE

Ster Cutter co

bull THIN RLM COATINGSWest Branch Industries

Subsidiary of Star Cutter Co2083 W M-SS Wast Branch MI486611

l-BaB-Resharp 1-888-737-4277Pilon (511) 345-2885 bull FAX (511) 36-5660

CIRCLE 1454 MAYJUNE 2001 GEAR TECHNOLOGY bull WWWgllllrrctlnologycom wwpOllflfulrnilmluloncom

SERVICE

GEAR TOOTHGRINOINIG SERV1CESSpUf - Helical- Double Helical

Capacity up to 16lS0_0 1 [I_p 2grStro~keAll ground gears certified up toAGMA Class 14+ on Zeiss-Hofler 16l2IGMM Inventory of grinders includesHoner BOO Hofler 11)00 Hofler 1253Supra Hofler 1500 and Hofler NovaCNC 11)00 (Fufiy CNC with on-boardCMM checker]

Kreiiter Gear1ech2530 Garrow St Houston TX 77003IPhone 713-237-9793 Fax 713-237-1209Contact Mr Willie WhittingtonVIsit our Website atwwwkreiter-geanech com

CIRCUE 1~

lndlUction HardeningSpecialists in Toom bV loothIContour Hardenilng of IntemallSpur helical and bellel gearsOur gear hardening equipmentincludes 5 NATGO submsrqedprocess machines and 5 AJAXCNC-controlled gear scanningmachines Tooth by tooth gearhardsninq from 5Dpmiddotl0DIP up to115 tons 200middot diameter

American IMe1a11Treatingl CompanyCleve lind Obio

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Breakdown SerVice AvailableCIRCLE $a

Reconditioned Cuttell Bodies$IGuaranteedl Cost Saviings $AW Systems can recondition AWSpiral Bevel Cutter Bodies to 100 like-new condition

Am Systems can sharpen Spiral Beveland StJa[ght Bevell Cutter IBlades Hobsharpeningl salViee also available

Rapid turnaround timeMost sizes available

For information alld quoteplease cnntact us at the following

AWSvstems CDmpany612 EIHarrisanl AveROYII OlLk-gt MJ 48061

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HOB SHARPIENIINGbull State-of-the-art eNC sharpening

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bull Wet grinding with frea-cutting CBN ordiamond wheels for Barn fHieH sharp-ening of carbide or high speed steel

bull Optional reeoating andstripping

bull Rush service available

Koepfer America LLC635 Schneider DriveSouth IElgin Il60H1

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bull BROACH SHARPENINGbull HOB SHARPENING

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PICK UP AN[I DELIVERY IN MANY AREAS

G~easonCUtting ToolsCORPORATION

1351 Windsor Road PO Box 2950Loves Park IlL61132-2850

Phone (8151877-89001Fax (815) anmiddotD264

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HSS amp Carbide up to 5 DiaStraight Gash

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GIROUND GEARSbull Precislon Ground Spur or Helical Gears up

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4864 Stenstrom RoadRockford IL 61109Phone (615)874~3948 Fax (815)874-3811

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Orillinal MAAG Parts for all Grinding Machinesbull Shapirngl Machines (8Mbull Inspection Machines

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CIRCLE US CIRCLE1~ po rtrnml bullbull IOIIcom 1ItI gutlchnololUCOm bull DEAR TECHNOLOGY MAVJUNE 2001 55

Shes working in wearable art fashion His interest was what acquaintedCommissioned last summer to create him wilh Chows work Hed seen her

the dress Chow tomed Wmzder Gears work in Chicago at the Museum offactory and took home a variety of plastic Contemporary Art where he serves onthepans inc]udingtile part wilh the internal museums permanent collection commit-gear spline As she recalls the square tee In spring 2000 he saw three dressesparts starshaped space intriguedlter-~t created by Chow in a museum exhibitadded another dimension Months later Chows new gear dress ~ ==~iinterest endOf

Chowobtaiaed about ] 500 copies of was featured at a fashion show-at unful plein oiraIe the part to make the dress She linkedthe Wmzeler Gear The show was part of the I IlfyoudidnatcerefDr1hisIl1lcIe 56 MAYJUNE 2001 bull GEAiR TECHNOLOGY wWIIIIgllllrteCllnorOtlY-com wwwmiddotpoWIlrtmiddotrsnsmlsslancam

Combining involute curves and bodycurves merging factory and fashionWmzeler Gear has transfonned one of itsproducts into gear haute couture WinzelerGear has created a plastic gear dress

1 was trying to come up with some-thing unusual to create a theme for our60th anniversary party says JohnWmzeler the companys owner and thatrelated to our already successful gear jew-elry campaign

Started in 1997 that campaign was aseries of elegant black-and-white photo-graphs of a fashion model wearing ringsearrings and bracelets-all made fromplastic gears The understated ads gracedthe pages of Auto World Design News andMachine Design

The new gear dress consists of manymany many copies of one plastic piece asmall square part with a star-shaped] inter-nal gear spline The part is used ina gear-clutch assembly which itself is used in anactuator motor forprovidimg lumbar sup--port inautomobile seats

Located in Harwood Heights IL aChicago suburbWmzeler Gear manufac-tures precision-molded plastic gears forthe appliance automotive and businessmachine industries

Wmzeler Gears latest piece of gearfashion was created by a Chicago fashionartist Cat Chow Winzeler describes Chowas an artist whos tryinglD decide whethershes a sculptor er a fashion designer-s-

weighs a 101 on a wom-ans body Winzeler I

estimates the dress weighs about 10 I

pounds-vlrs a littlebit on be heavy side

In addition thedresss weigha limited JC~~u ~

WOIi Ib IUiol Dlodel -its length Chow mig- Ttfllfty[righIlWirmlerllllr1inallytalked about it plUllcpif dna II lip

being a long dress DI_11 plHlIe ptrt Ibl r UII lIIIrmiddot~pld inllmelBut a long dress _( ~would have had structural problemsChow estimates that a long dress mighthave weighed as much 20 pounds ormore the dress would have been tooheavy for its rings to hold together and for Iits wearer to stand up I

It became a short dress Wmzeler saysito creating the dress Chow turned the

square parts so they looked diamond-shaped11urning them allowed her to cre-ate the dre ss V-neckline its front andback V-hemhnes and its V-shaped sleevesShe explains that creating the V-cutsaccentuates the part itself

It made it more interesting to have thepart turned the diamond way Chow saysabout the dress She adds thatmming theparts also broke the fabrics rigidity gavethe parts more depth and made the dress

oompanysanniversary party held Oct 2-0That day the main aisle in WinzeJer

Gears factory became the runway for tilefashion show Professional models woreIbe gear dressmd olber dresses created byChow The dresses included one made ofo-rings and another made of a single [IX)

yard-long zipperWben we do a commission we do not

want to stifle the artists creativityWinzeler says We commissioned her 10

do whatever she wantedSince the party the dress has been

shown at some trade meetings AI-aWinzeler expects to display the dress atupcoming plastic shows Its currently dis-

I played in Winzeler Gears lobby alongwith pictures ofthe gear jeweJry

Like the jewelry the dre S ID-ltly becomepart of a WinzeJer Gear ad campaignWmcZeler has aheady started to work onplans for such a campaign

The campaigns purpose To make surepeople remember who we are Wmzelersays He adds hat whether people likelhecampaign or not they will be talking about itA business-writer friend of mine calls itwomp word-ofmouthpotential 0

more excitingWmzeler says he commissioned Chow

10 create a dress because of his interest in

FerliBfIIlll r iisplinl IDBdliru palmlts all us tllIlBYOur 5111I1I1IIIIUI1l Ioot 8taBmiddotI~tlrB~nlIJIIIIufletaring facilityambind with n UJlmntl~oil nruilIlIIlWI lUllrinig BndBlIgin will uIIyur Bl1Iviu101lur_wrtGtyJa I ling ~UIIIIUIgJmuerioD joll~ _II III trIflJ III~IH arln III bullbull

wwrrYI II_II WI tBn hll

Perry It1thnlIlogy Corporlltilln lO Box 21 291dultII lIk ROlld

New BItID11I CT OBOS--~

Revolultionary EllectlronicGuide System ellmlnatescostllY meehanleal chlangeover~Small-lot helical gear production winnever be the same not for users of theGleason Pfauter GP 300 IESGearShapero Imagine adding hundreds ofhours a year in valuablechip-making time to youroperation simply by

eliminating the time and effortyou now require for changingmechanical or hydrostatic guidefor every new workpiece lead

The GP 300 ES does this andmore In addition to its normalCNC axes the GP 300 ES uses a cutterhead with a backlash-free direct drive for

controlling the cutter spindle rotation(Esaxis) through a torque motor andsoftware Almost any helix anglewithin a wide range of stroking ratesand face widths can be createdsimply by changing the CNCprogram

E-Axls and softwaJfI forcontrolling cuttefspindle

rotation enable the GP 300 ESto produce helicaJgears

without a mechanical guae

End resultYou can handle newworkpiece leads -and shorten leadtimes -like never before

For more inpoundormationcontact

Tlhe Gleason WOlrksWOOUniversity Ave PO Box 22970

Rochester NY 14692-2970 USAPhone 716473~WOO Fax 716461~4348

Web site wwwgleasoncomE~Mail salesgleasoncom

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MAYJUNE 2001

FEATURES



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(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































bull t bull bull

MAYJUNE 2001

FEATURES



211

DEPARTMENTS

11

56





















OLS


Michael Goldstein






Dan Thurman












BIPA_11OML

W

INACHi









CIRc~n4























bullIng











Ph (320) 762-8782Fax (320) 782-5280














CIRetIE 109

~-~ -- - ------------------









CIRCe -1$8

REVOLUTIONS -- _














Wecome to Revolu-






sefid them to Gear












































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----










Design Forrnulasfor Evalullting Contac1 Stress in Generalized Gear Pairs 1Q amp A Dynamic Loa~sWorm GeBrsamp Geometry Factors Page 39Load Distribution in PIanetary IGears w Page 41


















David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































MAYJUNE 2001

FEATURES



211

DEPARTMENTS

11

56





















OLS


Michael Goldstein






Dan Thurman












BIPA_11OML

W

INACHi









CIRc~n4























bullIng











Ph (320) 762-8782Fax (320) 782-5280














CIRetIE 109

~-~ -- - ------------------









CIRCe -1$8

REVOLUTIONS -- _














Wecome to Revolu-






sefid them to Gear












































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----










Design Forrnulasfor Evalullting Contac1 Stress in Generalized Gear Pairs Page 31Q amp A Dynamic Loa~sWorm GeBrsamp Geometry Factors Page 39Load Distribution in PIanetary IGears w 1


















David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I











































OLS


Michael Goldstein






Dan Thurman












BIPA_11OML

W

INACHi









CIRc~n4























bullIng











Ph (320) 762-8782Fax (320) 782-5280














CIRetIE 109

~-~ -- - ------------------









CIRCe -1$8

REVOLUTIONS -- _














Wecome to Revolu-






sefid them to Gear












































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































INACHi









CIRc~n4























bullIng











Ph (320) 762-8782Fax (320) 782-5280














CIRetIE 109

~-~ -- - ------------------









CIRCe -1$8

REVOLUTIONS -- _














Wecome to Revolu-






sefid them to Gear












































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I





























































bullIng











Ph (320) 762-8782Fax (320) 782-5280














CIRetIE 109

~-~ -- - ------------------









CIRCe -1$8

REVOLUTIONS -- _














Wecome to Revolu-






sefid them to Gear












































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I












































CIRetIE 109

~-~ -- - ------------------









CIRCe -1$8

REVOLUTIONS -- _














Wecome to Revolu-






sefid them to Gear












































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































~-~ -- - ------------------









CIRCe -1$8

REVOLUTIONS -- _














Wecome to Revolu-






sefid them to Gear












































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































REVOLUTIONS -- _














Wecome to Revolu-






sefid them to Gear












































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I




































































II





Cirde302

Tbullbull V


~

l1~~











































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I
















































































CIRCLE 1Ji








I



S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































S- Amcricllinc








AGMAAja M~ Corp


Applied Pmctss lee





Flluler Corp






Inducloheai





iagllIll Gear Corp






111116

179123167

153169136183109144

170146171

122158

172125I 82911295

115

105154173

110[74142

185161147

ISS119188

143

156

157

192

137299

1411149160

114176162127141

151134297189

108182

130

18416]

178

107

152

166

J31

4655

33385]5552

4

559

53

524352

SO10

5235

6

53

53

28middot29

lIe5552

FCmiddot[52

3254141754

UJ12-13

55

555551314337S4

S5254514

33[BC

5316

3052

385554

15

5545

254

261754

45

1f~ 1_ amp bull r ~

i r ~ - bullbull I





ORPORATION


CIRCLE 1141








FAX 3039388572

















































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I






















































































































This paper was p~-





















































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I













































































1- --- --



Bhn minimum

































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I






























































ID Toml1611205964905174


Totai


44921111198381

5962188

272


Class 2 3 4



Minimum Gear

Strength SF 125 175 250 300








-----




























David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I
































































David B Dooner





bull Itooth

~ ccntaet nermalI







CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































CIRCLE



yields

Pi = Rsincentl (Ia)

Ob)


w ])~K= +-- Po bull(2a)

or

81( 1( -R + ) Ini 0 SLn

(21))











(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I











































(wp = -wpo)



where







(3a)

(3b)







CERTIFIED

CIRCLE~79

(4a)

(4b)

(Sa)

(5b)




CIRCLEli1(6a)




ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I










































ellipticalccntact



HVpoid


Figi-Gear pairs







01]1=8 s

F2 + Fo2 p-o~ ( 2Pd r 15

a+b I ---p-

(7a)

(7b)






I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I









































I(8a) i NC

i ~g 300Il00 ~i ID

(8b) ~ ~ 200000ILl I ~






II



500000

100000

400000



where

II IlOti

35 411 45 Ih 1


Contact Stress



CIRCLE 125


















ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I
























































ra= [c (~ t4 KJ W





315 l25 315 315 1695 3525 2914 300




up Idegrad) 0 0461 0369 02341 Wli 0 ru











0076 0Jl56 001III 0074









3n P0=--- -----~----c 4 nrrb

(12)



















Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I
























































Tell Us Whet V_niM







FAX fal01 J548926







cmCLIE2S9

CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































CIRCLEUO

GEAR



------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































------ -- ----- IQMII _














j

l








(703~ 684-0242 or by I-mlil It

techgm bull org


j


_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































_-----------aampAII _


----+------+--- ----

bull







Where








Where







i




Lewis form factor


iI





Cl815 S d S QI87S

30 16













GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































GEARDESiGINFOCUS _



















BaSil helix angle
















lation







I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I









































I

-



I I

I




14


H3

S2HI1 S2Hi2 S2H3

S3H3


11

100


1~ __ ~~~--~~--~ ~~~ __ ~

30 ~ eo 70 80 110

~~ II Imml - ~

I~~----------~-----------------bull uus

KK uf---~r--- =~=J125

12

1181t~-===--1015


011bill

11


IKK

IlIIIPI 1M Amon417

722482

3(11

V 1mIll





















121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I






















































121181UI

KKl1411211

111111081041(12



~ - - V~ -

I r -==--t

100

9






2 e



14--------------------I 135

13middot

K 125

12

v 8tH-tKl1m_m

110E -287 200 Nmn

2 e 1 e


30 110

bull [nwnll70









~

I


i













Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I










































Ga~ Division

d Tool _I

9 ODS ID

I


CIRCLIE 13jt












I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I













































I till Us DIIIk

I

IIj

I




I













Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I











































Address _

Address 2 _


Phone Fax _






























PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I




























































PLEASECbullbullbull


bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































bullbull ~- kr

Company Name











o Miter Gear Drives
















clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I
















































clnIe 327








corpcom






cirde328








DistribvIH by~


SLMunsonamp Company


---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































---------------- --------

- - -------------------



drde329







drele330





































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I
































































LITERATURE







CIRCLE fia


I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































I CLASSIFIED-

SERVICE








IIEIJ WANTED







SERVICE



httpwwwtae-Inccom



CIRCLE1~



1 0IP16 face









ESTABLISHED 1960













-







Stodling Programs

800-447middot2392Fa 71H74-t003

~com





Ster Cutter co





SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































SERVICE




CIRCUE 1~











IPhone (248) 513852IFax (248)544-3922


















Quick Turnaround



CIRCLE 154


CIRCLE 15-7--






_ 1I)eugear com




-- - ------


CIRCLIEuia

FELLOWS I







































May/June 2001 Gear Technology

Documents

Transcript of May/June 2001 Gear Technology