HERE'S How:(!f It's faster. With CBN wheels. it's three

or four times faster; in fact The PHS 254features electronic probe alignment forfast, accurate setup; 4-axis CNe contml;10 lIP variable speed grinding spindle;and much more-all standard.

I!f It's versatile. It handles both bore andshank-type spiral-ffuted hobs up to 10"x 1.0",and an optional 5th axis is available. And itssmall, compact. footprint makes it. ideal foreven job shop applications.

[!{ It':s 'easy to operate. User friendJyGE FANUC 16'CNC control and on-screenprompts allow an operator to program and runthe PHS 254 with only an hour's training.

I!fBest of aU, it's a Pfauter. So it's built here in the U.S ..by the world leader in bobs-and hobbing-tedmology.

~.

CHICNlO,1!iB"T'EI!iIBE7111. '1IIi"

'lfl.n ,our booth 4700'IIcConnick ,.1_ Ea.' 1351 Windsor RoadLoves Park, IL61132-2698 U.S.A. Phone: 815-282-3000Telefax: 815-282-3075

CIRCLE A·1 on REA'DER SERVICE CARD

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

FEATURES---------- -

Effect of IExtended looth Contact on theModeling of Spur IGearlransmissionsHsiang Hsi UIlCInd Jife ng WangMemphis State University, Memphis. TN

Fred .8. Oswald and John J. CoyNASA Lewis Research Center, Cleveland, OH " 18:

Gear IFundamentalsC'omputerized Hob,Inspection '& .Applicatio:ns - Part IIYefi m Kotl y arGlobal Gear. Downers Grove. Il. 26

Cover photo courtesy ofFette Tool Systems ..Inc.,Brookfield. WI. SPECIAL FEATURES

IMTS - All You N'eed'ToKnow.:Dates.,llmes,PI'aces, Who!s, Who & What!s What Pilus .Exhibitor Index and Directory 8

Making the Most of Your Trade Show Vi:sitPhillip M. Perry 1·0

D'EPARTMENTSPub!lisher's Pag.eEvery Reason in the Worl!d to Go ..1

Malnagement Matt'ersISO '9000: The' FrugallCertification ProcessA.my ZuckermanIN/EX Information Export. Pelham, MA 37

Clas·sifiedsProducts, services, and information you can use 46

1U)['1jJ[1' A SOW

Fh''E (lOWBOY ARTJrrJ.IlTS

bridles '* buckles *' horsehairbits *' books *' betn * boloschaps '* spurs '* saddles

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CIRCl.E A·5 on R,EAJ)ER' REPLY CARD

CIRCLE A·S on READER !REPl Y CARD

4 afAR TECHNOLOGY

GEAR TECHNOLOGY

EDITORIAL

Publisher & Editor-in-ChiefMichael Goldstein

Associate Publisher & Managing EditorPeg Shor~

Senior Editor Nancy Bartels

Editorial, Assistant William R. Stott

Technical EditorsRobert Errichello

W.iUiam L. Jannfne 'Don McVittie

Robert. E. Smith

,\RT I--- - ---

A:t1Director Jean Bartz

,\nv ER'I'ISI:'\(;

Advertising Sales ManagerPatricia Flam

- - -

CIRCllIATJON

Circulation CoordinatorDeborah Donigian

IUND,\LI PlIIH.lSIII:\'(; ST.\FF----------

President Michael Goldsf.ein

Vice President Richard Goldstein

Vice President/General ManagerPeg Short

Controller Patric;k Nash

Accounting Laura Kinnane

Art Consultant Marsha Goldstein

RA:'\l DALL PllBI.l SIII:,,\(;, I:-":C.------------

1425 Lunt AvenueP.O. Box 1426

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\'01.. 11.:\:0, 4GEAR TECHNO,LOGY. The Jouro.AJ or Gtllr M'",-nuflildurlnl(lSSN 074:J--tiS.!'i8)ls publ iShed bimonr.hly by Randall Pubhshln8~htc .• 1425 'WLnl AlIfnul:. P.O. SO)l .426. iE1k Grove: VjlhllC. ILr.ooJ7. SubsrnpO'oo rees are : S40.oo in !he U,S.: UO.OO in Canoda:SS5.00 in alJ ol:/'ter countries, Second-Class postage perd Itt ArlingtonUeigh1S. Il., and ttL additional mailing office, Randall Publishingmikes every e:ffg!1 !O Cil:!iUTC lhHE tlii; processes de!!cri~d in GEARTECRNOLOGY!':oillgml to souud c!1ginecrin,g ~1i!;(:. Neither theaurhcrs nor Ibe pu.bli.sher can be' hetd respcnsjbfe for injuriessum.ined whi(.e- following the procedures described.Pesrmaster: Send IIddtelis c.han£t'lo III GEAR TECHNOLOGY. TheJournal ofOco!!l M~!lufacturin&! 1425 Luor Avenue. P.O. Box 1426.Elk Grove Viii olio. Il.liOOO7.CComenis ;:opydghl:ed by RANDALL PUBUSH1NG. [NC., 1994,Articles appeannlln GEAR TECHNOLOGY rna)' IlOI be reprodUiCedin whole Of' in p3f1 WJrMul IhI: ~i"~~ pe:mtrssmn o.(thc pubJishe.r or'rbe BUtbor.

For Maximum

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Tha1's,whyGMJ~-Kanzakllisthe premierchoice whenmaJdng Icruclaldecisions ,aboutIgear flnishinglleQuipment.

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and mgged construction for consistent high

quality production and longer tool life. They

deliver superior technical suppOril: to ensu re

minimal set up and peak per1ormance. They

also deliver something: you don't take for

granted .... Ieading edge technology.

This sophisticated equipment offers

optimal performance and accuracy, resulting

in increased shop profitability.

When your success is dependent upon

your cholce of major equipment, settle for

nothing less than GMI·Kanzaki. With GMI·

Kanzakl, gear finishing equipment is one

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THE AUTO LOADER AND GAUGING OPTIONAn example of.this leading edge technology is the Auto Loader and

Gauging option for the GFB-2S0 hard gear finishing machine.This technology enables the machine to automatkalfy load and unloadgears, and to introduce dressing as needed. saving /abor costsand mainfiJjning accuracy.

And allto gauging ensures finished gears arB within toleraf/C8S.If not the auto dressing function implements modifications to (}uaranteesubsequent pieces.aro meeting specifications.

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Gear down your p-ocesscontrol costsAHo!nI'abl'eanaly 'i~

The new PC-based QC 1000 gear inspection system performs fast,repeatable and highly accurate index, lead and profile tests on internaland external spur and helical gears and splines, And it: does all this soeconomically chat even a small shop now can replace several manual gearcheckers with a powerful, easy-to-use CNC gear inspection system.

F'ulill 4·'.][1- s valueUnlike some competitors' .3-axis systems, me

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... SYSTEMS CorporationAN ACME·CLEVELAND COMPANY

CIRCLE A·3 on, READER :S'ERVICE CARD,

ImTS '911i, the Association for Manufacturing Technology'sbiennial machine tool extravaganza opens September 7 at

McConnick Place in Chicago. As always, the size of this show is

astonishing. Over 100,000 visitors, enough to populate a medium-

sized town, will converge on Chicago's lakefront to visit more than

1,200 exhibits spread over the entire McCormick Place complex.

~MTS is a major marketplace. On-site sales at the 1992 show

reached $407 million, and the majority of visitor at [MTS 94 are

expected to be decision-makers ready and able to buy. Exhibitor

have come prepared to do business, and the show, with tile latest

equipment on display, is a good place to research your next pur-

chase and, perhaps, close a deal.

Business in many areas of the manufacturing sector seems to

be picking up. You may wish to consider making the upgrades in

your equipment that you put off during leaner times. There are

few places besides IMTS where you will

find more of the latest equipment and

information aU gathered in one place. In

this issue we have included some sugges-

tions to help you. maximize your returns

from visiting the show. A carefulty

planned fact-finding trip can save both

time and money.

Gear Technology will be at ~MTS for

the first time this year. We are locking

forward to meeting and talking with you,

about your interests and concerns re-

garding our industry. Drop by at Booth

N2-7193 (on the same floor with most of

the gear manufactur ing equipment

exhibitors) and say "hello."

-----

IJU B 1.1S IIE,H .5 IJ" I ~l:Information has never been more important to success in manu-

facturing than it is today. The people who know the most about

what's happening in their industry are in the best position to pros-

per. IMTS is a great place to gather some of that information.

Seeyou" Ih"how... ~ ~ •

Michael Goldstein,

Editor-in-Chief

JULY/AUGUST 1994 7

,rl"~D;-rrv

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The biggest industria'i badel show in the,worldl this year and She manufacturing machinery lindustry's mott

imponanl marketplace-win be at McCormick Pl'aee linChic:ago September 7-15\

lhe, Association for Manufalcturilng Jechnollogy'. thesp,onsor o,f :IMlTS 94. e,xpects, more than 1,0001

exhibitors and more than 100,000 visitors at the' biennial ,event .Allof McCormick. Place, nearly one miUion

square f,eet. wiU be turned into "'81 f,actory of the Mu"e"fo.r the nine' days, VIsitors; from all over the world willwa'ik the' aisles, reviewing billions of dollars' worth ,ofcutting-edg,elechnol'ogies.

ThefoUowingl,Gear Technologyadvettisers wm be showingl,a wide variety of thel latest eq,uiipment and

processes at their booths.

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American Pfauter Limited Partnership ofLoves Park, lL (Booth E3·470() will feature thePHSO bobbing machine, the PSA300 shapingmachine, the PHS254 hob sharpener, the PfauterMikron AIS gear bobbing machine, the CTX twinspindle machine. the GM16AC automatic lathe,r,he GLD20 sliding head automatic, the 'GAC65.the Hes app nVH25 verticalmrmng machine, theKapp VA 61 and GAS5] grinding machines.along with Pfauter-Maag culling tools,

Bourn & Koch Machine Tool Company,Rockford.,IL (Booth E2-2003) will feature theCBN gear grinder, a remanufactured CincinnatiI.2C . lant bed lathe with a NUM CNC Plus controland a multitude of other manufacturing solutions.

Fellows Corporation. Springfield, VT(Booth N2.7182). Fellows Corporation. J&LMetrology and Bryant Grinder Corporation arefeaturing advanced technology at the VT USAbooth. Stop by our booth for the late tgear shap-ing machinery. gearcutting tools and CNC opticalcomparators with internal edge sen ing. See thenew Bryant Ultraline UL2 high-speed precisionbore grinder.

Fette Tool Systems Inc., Blrookfidd. W~'l8ooth N2-650J), will feature Fette cobalt rough-ing and finishing end mills for end and centercutting. profiling and pocket milling. Ala. theywill have carbide indexable tools, including Uni-vex and TwinCUI. developments, heavy dutyroughing and finishing hob. hobs with inter-changeable egmems and thread rolling axial.radial and tangential head for faster output thanthread cutting.

The GI.eason Works. Rochester, NY (BoothNl-6911) w.ill demonstrate the latest CNC hob-bing. gear grinding and honing machines. as wella CNC gear cutting, lapping and cham-ferirtgldeburring machines, plus innovative tool-ing and workholdmg, Come see .15-second hobchanges. totally automatic dressing and grindingand more. Complete gear processing technologyfor spur, helical, bevel, or hypoid gear.

GMl. Independence, OH(8oot11 Nl-5228)will di play the GB,-2S0/CNC-S five-a i .hardgear fin:ishing machine, with new feature to satis-fy the requirements of gear manufacmrers :forsuper-flne surface finishes on gears.

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'), rJ'...,.r'"rJ'r...Inductehea! Inc., Madison Heights, MI

(Booth Nl-64S5) will feature an interactive,multi-media display system showcasing a widevariety of our induction heating capabilities,including standard and custom equipment arne!power supplies for heat treating. hardening.

, j..... tempering, brazing, annealing and more. Our'£;9 flexible, self-contained stariscan for vertically

scan-hardening a wide variety of parts will alsobe on display.

Kanzaki Kokyukoki Manufacturing Co.,Ltd., Amagaski, Hyogo, Japan (Booth NI-5228)

"'" will display the GFB-250/CNC-5 five-axis hard'J'~~t7gear frnishing machine, with new features to' satis-

fy the requirements of gear manufacturers forsuper-fine surface finishes on gears.

Liebherr, Saline, MI (8ooth N2·6953) willfeature the revolutionary LC82 CNC gear hob-

~ bing machine from Liebherr, designed for dry cut-,.;p---'~..~,., ting at high speeds. Also on di play at. the booth

."£1will be a Klingelnberg gear inspection station, aLorenz gear shaper, all LS 1.54 CNC and Oerlikon

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. equipment.Mitsubishi Machine Tool USA Inc., Itasca,

IL (Booth EJ-4299) will be introducing their newCNC gear grinding machine. It uses either CBNDr vitrified wheel technology along with optionaldressing capability. Also, they will display theirnew GC2D CNC gear hobber with state-of-the-artautomation and carbide cutting.

Pfauter-Maag Cutting Tools, Loves Park.IL (Booth E3-47fJO) will display its line of hobs(including the Wafer Hob and Opti-Gash Hob),hapercutters (including the Wafer Shaper Cut-

ter), milling cutters and! shaving cutters.Sala & BLM Corp., Elk Grove ViiUage, IL

(Booth Nl·6782) will feature CNC tube bendingand endforming equipment: tube loading, sawingand deburring systems; circular saws for solidreel and tubing; and high- peed saws for alu-

minum and! plastic.WMW Machinery Company, Inc., Wiest

Nyack, NY (Booth EJ-429S)" NILES Berlin,exclusively represented by WMW MachineryCompany, Ine., will exhibit the new Profile geargrinder. Its two independent CNe-controlledgrinding wheel slides, menu-driven CNC controland integrated software guarantee highest produc-rivity, FDr additional information, please visitWMW Booth E3-4298 .•

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Making the Most ofYour Trade Show Visit:

[6oing to IMTS? Beware, It'sI ea y to make any number of

'I I common mistakes that canturn your productive buying

trip into an expen jve bomb."Attending a trade how IS an

investment in time," says SteveMiller, who runs a consulting firmcalled Adventure of Trade Shows inFederal Way, WA. "And time rs thecurrency of the ]990,"

How true. 'Given the businessopportunjtie you forgo to attend the. how. the hours you pend navigatingthe aisle can be more expensive thanthe actual cash outlay for flight andhotel room.

So how can you get a solid returnon all this investment in lime andmoney? Seven trade show consultantspinpoint the most common errorsmade by trade show visitors - thentell you how to avoid making them,

Phillip M. Perryis Q Nev: York-based writer

sperializing ill businessmanagement and law. His

business articles IUll'1!

appeared in plibliC'afiofls

such as World Trade andInternational Business. H~is lire former Complll(!r and

finance editor of a majorindustry newspaper.

'101 GE.AR TECHN·OLOGY

PhH.lip, M. Pe.rry

1. Neg,lec.tillg advance p.lalll.lillg."I would really stress the jmportanceof preparing for your visit far inadvance:' ays Richard J. Brunken,president of Human Resource Devel-opment. Milwaukee, WI.

Indeed, most consultants cite thelack of ufficient advance planning athe number one reason why tradeshow visitors spin their wheels, Theyadvise marking your calendar a monthprior to the trade how. That' whenyou should start thinking about twothings: your goals for attending thehow and your strategy for reaching

those goals.2. D~fi1lillg goals tlJat are too gen,·

erato When deciding what you wantfrom the show, avoid general slate-rnents such as "seeing what' new" or"seeing our suppliers." If you don 'tset. specific goals, the show may endwith you feeling as though you failedto accomplish all you could.

which manufacturer can I get the bestsupport and customer service?

One question or a series of similarquestion will keep you focu ed onwhat you really need to accompli h at

3. Not developing a strategy 10reach goals. You may fail to reachyour goals because you did not plot 11detailed trategy. "Define a game planso all your steps are laid out. beforeyou arrive at the show," say JoAnnR. Hines, who attends do e to 2.0shows every year as president of theconsulting firm of Hine & As oci-ates, Ackworth, GA.

The steps in rhe straeegy . houldresult itn achieving your staled goals.Example: See x number of vendors tofind the best sources for a specificproduct or type of equipment.

Part of II successful strategy is toallocate tasks among coworkers whowill be attending the show. Do this

Steve Miller sugge rsa better way: early enough to avoid the duplication"Ask yourself what. is the biggestproblem you have ill your business,Write thi down in the form of a que -(ion. Theil take this que lion to theshow with the idea of getting answersfrom fhe staffers in the booths,"

For example, how can .I get greatercutting accuracy and longer tool Iife?Who offer: the highest productivitywith the lowest per piece co t7 From

of effort that would otherwise resultwhen different people plan to aceom-plishthe arne goal,

4. Failing to get a floor pial' alldbooth directorrinadvance, Mostshows have floor plans that list boothnumerically and directories that Iistexhibitorsalphabetically. Wen inadvance of the show, a 1

"Cross-reference the directory withthe floor plan to layout a walkingplan which maximizes the time youspend at the show," says Hines. Thesavings in hours will ensure that youreach your goals. "Most people justturn to the right and go down the aisleto start the show," says Hines.

And what if an advance copy ofthe directory is not available? "Manyshows that don't send out directorieswin send you theirexhibitor registra-tion Ii ts," advises Hines.

Indu try trade publications willusually include advance directory andbooth information (see p. 9).

S. Not pri;oritizing sections of thefloor plan, Try to estimate how manybooths you will be able to visit duringthe time you have at the show. "Tileaverage attendee spends about 13minutes at each exhibit targeted for avisit," ays Brett Fisher, marketingmanager of the Trade Show Bureau, aDenver, CO, association that studiestile industry .. He adds: "To that youmust add your walking time, eating.resting ancl the chance encounterswith peers."

Considering that slack time, figureyou can visit maybe three booths eachhour. These are booths run byexhibitors you specifically want tosee, not unknown booths where youstop for quick looks while walking lipand down the a:isles.

Okay, That comes to ] 8 booths in asix-hour period. Selectthese booths asyour "Priority l ' selections and markthem with a green marker. Write gen-eral guidelines for eeing x number ofthese booths per hour, You want to seethese exhibitors without fail.

Select a number of "Priority 2"booths and mark them with yellow.You see these booths during slacktime between the green booths. Thenlise a red marker for the new vendorsin whose products you might be inter-ested and for those whom you'd liketo see if the opportunity arises.

Now you have a visual aid for

walking the floor. YOIl can check offthe booths as you see them and moni-tor your progress in getting throughyour top priority stops.

6. Making tO'O" many appoilU-ments .. Don't get carried away whenyou make appointments. Trying tosqueeze too many in one day canactually make you less effective onthe floor ..That's because you caneas-ily fall behind and start rushing fromone appointment to another beforeyou have all the information youintend to gather.

"Rather than setting definiteappointmen; times, I suggest you tellthe booth staffers you will drop byduring certain. windows of time." saysHines. "Say someth:ing like, '['II dropby between this and that time .... '" Ifthe staffer is busy when you drop by,don't waste time hanging around.Leave word about the next window oftime in which you'Il drop by, thenmove on.

7. Ca.rryillg too much, Travellight. Hauling a briefcase and otherunnecessary items can slow you downand tire you out, making you lesseffective in the booths. If possible,carry only what. you need to takenotes, along with your specific ques-tions and your floor plan.

And don't weigh yourself downwith lots of product literature from thebooths. Take advantage of whateverfacilities the how has to check yourpile of literature, Some shows alsohave shipping services, even provid-ing the cardboard boxes ..

8..Weari1lg the wrong shoes ..Moreof a problem than you might think,wearing the wrong shoes was univer-sally cited asa damaging error thatcan erode productivity,

"Select a good walking shoe thathas a compliant outsole," advisesSteven I. Subotnick, a podiatrist inHayward, CA. "That means that thesole is not hard leather, but is soft andrubber-like so that it absorbs shockseasily."

The' ans-we·,-- 10· ~-c, -_ ___ r ryourmost demandiiriglg'ear app.lications.,!Fortoday's tighter specs, conventiona Igear manufacturing methods justdon't cut it. - -

Niagara Gear does.As ground gear specialists, we usethe latest grinding wheel technologiesand aJI electronic Reish

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12 GEAR TECHNOlOGY

You should also select a shoe that you will be talking wkh staffers whoha arches that match your foot, espe-cially if your arches are either unusu-ally low or high. Better quality shoestores have certified shoe fitters toadvise you.

"Women should avoid pointedshoes," says Subotnick, "Their shoesshould have leather that stretchesover the toes and is not so firm that itwill cause corns and callouses."

9'. Omi/ling all "early bird" visit.If YOLI visit the show building early inthe morning prior to the official open-ing time, you willfind lots of maga-zines and product literature waiting inbins. "Gather it up, pack it in a box,and check it before the show begins,"says Hines, 'Then it's out of theway." The s110w may also ship it toyour office for you. You haven'tmissed anyth ing, and you won'tweigh yourself down with materialnonessential to buying.

Some literature, such as the mar-ket publications. you can review rightaway. "Scan them to see if there areany interesting product announce-ments," advises Bob Donath, a tradeshow consultant in White Plains, NY."If so, mark where the booths are andhit them at an appropriate time."

10. Not previewing the show.Schedule some time to "scope" theshow before you start the walk thatyou have laid out. Walk the entireshow floor quickly, looking for unex-

are not already crowded by other buy-ers. You will be able to cover a lotmore booths right off the bat."

12. Ignoring the newer bootllsllines. While you don't want to spend'100 much time at them, the smallerand newer booths can provide leadsfor new products that can make yourvisit even more successful. "You'llsee lots of interesting products fromexhibitors who are new to the show,"say Donath. "The e booths are greatfor generating ideas."

Don't make the mistake of ignoringthem. The trick is to cover a lot of themfast, Get in and get out quickly, takingnotes on new products you can use.

U. Attendil,g too many seminars ..Be judicious w.hen attending work-shops. Ask two questions: "Is thematerial covered by the workshop sounique that I cannot obtain it else-where?" and "Does the subject matterrelate directly to my job and to why Ihave come to the show?"

A seminar on time managementmay be appealing to you, but you willlikely answer "no" when you ask thetwo questions. Unles there is anothercompelling reason for you to attendthe workshop (like your boss orderedyou to), avoid it.

14. Not steerilzg the conversatiollat the bootlls. "As the buyer, you arethe one in control," says Robert F.Dallrneyer. president of R. D. Intema-

peeled exhibitors or products. Take tional, a Los Angeles, CA, consultingnotes on what looks interesting. Thensit down and adjust your color-codedfloor plan and walking path toinclude them.

n..Followi"g .tlIe crowd. You areshowing your independence from themob by planning a productive tradeshow visit. Take that one step further:Walk the show in reverse. "You wiuget faster attention from the boothstaffers if you walk against the traf-fic," says Donath. "Most visitors startin the front of the show and crowdthe booths. If you start in the back,

firm. "Never forget that, Don't beafraid to exerci: e your control bysteering the conversation at thebooths."

That means interrupting a boothstaffer who is waxing eloquent onsome features of his product thatdon't concern. you and navigating theconversation toward benefits that willhelp you make more money.

Here's where your goal questionsreally come in handy. Miller suggestswriting the questions on severaldozen 3 x 5 inch cards. When you get

- - -

IMITS Survivel Gu,i;,de----- ---- -- - ---

On September 7, the equivalent of a medium-sized town will be dropped on Chicago's lakefront,Finding your way around this mall city will requiremore than strong legs and a good sense of direction.Gear Technology has assembled some basic informa-tion about IMTS to help you get the most from yourshow visit.

IMTS BasicsShow Dates: September 7 -15Location: McCormick Place, Chicago. [LHours: 9.:00 a.rn. to 5:00 p.m, except Sunday, Sept.11, \0:00 a.m. to 4:00 p.m. and Wednesday, Sept15,9:00 a.rn. 104:00 p.m.Registration Information: Call 8oo-322-IMTS.

The Complete TravelerGetting TlI'erejrom Here. Shuttle buses, taxis and

the CTA all will have routes between McCormickPlace, downtown Chicago and both O'Hare and Mid-way airports, Costs run from $ L50 for a CT A RapidTransit ride from O'Hare to downtown to $28.00 fortaxi service.

Shuttle will be leaving McCormick Place forO'HaIe approximately every 30 minutes during theshow. You may also reserve a ride from the show toand from Midway Airport

Special. bus service has also been arrangedbetween McCormick Place and all official IMTShotels. Discount passes are available. For more infor-mation, call 800-322-IMTS.

Phoning Home. Messages may be left at the Mes-age Center on the mezzanine level of McCormick

Place North. The number there is 312-808-2055, Theexhibit halls have no paging facilities, and messagescan only be checked and picked up at this location.

Pull-service business centers are located in boththe East and North buildings. They offer ecretarialand postal services, photocopy machines, fax. facili-ties and package handling. Souvenir and gift shopsare located near both centers.

Meat a.nd Drink. Levy Re taurants has severalrestaurants inside McCormid:. Place, featuring avariety of items from pizza and hot (logs to full-course dinners. Specialty carts selling tacos, orientalfood and snacks will be located throughout the exhi-bition halls.

Cash Crop..An ATM Money Machine is located

on Level 2 of McCormick Place East. Lakeside Bankis located al the corner of 22nd Street and KingDrive, west of the North Building.

Fun and Games. Sports Museums ... Livetheater . , . Great architecture The lakefront ...No one lacks fOI" amusement in Chicago. To help youfind the best entertainment, Chicago InformationBooths are located in both the North and East build-ings. You can also call the Chicago Convention andTourism Bureau at 312-567-8500.

Getting to the Good StuffMany, but not all. of the exhibitors of gear-related

products and services will be located in either theMetal Forming & Fabricating Pavilion or the Tool-ing Systems Focus Area, both on the upper level ofMcCormick Place North.

To make sure you don't miss any exhibits ofinterest, use the Electronic Product Directory. Justinsert your Expccard (part of your registration pack-et) in one of the computers located throughoutMcConnick Place, select. the product of interest toyou and get a printed list.

And to help you keep your bearings. the carpets inthe exhibition hat!

to each booth, hand the cards to a repand a k how the company's productscan solve yoorproblem, That narrowsdown the dialogue to basic matterspronto. iII the staffer doesn't have ananswer right away, say you'U returnlater for the informatiort,

Alternatively, use a uaiemem sucha , "I need to make a busine s deci-ion" to shift tile booth staffer s pitch

a w.ay from product features and

toward your needs, Explain what thebusiness decision is; then ask how theproducts at the booths can help youmake that decision ..

"If you find you know more aboutthe products than the salesman does.move on quickly to another booth,"says Human Resources Develop-ment' Richard Brunken. You may jotdown the name of a better qualifiedperson who is expected later.

"Aliso find a way of verifying whatthe staffer ay the product can do,"says Brunken .. "Get the name ofdesigners or other technical peoplewhom you can call after the show."

IS. Writing sloppy notes. Jottingnotes on the back of business cards ...in the margin .of bow directories . . .along the top of product literaturesheets .... Show visitors can think ofas many ways to confuse themselveslater as there are blank spots onpapers. Avoid them all. If you returnhome with a bunch of sloppy notes onall kinds of paper. you'H never getthem organized enough to achieve thegoals you et for the show,

"If you need to take a lot of notes,then atape recorder is good," saysJoAnn Hines of Hines & Associates."If you want to jot down short personalre ponse to what you . ee, then use asmall note pad that fits in your pocket"

16. Not exploiting "slaw" IIours.Every show bas its hours when theaisles are as calm as a country pond atmidnight, ami the booth staffer tandaround yawning and staring at eachother like owls, "This is the best timeto make appointments," says Adven-ture of Trade Shows' Steve Miller."especially with your high-prioritycompanie . whom you really must see.Find OUI when the low Limes are bycalllag ahead and asking theexhibitor or others who have attend-ed the show,"

Hine recommends Sunday as theleast crowded day if tile show startsthat day. "A lot of buyers don't comein on Sunday, so you have more limeto talk with the booth staffers." shesays, "It's also 1'1 good time to scopeout the how."

]'7. Not rI.IDrlitoring pr.omises to/OllOW-flp. Don 't let the exhibitor for-get to contact you with requestedinformation, According to Miller 8091of exhibitors fail to folfnw up aspromised after the how has dosed itsdoors. That means a lot of wa ledlime, You may never get the informa-

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tion that you need to make better buy-ing decisions.

To solve the problem, Miller hasdeveloped what he calls a "buyersguide." This is a long vertical cardroughly 4 x 8 inches. The buyerscarry a couple of dozen such cards asthey walk the show. At each booththey pull out a card and fill it in withanswers that the representative givesto their questions.

Lines are included for informationsuch as specific products or servicesseen, type, quantity and!delivery terms.Way down at the bottom is a question:''Wh.al is the action step agreed to afterthe show?" Answers may include mak-ing a telephone call, a personal visit orsending literature.

Trade shows are busy times forexhibitors and visitor alike. Withhundreds (or thousands) of peoplecoming and going at each booth.jt'seasy for records to get lost in theshuffle, "By using such a card. youhave a persona] record of what theexhibitor promised to do," saysMiller. Two weeks after the show, gothrough your cards and call anyonewho did not follow up with whateveraction or information you requested.

18. Not updating coworkers. Pre-pare a brief report for your cowork-ers, What are the trends you spotted?The applications you saw? The newproducts and technology introduced?"Your sharing will not only spreaduseful and enlightening information,but will reinforce your learningprocess as wen," says Brett Fi her ofthe Trade Show Bureau.

In summary, to get the most fromyour visit to a trade show, think of itas a research project rather than arecreational browse through a shop-ping mall. Have clear goals in mindwhen you go, a dearly thought-outstrategy for achieving those goal .and a specific plan for follow-up afterthe show is over. That is the best wayto make your mvesnnent of time,money, and effort payoff .•

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Effect of Extended Too,thContact on the Modeling ofSpur Gear Transmissions

Hsi:ang H!si:Un & Jiteng WangMel11phis Stat'e Unive:rsity

Memphis, TN

Fred B..OswaldS; J'ohn J. Coy·NASA iLew;is Research Center

Cllevelandl. IOH

AbstractIn some gear dynamic models the effect of

tooth flexibility is ignored when the modeldetermines which pairs of teeth are in contactDeflection of loaded teeth is not introduceduntil the equations of motion are solved. Thismeans the zone of tooth contact and averagetooth meshing stiffness are underestimated,and the individual tooth load is overstated,especially for heavily loaded gears.

This article compares the static transmissionerror and dynamic load of heavily loaded, low-

Ed

EsEpE/KilQO. Qb, QCRal• Ra2

Rbi' Rb2

R1,R2Sa. s,W

Nomenclature

gear error due to tooth deflection, mm (in)

tooth spacing error, mrn (in)

tooth profile error or profile modification, mm (in)

statictransmissien error of gear pair. mm (in)stiffness of gear mesh, N/mm (lb/in)

meshing compliance of tooth pairs a, b and c. mm/N (inJlb) Iaddendum radii of gear I and gear 2,. mm (in)base radii.of gear 1 and gear 2. mrn (in)pitch radii of gear 1 and gear 2, mm (in)separation distance in approachand recess, mrn (in)

total static transmitted load, N (Ib)WO, Wb, we static transmitted load on tooth pairs a. h,and c, N (Ib)

Ll.I separation angle: rotation of gear 1 (gear 2 fixed), fad

n.2 separation angle: rotation of gear 2 (gear 1 fixed), fadSubscripts:

contact point of meshing tooth pairdriving gear

driven gear

j

2

18 CHAR TECHNOLOGY

contact-ratio spur gears when the effect oftooth flexibility has been considered and whenit has been ignored .. Neglecting the effectyields an underestimate of resonance speedsand an overestimate of the dynamic load.

IntroductionIt is well known that. the dynamics of gear

systems can be influenced considerably by thestiffness of the meshing gear teeth (Refs. 1-5).A principal excitation for gear dynamics andvibration is the variation of [his stiffnesscaused by teeth entering and leaving mesh.This stiffness variation isa primary cause ofthe time-varying component of static transmis-sion error .. The static transmission error isdefined as relative displacement of the drivinggear with respect to the driven gear along theline of action. The static transmission erroralso can be affected by gear errors such astooth prefrle and spacing, runout, alignmentand deflection under load.

An important task for developing a geardynamic model is the determination of whichpairs of teeth actually are in contact at anyinstant. In some models, the gear teeth aretreated as rigid when contact conditions aredetermined (Refs. 3, 4,. 6-9). However, in allactual transmission, the load-carrying teethdeform elastically. This causes the incomingtooth pair to enter contact earlier than the theo-retical start of contact. Similarly, the loadedoutgoing teeth will leave contact later than thetheoretical end of contact. This extends the

tooth contact zone and increases the averagemesh stiffness.

In this article the effect of extended toothcontact on heavily loaded spur gears is exam-ined. The static transmission error and dynam-ic load were calculated for gears of moderatecontact rano 0.64) a wen as for somewhathigher contact ratio (L 95). The calculatedresults were compared to evaluate the influ-ence of extended tooth contact on the static anddynamic loads of a low-contact-ratio spur geartransmission. The findings may form the basis:for improvements in the spur gear dynamicanalysis code [)ANST (Dynamic ANalysis ofSpur gear Transmissions).

Theory and AnalysisTwo sets of low-contact-ratio gears were

considered for an analytical study. The twosets are the same except for the tooth adden-dum. which wasadjusted to provide contactratios of 1.64 and 1.95. Parameters for thegears are given in Table 1. The analyses wereperformed using the NASA gear dynamic code[)ANST. The analytical procedures aredescribed in the following sections.

Gear Sy .tem ModelFig. 1 shows a four-degree-of-freedom,

lumped-mass model for a typical gear trans-mission. The model includes driving and dri-ven gears, connecting shahs, motor and load.The equations of motion were derived frombasic gear geometry and elementary vibrationprinciples. The dynamic process is studied inthe rotating plane of the gears, and gear toothcontact is assumed to be along the line ofaction. The model and differential equationsof motion are describedm more detail inRefs. ]0 and 11.Meshiing Stiffness and Transmission Error

(Neglecting Extended Tootb Contact)To study the static transmissionerrcr and

meshing stiffness of a low-coatact-rasio gearsystem, we designate three consecutive toothpair - a, band c - and begin our analysis atthe moment in which pair a is carrying theentire load (single contact zone) and tooth pairb is just about to enter contact. The initial con-tact of tooth pair b occurs at the point wherethe addendum circle of the driven gear inter-ects the Line of action. At this instant, double

contactbegins. As the gears rotate.jhe point ofcontact moves along the line of action. When

TM

{ (' Motor

8M

Fig. 1- Gear transmission model.

tooth pair b reaches the theoretical point oftransition between double and single contact,the leading tooth pail" a disengages, leavingonly pair b in single contact. When tooth. pair breaches the next theoreticaltransition point forsingle and double contact, tooth pair c comesinto contact and begins to share the load (dou-ble contact); thus, the meshing action alter-nates between double and single contact zonesas the gears rotate ..

To investigate the effect of tooth flexibilityon t.he zone of tooth contact" we wi\! examinein detail. the first double tooth contact zone(where tooth pairs a and b are in contact). Withthese two tooth pairs in contact, the statictransmission error Et and the shared tooth loadWj for each individual tooth pair at contactpointj may be expressed as:

(EY)j'" (Ej])j + (E:n)j + (E/~I)j + (E#2)j (1)

(E?)j= (E'I)j+ (E~)j+ (E;I)j+ (E;2)j (2)+ (E~l)j+ (E$)j

W=Wf+ Wl

The tooth spacing errors above are deter-mined with reference to tooth pair a (which istherefore assumed to have no . pacing error).These spacing errors are due to manufacturing.The error terms are expressed as linear dis-placements along the line of action, The statictransmission error E, is the total relative dis-placement of the driven gear with respect tothe driving gear along this line. As long as theyare both ill contact,. the static transmission errorof tooth pairs a and b must be the same. There-

ID,r.Hsiang: Hsi LinIs associale professor ofmechanical engineering01 Mempliis Stale Uni-versity. He is a member0/ ASME alld AGMA.

Jifeng WangIs a doctoral candidateat Memphis State Uni-versity. He pre~'iouslystudied at the ResearchAcademy of MechanicalEngineering and IheNortheast Hem.'}'Machinery Institute,People's Republic ofClril.la.

(3) !Fred lB. Osw,alldis a research engineer atNASA Lewis ResearchCenter. He is Ihe authorof more Ih('1fI 20 papers011gear and IraIJ'Sll'li,-sian subjects and is amember of ASME.

Dr. J10hn J. Co,yis the branch chief,mechanical systemstechnology, NASA L~ .....isResearclr Cente«. He' islhe author of more than80 technical papers onseari/IS ami relatedsubjects.

JU~VI"'UClUST 199~. 119

Fig. 2 - Separation angles of a tooth pair in approach.

Fig. 3 - Separation dlstaneeealeulatlen for a. tooth pair in .approach(gear 2 fixed).

2D GE."R TECHNQLOGV

fore, from Eqs. 1 - 3,

where

(EJj= (.~:Sl)j+ (E~2)j (5)

(Ep)j= (Epl)j+ (Ep2)j (6)

(Ed)) = (Ed1)j + (Ed2)j= Qj Wj (7)

The gear meshing stiffness Kg at contact. puintj is then

(8)

In the analyses above and those to follow,the position of the contact point j on the gearteeth is expressed in terms of the roll angle ofthe driving gear tooth. In the single contactzone, the transmission error and meshing stiff-ness equations are much simpler and can bederived by similar procedures.

Gear Teeth Separation DistanceWe define the tooth separation distance as

the distance between apair of teeth just out. ofcontact during approach or recess if there is noelastic deformation, This distencecexpressedalong the line of action, is equal to the productof separation angle and base radius of the gear.The separation distance will be compared withthe static transmission error to determine tbecontact condition.

To calculate the separation distance, weintroduce the separation angle (exaggerated forclarity in Fig. 2) fora pair of teeth (pair b) inapproach, where gear 1 represents the drivinggear and gear 2 the driven gear ..The separationangle is not the same for the two mating gears.If gear 1 is held stationary, the separation angleil2 is the angular rotation required for gear 2 toclose the gap between the teeth of pair b..Like-wise, .6.1 is the required rotation of gear I whilegear 2: is held stationary. The actual tooth con-tact will start ala point where the separationangle of the incoming tooth pair is equal to theangular deflection of the preceding tooth pair(s).

The equations for the separation distance asa function of the separation angle can be

derived for a tooth pair in approach using Fig.3. In Fig. 3, the driven gear (gear 2) is regardedas fixed. Point A represents the theoretical startof contact of a tooth pair .. point B the theoreti-cal end of contact, and point P the pitch point.when no load i. applied. To find the separationangle .11, the two gears were rotated backwardto a position jl.lst before contact at 91 and 92•respectively. The tooth pair will make contactat point D if the ela tic deformation of the pre-ceding tooth pains) caused the driving gear(gear J) to. rotate an. angle of .11, The equiva-lent separation distance along the line ofaction, 51' between the incoming tooth pair dueto the rotation of gear I can be found from:

where

81= inv PI - inv YI

jjl == tan -I (. Ra2 sin jj2 ')1C - Ra2 cos fJz

112= cos -I ( R b2 ) - tPR 02

_ -1 ~ Ra2 sin (,62 + (Jz) )at - tan. C - Ra2 cos (62 + (Jz) .

p= cos -I ( RbI )I DOl

DOr=

Similar expressions can be derived for the linearseparation distance 52, where gear 1 is fixed andgear 2 rotates to dose the gap. Likewise,expressions can be derived for the separationdistances S L and S2 of a tooth pair in recess,where S I and S2 are defined for tooth pair a.

Fig. 4 shows the variation of the separationdistance during approach and recess as 11 func-tion of the rotation angle (9] in Fig. 3) for a1: I. ratio gear pair as described in Table ] andwith contact ratio 1.64. The zero rotation anglein the abscissa refers to the gearposition at thetheoretical start (or end) of tooth contact inapproach (or recess). The separation distancesS I and 52 differ, and the difference grows larg-er a the rotation angle increases .. The magni-

(9) tude of S 1 is less than S2 in approach andgreater than 52 in recess ..Since there is no par-ticular reason to consider either the driving orthe driven gear to be fixed, an average velue of

(10) S 1 and 52 has been taken as the separation dis-

(II)

(16)

1.0

0.8

0.6

0.4

0.2

a2 3 4 5 6

(a) Approach

1..0

0.8

.0.6

0.4

0.2

.02 3 4 5 6

Angle ofrotation, deg

(b) Recess

(12)

(13)

(14)

(15)

Fig, .. - Separation distance calculated 'for approach and recess.

(17)Table W.'- Sample Gear Pa.rame~ers

Number of teeth 2&.28.Pressure angle, deg '2.0'Module. mm (dia:metral pitch. l/m) 3.18 (8)Backlash, mm (in) 0.0'5 (0'..002)Face width, mm (i11) 25.4 (1.00)Design torque. N-m (lb-in) 373 (3290')Normalized tooth addendum LaD or 1.20'Theoretical contact ratio 1.64 or 1.95

JUl Y',",UiJUST l' 99' 21

Lance. Sa i designated a the separation dis-tance during approach and Sr is that for recess.

The computer program DANST was used tocalculate the static transmission error for thegear system described in Table 1. To simplifyIhe analysis, only unmodified gear are consid-ered here, D.ANST is based on algorithmsdeveloped in Refs. W and 1L

Fig . .5(a) shows [he theoretical (extendedcontact ignored) static transmission error forgears of contact ratio 1.64. The static trans-mission error COil i ts of manufacturingerrors added to the deflection due to load. hlthis study manufacturing errors, such as pac-ing and profile errors and runout, are neglect-ed ..This is a reasonable assumption fOT high-quality, heavily loaded gears; therefore, thestatic transmh sian error represents the 'elasticdeflection of the gear teeth and gear blank.The honzontalaxi in Fig ..5(b) is calibratedin terms of the roll angle for tooth b ..This isthe same as the rotation angle (used in fig. 4)except for a constant offset.

E 30;1,

.: 250Jj

20c.9'" 1.5'E'" 10c'"..l- Su.~~ 0'

S

I S,Sa II I

~ I ! :I II I, I

11 "'"" ,1--- 'r IV':! :

r-- .......'..-'--I ! -~: ': I i: : v:: :IIH • :III, 8,J8 clir D'

(a) Theoretical Static Transmission Errorand Separation Distance

Extended "'\Tooth ContaC\rIgnored :

I

I :1·-----L E tended Tooth

Contact Jnchirled

10 15 20 25 30 35Roll Angle, deg

(b) Comparison of Static Transmission Error withEffect of Extended Tooth Contact Both Includedand Ignored

Fig,S - ·tatic transmission error and .separaUon dlstanee for gear wUiIl,contact ratio = ],64. -

22 GEAR TECHN.O~OGY

Meshing Stiffness and Transmission :Error(1nduding Extended Tooth eon tact)'

Superimposed on the transmission errorcurve in Fig. 5(a) are separation distancecurves Sa and .Sr. The actual point where theapproaching tooth pair b make. contact is thepoint labeled C. where the separation distanceequal the tatic transmission error. Likewise,tooth pair a, in recess, leaves contact at thepoint labeled .8' ...

Five regions (designated Ito V) are identi·fied LIl Fig. 5(a). Regions I (AB) and V (CD')repre ent double contact zones; region IU(B~C')is the ingle contact zone; and regions WI(BB') and IV (C'C) represent the Increaseddouble (or reduced single) contact regions due1.0 the effect of tooth flexibility. This effectincrea es the contact ratio of the gear pairaOOI.l.15~ (&om 1.64 to 1.72).

To evaluate the static transmission error ofregion II. we adopt an analysis similar to thatpresented above. W,e begin at the momentwhen tooth pair b is in contact at the pointlabeled .8 in Fig .. 5(a) .. (This i the end of thetheoretical double contact zone.) Elasticdeflection causes tooth pair a to remain in con-tact until breaches B'. The total transmittedload W shared by tooth pairs a and b in thisregion is:

w;; (E~r(S~)j 01- (Et'j (20)Q/ Ql

where the first term. at the right-hand ide ofthe equation represents th - load on tooth paira, and the second term repre. enrsthe load ontooth pair b at an arbitrary contact point).

The static transmission error of all toothpairs in contact must be equal; therefore, theIran mission error of b in this region can becalculated :from Ref. 13:

Q!(S~)j+ QjQ}'W

Q!+ riJ(21)

When E!J, the static transmission error of toothpair b, i less than the separation distance. Sr'l,tooth pair a leavescontact. This occurs astooth pair breaches B'..(This is the beginningof region m. where b is the only tooth pair in

contact.) The gears remain in single contactuntil tooth pair b reaches point C.

At (he beginning of region IV, when barrives at point C, tooth pair c engages andgradually increases its share of the total trans-mitted load. The shared tooth load and statictransrnissjon error of tooth pairs band cchange with respect to the rotation of gears.They can be determined from the followingexpressions:

W=(E~)j

+(Ef)r (sg)j

(22)b cQi o;

Qj(s~)j + Qj'QJWQf+ Qj

Fig. 5(b) compares the transmission errorcalculated with extended tooth contact includ-ed (solid line) and ignored (dashed line).

If the tooth addendum (and hence the heightof the teeth) is increased, the contact ratiobecomes greater. The increase in the contactratio reduces the lone of single contact. Thewidth in the step in the static transmission errorcurve win be reduced as the separation dis-tance curves Sa and S, approach each other.These effects can be seen in Fig. 6(a).

If the theoretical contact ratio is increased toslightly less than 2.00, the increase in contactlength due to extended tooth contact may causethe single contact lone to completely disap-pear. This isillusjrated in Fig. 6{b), in whichthe tooth addendum of the gears was increasedby 20% over the standard value to increase thetheoretical contact ratio to 1.95. The actualcontact ratio (after consideration of tooth flexi-bilityjis 2.02.

fig. 6{a) shows the statictransmission errorfor the gears with theoretical contact ratio of1.95. The single tooth contact zone (regions Ilto IV) is so narrow compared to regions I andVlhat the figure was plotted at an expandedscale. (Only portions of regions I and V areshown.) For regions I (AB) and V (CD), thestatic transmission error curve is similar to Fig.5(a). Regions n (BC,) and IV (B'C) are extend-ed zones of double tooth contact (similar to' thecorresponding regions in Fig ..Sea)}. The trans-

s,, ,,

v,!.,,'A

I

20 21 22(a) Theoretical Static Transmission Error andSeparation Distance (Note: The mil angle axis isplotted at an expanded scale so the single toothcontact zone may be seen.)

e 30::!...: 250t:

r..J 20I:::0.:;; 15.§II>

IO0:::

1.4

1.2

(a) Contact Ratio = 1.64

1.6

1.4

1.2

1.0

0.8

0.60 5,000 10,000 15,000 20,000 25,000 30,000

Speed, rpm(b) Contact Ratio = 1,95

Fig. 7 - Predicted dynamic load fac~oli'of gear-s as .3 function of speed,wiithand without the effect ofextendedtooth contact

1.92 §~§S~~~;;::--:1.86 ~:=::~~~1.80

l.74

1.68

1..62

o.~ I..50 P'J..J.......::r:::.._4-..J-...u;_U!.Ju.a.....;;....L..:.~WI~ -I8 1.98

1.92

1.86

1.80

1.74

1.68

1.62

1.56

1.502,000

(a) Including Effeci of Extended Tooth Contact

11,000 20.,000 29,000Speed, rpm

(b) Neglecting Effect of Extended Tooth Contact

Fig. 8 - Predicted dynamic load factor of gears as a function of speedand ,eontad ratio.

24 GEAR TECHNOLOGY

The predicted dynamic excitation of this gearpail" will be similarly reduced from that calcu-lated with the extended tooth contact neglected.The difference isgreater for gears with a.highercontact ratio (which genernlly have more flexi-ble teeth), especially at heavy load ..

Results and DiscussionDANST was used to calculate the dynamic

load for our sample gear system. To comparethe dynamic load predicted under differentconditions, we definea non-dimensional termcalled the dynamic load factor. This is (he ratioof the maximum dynamic load divided by thetotal static load. The total static load is thetorque divided by the base circle radius. Forgears with contact ratio greater than 2, thedynamic load factor may be less (han 1.

Figs. 7(a) and (b) contain many individualsolutions for the dynamic load factor arrangedin the form of speed surveys. The speed sur-veys are shown two ways - with the effect ofextended tooth contact neglected and included.Fig. 7(a) is for a set of sample gears with stan-dard tooth addendum (l!DP). The theoretica)contact ratio (neglecting extended tooth con-tact) is 1.64. The response of the gear systempeaks at the resonant speed near 25,000 rpm.There are also smaller peaks at submultiples ofthe resonant speed.

Including extended tooth contact. in themodel increases the predicted system resonantspeed from approximately 23,250 to 24,600rpm, while the predicted dynamic load factor atresonance is reduced from about 2.'02 to 1.84, a9% reduction in dynami.c load. Bxtendedtoothcontact results in greater load sharing (increas-ing the length of double or triple contactzones), which, in turn, increases the averagemesh stiffness. Other effects include anincrease in the system resonant speed and areduction in the maximum dynamic load.

Fig. 7(b) illustrates the results fora set ofgears with tooth addendum increased by 20%(to I.2/DP) over the standard value. Thisincreases the theoretical contact ratio to 1.95.Includingextended tooth contact in the analy-sis reduces the predicted dynamic factor atresonance from 1.42 to Ll 0, a reduction ofnearly 23%. Unlike the example above, thereis little change in the predicted system reso-nant speed (25,000 rpm), Apparentlyelimina-tion of the very narrow single. contact zone

(Fig .. 6) has little effect onthe average gearmeshing stiffness.

Figs. 8(a) and (b) arecentour plots whichillustrate the effects of both speed and contactratio on the predicted dynamic load factor. Thespeed was varied over the range 2,000 to30,000 rpm,. and the theoretical contact ratiowas varied from ~.50 to 1.98. (As. above. thecontact ratio was varied by adjusting the toothaddendum.) These figures show how both fac-tors affect spur gear dynamics.

Fig. 8(.a) shows the predicted results ifextended contact is neglected. The resonantresponse at 23,000 rpm shows the highestdynamicloads for contact ratio of 1.52 andL70 ..In Fig. 8(b) the analysis was repeatedwith extended tooth contact included. Fig. 8(b)shows an overall lower levelof dynamicresponse than Fig. 8(a), The re onant responsehas shifted loabout 25,000. rpm, and there isIe s effect from changes in the contact ratio.

CondusionsThe NASA gear dynami.c code DANST was

used for an analytical study of the influence oftooth flexibility to extend the zone of toothcontact for heavily loaded spur gears. Thiseffect was both neglected and included as thestatic transmission error and dynamic loadwere calculated for low-contact-ratio spurgears, The following conclusions were drawnfrom. the investigation:

I..Neglecting the extension of the contactzone results in underestimating resonantspeeds and overestimating the dynamic load,especiaUy for heavily loaded gears ..

2. The effect is more significant for gearswith a theoretical contact ratio nearly (slightlyless than) 2.00. For these gears, the increasedzone of tooth contact may extend the actualcontact ratio beyond 2.00.

3. For the cases studied i.nrhis article.jgnor-ing the effect results in. an underestimate of thecontact ratio by about 3 to .5%.•

R.eferences:L Harris, S. L "Dynamic Loads on the Teeth ofSpur Gears." Proceedings of the institute ofMechanical Engin.eers, Vol. 172, No.. 2, [958, pp.87-H2.2. Terauchi, Y., H. adaao and M. Nohara, "Onthe Effect of the Tooth Profile Modification onthe Dynamic Lcadl and the Sou.nd Level of theSpur Gears." JSME Bulletin, Vol. 25, No. 207,

1982, pp. 1474-148L3. Cornell, R. W. and W. W, Westervelr,"Dynamic Tooth Loads and Stressing for HighContact Ratio Spur Gears." ASME Trans .. Jour-nal of Mechanical Design. Vol. 100, No.1,. 1978,pp..69-76 ..4. Lin, H. H., D. P. Townsend and F. B. Oswald,"Dynamic Loading of Spur Gears with Linear orParabolic Tooth Profile Modifications." Proc. ofASME 5th bu. Power Trans, and Gearing ConI,Chicago, IL, Vol. L 1989. pp..409-419.5. Tavakoli, M. S. and D. R. Houser. "OptirnurnProfile Modifications for the Minimization ofStatic Transmission Errors of Spur Gears."ASME Trans., Journal of Mechanisms, Transmis-sions, and Automation in Design, Vol. UJ8, Mar.1986, pp, 86-95.6. Yang, D .. C. H. and! Z. S. SUIl. "A RotaryModel. for Spur Gear Dynamics." ASME Trans.,Journal of Mech., Trans., and Automation inDesign, Vol UJ7, Dec. 1985, pp. 529-535.7 .. Velex, P. and! D. Berthe. "Dynamic ToothLoads on Geared Train ." Proc. of ASME 51h Ins.Power Trans. and Gearing COllf. Chicago, IL,1989, pp, 447-454.8. Kubo, A. and S. Kiyono, "Vibration Excitationof Cylindrical Involute Gears." JSME Bulletln,Vol 23, No..183, Sept. 1980, pp, 1536-1543.9.. Terauchi, Y. and K. Nagamura. "On ToothDeflection Calculation and Profile Modification.of Spur Gear Teeth," Int. Symp, 011 Gearing andPower Trans" Tokyo, Japan, 1981, pp. 159·164.10. Lin, IH. H., R. L. Huston and 1. J. Coy. "OnDynamic Loads in Parallel Shaft Transmissions:Part ~ - Modelling and Analysis." ASME J. ofMecn., Trans., and ALllomation in Design, Vol.110,0.2, 1988, pp. 221-225.11. Lin, IH. R .. R. L. Huston and 1. J. Coy. "OnDynamic Loads in Parallel Shaft Transmission. :Part U - Parameter Study," ASME F. of Mech ..Trans., and Automation in. Design, Vol. ItO, No.2, 1988, pp. 226-229.12. Seager, D .. L. "Separation of Gear Teeth inApproach and Recess, and the Likelihood of Cor-ner Contact." A'sLE Trans., VoL 19, No.2, May1975,. pp. 164-170.13. Tse, D. and H. H. Lin. "Separation Distanceand Static Transmission Error of Involute SpurGears." AIAA Paper 92-3490, AlAAjSAE/ASMEIASEE 28th Joint. Propulsion Conf., Nashville,TN, July 6-8. 1991.

Ac:know.ledgement: Originally presented at theAIA_ArSAErASMErASEE 29th Joint PropulsionConference & Exhibit, 1993, Monterey, CA. Avail-able as NASA Technical Memorandum 106/74.

JUL.YIAUGUST 1994 25

Computerized HobInspection & Applications

of Inspection ResultsPart III

Yefim KotlyarG!lobal Gea'r

Downelrs Grove,.IL

Editor's Note: The first half of this articleappeared in our May/June 1994 issue.

Flute IndexFlute index or spacing ]s defined as the

variation from the desired angle between adja-cent or nonadja.cent tooth faces measured in aplane of rotation. AGMA defines and providestolerances for adjacent and nonadjacent flutespacing errors ..In addition, DIN and ~SO stan-dardsprovide tolerances for individual flutevariation (Fig. n

Individual FluteVariation

12345678

Adjacent FluteSpacing or Flute-to-

FIute Variation

Non-adjacent FluteSpacing or Cumu lativa

Flute Variation

12345678 12345678

,26 GEAR TECHNOLOGY

-

Fig.1

There is a slight. inconsistency in the ANSIB94.7 definitions of flute spacing variation andflute spacing tolerance. The variation refers toan angle variation: however, the tolerancerejers toa linear displacement.

A flute index error caused by inaccuratesharpening creates unequal. height and thick-ness of cutting edges, Unequally positionedcutting edges produce a "drunk" involute (Fig.2). The effect of a flute index error can be cal-culated (Fig ..3)_

1\" ~ - vFlute spacing error causes involute distortion.

fig.2

Adjacent or nonadjacent flute spacing errorswin affect changes in the radial position of acutting edge:

Radial misposition::::(cumulative spacing error)

• (cam size). (number of flutes)• correction/ln • (index measuring diameter)]

Correction e 1 for stra:ight flute hobs,

For helical flute hobs, the correction couldbe determined as follows:

Correction ::::HN/(HN ± H)Where: HN is the flute lead,

H is the thread lead,(-) is used when flute and thread lead

have the same hand.

The gear's involute variation caused by hobflute index error can be calculated as follows:

Gear profile variation::::(radial misposition)

• sin(axial pressure angle)

Fig. 4 shows the result of the inspection. Itshows the total flute spacing variation (nonad-jacent by AGMA definition, cumulative byDIN definition), adjacent flute spacing andindividual spacing variation (specified only bythe mN standard). The inspected errors, toler-ances and actual quality are displayed.

Flute LeadFlute lead is the axial advance ofa tooth

face helix in one turn around the axis of thehob (Fig. 5). The amount of flute lead is usual-ly a very large number or even an infinity inthe case of a straight flute hob; therefore, onlya fraction of flute lead is usually inspected. Inany case the inspection length cannot begreater than hob length. DIN and [SO stan-dards, for instance, prorate flute lead tolerancein relation to 1.00 mm of hob face width. TheAGMA standard specifies lead tolerance insteps relative to hob face ..

Flute lead error causes involute distortion(Fig. 6). It can also cause an inconsistency ingear tooth size during hob shifting, but only afractional amount, depending on radial relief.Fig. 7 illustrates the relation between flute lead

Radialmisposition

FIutespaci~-I+:::-)Brrori~ L

InvoluteRi\'dj'l~jtion

error .r----- \I.

Radial Mispositiun Cumulative Error • Cam Size ~ Nymber Flutes • CorrectionIt • MeaSUring Diameter

Gear Profile Error = Radial Misposition • SinlAxial Pressure AngleJCorrection = 1 - for Stra ight Flute Hobs

HN/\HN ± H) - for Helical FIute HobsHN= Flute Lead H = Thread LeadH is useti when ilute and tnman have the same hand

Relation Between FluteSpacing Error andGearProfile Error

Fig.3

Hob ID 4191 Left Contact

Right 'N PA 20.000000

N.D.P. 1.236467 Left NPA 20.(I()OClJO

RightSerial 001

Operator Ed

Probe O.07847L

Axial Lea d 0.8660000 Lead Hand

Whole Depth 0,23622 Gash Hand Left1-----------------+----------------1

Number Gashes to Required Quality AGMA: B1-----------------1-------- -~----

Number Threads c:~Roto Hob\HB006.HOBIMSOO9.MESInspe cted 04/15/93 09:20:48

Metric/Inch Inch Magnif 2000.00 Scale 0.40

, Hob Gash Iindex Inspection! _-< •• - •••••••••••••••••••••.•••••••••••••••••••••••••.•••

1 ••••••• • •••.•.••••••••••••••• • •••••••• • •••••••••••• ·••• ·· •••••• ·r;§=: !,ll····························· .. ········· ..··.······,···" , .l"d T ., " II ·c ····1

i,,:::,::,:,·::.:.:.::.:.·:.:::::.:::·:·:::::.::·::·:··:::\;::::· ••:••·.:·.::,'·: •.::1I' · c c !i:.:::: :~:::::::~: " or ••• " ••••• ~: ::~: ::::: :~:: :~:: ::.:::::: :~:: :::: :~I

fig.4

Gash/Tocth Toler.Total 0..00500VariationAdjacent Gash 0.00150Actual Quality

1/20.00242:A

-0.00127000228:0o

---£-t.~---: r /:: 1/:, " I

: A J, ", 'II I'"1/'/""

¥efilm Kotlyaris a manufacturing engi-neer with Global Gear inDowners Grove, n: Hehas also worked forAm.erican Pfauter, L P.,Loves Park.IL, and Row-Technology. Inc .. Dayton,ON. He is the author ofnumerous papers allgearing subjects.

JULY/AUGUST 1994 27'

Cutte r Tooth Gear Tooth

Flute lead errordistorts invol ute. J\V

Fig.6

Radial MispositionI

Radial Misposition

Flute Le_ad7t'Error .,J.

\

(' ..cam

Radial Misposi lion = FlU1eLead Error • Cam Size • Number Flutes • !;Q[rectipoIt· Hob Outside Diameter

Gear TDOlhThickness Error = 2 • Aadial Mlsposilion • Sinifu;ial Pressure Angle)Currecnon = 1 -lor Straight Flute Hobs

HN/IHN ± Hi-for HelicalFluteHobsHN = FI ute Lead H = Thread LeadH is used when flute and thread have the sama hand.

Relation Between Flute Lead Error and Generated Gear Tooth ThicknessFig.1

Inspection DepthFrom O. D.

Fig.8

Hob ID 78549·008·2·10 Right N'.D.P. lB.581lZ26 left NPA 14.1XKlOOOSerial 1234 Axial lead 0.6783590 Lead Hand Right

--- -

Operator Ed Whole Depth 0.13500 Gash Hand Straight--Probe 0.07874R Number Gashes 12 Required Quality AGMA: B

Inspected 03122193 10:50:35 Number Threads c:\Roto HoblH B004.HO BIMSOI2.M ES

I Melric/lnch Inch AightNPA 14.000000 Magnif 250.00 Scale 2.0

Bottom0.56250 Gash Lead Inspection Depth'" 0.14033 3.18750

':::::1::::' :::: ':::'::::"::::.:::::::::::::::::::::::::':::::::::::':::::::::':::.::j::::-[ Top........... T. __ i··· i

t:::0

'Ci],

:~ +'C....

1

above the root.Lead. and Thread-to- Thread Errors

Lead error is most commonly checked by ahob manufacturer since it isa very imponantcharacteristic that affects hob performance.Hob lead is an axial advance of one revolutionor hob thread (Fig. 5). Axial distance betweencutting edges can be calculated as shown inFig. ] I. In this figure, n = number of cuttingedges, i = number of gashes, correction = gashhelix correction factor (see section on fluteindex). The task of hob lead inspection is tofind variation of cutting edges in relation totheir theoretical positions,

Lead inspection over cuuing edges showsthe combined effect of any runout, flute lead,flute index and lead error itself. Lead error,measured over the cutting edges within thegenerating zone, reflects the potential gearinvolute variation almost directly. The onlyadditional. factor influencing gear profile varia-tion is the quality of hob pressure angle. Theeffect of lead error on gear profile accuracy(FJ.g. ]2) can be calculated as follows:

Total profile error.. (leaderror within generating zone)

··cos(axial pressure angle)

Sometimes it is important to analyze thelead variation in different hob sections, sincedifferent hob sections generate right and leftflanks. If one needs to pinpoint a lead erroritself, a behind-the-edge lead inspection shouldbe performed. This type of inspection wouldhelp to find out the inherent lead error intro-duced during manufacturing without the effectof sharpening errors.

Lead inspection is perhaps the most com-prehensive inspection after the action line, Theonly missing link to the complete understand-ing of hob performance is accuracy of hobpressure angle.

A CNC inspection machine may combinelead inspection with thread-to-thread inspec-tion for the multi-start bobs. The adjacentthread-to-thread error and thread variation canbe mathematically determined within the spec-ified hob section.

Lead averages of all threads are comparedfor the thread spacing determination. Threadsbetween which the maximum adjacent error

II HoblD 4191 Left Contact N,D,!', 7,236467 leftNPA 2D,0C0lX)SeriBI 001 Axial Lead D.861l0000 lead ~and Right

Operator 'Ed Whole Depth 0,23622 Gash Hand LeftPrObe Q,07874l Number Gashes 10 Required Quality AGMA:iB

Inspected 04/15/93 09:20:48 Number Threads 2 c:\Roto Hob\HBOO6.1l08IMSOO9.MES

Metric/I nch Inch Right NPA 2D.OOoooo Magnif250.00 Scale 2.0

Gash Toler. 1 4 7Total 0,00544 0,00538 0,00327Form OJ);)349 0.00382 0,00269Sklpe 0,00250 O.OO240:A O.00221:A 0,OO113:ASlnpe!llXlmm 0.00545 000501 0,00257

Fig. 111 _

Distance" In • Lead Ii) '. Correcnon

Fig. 111

Gear profile generation takesplace along lines of action.

Hob lone Generating Gear Right FlankHob Zone Generating Gear Left Flank

Gear Profile Error = Lead Error Within Generating Zone- Cos (Axial Pressure Angle)Fig. 12

JULY/AUGUST 1994 29

+

!

PHOb10 4191 Left C__a_nt-;::ac:;;-t-+----;-N.-:-D;-;P.----;-.;-:7.23646==1:--+"';'L_Bft~N~P-A_;__-- 2O.1mOOO 1:1 Serial 001 Axial Lead '0.8660000 Lead Hand IRightil; Operata r Ed Whole Depth '0.23622

I Probe 'D.07874L Number Gashes 10

Ga sh Ha nd left

Required Quality AGMA B

C:IRDto Hob~BOO6.HOBIMSOO9.MES1-. S ..Magnl! 500.00 cale 2.0

I Inspected 1Jo4I15/93 09:20:48, Number Threads 2~~----~~~~~~Metricflncn Inch Right N PA 20.000000

fig. 13

Thread/FlankTotalAdjacent1 Axial Pitch3 Axial PitchesSlopeThread VariationAdjacent ThreadActual Quality

i3Dtlom

Hob Lead Inspection Over Ed,\l!.- 2.'05360

1..··· ·.····· ·.· tJljFI.' Top: ;·'1"1+·· it:l!lI::P:U:!::f:l:::::::::::::·::·'::::::n +'I. ', .. • .. "·· .. ,, .. • .. · ...... '::::::::i.j::.l ..lf11 +.1:::::::: ::::::::::::::::::::;:QJJ£l~ +

f?')t"';;:~llijll.,::t:p.::7:::::::::::::::::::::::.::::::::::.::~::ll .'!.. ··· · · ·,,· .. ·· .. ·.... ·I ..ilj.."i" .:.I" , .r..:.:.::t±±:L ,-j,..I"tJ·nI~ · · ·!..l +I..l. +·1· · · · · ·1' ...1,; 2.14423

2/11

lfR

III

21L

0.52037

Toler. III0,00271

-0.00066:0O.00118:C0.00249:0-000259·0000051/2 = 0.ooOI0:Ao

llR0.00257O.00059C0.'00134:00.'00248:00.00257

4),000011/2 = 0,00001:Ao

2fR000287o 00052:C000136:00.0'0273:00002B90.000012fl : ·IHlOC(l1:Ao

2/L'0.'00251

·0.0008500.00145:00.00251:0

.().OO2600.00005

2{1 ~ ·0.0001 O:Ao

0.0005'00.000800.00120

0.0008'0

Hob ID 4191laft CMtacl N.D.P. 7.2364BJ lehNPA 21),ocro:lO

ISerial 001 Axial lead O.:8Il6OOOO Lead Hand RighIOperator Ed Whole Depth 0.23622 Gash Hand Left~-'Probe O.07B74L Num bar Gashes 10 Required Quality AGMA:.B

Inspected 04115/93 09:20:48 NumbsrThreads 2 c:\Roto HobIHB006.HOBIMSQ09,MESMetriclTnch Inch Righi NPA 20.000000 Magn~ 500.00 Scale 2.0

Hob Lead: Inspection Behind Edg;e Depth. :.- 2.05350

!....""" .""." ..... ""." " I' "Tt1lj TopI"'''''''~'] l·h'l ~hr'.;]:2/R li~:l::~::==:::·::::::':::::::::::::J:J

!·..,···..··,·....···.....·......··....···JlIl1

::~1/I!jlilI.U.."..."...."......"....""...."...+"

" 1~;·;,;!i;JUl t0.51891 ';::.'.: ::::::. ::::::::::::::':::::,::::,::::::, ,J:] 2+'4270

Bottom

+

t

Thread/Flank Toler. III 2IL 1/11 2/RTotal 0.00227 0.00197 D.lmoo /).00180Adjacent 0.00050 ·0.00068:0 ·O.D0055C O.'OO055:C 0.00048:81 Axial Pitch 0.00080 O.OQ1Q2:C O.00101:C 0.OOO93:C O.OOO84:C3 Axial Pitches 0.00120 0.00227:0 '0.00197:0 0.00205:0 O.COI74:CSlope ·(1.00221 ·0.001B1 ·O.OOIBl 0.00186Thread Variation .().OOO02 0.00002 ·000005 0.00005Adjacent Thread OOIlO8!l 1/2 = O.OOOO4.A 211 ~ ~.OOOO4:A 1/2 = 0.00011:A 211 = .Q.OOOI1:AActual Duality 0 0 D CFig. 14

30 GEAR TECHNOLOGY

occurs should be identified for both right andleft flanks,

In addition to the lead characteristics speci-fied by DIN. AcGMA and ISO standar-ds (totalvariations, adjacent variations and variationswithin 1 and 3 axial pitches), a lead slope errorcan be determined, This value can help to cor-rect a setup on a hob grinding machine.

The automatic lead inspection and evalua-tion can be performed on any section of thehob. The inspection plot should provide refer-ences to the inspection and evaluation area(Figs. ]3 and 14).

Outside Diam.eterRunout of hob outside diameter may not be

important for orne applications, The tip of thehob tooth does not generate a gear involute,But when the gear root form is acensideration,the hob 0.0., inspection may be useful. Fig. 15shows hob inspection at the tip of the hob.Somet.imes it is important to check hob runoutbehind the edge (Fig. l 6). This type of inspec-tion would show D.D. runout without theeffects of hob wear and sharpening inaccura-cies. Sometimes for special. form hobs, it isnecessary to offset the probe position from thetooth center (Fig, 17).

Figs. 18 and 19 show the outside diameterinspection results in circular and linear for-mats, Results of the inspection and evaluationmay include total runout, out-of-round, con-centricity errors and average diameter. Theaverage hob diameter may be helpful for setupadjustments of a bobbing machine.

Pressure AnglePressure angle jnspection is the inspection

of a hob tooth profile (Fig, 20)., Frequently, thehob tooth profile angle is the same as the gearpressure angle at the pitch diameter.

Usually the tooth profile is measured in theaxial direction (Fig, 21). However, sometimesresults may be presented normal to the axialpressure angle (Fig. 20).

Pressure angle accuracy directly affects thegear profile. The task of inspection is to findout the profile deviation fr-om the specifiedgeometry. Most straight gash hobs have astraight line profile. Some coarser pitch hobsmay have an exvolute profile.

Line of ActIonThe action line is the tine that crosses gen-

erating points on the hob cutting edges within

- -

Fig. 15

0.0. Inspection Behind EdgeFig. 111

Probe Vertical

-----

Fil!l17

113641i7 teft NPAHob 10 4191lefl Conlact N.D.P. 20,000000

Serial 001 Axial Lead 0,8660000' Lead Hand Right

Operator Ed Whole Depth 0,23622 GashHand left

I

' ~ ------u.o7874l Number Gashes 10 Required!Quality AGMA: B

Inspected 0!\/l~3 09:20:4lI NumberThreads c:lRoto HobIHBQ06,HOBIMSOO9,MES

I Metric/Inch Inch Right NPA 20,000000 Magn'l! l000J)() Scale 15.0 I

Hob 0.0. Inspection Over Edge

1-

8

Gash/Tooth Toler,Total Runout 0.00150Out-of·lloundEccentricityAverage Diameter

1140,00132:B0.001.00.000262..'52253

Fig. 18

1/40,00132;80.001400.000262.52253

N.D.P. 20.0000001Rigltt -I

7.236467 Left NPAI--------j----- ,-1--,,---,...-

Serial 001' Axial Lead D,8660000 Lead Hand~-------4Ed Whole Depth 0.23622 Gash Hand

- - -,----==-:-:-::--1Probe O,Q71l471 Number Gashes 10 Requir,ed !Quality AGMA: B

Inspected 04/1~3 09:20:411 Number Threads 2 I c:lRoto Hob\HBOO6,1I0BIMS009.MES

Metric/lnch Inch Aight NPA 20,000000 Magnif 1000.00 SeaIe 0,40

Operator

Hob 0.0. Inspection 'Over Edge

L:~:~:::~:~:~::::::::.:.::~:::.::.::::.::.::~~::'~::~~::::::.~:~:~::::::::~:::.:::~:.~~::J! , .,1 .. ·· .. ·•••••• .. •• .. ••· .. ·••• .. · .. ··· .. ·· .. ··· .. ·· •· .. •· .. ·•· , ..',.., .1.. ·· .. · ··• .. · .. ·· .. ·· · .. ·· · · .. · • .. ··· .. ·· .. · ·· .. ··•· .

~.!1/4R,~~;t+. ~ 2 =::?E 1~ ' , _- '§ 1::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: I,0 ! .

I:::::~::::~:::~::::~::::~:::~:::~::::~:::~:::~::::::::~~::::::~:::::~:::~:::~~:::~::~:::~i··············· ..····································· , .1····················· ..··· ..······· ..···· ..·····,········ .1".·· ············· ·.·."~n ,' " .i ········· · u .r::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::GashlTooth Toler.Total Ruoout 0.00150Out·o!'·Rou ndEc centri cityAverage Diameter

---

Fig. 119

Pr'essureAngle Inspection

Pressure Angle Inspection- ---

Fig.21

JULY/AUGUST'199& 311

left

-- ---

Fig.22

Right Hank Contact RegionLines of Action

- -

Fig. 23

Gear profile generation lakes place along'-". lines of action.

\J_/

J

Hob zone generating gear right flankHob zone generating gear left flank

Action line inspection can reflect involute generation variationsonly in a specific single hob position.

Fig. 24

Radial relief angle

~- ,A\\

Axial relief angleLeft flank

'\=~ :~;~I'Axial relief angleRight flank

----»-«:

+

32 GEAR TECHNOLOGY

the contact region (Fig. 22). A variationbetween theoretical positions of these pointsand their real positions is the action line error.DIN and ISO standards specify tolerances forvariation between two adjacent cutting 'edgesand the total variation within a contact region(Fig. 23). Some specifications use the term"base pitch" rather than "action line."

Action line is perhaps the most. significantinspection. This inspection combines the'effects of all single hob accuracy characteris-tics that influence the gear accuracy. For gearsthat were cut with a low feed rate, there is adirect relation between the accuracy of the hobaction line and the generated involute .. Thefollowing single geometrical characteristicsare combined! in an action line check: amyrunout caused by mounting or manufacturing.rake, flute lead, flute index. hob lead and pres-ure angle. Thus. the combined effect of the

above characteristics on gear involute can bedetermined in one action Ilne inspection.

Sometimes, in order 1'0 reduce overallinspection time, only line of action is inspect-ed. However. in order to locate the source of aspecific hob problem, the inspection of the lineof action only is not sufficient. In this case,inspections of other hob characteristics have tobe performed. There is another drawback ininspecting just a line of action .. Line of actioninspection can only show variation of cuttingedges in one specific hob position. When thehob is shifted, different cutting edges or differ-ent points on cutting edges generate the invo-lute. Since all the hob characteristics affect lineof action variation, the inconsistency of errorsat different hob positions can be rather largewhen the line of action is inspected. In con-trast, the error inconsistency of other hob char-acteristics is usually of lesser magnitude, Forexample, a rake error on different hob teeth islikely to be more consistent. In short, the lineof action inspection can be very effective ifperformed at the apex point as the hob ismounted on the hobbing machine (Fig, 24).

Radial and Axial ReliefAxial and radial reliefs, shown in Fig. 25,

provide clearance during thecutting action.These characteristic' are not classified by anyknown standards. Nevertheless, some peoplecheck these characteristics for various purpos-es, mostly research and development.

Tooth ThicknessHob tooth thickness, shown in Fig. 26, is

usually specified in reference to the tip of thetooth. Thai. is why the current tip diameter ofthe hob bas to be determined prior to tooththickness measurement. Hob tooth thickness isan important characteristic if gear root diame-ter is to be controlled precisely or if the geartooth has a tip or root modifications. Other-wise, a small variation of hob tooth thicknesshas no significant effect on gear involute aslong as that variation is consistent. The consis-tent tooth thickness variation can be compen-sated for by adjusting the center distancebetween 111ehob and thegeaJ' blank.

CNC and. Mechanical HobInspection Machines

Prior to the introduction of CNC machines,there were various types of mechanicalmachine available for hob inspection. Theywere usually limited to in pecrion of only afew hob characteristics. Data acquisition andanalysis were tedious and very much depen-dent on operator skins. Nowadays, there aresystems that perform all in pection and evalua-tion tasks automatically.

Data ProcessingThe ukirnate goa] of data processing fea-

tures i to make the inspection and evaluationsystem more capable and impler to use.

Only ten to fifteen years ago, computerizeddata processing techniques for hob inspectionwere either nonexistent or very primitive.Today there is an explosion of data processingfeatures developed for hob inspection that wereinspired by the latest advancements in comput-er and software technology ..Some of these fea-tures are di cussed below.

An assonment of evaluali.on capabilities.These include (I) the ability to select or modi-fy an evaluation range within the inspectionzone; (2) the ability to determine tolerancesbased on a elected class and to determinequality level based all, the inspection result ;(3) a built-in library for AGMA, DIN and ISOstandards; (4) the breakdown of surface varia-tion into basic components - total, formandslope; (5) the abmty 10 present results in thesuperimposed format; (6) theability to switchbetween metric and inch measurement; and (7)the ability to automatically select magnifica-tion and cale.

FrtU scr.eenedilin.g. This includes the abili-ty to go forward and backward through thefields and screens; full cursor control - up,down, len,right, delete, and insert; dear andseparate screens for the part geometry and theinspection and evaluation conditions; and mul-tiple language support for descriptivetext,

Data entry validation jeatur~ that detectsgmwth errors and advises corrections, Thisfeature tests every parameter entered and pro-vides the validation range on the screen, Everylogical combination of the data can also betested for compatibility on every screen.Incompatible fields can be displayed.

Dejault jeatu.res to minimize data erdry.These include the capability to override defaultinspection and evaluation criteria.

OH-lin,e aflalysis. This feature opens animmense opportunity for data manipulationand enables the reevaluation of the previoulyperformed inspections. It provides capabilityfor (I) storing, sorting, and displaying the listof stored inspection results; (2) moving theinspection data to another computer for reeval-nation; (3) applying different evaluation crite-ria after the completion of the inspection,including a circular, linear or superimposedgraphical presentation, an evaluation range,magnification, scale, output devices, tolerancesysjems, etc.; and (4) paperless storing and fil-ing of inspection results.

Data output. Many systems provide achoice of output - printer, plotter, screen orfile ..Some systems have thecapability to printor plot several characteristics on a single page.

Part s,tora.geand retrie'ial. This featureshould include storing, sorting and displayingthe list