It·s the RPM of1be bob 1bata..the geu:z1liDB speedofhobhifta.SmaB-dameb diBp(abJe ~bobs frool Pfauter..Maag running at400-5(X) SFM can mean bob RPMsfrom 700-1100, aIKl wa:trabIe RPMsfrom 5()..500. deperr:ting 00 the nmn-her of teeIh in the wakpiece.The American Pfauter/Pfauter-MaagWaferN Hobbing System for high-production gears and pinions offershigh-efficiency hobbing using:• Small-diameter shank-type

Wafer1'oland Opti-Gash'" bobs

Hob DataDiameterLenglthNumber of

ThreadsClassMaterialCoating:Cycle DataF,eed RateFeed Scallop

DepthCutting SFMCutting RPMFloor to Floor

Time (lMin.)Pieces per

Waferi"M Hob

Wafer™2.0"7.5,"

3ACPM HEX 76Tinite™

0.06"

0.0002"400765

0.25

27000

• 2_1a1dAriW -' I•..-......O",Crnadine desip BIDJIlo-tmaI tlocr spatZ

• Higblyreliable G.E. FANUC 150fC c:ontrol anddigilal

CuttingIntroduces ...Opti-GashTM HobsIn response to industry's demandsfor higher production and accu-racies. and as a result of thesuccessful introduction of ourWafer concept for throw-awaytools, PMCf has developed theOpti-Gash " hoh.This hob. designed for a specificproduction application, optimizesthe hob desien for maximumbenefits in p'foductivity andgenerated gear geometry.Until now, most hobs have beendesigned with the minimumnumber of gashes to produce arequired gear tooth geometry cou-pled with the maximum numberof available resharpenings.Today's high costs of operationdemand higher production mtes

of greater accuracy gears onfewer. more expensive machines.The Opti-Gash hob has beendeveloped to meet these demand-ing and conflicting requirements.Our engineers desianed thi .. hobarollnd~a specific chip load andcreated a tool having an optimumnumber of gashes at a diameterand length (0 suit the machinecapability and part requirement,The result is a hob which willproduce a high dCb'TCC of Iormaccuracy - and a machine cuttingload generating low-spindlelOflJUCS - producing as a conse-quence the highest possible leadand index accuracy.The low chip-load, high-qualitytool steel and coatings. along with

efficient cutting geometry resultin higher cutting rates and manymore pieces per sharpening thanwith conventional solid orsegmental hohs,The resulting reduction in machinechange-over time, resharpcningand recoarina costs more thancornpensatex for the reducednumber of available sharpenings.Accuracy? TIle Opti-Gash isavai table in all accuracy classes -better than AA DIN or AGMAstandards if required. For a spe-cific proposal on all Opt i-Gashhob for your application, sendfull part and machine data to yourlocal representative or contactthe PMCf sales engineer foryour area.

Pfau'e,- aag Cutting To sLimited Partnership

1351 Windsor Road, P.O. Box 2950. Laves F':ark. IL 61132-2950 USATelephone 815-877-8900 • FAX 815877-0264

C'IRCLE A-2 on READE.R REPlli' CARD

ItSWe'veadded a newdimension in serviceand support to ouradvanced 3-Dgear-measuring machines.

'If you haven't looked at us lately, here's some big news:Hofler CNC gear-measuring machines and softwa~e now comefrom the Industrial MeasurIng Technology Divisionof Carl Zeiss, Inc., a wor;ld leader in coordinatemetrology equipment

As the gear experts at Zeiss, Hofler isnow more responsive than ever. Our full-serveeIDeations across the U.S. provide whatever youneed-sales, operator training, maintenance orreplacement parts.Anextra dimension in speed and precision,

All Hofler machines feature a unique three-

I,,\- . ... . j.~~&fl dimensional probe head: that allows faster, more accuratetesting of profile and ,lead. Even the simplest Hofler modelis more precise than any competing machine in the industl)l.Hofler products include the ZME series for cylindricalgears, the EMl series for universal gear measuring, and' theZMC model for your most demanding. laboratory, 3-D andbevel-gear applications. You can also choose from threedistinct software packages that run on a networked or stand-alone IBM AT-compatible or Hewlett-Packard computer.Calltoday for literature or a demonstration.

1-800-,888-19,67Ext.51Or see your local Zeiss represenlative.

Carl Zeiss, Inc.

IMT Division7008 Northland DnveMinneapolis. MN 55428612- 533 • 0225

Cover photo courtesy of WMWMachinery Inc. Blauvelt, NY.

CONTENTSJAt\UARY/FEBRUARY,llJ')2

-

FEATURES

D,esign Guidelines for Hiigh-Ca:pacity BevellGear SystemsBy Raymond 1. Drago

Boeing Helicopter, Philadelphia. PA , ,.. , " 116

O f- .- S-ht Po' S- - -T-t'-· port IIIpJmum "0 eemng· pecucalon- I a ..8y Mark l.uw e re n zMetal Improvement Corp ... Inc., Milwaukee, WI

l m an ,'S Ek is

Ford New Holland. New Holland, PA ., 30

SPECIAL FEATURES

IGear FundamentalsThe Rilght and Wrong 01 !Modem Hob SharpeningBy Robert Modero",

fTW, Illinois Tools. Lincolnwood. IL. , , ""."" .. ,,, ,,, ,, 34

D'EPARTMENTS

Publisher"s PageThe Nii'na,The Plinta!,,and the American Gear Industry .." " Ji

!Management Matt,ersPlroduct liabillity DefenseBy LalV(!r(!ll'ce-M. Ko h n ..'13

Shop Floor,A Clockwork IGearBy Will i am L. 1a Ill! j tr c k " ., ..., .. " " " , '41

.Advertiser IndexFind the products and services you need ."., "." ., ,42

ClassifiedsProducts, services, and information you can use 46,

Cal~endarEvents of interest. , , 4,1

Tired of rejects?

Tired of inadequateinspection capabiHties?

Tired of promisesand no action?

Tired of gear suppnersthat make you look bad?'

Tired of justsm'ooth ta'l'k?

O,u,r qu,iet ge,ar'sd',o ,al,1th,e

tal,ki,ng for' ,us'!'• Crown Hobbing for noise reduction and misalignment compensation.• Hard hobbing with carbide hobs after heat treat as a substitute for gear grinding .•, CNC hobbing and shaping alignment proqrarns for varying teeth and pitches and special

forms such as fi'exible coupl'ings or hi,gh helix worms and camshafts.

New Se,rv,ices!! CNC analytical gear inspection.!! Double flank. mil checking with SPCof individual elements: total composite error;

tooth to tooth error run out and average center distance.!! Hob Sharpening: carbide and' spiral gash, capability.

CIRCL'E A,·4 on READER REPLY CARD

RO., BOX 8011 71' 5 MAIN ST.,ROSCOE, ,It 6J 0'73,fSl 51 ,623-2 J 68FAX liS 15) 623-6620

Member of theAmencan ~arManufacturers ....sseoeuon

GEAR TECH:,\OLOGY

EI)ITOHl:\I,

Publisher & Editor-in-ChiefMichael Goldstein

Associate PUblisher & Managing EditorPeg Short

Senior Editor Nancy Bartels

Publishing Assistant Donna-Marie Weir

Technical EditorsRobert Errlehellc

WilJj!LmL. JannlnckDon McVitUe

Robert E. Smith

:\RT- -

Art Director Jean Sykes

Art Director Jennifer Goland

;\D\'ERTISI:'\G

Sales Manager ~alrida Flam

Sales Coordinator Mary Mlchebon

R\:\'[),\LL PlIBLISIII;\;(; ST.\FF

President Michael Goldstein

Vice President Richard Goldstein

Vice President/General Manager Peg Sbort

Controller Pal rick Nash

Accounting Laura Klnnane

Administrati ve CoordinatorDeborah Donlglan

Art Consultant Marsha Goldst:eln

IU'-.;" \1.1 l'l'BLlS11I;";C, 1'-.;C.

1425 Lunt AvenueP.O. Box 1.426

Elk Grove Village, IL 60007(708) 437-6604

\'01.. 9, xo. 1'GEMl '!'IiCElNOUIIG\', Tho J""""'" '" c..r lld__ o!l!ctmIJI:

(lSSN' 074J.tM8) u.pubhsbed biiilOlldll'J b)' Rooall Publi!iblnJl. [nc •. 142::5tunl AvtnlJt. P.O. BOA 1426. Ell: Grave VlliuSe., n.. 6OC01. Subscriplioil1'Il1I'5are: SoMl.OO ~nme U.5_: lSO.Win CiruIJ;I: ~U500 i..allOlhlrcoumml..So.:orJd...CW.! pil!na~ piJd iii " ..hnguJII tkl!lit"lL.udatakinlun3lmaihnjoIf"xe:. JI.&OOIJI ~IKh!'&1 ~ CVeQ' c:ffon II) cu.5IR IhI!; ~be ~deii;:ribciliU GEARTECHNOL.OOYwnrnttilolo'SC.-ndenglnet.flns ~Neitber [he IYlOOn: nnr ibc p-iblisber "lUI be hc'Jd ~pons:lbh: for trruriessu..~w.intd wbHc roUo-wlnj ~M JJrOCeduro dc!iCribcd.

Pmlma:.1OI.rr: Send ~ ch...,..gc-, 10 OBAJt 1'E.(ltNOLOOY. 'J'he.Joun.Ii I:!f Gw M~~Jlj. 1425 Li.n:ll Ii.~. IP.O .HDII 1426. En.arulit' Villi •• n,6(0)1.

ecoo~C!nil. cop)Irightcd by RAND ...U JlUBUSl-UNO, fNC,. 1m."nkl~5 appeurinl in GEAR IECHNOLOOY 'm.li.ynot be reproduced Inwbulcor iill piiil widlOUl t.l!e6Pfts:8:pe.nni:!.S.1onoflhclJ'Llblisliltrorthc- aut.hor

HIGH NOON;, WESTERN COLLECTIBLES"

Bougbt & :Sold:'* Bridles'* Buckles.. Clothingi* lBits* Books

*BellS.. Bolos* Chaps* Spurs* Saddles

'(2131202-9010 br IppoinLmenl(2131,202-1340 \fax 1

CIRCLE A·19 on READER REPlV ,CARD

ClDTIBEFEATURES:./ Accuracy- All grinding

operations completed in asingle step

./ Rapid Setup or Changeover-Bodies to blades, roughing tofinishing, other diameters.

./ Full Probing Capabilities-For born part and wheellocation.

./ CBN Wheel- For bettersurface integrity and finish,longer tool life.

lihese features res'u'lt 1111'1II11prec'edented productiV.ity.

CONTACT US FOR FULL DETAILS

.£ELK RAPIDSENGINEERING

Ji7 Subsidiary of Slar Cutter Company210 IIndustrial Park Drive. P.O, Box 728. Elk Rapids, Mil 49629- Phone 616/264-5661'. Fax 616/264-5663CIRCLE A-S,on RE.&J)ERREPlVCARD

J~NU~RY/FSBRU"'RV 19.92 5

ADVERTORIAL

Bourn &Koch Machine ToolCompany, Rockford, TIlinoisProvides Unique Solutions

to Solve GearManufacturing Problems

Problem - A small fractional horse-power rnoior manufacturer required quieter gearsfor his speed reducer gear boxe . These motorswere used in office and computer products andwere 100% impecl.ed for noise level prior toshipment.

After the exisringmanufacturing equip-ment and method of processing wm; evaluated.Bourn & Koch determined that the BEST FITSOLUTION was to better utilize the equipmentby providing a gear manufacturing solutionsseminar ..

A one day seminar was presented withemphasis on controlling the design, processing.blank. and hobbing quality. as well as the itemsI.halhad an influence on gear noise transmission.

The semi nar was presented to the opera-tors, inspectors, engineers, and supervisors in aclassroom type of setting. Each attendee re-ceived a text book for reference ill olving futureproblems.

End Result - Bourn & Koch Best FitSolution provided a. better understanding ofgear manufacturing and the factors most im-portant on producing quieter gears. lass AAhobsere now being sharpened 10 Class AAtolerances, and blanks being controlled by gearquality requirements.

Problem - A portable electric 10.01manufacturer wieh many mechanical Barber-Colman Hobbers required more accurate changegear set ups that worked the first lime and fit thegear boxes without trial and error.

Helical pinions. and gears required"hobbmg 1.0 green leads" dueto heat treat di tot-

tion after hobbing,On differential type bobbing machines.

an accurate method of calculating ratios with fourgears, using change gears from 20 to 100 teethwas also. necessary.

A BEST FIT SOLUTIO was to pro-vide four computer software programs which

provided the set ups arielthe processing infonna-non with the routings.

End Result - customer now has severalpeople trai ned to use the gear software for changegear set up '.production estimating. The cus-tomer can also calculate four gear ratios whichwill achieve pecific accuracies using a tandardcomplete set of change gear .

Application determinesthe BEST FHSOLUTION. Not every application can be ad-dressed by new single purpose or new universalproducts. Even though Bourn & Koch has a fullline oleNC and manual hobbing and gear shap-ing,machines. we evaluate she applicanonand leithe solution determine whether new equipment orbener utilization of existing equipment is the bestsolution.

Your BEST FIT SO' UT]ON my notalway be as ea yto define as these. but with thehelpof'industry recognized personnel from Bourn& Koch. we will strive to provide the type ofservice that gives you unique solutions to yourgear manufacturing problems.

O,OU,Rn'& '1,"'OIC:~I-ImaC:'I~lneTQQL 'C:O.2500 Klshwaukee St.Rockford, lL 611 048151965-4013 FAX.8151965·0019

16 GEAR TECHNOLOGYCIRCLE ,A·9 on READERi REP,LY CARD'

CIRCL.IE A·10 on REA'DER REPlV 'CARD

BOURN & KOCH MACHINlE TOOL CO.,a manufacturer of precision products since 1975adds new dimensions to the Hobber & Shaperline acquired from Barber- Colman. Company.Tapered Root spline hobbing, automatic hobclamping. and water soluable coolant capabilitiesare our standard options.

ModeI16HCNC·56

16HCNC SeriesAvailable in 16,36 and 56 ModelsMax. Work Diarneter.. 16"Max. Work Length 16",36",56"Max .. Hob Diameter " 6"Max. Hob Length 7"Crowning, Double Cutting, Radial!Tangential worm gear cycles.

The machines are controlled by a 32 bit NUM760E Gear Hobbing CNC Controller which isespecially designed for bobbing.

Model 300HCNC

300HCNC SeriesAvailable in 300,400, and 600 ModelsMax. Work Diameter, 12". 16",25"Max. Work Length 40", 48",144"Max. Hob Diameter 6"Max. Hob Length 7"Also offers Carbide Hobbing capabilities.

macHIM.e TOOL CD'.

2500 Kishwaukee StreetRockford. n, 61104(815) 965·4013Fax (815)965-0019

Before you buv» CNCGearInSp,ection System, ask

these fo,ur Questions

1'.Can we get complete inspection ofboth gears and cutting tools?With the M & M QC 3000 System, the answer is~. The system will test lead and involute profilecharactertsttcs of internal or external gears and splines.It Is the only universal gear tester available which providestrue index. testing without expensive attachments. In addition,we have fully-developed software for checking hobs, shavercutters, shaper cutters, and other cylindrical parts such asworms and cams.

Hob Pressure Angle Check. Shaver Cutter Lead Check

2. Can you customize software to meet our quality~inspection specifications?At M &.IMPrecision, we write and develop our own lnspecnonsoftware. Our technical team can and has implemented in-spection specificaliions into specmc software for individual re-quirements. Our current library includes line/curve fitting aswell as modified K-chart analysis routines.

Line/Curve Fitting Modified K-Chart Analysis

3. OK, you can inspect gearsand cutti;ng tools. What else is available to

aid us in quality control of the manufacturingprocess?

At M & M Precision, we have fully integrated such advancedsoftware packages as Statistical Process Control and ToothTopography into our standard t·esting software. Our SPC pro-gram can identify non-random variations and provide earlywarning, of variations which are approaching tolerance limits ..Our Tooth Topography software features automatic testing 01lead and involute at multiple locations and provides two- andthree-dimensional graphics.

SPC Hun Chart Topological Map

4. IDoyou have the technical support team and lin-stallation experience to back up the hardware andsoftware provided?At M & M Precision, we have a technioai team with over 45man-years of experience in developing CNCgear 'inspectionhardware and software. All software for our QC3000 Systemhas been developed in-house. In addition, we have workinginstallations at these leadi:ng companies:

• General Motors • Oincinnati Milacron• THW. Chrysl'er• Ford Motor • Pratt & Whitney• Warner Gear • Rocketdyne

For details on our advanced QC 3000 System and availablesoftware, contact M & M Precision Systems, 300 ProgressRoad, West Carrollton, Ohio 45449,513/859-8273.

LI/YIliMM PRECISION_SYSTEMS

AN ACME-CLEVELAND COMPA.NY

·OIRCI..'E A-11 on READER REPL. Y CARD

ext year will be the SOOth

I anniversary of Chll'i topherCclumbu 'ramoll "dis-covery" of America. Poor

Columbus has fajlen 011hard time of late. whatwith revisionist historians

smacking their lips over hismore notable failures and reminding us

thai. American natives have a vas flydifferent point of view an this Great

American Success Story. Bill. beforewe relegate the Great Navigator to. the

scrap heap of trashed-over heros. let'take one last look at some of the pas i.-

rive lesson to' be learned from theColumbus experience - onesthat couldbe instructive to our current situation

in the American gear indu try.Whatever other complex factors moti-

vated Columbus amdhi fellow explor-ers to travel, and the various kings,

government. and bankers of Europe '10

finance their adventures, one undeni-

able goal was the opening of new mar-

kets. Our European ancestors got intothe exploration busine s to make money.

They were looking to open up traderalites to Asia. What they found, ofcourse, was omething el e entirely.but those trade routes were what theywere looking for to begin with.

The decision to finance olumbus'

voyage was a busine deci ion too. Itwas based on LheLime-hollored rule 'Lhal.

ri.sk and reward tend to be proponioaal -the bigger the risk. the bigger the pos-sible reward al theend,

And never doubt the nature of therisks. It wasn't just that no one in Eu-rope wa eertainefwhat layjnthewe t-ern Atlantic, and lilat most contempo-rary maps showed a big, blank. pacethere and the ominous warning, "Herethere be dragons." Nor was it justthateven a state-of-the-art ship of the daywas one most of u would be reluctantto take for an afternoon sail in a mild

chop off Oak Street Beach in Chicago.

The Nina,The Pinta,

And The AmericanGear Industry

Some of the rrsks would soundquite familiar to us today. The "beancounter " in the Spanish court were"bottom line" men too. They werebeing asked to payout a 101 of money

with onlya dubious promise of ome-

thing in return. And they weren't allthat familiar with the markets they were

tryi.ng to break into. Contemporary re-ports were vague, closer to fairy tales

than hard data ..Allthey knew for surewas that vast wealth was to be had bythe person willing [0 overcome 'theobstacles, but that these were formi-dable. There were different languages

and customs that could gel the unwaryinto trouble-if not eaten-and sophi ti-catedv knowledgeable traders whowould strike a bard bargain and werereluctant to let. newcomers share theirmarkets. Even ifone survived the voyage

and the dragons, the competition couldbe,literaUy. killing.

The more cautious among them had

other good reasons for not straying farfrom their home market. It.wascenainlyeasier and safer and cheaper 10 do busi-ness with their familiar neighbors. Theyalready had established customers. Theolder trade routes maybe weren't thebe I, but they were familiar. The riskswere at least known ones.

PUBLISHER'S PAGE

And what happened if Columbus waswrong? What if he got eaten by thosedragons? What if the earth really didhave an edge. and he and hi shipsailed over it into nothingness? What ifthose "Indians" wouldn't sell them theirspices, and who knew how to peakChine e anyway? Sure, there might be

all the riches of a ast, wealthy contl-nem if they ucceeded, but what if Ihey

JAN UARYIFEIlRUAAY '8112 9

110 GEAR TECHNOLOGY

someplace else .. He never did find the luctant to take the risk of marketing

market he was really looking for. He ourselves aggres ively - either at homeand his followers made a lot of expcn-

si vc, tragic mistakes in opening the mar-

kets they did find. But they persevered.

They learned. And in the end, the sue-

10SI their investmenr?The decision toenter new markets

hasn't changed. It's still a voyage into

unknown territory, full of risks and UIl-

foreseen problems. The dragons may

have changed the color of their cales,

but they're till waiting au! there, andnobody', inve tment is guaranteed.

But the reward haven't changed ei-ther. For the courageous, patient, and

peri tent, they can more than cover

the risks and expenses.

In the Spani,sJil court, the risk-takerswon out, and the rest. as they say. ishi tory. True. the COUf e of success wasnot smooth. Columbus was lost for

much of his voyage to the ew World.After he landed. he thought he was

cess was of epic proportions.Our situation in the American gear

industry is not unlike thai of those bean

counter in Queen Isabella's court. Forevery powerful motivation we have for

seeking out new markets overseas. there

seems to be an equally good rea on for

Slicking dose to home. Money is tight,

The economy is shaky. The foreigncompetition is stiff. The economies in

some of our most likely markets arc com-

plete wrecks, and the paperwork neces-

sary to get into foreign markets couldreforest a small. third-world country.Can we afford to spend the money we

have on risky ventures that :might take

years to pay offor might not payoff at ull':'

Can we afford not La?

What the visionaries .in the Spanish

court in 1492 knew was that, risky or

not, they really had no option. The

push to explore was on. I conomic and

social pressure a.II over Europe weredemanding the widening of vision 10

include the rest. of the world. If the

paniards didn't reach for the new mar-

kets, one of their neighbors - Portugal,

France, England - would.

The situation is the same today. The

pre. sures of history dernand fhat we

broaden OUf horizon again. Like it ornot, we live in a global village, and

plenty of OUI:' neighbors are already ag-

gressively exploring the opening mar-

ket. of Eastern Europe, Asia, and

South America. With our own market

at home shrinking lind our industry

growing mailer and smaller. can we

afford not to develop new markets both

at home and overseas?

Much of the American gear industry

eerns 10 me 10 be stuck in a timid,conservative mind-set where we are re-

PUBLISHER'S PAGEorabroad. Like some of Queen Isabella's

bean counters, we see the world as lim-

Ired to our own corner and are content toleave il that way. Let omeone el e runthe risk of sailing off the edge.

This timidity w.ill be OUf undoing. Inthe tough economic climate we face 10-

day. the gear manufacturers who aresucceeding are [he ones willing to take

the risk. and face ihe unknown . They

are willing to explore new markets here

at home or ill Eastern Europe. Asia. andSouth America, and never mind the factthat the profit might not be instant, or

that they might make some mistakesand have some colossal failure .They re gambling all their ability 1.0

find and develop these new markets.It's a necessary gamble. We either

gel out our maps, load our ship. lind

gel moving, or be left behind by the

people who do.

~~Michael Goldstein

Pub1isher/Editor-in-Chief

ADVER:TORIAL

Technological Advances.aMajor Benefit Of

Gear Industry Mergers

••

To attendees of AGMA' sGear Expo '91 (Detroit) it wasobvious that spiral bevel gear producers are due for majoradvances in gear making and testing equipment. Nowherewas it more evldentthan at Booth .10],where Klingelnbergand Oeriikon demonstrated some oftheir capabilkies, The(March, '91 )joint venture of West German-Kllngelnbergwith Swiss -Oerlikon consolidates some of the best gearequipment technology in the world,

Together. Klingelnberg and Oerlikon will optimize theirtechnologies to benefit all gearmaker , Oerlikon brings

savvy from highvolume, automo-tive-type produc-tion of smaller di-ameter Spiral Bev-el . Klingelnberg'universal cuttingsystems cater totheneeds of smallerrun, high quality,larger 00 produc-

At Expo '91, the combined companies demonstrated aKNC-60 Gear Generator, (Figure A) and numerous GearTesters (Figure B). The new OPAL parallel axis geargrinding ystem also attracted buyers' anention (FigureC). The OPAL delivers exceptional accuracie and ha .CNC controlled dressing of either conventional or CBNgrinding wheels, This added flexibility permits cost-ef-fective production of small-to-medium quantities of Spuror Helical gears for the Automotive, Aircraft or MachineTool industries.

The Klingelnberg-Oerlikonjoint venture will also chan-nel development energy on 11 common path for vibrationcontrol, noise reduction and software development. Intoday's climate of global com-petiti veness, the importanceoftechnology has never beensuch a critical issue. The com-bined companies. working to-gether, will set the pace forgearequipmentinnovarioaforyears to come.

KNC-60 Gear Generator producesSpi ral Bevel gears tip 10 600 mm.

Hou ed inlhe KlingelnbergGear Technology, Inc. head-quarters at Strongsville (OM),

The OPAL 420 control systemspeeds grinding and changeoverof Spur Gild Helical gears.

offering , gearmakerswill be the beneficiaries,The results will lie withshorter, more cost-effec-tive run cycles; fasterchangeoverumes; higherquality levels; coordi-nated testingequipment.

the combined re ources ofKlingelnberg and Oerlikon offer a single source for sales.tecbrucal service and maintenance for all their productlines.

For further information, contact:Klingelnberg Gear Technology, Inc.15200 Foltz Industrial ParkwayStrongsville, OH 44136

Phone (216) 572-2100 FAX (216) 572-0985Testing and

documemationis q!4icker and more

accurate 011 a PNC 60.

CIRCLEA·7 on READER REPLY CARD'

JA'NUARY/FEBRUARY 1992 111

111111

Ask us about the GMI differenoe and our innovativenew product .. .the Mutschler Model4S0 Chamferand !Deburring Machine Tool.. It features state-of-the-art controls, up to four Rotex arms, for pre-program-medfilnlshingl operation on up to 20'" OlD gears.Oet complete detaiils. Call Bill McElroy at ourClev,eland offices. !Hewill put GMI geallTlaik,ingexpertise to work for you!

Gsarrnakers today face many chalienges-qlJality,service, r,eliability and pricing are probably the mostcritical. Those who succeed lin today's competitivemarketplace often align with vendors. that deliverextraordinary value=conslstem high qualityproducts, pertinent technleal support and personalexpertise. OMII is such a vendor.

=.o. Box 311081670811vandaleDr., Cleveland', OHI 4413,1Phone (216) 642-0230 FAX (216), 642.-0231CIRCLE A·112 on, READER RE'PL Y CARD

Product Liability DefenseSeven strategies tor minimizing your risk

D t's every gear manu-facture.r's. rughtmar.e.Your company has__ been named as a de-fendant in a product Iiabili.tysuit - one involving seriousinjuries and death. You'refacing endless court appear-ance , monumental legalfee, and, possibly. seven-figure settlements out ofyour coffers. The very ex-istence of your businesscould be on the line. Thequestion is. how do you pre-vent this nightmare from be-coming a painful reality.

Recently Gear Technologytalked to mliott Olson, a part-ner in the Los Angeles fum ofHaight, Brown & Bonesteel,lawyers specializing in prod-uct liability defense, aboutprotecting your firm from ru-inous product liability suits.He recommends the follow-ing seven strategies: Indem-nification. Compliance, De-tachment, Commitment, Con-trol, Warning. and Defense,

Indemnification. First tryto get a contract with the finalproduct manufacturer to in-demnify you in any lawsuitsthat involve your product. IfYOll have indemnification, heis responsible for tl:tedefensein the event of a suit At thesametime, that defense canbe somewhat simplified; andthe more complicated a suitis, the more protracted - and

Lawlren:ce M. Kahn

expensive - it will. be,The risk of such indemni-

fication to the final productmanufacturer is small, espe-cially if you are a long-timesupplier. It has its own inspec-tion procedures and presum-ably knows your product aswell as its own. The costs ofadding your defense to its in-urance is probably not sig-

nificant, and may also enablethe manufacturer to buy com-ponents at a lower price, sinceyou win not have to add thecost of additional insurance toyourprioe.

If such a deal. can be ar-ranged, the wording of thecontract needs to be very spe-cific. Olson warns, "It is aslight trick to properly drawup such a contract, The bestway to do it is to get the finalmanufacturer to 'indemnify,defend. and insure againstall claims. liability, etc., in-eluding those arising fromthe sole negligence or defectof the product manufac-tured by the gear company. '"

But what if you do not haveor cannot get such a con-tract? Then how do you pro-tect yourself?

Complia.nce. Make sureYOl.U product complies withall government regulationscovering :it and with any ap-plicable voluntary standards,such as those of ANSI, SAE,or AcGMA This provides an

---

MANAGEMENT MATTERSexternal, objective indication Managing a businessof quality. A wen-run quality ~ today is hard work. letcontrol department is also an ~ "lManagement Matters"im f'lo·...ant defense Olson says- : - - - -- -

-1' .""-- --' . _. --- , : l,endahand!.T1elluswhat"Obviously, the proper qual-ity control is essential," Fa:il-ure to comply with your owncriteria can be fatal.

Detachment. A third de-fense is toestablish an ap-propriate distance betweenyour company and the finalproduct manufacturer. Youshould be aware of the finalproduct application andwhether the it goes beyondthe limits of its design criteria ..Olson explains, "",the tractoror whatever was designed topull a plow, and it's now being

management maltterslin-: terestyou. Write,to us.,at

P.O. Box 1426. !Elk Grove,.Il.I60009, or calli 'our staftat ~108;'431-6604.

the contract of sale a statementthat the gear use should belimited to the specific purposeintended, "The gear rnanufac-turer should at.least have somespecifications to which it imanufacturing the gear andmake sure that the componentis designed beyond the endur-

used as a battering ram, and . ance limit of those specifiea-the gear manufacturer knows : tions," says Olson.that hi gear is not adequatefor that use, he should takesteps to protect himself. eitherby warning the manufactureror final user not to use it forthat application, or by beefingup the gear,"

However, since the likeli-hood of this prior knowledgeis slim. you should include in

Law!rence M. Kahnis a Los Angeles-basedmarking consultant, writer.and media personality. Hespecializes ilr business-related subjects and wasthe host of KIEV Radio's"It's Your Business",Among tire subjects of hisinterviews has been formerpresident, Ronald Reagan.

JANUARY/FeBRUARY 1992 13

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TECHNOLOGY

On the other hand, be wary in safety should come at theof becoming too closely in- design stage, not later in thevolved in the design of thefinal product. According toOlson, the danger is thi :"Each entity in the stream ofcommerce of a product is li-able if the product is defec-tive. If the tractor has a char-acteristic which causes it tolose steering, yet the gearsprovided are adequate, thetractor manufacturer and allentities down the line, including the distributor and thedealer, would be liable, butthe gear manufacturer wouldnot be, as long as the gear

With this new gage you no longer have to question thecomparability and accuracy of separate masters for eachmachine - one gage does it all.• NIST-Certified f'""""------- .......II• Accurate to ±O.00005"• Measures flip-flop on

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Centrol, A fifth strategyi to maintain careful controlof documentation. Sloppilyworded documents can be fi-nancial time bombs. Be waryof the wording of justifica-tions for design changes.Phrases like, "change madeto avoid field failures," or"change made in order toprevent lawsuits," are deadly.Eitherdon' tdoeument the rea-son at all or give other validreasons, such as cost cutting,maintenance simplification,

-----

MANAGEMENT MATTERSdidn't fail or break, or unlessthe gear manufacturer par-ticipates in the enterprise insome way, such as recom-mending how the gears shouldbe used, how the tractor shouldbe used, or making recom-mendations as to. the owners'

or performance improve-ment. Don't admit to safetyproblems that don 't exist.

Every company needs arealistic document retentionprogram so that useless orpotentially damaging papersare not kept around for long

Ph: 708 377'-2496 FAX 708-377-.2546Call today for infonnalion or to let us certifye=~:~:;i:;~~;~'

manual, etc .." periods of time. One suchCommitment. Commit- document is what Olson calls

ment to safety is the fourth the "God-help-us-if-some-defense. No one sets out todeliberately make 11 productthat will kill or injure some-

thing-goes-wrong" memo.Such documents, usually cre-ated in the heat of discus-

one, but sometimes safety sionsoveraprojectedchange,concerns are lost sight of oroverridden by other consider-ations. Management mu t in-sti II an overall sense of com-mitment to safety in all de-partments. Simply put, a bal-ance has to be struck betweenputting out a product that'stoo expensive and one thatwill cost more in. the long runbecause of some catastrophicfailure in the field that willcost life and limb. Olson says,"One of the rna t expensivethings you can do is killsomebody or make someonea quadriplegic." Investment

CAN WE USE IT IF WEDO'N"T ABUSE IT?

are also potentia] disasters.Of them Olson says, "Thereis no need to create such adocument or to keep it,"

This is not meant to dis-courage discussion of safetyquestions,and unsafe prod-ucts shouldnever go to mar-ket. Where the problem arisesis in the careless use of lan-guage. Olson recommendsthat all employees be madeaware of the potential dan-ger of the kinds of th.ingsthey write. A careful programof education of employees inproper documentation can

save a lot of headaches.Warning. A sixth strat-

egy is to be very carefulabout the wording of anyproduct warnings, installa-lion and operating instruc-tions, etc. Don't :fall into thetrap of thinking that warn-ing against every conceiv-able danger will protect youfrom suits. You cannot pos-sibly warn against all thepossible danger .and over-warning degrade the valueof the notice.

Warnings hould cover theunexpected. Says 01 on,"Don 'Iwarn. against obviouthings. Don't warn driversnot to run into people whiledriving. On the ather hand, ifyou have a clear. odorlessliquid that is a deadly acid,the bottle should containsome kind of warning."

Depending on the prod-uct, having itreviewed by aproduct liability lawyer,preferably one with productliability trial experience, allengineer with product liabil-ity experience, and, perhaps,ahumanfactor engineerrnaybe a wise move. Olson says,"Sometimes defects can beeas i]y corrected if discoveredby such ,a review .."

Defend. Suppose youhavetaken all these precau-tions and till find yourselfconfronted with a product li-ability suit. Olson' advicein this case is to be preparedto aggressively defend your-self and preferably take COIl-trol of the defense. Don'tjust turn the defense over toyour insurance company,thinking, well, we pay a lotof money for this policy, solet them worry about it.Many times insurance com-

panies are tempted to takethe safe way out, settle theca e,and then later raise yourrates or drop' yourcoverageentirely. This could be unfairto you in a number of ways.Chance are, nothing iswrong with your product. Itsdesign is based on sound en-gineering practice. It meetsall the standards. codes.andregulations. andtbere' snothing wrong with it, ex-cept someone has misusedit Accepting a ettlernent insuch a case can cost youmoney you shouldn't haveto pay and can hurt yourcompany' reputation.

The decision to launchan aggressive defenseshould be made long beforethe possibility of a law suitarises. It should be discussedwhen you are negotiatingyour liability insurance cov-erage. "That's the time tonegotiate the right to iden-ti fy your own counsel,"says Olson.

Once you've made the de-cision to aggressively defendyourself in such suits, youmust al 0 be prepared topresent witnesses and com-pany personnel 10 assist inthe preparation and defen eof cases. But this investmentmay be well worth it in termof a final settlement.

Protecting your companyfrom product liability suits isa complex. ongoing process,It requires forethought, care-ful planning, and a long-termcommitment, but ultimately.that extra planning will payoff in added protection whenthe worst happens. I.For allswers to questions aboutthis article, circle Reader Ser-vice No. 79,

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JANUARY/FEBRUARY ;992 15

16 GEAR TECHN,OLOGY

Design Guidelines forHigh-Capacity Bevel

Gear SystemsRaymond Ji. Dlrago

Boeing IHelico,pter. Philade'l'phia, PA

Abstract: The design of any gearing system is adifficult, multifaceted process. When the systemincludes bevel gearing. the process is furthercomplicated by the complex nature of the bevelgears themselves. In most cases, the design isbased on an evaluation of the ratio required forthe gear set, the overall envelope geometry, andthe calculation of bending and contact stressesfor the gear set to determine its load capacity.There are, however, a great many other param-eters which must be addressed if the resultantgear system is to be truly optimum.

A considerable body of data related to theoptimal design of bevel gears has been devel-oped by the aerospace gear design communi ty ingeneral and by the helicopter community inparticular. This article provides a summary ofjust, a few design guidelines based on these datain an effort to provide some guidance in thedesign of bevel gearing so that maximum capac-ity may be obtained. The following factors,which may not normally be considered in theusual design practice, are presented and dis-cussed in outline fonn:• Integrated gear/shaft/bearing systems• Etfectsofrirn thickness on gear tooth stresses• Resonant response

Nomenclature

0" Harmonic index, integer D == 0, I,2 ...

f'" Tooth mesh frequency and harmonics

k" Integer multiplier, k" I, 2, 3 ...

n = Number of gear teethN" Rotational speed, revolutions per second

Q= Number of mesh points on gearW D = Weight of helicopter damping ring, pounds

W G" Weight of gear rim, poundsn" Natural frequency, Hertz

Integrated GearlBearinglShaft SystemsBevel gear are typically manufactured as

blanks and then attached to their shafts by avariety of techniques including keys, bolts,splines, and the like. The existence of thesejoints increases the weight and complexity of thefinished assemblies while reducing their reli-ability, accuracy, and effective load capacity. Inspite of these limitations, the two-piece shaft andgear assembly remains the most common con-figuration because it is the easiest system todesign and manufacture. In addition. bearingjournals are provided for assembly of bearingraces, resulting in a multipart gear/bearing shaftassembly with many potential faying surfaces.

In applications in which weight and reliabil-ityare critical considerations, these joints andfaying surfaces have been the subject of con sid-erable research. The primary operational prob-lem with these joints is fretting. Under the com-bined conditions of high stress and a frettedsurface, a crack can initiate at this joint and, ifundetected, can progress to failure. This prob-lem is significant forthe typical hel icopter appli-cation; thus, much effort has been devoted tocoatings, platings, lubricants, and imilar de-vices aimed at reducing the long-term effects offretting and the ensuing corrosion. The obviousfinal solution to the problem is, of course, theelimination of the joints a.nd faying surfacesaltogether. This can be accomplished either bywelding or by designing integral gearfbearinglshaft configurations. The former techniqae hasworked well in many applications, but intro-duces potential. new problems associated withthe weld itself. The optimum solution is, there-fore, integral design, Because of the complexgeometry of bevel gears and the offset generat-

fig motions of the cutting and grinding ma-chines, this is easier said than done, especially inthe case of complex shafts with projections atboth ends of the gear.

The original impetus behind the growth ofthi technology wasthe development ofthe CH-47D helicopter. A decision was made to elimi-nate all bolted bevel gear joint, either throughintegral de ign or welding, Integral design waselected because of lower developmental costs

and greater inherent reliability.The first step in the design of complex, :inte-

gral- haft spiral bevel gears i .the definition ofthe path of the cutter with respect [0 the gearblank, We have developed a.computer programwhich uses manufacturing machine settings toproduce plots of the path of varia us points on thecutting and grinding tool • as Fig. I shows.

Fig. ~ • CH47D Jorward sunlbevel ,gear wilhgrlDdi~ngwhe~1 tiip' and body point ploLGraphic layouts and model check . are used toensure Lhat at proper cutter and haft design canbe obtained in orderto achieve an integral geardesign. Machine and cutter rnodiflcanoas have

- Ibeen developed to achieve the ere ults ..

Based upon these developmenrs, all of theCH-47D spiral bevel gear were de igned toeliminate all boned or splined joint . Atypicalcomparison of the CH-47C and CH-47D for-ward transmission sunlbevel. gears is shown inFig. 2. The concept of integral design was ex-tended beyond the elimination of the bevel gearbolted joint to total integration, For thi. gear thisincluded the integration or an accessory spurgear and a journal for bearings. The final designof the CH-47D sun/bevel gear incorporared threebearing journals and three gear (two spurandone bevel) into a single integral haft/gear design.

Fig. 3 also shows the integral bevel gears forthe aft and engine tran mi sions. The enginetransmission bevel. gear required a significantdesign change in the center portion in order to

BEVEL GEARINTEGRALWITH SHAFT

AtCESSO RY DRIVEG EAR INTEGRALWITH SHAH[THREAD, KEY. ANDLOCKNUTASSEMBLYElIMINATEDI

ACCESSORYDRIVE GEARKEYED TOSHAFT

lJ.a·INCHPITCHDIAMETER

SUN GEAR INTEGR_Al WITH SHAH

CH'-41C FORWAR P' SUNlBEYEl CH-gID fORWARD SUN/BEVEL

Fig...2 • Comparison (If CH47C and 0-4m gears,

ENGINE TRJl.NSMISSION

Fig ..3,· Representattve ,example of_ integral spiral bevel gear_. for theCH·47D beUcopt,er.eliminate canerinterference,

Furthermore. the power tran mined per poundof gear has been increased. as shown in Table 1,by at least IO~ and a much as 20% for thegrowth power level of the CH-410 bevel gears(lO,OOO-hp system as compared to the CH-47Cgears. ~6.000-hp .y tern). The philo ophy of in-tegral design has been taken several steps. furtherin theCH-47D transmission .permitting a morecompact (relatilve to power tran m itted) and morereliable drive system than that of the CH-47C.All of these improvements have been made with-out significantly increasing the gear tooth stresslevels over tho e of the CH-47C.

The projected production acquisition cost of theintegral CH-47D gear is virtually the arne asthat for the conventional bolted shaft assembly.while the life-cycle cost w.iU be significantlylower because of reduced rejections at overhaulfor joint-related problems. Therejecti.on rate isquite high for such problems; thus, eliminatingthe joint will greatly lessen rejects. This conclu-

Ra,ymondJ ..D.~ago'is A.~soci(llt' Tedmicolfellow. Dynamic SY.flfITUTechnolog),. at Boei1JgHelicopters. He is .th~author of numerous b()nksand paper.\' an gel/rillgsubjects.

JAN.UARYlfEIBRUARY IIH2 11

Table 1Relative Wei.ghls ofCH-47C Bolted Flange and

CH-47-D Integral Bevel Gears

IICH-47C CH-47D

I(6.000-hp system) (I O,OOO-hp system) Percent

Transmission Ibp/lhJ (hp/lb) ImprovementForward 89 1:02 15

Afl 96 1.05 10Mix 123 147

II

20 I

I Engine 175 209 20 I

sion must be tempered somewhat, since with theintegral gears a non-repairable defect on the gearor shaft will result in the entire component'sbeing scrapped, whereas with separate parts, this isnot the case. This is a small consideration within thecontext of the overall system and is far overshad-owed by the improvements in weight, reliability, andlife-cycle cost

Effects of Rim Thickness on Gear ToothStresses

Many investigators have indicated that the ac-curacy and applicability of currently availableequations for predicting gear tooth bending stressare limited in some applications. Testing and ac-tual field experience have verified the fact thatgears which are constructed in such a way that therim supporting the gear teeth is less than rigid havetooth root stresses that differ substantially fromthose predicted by conventioeal theory.

In order to overcome the shortcomings of theexisting analytical tools, several researchers haveaddressed the problem in a variety of ways. Somehave proposed new approaches based on varia-tions of simple beam theory, while others haveused finite-element methods (FEM). In addition to.these analytical efforts, many photoelastic andstrain survey investigations have been conducted.

Unfortunately, the vast majority of the research(both analytical ami experimental) has concen-trated on the gear-teeth themselves withourregardto the blank: configuration ..This research has beendemonstrated to be inadequate for lightweight,thin-rimmed gears ..In order to better understand

NOTE'BACKUP RATIO = BACKUP

WHOLE DEPTH 0.25

Fig. 4 - Phuteelastic test specimen configuration.

'18 GE"R TECHNOLO(lV

this phenomenon, a series of investigations wasundertaken with a simple segment model There uIt of this testing clearl y indicated that the rootstresses become much more significant as the gearrimthickne s .isreduced.

In order to accurately evaluate the effect ofrim thickness, three different pitch diameterscombined with five rim thicknesses wereevalu-ated, as summarized in Table 2, in an extensiveseries of photoelastic tests.2-3 In order that thedate from each test specimen could be directlycompared, the gear tooth configuration was thesame on all specimens, as shown in Table 3.

The gear blank. construction was also de-signed to be representative of an actual blank, asshown in Fig. 4. The pitch diameter CD) and shaftbore diameter (d) were the parameters variedduring the test, Radial support wasprovided forthe model at each end of the shaft, and one endwas clamped to provide torsional restraint.

In contrast to these test specimens, virtuallyall photoelastic gear testing done before thisinvestigation was conducted with large tooth-segment specimens. For example, in theirlandmark work on stress concentration fac-tors, Dolan and Broghamerused two-pitch, l 4.50

and 20° pressure angle tooth segments. (Fig. 5).The gear tooth form for each specimen was

defined by a computer program developed as apreprocessor for a gear FEM analysis system."This program provided accurate point-by-point coordinate data for both the profile andfillet areas. These data were transferred to aGerber 4400 plotting system on magnetic tape.This computer-based system then scaled upthe data bya factor of 10 and provided se-quential tooth plots Olil Mylar." The systemenabled the plot accuracy to be controlledwithin a few thousandths of an inch. The eplots were subsequently used to manufacturethe actual specimens.

A line-master copy milling machine was usedto cui the gear teeth on all specimens. The 10-times-size gear tooth plots were placed on thecopy mill tracer table and converted opticallyback into digital coordinate data. The machinethen reduced the digital data to actual size andused the signal thus produced to guide an end-milling cutter which cut the actual tooth profile.The speed of the cutter was kept high and thefeed rate low, so that the resultant parts hac!goodaccuracy and finish; the accuracy of the finished

parts was about AGMA Quality Class Q 11.Two-dimensional models were fabricated

from annealed polycarbonate plastic for the8: 1 through 2:] specimens. These gears werethen bonded to aluminum-filled epoxy shaftswhich were modulus-matched to the plastic blankmaterial (solid aluminum shafts were, however,used for the 4- and 8-inch pitch diameter, 7.5: 1and 3.8: 1 backup gears, respectively, to preventexcessive lateral haft deflection),

Three-dimensional models were required forall the 0.45: I specimens because the rim thick-ness was only sligbtly greater than the shaft wallthickness. The 3-D specimens were cast from anepoxy-based resin system employed phthalicanhydride and amine hardener : the castingswere then machined to the appropriate dimen-sions. In order to facilitate cutting the teeth onthe copy mill. the 3-D shafts were parted near thegear tooth area and rebonded after the teeth werecat. Fig. 6 shows a variety of the specimens used.

The 2-D model assembly - model, load arm,and model restraint - was placed in the opticalpath of a transmission polariscope, which per-mits the analysis of the isochromatics (lines ofconstant color) through the use of circularlypolarized light. The shaft was restrained radiallyat both ends and torsionally at one end, while theload was applied to. the central. tooth of the five-tooth cluster. Load was applied at three separate Fig. 5 . Dolan and 8roghamer~est setup.

locations along the tooth profile: low point of 4.IN. P.O., 20, 2:1single-tooth contact (LPSTC). pitch line (PL).,and high point of single-tooth contact (HPSTC).An isochromatic color photograph (35mm slide)was obtained at each load location for subse-quent analysis and documentation. The modelwas then modified to the next configuration byremoving the gear from the shaft. enlarging thegear inside diameter, and bonding to' a shaft oflarger diameter (2: I backup ratio).

The 3-D photoelastic models were loaded asshown in the test schematic in Fig. 7.. All threepositions, LPSTC, PL, and HPSTC, were loadedsirnultaneou Iy to conserve time becau e of the"stress-freezing" procedure. which involves adetailed heating and cooling cycle. Subsequentto the "stress-freezing" procedure. the modelwas sliced by machining off the ends ofthe shaftso that a constant-thickness, 2-D model throughthe gear tooth section remained, The slice wasplaced in the polariscope and analyzed exactlyas the 2-D specimens were.

Tallie 2I

Photoelastic Test Specimen Configuration Gear

Shaft

II

!

Dia.D Din. d Backup Dash Model(in.) (in.) Ratio No. Type

16I

8.70 8:1

I

1 2D16 14,00 2:1 2 2016 I 15.40 0.56:1 3 3D

8 0.75II

7.5:1 4 208 6JO 2:1 5 2D8 7040 0.56:1 6 3D

4 0.75

Ii

3.8:1 7 204 2.10 2:1 8 204 3.4{) 0.56:1 9 3D

Tallie 3Test Gear Tomb Geometry

Diameiral Pitch 5.00025.000

0.200

0.245

0.06·2

0.310Involute

Circular fillet wilh noundercut

Pressure Angle

Addendum

Dedendum

Fillet Rad ius

Tooth ThicknessTooth Form

Root Configuration

8-IN. P.D.•.. 2D,2:1

a-IN. P.O.,30.0.56:1

Fig. 6 • Comparison of 2·Dand 3-D test specimens.The photoelastic stress analysis was perform-

ed by the color-matching technique, wherebycolors of known magnitude are matched to thoseof the projected image. The ability to discernpartial fringe orders is typically ± 0.1 fringe,assuming an initial friage order of approxi-mately 0.7 or more. Therefore, the accuracy ofthis technique is directly related to the magni-tude of the observed fringes. Throughout thistest program. the majority of analyzed fringeswere 2 or more, which re ulted in an accuracyof ± 5% or better.

The data obtained from the experiments were

16-IN. P,O.,20,2:1

4-IN.P.D ..30.0.56:1

JANUARY/FEBRUARY 1992 19

reduced and convened into stresses. The magni-tude of tlre : tresses of and by themselves are oflittle consequence, since we are primarily seek-ing trend. Furthermore. since the models wereplastic. the load and the re ultant tresses werequite low relative to those which one wouldexpect on a metal gear of the same size, Despitethese facts. it is always interesting to compareexperimental data 'to orne knownpoints, Wehave already indicated that for gears with rela-lively large rim thicknesses. the conventionalequations predict the maximum fillet tensionstres with reasonable accuracy. In order toverify thi observation. measured fillet tensiontres e for the test specimens with the largest

backup ratios were plotted as functions of loadposition. This plot, Fig. 8, shows that the tensionstress at the highest point of single-tooth coo-

Fwg. , ,0 ScllemaUcof 3·D test setup,

PITC11PQINT SOUDSYMBOLSINDICATE

~ ~~

In our analysis of these data, many param-eters were plotted and evaluated .. Perhaps themost significant are the fillet and root alternatingstress and the alternating stress for fully reversedloading shown in Figs. 10-12.

Although many subtle effects may also benoted, the main trend shown in these plots isquite apparent the stress increases dramaticallyas the rim thickness-to-whole depth ratio drops

iii 1.0

; oJLLI;a:;;I-

'"Cl 0.6Z~ I

§ 041

~ I« 0.2 I~ I

u: 0 ~D.2~O::l:.l~O.1:-4~O.1:-6 .LO::l:.8,1,1~.O"---~2,::-O"""""3.1:-0""4~.O--'6~.O...J..-}.,8.0,...L"""10.0BACKUP RATIO

016 IN.o BIN. PilCH DIAMETER0, -tIN,

below 2: I. The conventional AGMA equations Fig. 1.0• Effect ,ofbackup ratio on find alternat.ing stress.show no such effect. It is also interesting to notethat the measured stresses remain reasonablyconstant as the backup ratio increases above 2: 1.

Another parameter which is of interest is thealternating stress that occurs when the gear issubjected to a fully reversed load, as is the easefor an idler gear. As expected. the alternatingstress level is substantiallyhigher than for eitherthe root or fillet location when subjected tounidirectional loading, For a given allowablestress level, the load capacity is thu lower whena gear is used as an idler, This fact is by no meansa tartling revelation. Most designers incorpo-rate a reduction factor when calculating idlergear load capacities. AGMA standards recom-mend that the allowable stress be reduced to 7'0%of its unidirectional value for bidirectional load-ing. Actually the allowable stre does notchange; rather, the magnitude of the alternatingsire s changes. Thus, applying the correction tothe allowable index stress in accordance with theAGMA standards is a convenience rather than afactor. In order to define the actual reduction tobe expected. we have plotted the ratio of rootalternating stress to the fully rever ed alternat-ing stress in Fig. 13..

Based on these data, it appears that the 70%suggested by the AGMA c tandards is a bitoptimistic for smaU diameters. but is certainlyreasonable overall.

We have clearly established the fact that themeasured stresses are quite different from thecalculated stresses, The calculated stresses are,however, stress indexes rather than exact stresslevels. The difference between calculated andmea ured would then be much less significant ifa can rant relationsbipexisted between the two ..It hould be obvious that thisis not the case,since we have already demonstrated that themeasured stresses vary substantially with back-up ratio. while the calculated stresses do not.

Plots of test data clearly indicate that a COD-

(;5 1.0>

the center section can act as a concentrationpoint for root stresses, further aggravating abad situation.

Resonant ResponseGear resonance is one of the most insidious

and destructive of all gear failure modes .. Itgenerally occurs quite suddenly and with cata-strophic results ..Since a gear often fails by theseparation of large fragments from the blank. thedamage is u ually extensive. e pecially whenhigh rotational speeds are involved,

The prevention of this type of failure is rela-tively simple once resonance has been identifiedas the causative factor. Either of two approaches

OIGIN.o 61N. PITCH DIAMETERI.l 41N.

:I\~-AGMA REDUCTIONFACTOR =70%

u OJ..,2--=O:l::-.3-'0.i:-4-L-=0~.6..1...::l0.~S"-:l.1:.D--......,;~L;;-.O-..:3.'lr0 -74.7I"-..oI..-I'6.:r'0'-::I:8.0~mo

B.ACKUP FlATIO

Fig. n - Effect of fuUy rev,ersed bending (idler gear) 00 root stresses.

BACKUP RATIO = RIM THICKNESSTOOTH HEIGHT

3.0

2.0

2.B

2.4

I RIM 2.2THICKNESS 2.0 _

I FACTOR Ke 1.8

1.6 '

1.4 I

1.211.0

o.o "--'-"'-.!----'--"'--":-----0.3 D.4 0.6 0.8 1.0 2.0 3.0 4.0

BACKUP RATIO

0, PHOTOELASTIC TEST DATA

• FEM ANALYSIS OATE

Fig. ~4 • Proposed rim thickness factor.

ALTERNATING STRESS AT 7.050 RPM ±3.800 PSI

ONE REVOLUTION OF GEAR

Fig. IS -Increase in alternating stress reseltlng from speed change to'excite resonant response,

22 G:EIIR TECHNOLOGY

may be taken: The gear can be redesigned so thatits natural frequencies do not coincide with anyoperational excitation condition; or the blankcan be damped so that even if excited at itsnatural frequency, the response of the gear issmall enough to preclude failure.

Resonance phenomena in gears, while notwidely treated in the literature. can be of con-siderable consequence in the design of high-speed, lightweight gearing. Should the blankbe excited at a frequency sufficiently close toone of its resonant frequencies, deflectionsand, hence, stresses can increase to levelswhere failure can occur within a relativelyshort time. Fig, 15 shows the increase .instressresulting from operation near a resonant fre-quency. Stress plots were obtained fromtelemetered strain-gage readings during dynamictransmission tests. Strain gages were located 00the flange of a. spiral bevel gear. It is interestingto note t.hat although the torque remained COIl-stant, a change in shaft. speed of less than 9%resulted in an increase in stress level of over73%. In this example. a further increase in speedof about the same magnitude would cause thestress level to fall again to the 3,800 psi range.The narrow speed band sensitivity is character-istic of gear resonance problems,

The origin of resonant failure is at or near theoutermost part of the blank in the gear tooth root,where the combined tooth-bending and blankresonance stresses are maximum. The crackprogresses through the blank as shown.in Fig. 16and returns to the gear outer diameter, thusremoving a wedge-shaped fragment from theblank, Gears which suffer this failure mode areusually, but not always, operating at high rota-tional speed; thus the high-energy fragmentcauses considerable damage. as Fig. 16 demon-strates. Because of the catastrophic nature of the

FATIGUE. ORIGIN

Fig. 16 - Typi.ca~resonanee failuer ..

failures associated with this phenomenon, it. ispossible that it will not be recognized as thecausa] agent, and a general beefing-up of allparts involved is undertaken as a fix for theproblem. In many cases, this will. solve theproblem, since the resonantfrequencies will alsobe altered; however. the resulting design is usu-ally heavier and more costly dian necessary. Hadthe resonant problem been recognized and dealtwith, the final configuration would have beenmore cost- and weight-effective.

Mode Shapes - WIlen a body is excited at itsnatura] frequency ..the body win assume an os-cillating deformed shape called a mode shape,For a body of revolution these mode shapes canbe generally classified by the number of nodaldiameters (diameters exhibiting zero displace-ment) occurring during the vibration deforma-tion cycle. The number of nodal diameters con-tained in a mode shape is referred to as theharmonic index of the mode. Classification ofmodes by their characteristic harmonic index ishelpful, not only as an aid in visualizing the modenape, ,bultalso in the del:erminati.on of excirarion

frequencies. In theory. 111 body of revolution iscapable of an infinite number of mode hapes foreach value of harmon icindex. These mode shapesare all unique and occur at unique characteristicnatural frequencies. The mode shapes consist. ofvarious combinations of circumferential or ringnodes, i..e., circumferential rings of zero dis-placement. Fig .. 17A is a sketch of the defonnedmode shape of a thin-walled cylinder (solid line)superimposed on the undeformed shape of thecylinder, This particular mode has a harmonicindex of 2. as evidenced by the number of nodaldiameters. Note the circumferential ring nodeoccurring at section B-8. Fig. 17B shows thecylinder again responding in aharmonic index =2 mode, but. at a higher frequency and with ringnodes at sections E-E and G-G.

Speed/Frequency {Campbell} Diagrams - h isimportant to note that the mode shapes shown inFig. 17 represent the displacements at an instantin time: at 112 cycle or 112m seconds later, the

n

displacements of the structure will be the negative(with respect. to the undeformed shape) of thedisplacements shown ..With this in mind, ircan beseen that for a. stationary (nonrotating) ciecalardisk or cylinder, a rotating, steady (non-oscillat-ing) force wiU induce constructive reinforcementof the displacement waves at a rotation speed of

N=± miD (l)By a simple change of reference system it

can be seen that this is also the case for a rotatingcircular structure subjected to a force stationary inspace. This relationship is valid for values ofharmonic index D ~ I, 2, 3... For the case of D =0, no nodal diameters (purely axisymmetricalmode shape), this criterion does not apply, sincea.nonoscillating rotating force will not excite thistype of displacement mode shape. The excitationforce for geartooth meshing forces are not steady.but oscillate with respect to a reference systemfixed to the rotating gear. The frequency of oseil-lation of the mesh forces and their harmonics is

(2)for k = 1. 2. 3 ....Hence, the criterion to produceconstructive reinforcement. of a displacementmode shape by a rotating, oscillatory, excitingforce is

m = knN ± DN = (kn ± D)Nn

A convenient method of displaying the rela-(3)

A ,...8 r-C

f;:,

-~,1--'

CA B

SECTION A·A SECTION B·B SECTION c-c

~Q~~ - NODAL NODALDIAMETERS CIRCUMFERENCE. DIAMETERS

ANATURAL FREQUENCY - 545 HZ

- -- - UNDEFORMED SHAPE

--- DEFORMED SHAPE

SECTION e-o SECTIONi E·E SECTION F·F

~QI?NODAL NODAL ~

DIAMETERS CIRCUMFERENCE DIAMETERS

S~.G

~CIRCUMFERENCE

~H

~DIAMETERS

BNATURAL FREQUENCY~. 6.840 HZ

Fig..l' - Sketeh of two mode shapes of harmonic index =.2 for hollow cylinder.

J Po N U A R Y I FEB H u A R Y 1 9 92 .23

iN, N2 N]GEAiR ROTATIONAL SPEED, N· HEVOWTIONS/SECOND -----7»

OJ = (kn ±Ol N

!O = [kn . D) N

i ([)= NATURALFREUUENCY OF MODEWITH HARMONICINDEX = 0

FOR 0 = 0, GEAR EXCITEOAT SPEED N2

FOR 0", D. GEAR EXCITEDAT SPEEDS NI AND N,

'IGEAR II

NATURAL IFREQUENCY, CO

- HEATZ

Fig. 18- Typical speed/rrequency (Campbell) diagram.tionship between gear natural frequencies andtransmission system excitations is with a fie-quency-versus-speed d:iagram. Excited frequen-cies are plotted on the vertical! axis and rotationalspeed is plotted on the horizontal axis as shown inFig. 18. Such charts are frequently referred to asCampbell. diagram .

Natural frequencies from bench test or analy-sis are plotted a horizontal lines. The lines (l) :::

n(kn ± D)N are then plotted for the values of Dcorresponding to the mode shapes of the naturalfrequencies under consideration. The points wherethe horizontal ro lines intersect the ro "" (kn ±D nD)N lines indicate the speeds at which the gearresonance w:iIl be excited. Should these speedsOCCUrwithin the operating speed range, a poten-tial gear vibration problem will exist Resonantconditions can also beexcited by harmonics of tiletooth mesh frequency; therefore, n = (kn ± D)Nshould be plotted for several of the lowest valuesof k, In addition, otherpotential sources ofexcita-tion must be considered. One which is of particu-lar irnpcrtance in the design of epicyclic gearsystems is the planet passage frequency. Notethat for modes witli a harmonic index of I orgreater, resonance conditions are excited at twospeeds for each tooth mesh harmonic. The caseof a harmonic index :::0 mode is excited only atthe basic tooth mesh frequency and its harmon-ics. In aU cases the frequencies at which the gearvibrates are its natural frequencies with respecttoa reference frame fixed to the rotating gear.It should be noted that the apparent stiffness ofthe rotating gear can be slightly altered bycentrifugal effects, thereby causing n to be afunction of rotational speed. If this function

,2'4 G.EAR TECHNOLOGY

can be determined either by test or analysis,the foregoing is still applicable. In this casethe 0), horizontal lines would become 0) ""n nf(N) curves, and the intersection points wouldbe determined as described previously. Forgear sizes and speeds typically encountered invehicle power gearing, these centrifugal effectshave been found to be negligible.

Evaluation of Resonance BelUlvior - The prob-lem of evaluating the resonance behavior of aspecific gear may be approached in many ways,however, these methods can be broadly classed aseither experimental or analytical. Experimentaltechniques provide very accurate data regardingresponse frequencies and mode shapes; however,actual hardware (or at least prototype gears) isrequired. This limits the correction of any prob-lem areas identified to either redesign or add-ens.The use of analytical! techniques, on the otherhand, allows these problems to be addressed andcorrected in the design stage. The basic datasought by either method are the response (reso-nant) frequencies, the mode shapes, and the levelof response; i.e., the stresses induced by operatingat a resonant frequency ..Both methods can pro-vide the first two pieces of the puzzle, frequencyand mode shape; however, the level of responsecan usually be obtained only thorough the use ofsophisticated strain-gage instrumentation du.ringan actual operational transmission run. Someprogress is being made in the ana.lytical definitionof response level Although. it would seem thatanalytical tech_niques are preferable in alII cases,advantages and disadvantages to both methodswill become clear as we proceed thorough thenext two sections. One of the biggest unknownfactors is the amount. of damping that occursbecause of bolted joints, supports, and the like.

Experimental Methods - There are manymethods forexperimentally defining the resonantfrequencies and mode shapes of gears ..The spe-cific method which should be used ill any par-ticular case is a function of component size,mass, ami the dollars available for test.

In order to evaluate the response of a part, anexcitation source and some means of detectingthe response and defining the mode shape mustbe provided.

The testing is generally conducted as follows:The gear is mounted in such a way that it :isisolated from its surroundings (eJastomeric pads,canis, etc.) and excited witha variable-frequency

II

source. A weep through the frequency range ofinterest is performed while the gear response ismonitored. Frequencies which produce substan-tial responses are noted. After the frequencysweep is completed, the gear is again excited ateach of the noted frequencies while the gear issearched or probed to define the mode shape.

The determination of frequencies to be search-ed can be enhanced by performing a simplebang test if frequencies have been calculatedpreviously by some analytical method, or shoulda frequency spectrum analyzer be available.Fig. 19 shows a typical spectrum-analyzer os-cillograph from gear bang testing. Note thenumber of frequencies which display high rela-tive response; these frequencies repre ent theexcitation frequencies near which gear reso-nant problems may occur. Note also the largenumber of resonant frequencies. A bang testconsists imply of hitting the gear once andevaluating the resulting response with the aidof a spectrum analyzer, A gear thus excited willring down at all its natural frequencies; with aspectrum analyzer,these frequencies can beseparated and identified,

This experimental technique actually deter-mines the free-vibration characteristics of thegear; however, the natural frequency of freevibration has been an excellent indicator of theinstalled and operating re onant frequencies ofthe gear and shaft. Fig. 20 is a Campbell diagramshowing the free-vibration resonant frequenciesof an integral spiral bevel gear and shaft, asdetermined from air siren testing vel' U shaftspeed. Also plotted on this diagram are thefrequencies at which increased response wasnoted for the component installedand operatingunder design loadings. These operating datawere obtained from telernetered train-gagereadings recorded during a transmission dy-namic strain survey. Note that the forced-re-sponse frequencies of the operating gear andshaft agree closely with the free-vibration natu-ral frequencies determined in siren tests.

The four main variables to be addressed in anexperimental investigation of the resonant re-sponse ofa gear (or any other part) are themethod of excitation, the method of detectingwhen a resonant condition has beenencoun-tered, the method of identifying the mode shapeof a particular response, and the stress levelassociated with a particular response. With the

1.0

0.9

w O.Benz 0.70"- 0.6en....a::LU 0,5::-t= 0.4Sw 0.3a::

0.2

0.1

(1

a z 4 6 8 10 12 14 16 1;8 2lIFREilUENCY· KHZ

Fig .. 1'9'• Typical plot of relative response amplitude versus fl',equencyfrom gear bang test.

TWO TIMESTOOTH MESH FREOUENCY

~ G~ro~M~z 6 }~EXCITATlON FREQUENCY~ 5 i _,--:>,30 3D= HARMONIC NO.3til f-".........=~'---....,....~"---y. 40 = HARMONIC NO.4

RP~ SWEE'P1RANGE 50" HA'RMONIC NO,. 5

;IMEAs,uRED RESONANCEOi~IOi:-:!;20:-:3II;\;--:40~50:-6II*""7~D -:'8IIi:-;!::90~I~OO;-lll 0

SHAFT RPM· PERCENT(100% = 8,000 RPMI

Fig. 20- Campbell diagram showing siren test and '0:11 rating rcsonaJl.tfrequency response.

II OSCI LLOSCOPE

FREQUENCV COUNTER

CY COUNTER,I

Fi!g. 21 - Electrom.agnetic exettatlon with detection by microphoneand oscilloscope.

J"NUARY/FEBRUARYI 992 2.'5

26 G EAR TEe H N 0 LOG V

exception of the stre s level, each parametermay be addre ed separately since, ill theory atleast. any excitation method can be used withany combination of detection and identificationtechniques, However, considerations of experi-mental setup and procedure will limit the combi-nations which are practical. Complete deserip-tions of the variou techniques can be found inRef. 6. An excitation source, such as the electro-magnetic setup shown in Fig. 2] or the air sirenshown in Fig. 22, is the first piece of equipmentrequired. A means of detecting the existence ofa resonant frequency, such as the micrcphoneshown in Fig. 21. or the accelerometer shown inFig. 22, is 3180 required. Finally. the mode shapeitself must be defined through the use of sand orglitter patterns (Fig. 23), holography, or by hand-probing with a microaccelerometer (Fig. 24).

If a strong excitation source is used. hand-probing (Fig. 24) with a microaccelerometer canidentify nodes and antinodes and, tbus, modeshapes. This technique does require some opera-

Fig, 22 - Air siren ,excitation source.

Fig. 23 - Modle sbape detectlon on a nat spiralbevel gear (17,939' Hertz).

Fig. 24 - Technician probing manually for modeshapes.

tor skill and practice on simple shapes. It can bevery useful. in tile evaluation of complex modeson complex gears.

Analytical Methods - The high costs associatedwith the reclesign of complex gears to improvetheir dynamic characteristics after initial proto-type fabrication and testing make necessary accu-rate analytical techniques with which to predictresonance. This would allow the design engineerto predict the dynamic characteristics of a particu-lar gear design while it is still on the drawingboard, thus enabling any changes to be incorpo-rated before fabrication and test

Because of geometrical complexity and thegenerality of configuration, the finite-elementmet.hod (FEM) was chosen as the most suitableanalytical technique. Recent experience usingseveral general-purpose FEM computer pro-grams and modeling techniques indicates thatexcellent correlation with experimental datafrom prototype resonant testing is possible. Themost efficient of these techniques has been anaxisymmetrical modeling approach. This methodassumes the gear to be symmetrical about itsrotational centerline and, hence, requires that. onlya single cross section be modeled.

The model definition required for sufficient-lyaccurate results (that is, within about 5· 10% over-all) is quite coarse relative to that required for toothor blank stress analysis. The teeth themselves, fm'example. are not modeled as separate entities;rather, only their mass is simulated. This is doneby increasing the root diameter to the midtoothdiameter and then modeling the gear teeth as asolid ring of this thickness; in most cases thismodeling system yleldsexcellentresults. Formanylowermode (which are the rno t important any-way) the accuracy is far better than that at highermodes; in mo t cases the error i less than 5%.

Some of the difference between bench anddynamic rig test results :may be because of cen-trifugal stiffening of the blank at normal operat-ing speed. However, when we consider the goodoverall correlations obtained at low to moderatespeeds, this effect can be con idered negligible.This may not be the case for very high-speed,large-diameter gears.

Most programs include the ability to produce aplot of each mode shape. which can be quitehelpful in determining which areas of the gearrequire modification to obtail!l the desired dy-namic characteristics. One such plot is shown in

Fig, 25, Each mode shape has an. associated har-monic index. This index represents the integernumber of nodal diameters characteristic of thenodal displacement shape of the gear. Fig. 25 alsoshows an axial view of the deformation of theintegral. spiral bevel gear shaft, indicating that theharmonic index of this mode is 3, The analyticallypredicted and mea ured re onant frequencies arealso compared. The correlation in thi.s particularcae is exceptionally good; in general, the pre-dicted values for the lower frequencies do notdiffer more than 5% from the measured siren testfrequencies.Modifying Resonance Behavior- Once thereso-

nant frequencie have been determined. it must beascertained whether the frequencies lie in theoperating excitation range. If resonances do occurin the operatingfrequency range, the design engi-neer is faced with a decision: He may eithermodify the design (change mass and/or tiffnessof the gear), or he may provide some form ofdamping to decrease the response of the gear nearthe resonant frequency.

Both approaches have inherent advantagesand disadvantage . A careful evaluation of thealternatives is required in order to decide whichmethod is applicable to any given situation.

Detuning - Modifying the geometry of thegear in an effort to change its mass and/or stiffnesscharacteristics is frequently referred to as detuning.The ideal approach is to design all gears so thattheirnaturaI frequencie are far from any potentialexcitation sources, especially gear mesh and itsmultiples.

Although this approach is not practical in allcases, .itcan be eminently successful, particularlyif the blank is relatively simple and the Campbelld:iagram is uncluttered; ueh a case i shown inFig. 26. The gear mesh frequency at overspeed(3,682 Hertz) is quite close to a narural frequency(3,764 Hertz). Adding material as shown increasedthis natural frequency beyond the overspeed exci-tation frequency. In this instance the next lowerfrequency did not increa e enough to bring il intoproximity with either the idle or 100%- peed exci-tation sources. In ca e such as tills, plots of themode shape we an invaluable aid in determiningwhere and how the gear must be modified.

Since each problem is unique, no hard-ami-fastguidelines can be given on the methods to be usedin accomplishing such modification, but it i .gener-ally best to make changes which increase stiffness

and, thus, raise the natural frequencies, rather thanto add mass alone. such as adding lump to the gearbore. This method has been shown to be the mostweight-effective for lightweight gearing.

This discussion is aimed at small perturbationsof a basically fixed design. If an analysis is per-formed early enough in the design cycle, it may bepossible to make a major change which will. effec-tively improve the situation.

Damping - If detuning is no! practical or notsuccessful, damping is a viable alternative. Damp-ing causes the amplitude of and, hence. stressresponse to the excitation forces to be reduced inthe installed and operating forced - response envi-ronment lfthe proper amount and type of dampingare applied at the appropriate places on the gearblank, thisapproach is almost always successful.There are many ways in which damping can beintroduced into the blank.In addition, the construc-tion of the gear itself may contribute 10 its dampingcharacteristics. If it i manufactured as a separatepart and is bolted, keyed, or splined to its shaft, thejoint will provide a small amount of dampingthrough the rubbing action (Coulomb damping)which is inevitable at such joints. Unfortunately,this motion, which is beneficial in adamping sense,can be very detrimental over the long tenn, since itmay give ri e to fretting. Frettedjoint can be thesource of cracks in either gear or shaft which leadultimately to structural failure. An integral shaftand gear design eliminates both the damping and

-_ .. UNOEFORMED OUTLINE

DEFO.. R.MED O...UTt.INE,. ;W.:. -.-- "'-[MODE SHAPEJ I. !NODAL DIAMETERS -. ,/HARMONICINOEX=3 ......-.,/

AXIAL VIEW

CENTER LINESIREN TEST FREQUENCY 7,294 HZPREDICTED FREQUENCY 7,180 ~2

-114 . = 1.56%Fig. 25 - Predicted. gea.r resonant freq,uendes.

ORIGINAL DESIGN MODIFIED DESIGN

~DE~

MATERIAL ADDED

~~HARMON1C NUMBER 2MODE 1FREQUENCY 3,164 HZBASELINE WEIGHT 30.5 POUNDS

HARMONIC NUMBERMODEFREOUENCVA.556 HZMODIFIED DESIGN WEIGHT 32.S POUNDS

Fig ..26 - Com pari on of original and modified. spiral bevel gear designs;modificationimpro\led resonant frequency chaeacterlstlcs,

J A (oj U A R Y I FEB ~ U A R Y 1 9 9 2 ,21'

SPONGVITON

Fig ...27- Hollow gear shafts rUled with elastomerand plugged.

• .-VISCOELASTICMATERIAL

STEEL STRAP

Fig ..28 - Thin elastomeric coating on gear webwith steel constraint.

BALANCESLOTS

REMOVALSLOTSIHOLES

C·SHAPEDHELICAL

Fig. 29 - Types of damping rings.fretting conditions and is preferable. since frettingc-anbe a major problem. and there are other lesssevere and more effective methods of applyingdamping. Two of the simplest methods are coat-ings and rings.

Coaril1~s - Coatings can be applied to 11OnfUllC-tional surfaces of the gear blank to reduce thevibration level. Both hard and soft coatings havebeen used with varying degrees of success. Softcoatings, such as bonded layers of an elastomer.have been used in a number of applications. Be-cause they are exposed to the hot oil environment.they generally must be either trapped as shown inFig. 27 or constrained as shown in Fig. 28. Theeffectiveness of either method depends upon main-taining the bond between the elastomer and the gearblank ..Other methods of coating. such as plasma-

28 GEld! TECHNOLOGY

spray coating orelectrechemically plating relativelyheavy metals like molybdenum or copper com-pounds on the appropriate surfaces, are more perma-nent and less likely 10 separate from the gear.

Any of these methods will work, particularly ifthe response is not overly energetic, and if the geardesign incorporates large, flat web areas; however,our testing has shown that whilethe noise level isreduced in many cases, the damping provided Isnot sufficient to reduce the vibratory stresses toacceptable leve.ls.1I

Rings - Damping rings are a much more effecti vemethod of providing damping. Solid, C-shapcd •and helical rings (Fig. 29) have been used success-fully. Solid rings are inserted into an internalgroove machined under the gear rim by heatingthe gear and cooling the ring. Helical rings, whichare actually modified common retaining rings, areturned into a similar groove in the gear rim. Bothdissipate energy through a mechanism which isbelieved to be largely Coulomb friction at thesides and, especially, the bottom of the groove.The helical rings provide considerably moredamping (about 2.5 times more, according toRef. 8) than.solid rings, and both provide an order-Of-magnitude more damping than most coatings.though they are generally not aseffecti ve inreducing noise as some coatings appear to be. Thesolid rings have less retention surface (limited bythe amount of gear expansion and ring contrac-tion at installation); Ilms, they are more likely tofall out of their grooves and cease their dampingfunction because of wear than are helical rings,which typically have relatively deep retentiongrooves. In addition, the force exerted on thegroove by a solid ring does not increase apprecia-bly with rpm because of centhfugat fo:rci(Cf).Since helical rings are not closed loops. they lendto unwind with increasing CF and exert greaterforce and thus, greater damping on the ring groove.In a simil'ar manner, the damping effectiveness ofhelical or C-shaped rings is not affected by wear,since CF will keep opening the ring so that contactis maintained with the groove. After solid ringswear, CF onlycontributes to increased ring stressand does not maintain contact pressure with thegroove; thus, damping effectiveness may decreasesubstantially. In order to yield maximum effec-tiveness, the proper amount of ring weight mustbe provided. The results of extensive dynamicstrain survey testing have been analyzed in aneffort to determine the ring weight required in the

general case. Sa ed on thi information, the fol-lowing empirical relation between ring weight andgear weight has been developed;9

Wn = 0.06WGO.75Q (4)

Equation 4 has been shown '10 work well forlightweight aiIcratt-type gears in the size range of6" to 33" pitch diameter and at pitch line velocitiesup to approximately 281000 fpm.

The importance of the proper choice of ringweight and placement can. be seen in F.ig. 30. Thefmal. stress level has been reduced by 50%, eventhough the transmitted torque increased by morethan 80%.

One of the mo t significant problems associatedwith damping rings is the wear that occur, both onthe ring and its groove. Although the groove wearalone is almost never evere enough to cause thegear to fail, slivers which can cause indications onchip detectors. indicating screens, and other debnmonitors can be generated. In addition the ringwears excessively when it cro section ire-duced, and the possibility of its faHure ari es. Theseproblems CaDl be reduced by hardening the groove.and using mukrple-wrap rings. The wearappears tobe caused more by the ring beingforced to rotate inits groove by the gear-load-induced deflectionsunder the mesh point than by its vibration in thegroove because of it re pon e to gear naturalfrequencie . It seems likely that the wear problemcould be reduced by decreasing these deflections.

The addition of damping ring Dr coatings doenot change the natural frequencies of the gear toany measurable extent; this has been verified byelectromagnetic and air siren te ling as well as full-scale transmission testing.

Cl:langi!lg Excitation Frequency - Our discussionthus far has been limited to modification of theresponse of a.gear to a given excitation source. It isalso possiblein some case to change the excita-tion frequency. This can be done in everal way.The easiest but usually the least practical methodwould be imply to alter the ystem speed so thatit does not. coincide with .any of the natural gearfrequeucie . Relatively large changes in excita-tion frequency can al 0. be made by changing thediametralpitch (module) or the gear set to increaseor decrease the number of teeth .thu changing theme: 11 frequency without changing han peed.Any change inpitch: hould be carefully evaluatedin. order to insure that the bending-fatigue capacityofthe gear set is not compromised. Several de igntechniques have been propo ed to employ gearing

-- ~19L9

GAG~( '0

ORIGINALCONFIGURATION

~L 1ft"GAGE GAGE,INTERMEDIATE FINAL

CONFIGURATION CONFIGURATION

-L"-t"W AlTsmss"ONE P . ~25.000 PSIf- REV-I'

'GAGE WAVEFDRMl60%TORQUE AT 8,000 RPM

--L~P'" All STRESSONEPER ~PSI

I- REV -IGAG,E WAVEFORM '60%TORQUE AT 8,000 RPM

\,#>-- - III 10NEP,ER I All STRESS.I-- REV -I:t 12.1lOD PSI

GAGE WAVEFORM110% TORQUE ATII.DOO RPM

Fig. 30 • Reduction Df transmission bevel gear response thrDugh in-creased da.mpi.ng.

with either more or fewerieeth than would ordi-narily be used on agiven sized gear.

Other alternatives, which would require rede-sign, are to alterthe number of planets in allepicyclic system or Itochange the relative ratiosused in each stage of a mulnpa system,

Condus~onsThree areas of significant concern to the deign.

ers of spiral bevel gearing have been identified andeli cussed. Each area is outside the normal designprocedures for such gears, but can be very impor-tant in the overall success of specific designs.

General de ign guidelines have been pre-sentedand references for further and more detailedstudies have been provided .•

References:I.DRAGO. R_YMOND J. "On th~ Design and Manufacture ofIntegral Spiral Bevel Gears for the CH-4iD Helicopter." Aero-space Gearing Committee Meeting, AGMA. March, 1978.2. DRAGO, RJ. and PIZZIGATI. a.A.·'Some Progress in theAccurate Evaluation of Tooth Root and Fillet Stresses in Light-weight ..Thin-Rimmed Gears." Paper 1':129.21. GMA ..October.1980.3. DRAGO, RJ. ami lUTTH'A S. R.V. "An ExperimentalInvestigation or [be Combined Effects of Rim Thickne,q andPilch Diameter on Spur Gear Tooth Root and FiUet Sin: se ."Paper P229.22. fall Technical Meeting. AGMA. October. 1981.4. DRAGO. R.I. "00 the Automatic Genemrlen off EM Modelsfor Comp