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January/February 2000 Gear Technology

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  • ISpur and helical gear productionhas never been in better shapeGleason Pfauter's new GP BOS CNC GearShaping Machine gives you '[he next-generationtechnology you need to take valuable time andcost out of the production of internal andexternal purand helical gears.

    Bul: that's not. ,aU. You'lI also benefitfrom the GP Series' revolutionary"common platform. modular-de ign"approach. which reduces co t, shortensdelivery leadtirnes, and promi es afaster Return on Investment.

    BoU.omline? No other machine in its,cia s delivers 0 much, so fast, for solittle. For example:

    II's equipped with a standard thermalcompensation system that automaticallyadj u ts pari, size in response to machinethermal changes.

    Its unique cast machine frame is designedwith highangle slopes for highly efficient

    chip removal,

    An axial slide provide automatic strokeposition adjustment.

    The workspindle is equipped with adirect-drive CNC servo-splndle motor .

    1The optional tail tock is motorized,eliminating the limit switch setuprequired with hydraulic cylinders .

    1 Gear tools to ujt any applicationrequirement are available from GleasonPfauter HIJI'IhCutling Tools.

    Advanced FEA d sign toolsIWefe used to nelp optimize'

    weighl and strength.

    _ U_ ,_tIBooth ',5742,

    w~-~~C"DD

    For more inrormation, contact:

    1000 University Ave., P.O. Box 22970Rochester, NY 14607-]282 U.S.A.

    Phone: 716/473-1000 Fax: 7~'6/461-4348Web site: www.gleaon.com.E-Mail: sales@gleason ..com

    http://www.gleaon.com

  • THEtATSTINNOVATIONIN HOSSING.SUPERIORQUAUn; SE.RVlCE.AND DE.lIVER)':

  • The'Journal of Gear ManufacturingJANUARV/FEBRUARY 2000

    FEATURESllow Vibration Design ,on a H!elital Gea,r Pai'r'A discussion of tooth modification and shaft deflectionand their effects on vibral:ion 18:

    IMillennium Outloo'kGear manufacturing's past, present, and future 26,Gear Expo follow-up , , , 3~

    31Reverse Engineering ,of Pure Iinvolute, CylindricalGears Using Conventional Measuremen1 Tools,U ing mea urement over wires andspan measurement to determine geometry 32

    Management Matters: Shop, Floor SafetyWhat you need to know about maki,ng your gear hop safe l~

    Software BiltsOur peeial edition of product. news devoted to gear software 43

    DEPARTMENTS

    Publ,isher~s, P'ag;e'Tile Bigger Picture 1'

    Rev,o~lutionsRainbow Coating. lndexabl Carbide In ert Hob anda Survey 011 Machinist Training, '11'1

    11 Technicall Ca'ienda'rMake plans now for these upcoming events 16

    Advertiser IndexTry Rapid Reader Response for nearly In milt info:nnation 11'

    Industry NewsWhafs new in the gear industry? 48:

    lruiteratule !MartFree brochures and catalogs from our advertisers , 501

    Produc1 N'ewsNew tools for gear manufacnirers , 52

    Coll.',lrtcaurtlQ'II'R'8~carGear 1& _lcblDe.Rockford. IL

    IClassiliedsServices. Help Wanted and mOI1e ,. 54,

    AddendumThe Saginaw Gears " ,..56,

  • CIRCtE 173,4 GEAR TECHNOLOGY

    GEAR TEC8NJ!~flQtEDITORiAl

    Publisher & Editor-in-ChiefMichael Goldstein

    Managing Editor William R. Ston

    Senior Editor Charles M. Cooper

    'Ieehnlcal EditorsRobert Errichello

    Don McvinieRobert E. SmilhDan Thurman

    ARTAFt Director Jean Bartz

    ADVERTISINGAdvertising Man.ager Patricia Flam

    Advertising Coordlnator Susan Brandt

    CIRCULATiIONI Circulation Coordinator Jennifer Beale

    IiINTERNET

    Enternet Editor Daniel Gonsiorowski

    Gear Industry Home P,age SalesPatricia. Flam

    RANDALIL PUBUSIHING STAffPresident Michael Goldstein

    Vil;e President Richard GoldsteinController Patrick Nash

    Accounting Laura Manionrt Consultant Marsha Goldstein

    Phone: 847-437-6604E-mail: [email protected]

    Web: www.geartechnology.comwww.powertransmission.com

    BPA~T-.

    WVOL. 17. NO.1

    'GEAR TEUIiNOLOGY, Tho J",rr ".I Qr GearM.nur.JI" Avenue, P.O.Box 1426. Elk. Greve Village.IL 60007. (847) 437-6604.Cov... price $5.00 U.S. Periodical postage paid atArlinglml Heights, ,IL. and ai, additional mailing effice.Randall Publishing makes every effort to ensure thut theP"""'''''' described in GEAR TECHNOLOGY conloem10 round engIDcenng pracrtce. Netrber 1he smh:orJ, nor thepublisher an be held responsible for injuries l=:Elilulinedwhile foUowing the procedures described, PosrmasterrSend address changes 10 GEAR TECHNOLOGY. TheJoomal of Gear MonllfBduri'l\, 1425 LUIlt Avenue. P.O.B". 14Z6,EI~ D,u" Village. IL. 60007. ec""tomL' c"PY-nglued by RAND ....LL PUBLISHING. !Nc.. 1'l1l'i Nopart or this publication may be reproduced or transmiuedin any Iorm or by any means. electronic or mechanical,inclw:ting photocopying, recording. or by '"'~ inFormntiOlllilur..igc lind ~eYIll sYh;ltm. 'id,-U.l'lDUl pernlJssiun In writ-ing from Lh;e [lubUF.her. Cornems of Bd~ are suhjfX'1 toPublisher's approval.

    mailto:[email protected]://www.geartechnology.comhttp://www.powertransmission.com

  • CIRClIl: 186

  • SAM 'UTENS!IILI RI1370 Form Gnnding' Unlimited Forms High Quality and Finish No Helix Angle Limitation Prototype or Large Lot Sizes

    FlexibilityBxtemal GearsInternal GearsRotorsWormsScrews

    integrated dressing systems for ceramic01' dressable CBN wheels for unlimitedwheel profiling

    Integrated inspection system for leadinllO/ute and index checkingduring the work cycle

    SU AMERICA INC.8775 ICapital1 AvenueOak Park, MI 48237PII.: ,(248) 548-7177Fax: (248) 548-4443E-Mall: [email protected]:SAMPUTEN5IU

    Ifred YoulngPresident ofForest City Gear

    FOREST ,CITY GEAR

    RO. Box 8011 71 5 Main Street,Roscoe, It 61 ,073-,0080Ph.: f815) 623-2168Fax: ,{BI 5J 623-662,0E~Mail.:www.fcgeal..com

    CIRCLE 138

    mailto:[email protected]://www.fcgeal..com

  • ------- --------------

    PUB'LISHER,'S PAGE -- __ ruMIL~LE;MNNUUJmMruDllUUTlIJJLIDlY]OH~-.

    --------.....,.ICTURElleamed much of what I know about tho! machine tool busi-

    ness from my father, who learned it from h.s father before him.One of the lessons he taught wasthat no matter how important thedetails seem, it's equally important to look at the bigger picture.

    For example, before Winspected a machine, I would study thecatalogs and make lists of all the features and sizes that. load to

    check. My father would tell me that after completmg my check-list, I should step back from the machine, walk around it. awayfrom the details, and see it as a whole, He aid forcing yourself to

    look froma biggerperspective often lets you see what you wouLd

    otherwise mi s.Very often, he was right, Once, when I in pected a cylin-

    drical. grinder, I forgot this le on. Somehow, I overlooked thefact that the machine was built special, without a reciprocating

    table-the bed and the table were one piece. I had covered all

    the details but overlooked what some might say was obvious.

    Sometimes the obvious is the hardest thing to see. Today Ireal-ize thai using a bigger perspective allows me to see problemsand opportunities I wasn't expecting 10 find or didn't. think to

    look for.m was reminded of my father' wisdom at this year's Gear

    Expo. As many of you know, Gear Expo i~the worldwide gearindustry's premier event. and it has grown with each incarnation.There were far more exhibitors al. this how than we've ever seenbefore. This means more money for the AGIVIA, which translates

    into' more and better services for the industry as a whole.But while the number of exhibitors has grown, the number

    of visitors dropped dramatically this year. Most people view theshow as a machine tooL show-a place to see, compare and buy

    gear manufacturing equipment. Wben Iwas down on the showfloor, walking througb the aisles, thi is how .I saw it, too. Butthen I tried a different perspective.

    The Nashville Convention Center. where Gear Expo washeidi, ha a viewing area above the show thor. From there, youcan ee the entire show. While I was up there, it struck me thatthis was much more than a machine tool stow. The full view ofGear Expo revealed to me the entire gear industry, all in oneplace. I realized that for four days, we had access to the finestgathering of gear talent anywhere in the world. From my perchabove the show, I saw gear manufacturers. materials suppliers,software vendors, consultants and cutting tool manufacturer,

    all of them valuable busines contact with knowledge about

    gears. Of course, the machine tool manufacturers were there aswell, not just with salespeople, but also with the engineers, tee II-

    nicians and field service people who develop, design, build andtroubleshoot the machines. For those who fell they needed evenmore gear knowledge, SME offered a series of gear clinics at

    the show.The value of these experiences cannot be overstated. The

    information, contacts and business opportunities made the trip

    to Nashville not only worthwhile, but essential to compete suc-cessfully in today's marketplace. By looking at Gear Expo asmore than a collection of exhibitors, Iwas able to reap the ben-efit of everything the show had to offer. AIl opportunity notseen i an opportunity missed.

    The gear industry is changing faster than ever, and acce 10mformation may be the key to ucce in the years 10 come. Withthis Millennium Outlook issue, we've tried to walk around the

    gear industry as if it were one of my father's machine tools,We've examined ourselves from different perspectives to see howother industries and global. events have shaped the changes in ourlittle industrial niche and how these factors will affect our future.

    Ourtalks with some of the leaders in the gear industry haverevealed how dependent we are on the rest of the world and, insome case, how defenseless we Me against it. The whims ofeconomy, politics, war and industry can ei ther carry us or buryus, depending on how quickly we adapt to change.

    The pace of change will continue to accelerate in the com-ing years, and our industry will have to keep up with these

    changes in both traditional and novel ways. We must challengeourselves to view our com-panies and our industry withfresh eyes and from differ-ent points of view. We can't

    allow the comfortable,familiar perspective of oureveryday routine to restrictwhat we're able to see,because what will seemobvious to us in the future isprobably lost in the detailsof today.

    Michael Goldstein, Publisher and Editor-in-ChiefJA.NU .... RVIFEBRU ... RV 2000 J

  • KAPP and NILES are manufacturers of gear and profile grinding machines for the

    automotive. aerospace and commercial industries: Innovative - reliable - efficient.

    Call us for details,

  • Representing KAPP, NILES and KAPP TECH:

    KAPP SALES & SERVICE LP, 2870 Wilderness Place,

    Boulder, CO 80301, Phone (303) 938-9737 Fax (303) 447-1131KRPPSALES" SERVICE

    CIRCLE 145

  • Introducing the completelynew revolutionarygear grinding machine

    You will not find a fastetmore accurate, moreflexible and morealfordable* gear

    din gnn . 9machine.,

    'please ask for a q~uote

    WelbankaD oormstomerswbo visited US at the

    ;. :.T~~~\~ ...

  • ______________ REVOW1l10NS _

    WiU Rainb_ow Coati"-g Le_adto IManufactulri:ng G'old?Gear manufacturers have u ed coated

    cutting tools to obtain dramatic increasesin productivity over thepasl. decade.Titanium nitride (TiN), titanium alu-minum nitride mAIN) and titanium car-bonitride meN) coating have becomethe norm for gear cutting tools.

    Space Age Concepts of Dayton, OH,claims to have the next generation ofcoatings for cutting tool applications, andaccording to company CEO DarylBlessing, gear manufacturers who havetried it have had great succe s.

    The Laser-Cut 964 Rainbow Coatingi made up of W elements. which areapplied in a single ultra-thin layer by tileprocess of physical vapor deposition. Theexact makeup of the coating i propri-etary. but the end result i a Rockwellhardness in the 92-94 range, a coefficientof friction of .027 and coating thicknessof 65 millionth. of an inch.

    Becau e of the number of elementsinvolved and orne special processingsteps, the coaling costs approximately25% to 30% more than TiN. Also. thecoati ng process takes about I0-1.2 hours,compared to about 3-4l:lours fotTtN.

    However. the combination of proper-ties achieved allow both faster cuttingand increased tool life. Blessing says.

    The coatinghas been applied to allforms of gear cutting tools, includinghobs, shaper cutters, broaches and bevelgear cutting blades. "Our gear manufac-turing customers get as much as three 10four times the tool life before the toolneeds resharpening," Blessing says.

    Also, because !he coating is so thin, gearmanufacturers can regrind !heir tools moretimes than with other types of coatings.Blessing says. "In some cases, they've seenas many as IOta 11 regrinds per hob."

    The coating can be applied 10 mostcutting tool materials. includ:ing stainlesssteel. tool steel and carbide. Coated toolscan be used 10 machine typical gearmaterials, such as 4140 steel, as well asa variety of more unusual or exotic mate-rials such as aluminum, titanium or high

    nickel-content steels used in aerospaceand other special applications. "You canbasically machine any material thatyou'd like," Bless.ing says.

    The combination of hardness andlubricity also makes the coating an idealcandidate for dry cutting, either with highspeed steel or carbide hebs, Blessing says.

    ibe Laser-CUI 964 R-.alnbowGaatlnglr-om Space Agel Concepts.

    Welcome to Revolutions, the col-umn that brings you the latest

    most up-to-datB Bnd essy-lo-reBd

    informBtion Bbout the people

    snd technololY ,01 the leSlindustry. Revolutions welcomesyour submissions. PleBle send

    'hem 10 Gear Technology. P.O.Box 1426. Elk Grove Vmale, It,60009. fax (847) 437-66tB Dr 6omB;1people@geartechnol'ogy.com. Ifyou'd like more information' aboutBny ,01 the amcl'es that ~ppea1,please circle the appropriate .num-

    bel ,on the Reader Service Card.

    The same combination of propeniesgives Laser-Cut 964 promise as a ,coatingfor wear parts. In fact. at least one majorautomotive manufacturer is using tilecoating to increase life and improve per-formance of internal engine pan,Blessing says.

    Circle 251

    Carbide Insert HobbiingVery large gears, !hose with 3/4 DP for

    example. present certain problems for gearmanliIfacturers. Such gears could have atooth height of 3" or more and be 40 feet indiameter. According to Ron Scllomanfl ofLMT-Fette, the surface speed ofa conven-donal high-speed steel hob has to be reducedto almost nOlhing on such a Iar:getooth pro-file. "If !he gear or pinion to be machined hasa hardness of approximately 300 I':IB. ihemachinability chart for conventional bobbingcalls for a surface speed of no more !han 10mimin (33 feet), The corresponding spindlerevolution ana 14" diameter hob would ihenbe as low as 8 []lID. With a feed! rate of 1-1.5rnm (.040"-,(160") and a gear face width of lmeter (40"), it is easy to imagine that themachining time becomes aslronomicallylong. We are not talIcing in tenns of hours. lttakes many days to complete a gear ()I' pinionof these dimension ."

    JAN,UI

  • REVOILUTlOiNiS 1 ----- _-- ----- -------------

    In order to speed up bobbing opera-tions of large gears and pinions,engi-neers at Wilhelm Fette GmbH, Hamburg,Germany, have developed a unique hobdesign that uses indexable carbideinserts. The cutter body has a precise hel-ical path on which the tooth segments areaccurately placed. To ensure maximumaccuracy tor the tool, these segmentsmust be precisely machined and placed ..For maximum rigidity, the insert seats arearranged tangentially. On hobs for DP5-2.5 (module 5-10), one long insertcovers the entire tooth profile. For IDP 2.4

    "..""" boundO~ of autorn;rlNe design c;xes!retched. the need arises for ever g"""'" reliobillfyand smaller toielances. while maintaining 01 reducing !he cost per piece. Whirling is""", C

  • Redefin'ing "Worldclass" 'lor a new millennluThe wOTld is tjuic:llly6egl'nnlng to, realize tim, tbe essenceo/l'1ACSTlIEle Is q.ru~UtJ' and senice. OU.r ellpodly forengtneered steel barsbns grou'lJ drrmUllicallJ' along U'ilbn hosl' of l'tdueadlil'd sert!ices Sllcb flS wnllnert:iD1 bealtreating and. tbe patenfed Nllrolee treatment 0/ our newNtl.roSleel bars. Ou, gonl, lIS we rtlOl'e .Inlo Ibe nf.t.:1millennium, Is .10 rontinlle 011' e.t.:traordJnary grouothwblle nwlnlaining our #1 posJlio1J in ,q#mlt.t)' and sen';ce.

    CIRCLE 104

  • _------------- RE.VOLUTIONS _Schomenn, after the above tests werecarried out. the too] was equipped withcarbide inserts for skiving a hardenedgear of similar size, "The 60 Rc gear wasmachined with 248 SFM and .160" feedrate per table revolution," saidSchornann, "There was no detectablewear on me TiN-coated carbide in enafter machiningeight gears, each with 61teeth and a face width of 5.5 inches,

    The initial cost of ICI hobs is high.

    but according 10 Schomann, these 1001become economical when you take intoaccount maintenance problems such astooth chipping. cracking or breakage;excessive flank wear; accidents anddowntime due to sharpening. "When allof the e factors are considered," saidSehomana, "the use ofa hob witlJ index-able carbide inserts becomes an econom-ical investment,"

    C!irele 252

    THE PURDYCORPORATION

    ISO 9002 CERTIFIED

    586 Hilliard StTeet RD. Box 1898,. Manchestet; ct 06045-1898 U.SA.Telephone: 860 649-0000- Fax: 860 645-6293

    Home ~age: http://www.purdytransmissions.r:omE-Ma#: [email protected]

    c I ~ THE P;JRDY CORPORATION

    CIRCLE 14614 GEAR TECHNOLOGY

    Ma,c!hine Tool Techno'liogyTra~iningSurvey

    The Teeling arid ManufacturingAssociation (TMA), a loeal not-for-profittrade association erving 1,600 plasticsand metalworking companies and suppli-ers in the Chicago area, asked its membercompanies to rank. several educationalareas for potential entry-level employees.The goal of the urvey was to aid schoolboards and local advisory council in theirdecision-making processes as related to.manufacturing technology programs. Theeducational areas designated were aca-demics. manual machining ..CNC trai,ningand CAD training. The respondents wereasked 10 rank each educational area inorder of preference with 1 being the mo timportant and 5 beingthe least importantattribute. TMA received 1.62 urveyre ponse from member companie and

    ix written re"ponsc .Study Procedure. The study exam-

    ines the Chicago precision metalworkingindustry as agroup, as well as by indi-vidual area. This includes precisionmachining, moldmaklng, diemnking andmachine building. The study also exam-ines influencing factors such as companysize. manual. and CNC machine usc.

    Results and OpiniollS. Chicago. areametalworking companies rank manualrnachiaing a tile mot preferred educa-Lion area, followed by manu a] machin-ing/CNC training. academics. CNCtraining and CAD training,

    The survey concluded that ihe beSIprepared students for the precision mel-alworking industry should have a. combi-nation of manual machining. CCmachining. and CAD training. Studentshould enroll in math classes tressingalgebra, geometry and trigonometry,Science classes such as physics andchemistry are also important.

    Fora copy of the complete survey,contact the TMA Educauon Departmentat (847) 825-H20. ext. 322 or e-mailDan Kiraly at dkirol},@tmanel.com.

    Circle .253

    Tell Us What You Think ...If you found these Revolutions of interestand/or useful, please circle 220.

    mailto:[email protected]

  • IIliP 11.,I:nt, 11111 Innllnll ,nr IIIlin IIIIlun II' lillPl--even plastic andpowdered metal-is an M&M GRS-2 Double FlankGear Roller System with iPC/'Nindowse-basedanalysis software.

    I .. nliin UII"'I U UIII'P. PerformtolalcompOSite, looth-Io-tooth, runoul and! nick or burrtesting in seconds with the push of a bunon. Yourmachine tool or cell operator can determine gearquality and monitor manufacturing processes withvery little training.

    In IIPI._IUI nl IlIlnlc nnlts clearlydisplayed on the monitor or printed on standard paper.For easy interface with spe software, test results canbe saved aulomaHcally in database formal. .And M&McompOSite roll testers, like all M&M functional gages,have a track record 01proven reliability and virtuallymaintenance-free service.W. aUI... IU!UPI. Please call (937) 859-8273or fax (937) 859-4452. E-mail info@mmprecisioncomand visit us on the web at WIY'N.mmprecision.com .

    .~.El:I.'.1I- 6gB

    t: ~II.A".1IC 2000 M&M P,ec/SfQ" Syslrms Co/pOlinO"

    iI

    A IIIIII GilD: p TYlpe, IOlcl dllng

    P II a :8 u C: ,ft n Id P 0-_ d Ie r e dl I:

    'TheSimpleSOIUIlionl

  • CIRCUE '19'16, GE.AA TECHNOLOGY

    IIBNOLDPrecision Technologies

    _TIECHNICAL ICALIENDAIRI _January 10-13. The Folk School. Milwaukee, WI. The

    Falk School is a four-day course designed to familiarize work-ing maintenance mechanics with field-practical, factory-

    approved installation, alignment, maintenance and failureanalysis procedures for Falk gear drives and couplings.Workshops are designed to provide maximum familiarity withlogical. hands-oil service techniques . and are deliberately keptflexible to accommodatethe interests and experiences of thestudents. Twenty-four se sion are cheduled throughout 2000,two per month. For more information visit Falk:'s Web site at

    wwwJalkcorp.com or call. (262) 317-1.420.

    January .24-27.ThreeCeurses from SME: Fundamentalsof Broaching, Heat Theating & Hardening of Gears, andBasle Gear Desi~ and Manufacturing. Detroit (Tiroy), MlThe: e three courses are o'lfered separately. The Fundamentals ofBroaching urtroduces jhe student to the broaching process;examinesthe care, storage and maintenance of broaching toolsincluding sharpeningand recondiaoning: discusse turning. heattreating and grinding and offers pointers on troubleshooting,Heat Treating and Hardening of Gears offers presentations onaustempering, induction hardening, paris washer management,minimizinggear distortion and gas nitridiogas applied 10 gears.Basic Gear Design and Manufacturing is also .31 clinic and itoffers presentations on gear basics, Cylkro angular face geartransmissions, manufacturing methods and mad'l:ines, shaving

    and broaching. There will also bea tOllr of the National Broach& Machine Company in Macomb, Ml These courses are spon-sored by the Society of Manufactllxfllg Engineers. For moreinformation contact Lynn Albertson at (313) 271-1500 or sende-mail to [email protected].

    }~ebruary 13-16. Melalform 2000. Nashville ConventionCenter. Nashville, TN. More than 250 exhibitors will! participatein Metalform 2000, with exhibitseovering 74,000 square feet ofspace. AU areas of metalforming win be represented includingtooling. tamping, slide foming, roll forming, fabricating,welding. assembly and automation. AUendance is expected toinclude more than 7,000 industry professionals. Sponsored 'bythe Precision Metalforming Association .. For additionaljnfor-

    mation call (216) 901-8800.

    Mal'ch 20-25. Hannover Fai;r 2000. Hannover; Germany.The Hannover Pairis the largest and most influential interna-tionaltrade show for industrial technology. Qualified profes-sionals including buyers, distributors, politicians and journalistscome from 100 countries to identify the latest products and.

    trends in every sector: Over 300,000 qualified attendee. 7,500exhibitors from 70 countries, 2 ..75 million square feet of displayspace. For moreintormatien contact Hannover Fairs USA. fuc.at (609) 987-1202 or I.og ontoiheir Web site at www.hjUsa.com.

    TeI.UI WMI V... TbIH ...H you found this .rIIe .. of intarast and/or useful, please circle 117.

    mailto:[email protected]://www.hjUsa.com.

  • ----

    ADVERTISER I,ND'EXFor more information about a product or service advertised inthis issue of Gear Technology, circle the appropriate number onthe Reader Response Card and put the card in the mail.

    For even faster response, use RAPID READE:R RESPONSE. Visitwww.ge8I1echnofogy.comJrrr.htm and have your requests forinformation delivered to advertisers instantl~ via e-mail!

    ADVERTISER RS # PAGE #

    Toolink Engineering

    AfW Systems

    Ajax Magnetbel'JIlic

    American Metal Treating Co.

    Applied Process

    Bari! International Corp.

    Becker Gearme isters

    Bourn & Koch Machine Tool Co.

    Colonial Tool Group

    Emuge Corporation

    EurocTech

    Fassler

    ~51 CilY Gear Co.

    GeneraJ ~I!gnaplale

    The Gleason Wor'ks

    GfeasonPfauter Hunh Cutting Tools

    Hofler

    Holroyd

    Inductoheat

    Insco Corporation

    ITW Heartland

    K:a.pp 'GmbH

    Koro Sharpening Service

    Kreiter Gearteeh

    LeCount, Inc.

    Leistritz Corporation

    M&M Precision Systems

    Maesteel

    Midwesl Gear & Tool

    National Broach & Machine

    Niagara Gear Corp.

    On-Line Services, Inc.

    Parker Industries,

    Perry Tec~nology Corp.

    Pro-Gear. CD., Inc.

    The Purdy Corporation

    Quality Transmission Components

    Star Cutter Co.

    Sudalint.emational 'Gear Works

    Hl3 46

    1.'4 50

    152 54

    [1'1 50'

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    105. 1.U1orof K6!!!g""", w....i'IoI

  • Low Vibration Design onA Helical Gear Plair

    Prlofessor Dr.. IEngl,Kivohik,o Umezawa

    elical gear pairs with narrow face widthcan be theoretically classified into threecategories over the contact ratio domainwhose abscissa is the transverse contact

    ratio and whose ordinate Is the overlap contact.ratio. There is a direct relation between vibrationmagnitude and shaft parallelism deviation. To clar-ify the effect of the tooth deviation types on thevibration behavior of helical gear pans, perfor-mance diagrams on vibration are introduced. Theacceleration levels of gear pairs are shown by con-tour lines on the contact ratio domain, Finally theperformance of gears with bias-in and bias-outmodifications is discussed considering the effect ofthe shaft parallelism d...viation with lise of thedeveloped simulator all a.. helical gear unit. nbecomes clear that there is an asymmetrical featureon the relation between the vibration magnitude ofa gear pair and the direction of each deviation.

    The Helix Angle and tile TransmissionBehaviors of,a Driven Gear. The author numeri-cally solved the deflections of a thick plate withfinite width (Ref. 15) and a rack shaped cantilever(Ref. 16) under a concentrated load (as shown byOlsson in Ref. 1) by using the finite differencemethod. Furthermore, the lead distribution alongthe line of contact and the compliance of a helicalgear tooth pair from the start of meshing to theend of meshing have been revealed (Ref. 17-19),

    When the face width is constant, i.e. threetimes the whole. depth, the relation between the

    \ I\ 6/, I

    c d..,~ l!."I \'\

    ,.qP ".....0,,6 ..0.4..0.2 0 0.2 0..4 0.6

    ~p.-I I- p .K(I) Spur gear (b) ~\4' (e) ~20" (d) .1}=30

    ~L48 Ea~L48. .=1.48. ..=1.48.",..0,44 ~~.66 ~=L10

    Fig; 1-The behaviors of the driven gear and the helix angle w.ilh b:1h'" 3.0.18 GEAR TECHNOLOG,V

    helix angle and the calculated behaviors of thedriven gear under loading is shown in Figure I,These results are analyzed assumingthat the 1'10[-mal pitch P 111' norrnalized with the whole depth, is0.6. Then the whole contact ratio is calculated foreach helix angle. The overlap ratio is calculatedfrom this whole contact ratio and the assumptionthat the transverse contact ratio is sa'" 1.4. Thiscontact ratio wa calculated for a spur gear pairwhen the normal pitch Pin is .0.6

    When the helix angle is 14 (Figure la), thesum of the transverse and overlap contact ratio issmaller than 2, Therefore, this parr of gears trans-mits load alternately with one pair and with twopairs of mating teeth. The load sharing ratio forthis pair of gear varies more smoothly than thatof spur gears. But sometimes knobs appear onthis curve when the meshing condition transitsfrom one pair meshing to two pairs meshing.

    When the helix.angle is 2.0.0or 300 (as shown inFigures lc and ld), the total contact ratio is over 2.The gears alternately transmit load wilh two andthree mating pairs of gear teeth, the load sharing ratiovarying smoothly.The behavior of the driven gear, orthe transmission error, also vanes smoothly.Especially when the helix angle is 30",the overlapcontact ratio is over 1.0 and the behavior changesvery smoothly with little fluctuation as shown,

    Three Categories of a parallt axes gear pair.Theoretical and experimental studies all staticmeshing behavior under load have proven that apower transmission parallel gear pair can be clas-sified into three categories on the contact ratiodomain based on its facility for reducing vibra-tion as shown Figure 2.

    Vibration Magnitude andShaft Parallelism

    The relation between vibration and parallelismof axes was investigated for three kinds of helicalgear pairs classified into three categories. Twokinds of shaft misalignment were implemented,in-plane and out-of-plane deviation. For realizingthe out-of-plane or the in-plane parallelism, thepedestal of the driving gear shaft was tipped inthe vertical plane or in the horizontal plane,

  • vibration. Woen the error increases to :Ollm, Fig. 3-Shaft misaligllmerlt setup..peak appear al the higher harmonic resonance, I ofa helical gear pair wa developed. Performance

    respectively. The vibration was measured I:>y twoaccelerometers attached directly to the driven

    gear blank surface.

    Dimens.wns of test gears and test apparatus ..Test gear pairs were designed to belong to eachcategory classified over the contact ratio domain,

    and are named Hl, H2, H3 and H4 as sh wn inFigure 2. lDimen ions of each gear pair are dis-played in Table I. All test gears were hardenedabout BreSS, and finished by the MAAG 3D-BCGear Grinder. Tooth profile and tooth traces are

    made with as little deviations as pes ible.Shaft misalignment set up. Shaft mi alignment

    was created by placing everal thickness gages onthe surface of the ba e plate or on it side s urfacefor the out-of-plane or in-plane deviation (Fig. 3).Thickness gages of 0.1.-0.4 mm were used a nd theangular deviation realized were about 05x10-3

    rad and I.Ix l0-3 rad. The amount of the cut-of-plane and the in-plane deviation was measuredwi.th two dial indicators. Gear shaft misalignmentwas introduced for both the leading and trailingside bearings.

    Influence of the out-ofphn.e deviation. Therelation between rotational vibration re ponse vs.

    speed and out-of-plane deviation for the gear pairH3 is shown in Figure 4. With proper alignment

    (as indicated by "no error"), acceleration increas-e. with the speed. Bei ng observed in the cases ofthe gear pairs Hland N2, the peak cannot be rec-ognized for these gear pairs without deviation.

    When 13J,Lmedge to edge deviation exists atthe lead ing side, the peak appears at about 2700rpm, which is ascribed to the second hannonicresonance. As the error increases to 29J,Lm,.aecel-eration increases over the whole speed range andthe peak occurrence shifts towards a. lower speed,However, when. an error of 14.J!IDexists on the

    lraJlin,g side. there is no remarkable increase in

    and the acceleration levels becomes high.

    Influ.e.nce of ,the in-pl(me d.e"iation~ For thegear pair H3, the relation between the rotationalvibration response and the in-plane deviat.on isshown in Pigure 5. In the case of an error on the

    trailing side, the vibrationof this gear pair is notinfluenced bythe error. With an error on the lead-ing side, the acceleration level become high. andhigher harmonic resonance peaks appear.

    However, the vibration behavior of the pair is nota inflllenced as with the out-of-plane deviation.

    Performance D.iagrams on Vibratiol!llTo clarify the influence of tooth deviations .0111

    vibration, a simulator forthe rotational vibration

    1.0

    OJ""

    .9~1:1.

    '""C!t0

    0.5

    1.51.0 2.0Transverse contact. ratio .ea

    Fig. 2-Classijication of parallel pairs.

    Table I-Dimensions of test gear pairs. I

    Gear pair I HI I H2 I H3 H4annal module 3.5 4

    ~-

    umber of teeth 30 29Helix angle (deg) 30 15

    -Pressure angle (deg) 20face width (mm) JO 1 20 I 25 =r:~---~- -Addendum modification coefficient --0.17 0Transverse contact ratio 1.4 1.57---

    1-

    Overlap contact ratio 0.45 0.91 j 1.14 0.58

    ,DrivtnGear

    DnvingGear

    M~DA+K (t,O)=W+F(t,3)

    Dr; ~iyo'hikoUmezaw,B(1918/998) was II pro/es-sor ill tile precision andilllelligence laboratory 01Ihe Tokyo Institute ofTechnology, Tokyo, Japan.All .the tnstina he used hisexpertise in gear design ..machine d namics, vibra-tion and acoustical meo-.mreml!'Mt to work 011 reduc-ing sound and vibration. illgear units. Dr: Umezawadied sudde.nly at the age oJ60 while on a hon vocationafter preseruing this papuat the AGMA /998 Fall

    (1) Technical Meeting.

    diagrams on vibration with acceleration levels

    shown by contour lines on the contact ratio

    domain are included.Theoretical Anlllysis on the Vibration

    of 8. Helical 'GearModel 0/ motion~ Considered along the line of

    action of a helical pair; imaging at the center line ofthe pLane of action, the rotational motion of a power

    transmitting helical gear pair can be treated .35 a sin-gle degree of freedom system similar to the case of aspur gear pair, i.e.,1he tooth is treated as a spri~g andthe gear blank as a mass, by the following equation.

    JANU"'~YIFEBRU"'RV 2DDD 19

  • 100

    lleodi - InIilI ~ -e (to tho lrtlilipg

  • Agreement between the calculated re: uhs from

    the simulator and experimental results is goodabout the waveform, especiatly the change in the

    numbers of vibration cycles within one toothmeshing period T:.atlldabout the behavior ofamplitude as th.e rotational speed is increased.

    The relation between vibration amplitude in

    RMS value and rotation peed is shown in Figure

    8. This was developed u ing a good quali~,.. pairwith deviations under 3~.lfn. and whose dimen-sions are the . arne as tho e in Figure 7 except forthe 25mm :face width.

    Nature ~/ dimensinnkss stijJness. Figure 9shows the stiffness behaviors along the line ofaction Kj (t,S) of two helicafpairs, (a) and (b), 'These

    are plotted at the same position on the contact ratiodomain (black dot in the lower left figure).

    Apparently stiffness behavior is different, espe-cially with respect to the mean value of stiffnessKi.mean' However. the behavior of the diInensionlessstiffness K('t,X), in. which the actual stiffm:ss isdivided bylhe mean value of stiffne s, is the same

    shown Figure 9(c) from the viewpoint of how to

    yntbe ize the performance of helical gear pairsbecause the difference among the first orderfourier coefficients of each dimensionless stiffnessare within 10 percent deviation on each pairbelonging at ihe identical point on the contact ratiodomain, The differences of the higher order Fourier

    coefficients are oflhe arne level. amplitude, andtheir values are smaller by one t1tird than coeffi-cients of the first.

    Performollce diagrams on Il.i"ration~0/ helicalgears. At each operating. peed and under eachdeviation condition. the vibration levels weresolved numerically by the simulator al 80 pointin the contact ratio domain, where the transversecontact ratio (ab cissa) was set at 8 points from].0 to 2.0 and the overlap ratio (ordinate) was at10 points from 0.2 to 2.3. Oonsequently, the

    solved vibration levels were expressed as contourlines on the contact ratio domam,

    Acco,u.nted deviatl'(ms .and modifications.Performance diagram were produced or. the

    seven kinds of pairs: the 110 error pair. the pairwith crowned tooth face, and the pairs having.respectively, pressure angle (prnflle tope devia-tion in ISO). convex. profile, concave profile. leadand pitch deviations, which are similar in manu-facturing and assembling gear units, The perfor-mance diagrams calculated under the condition

    that the relative deviations between meshing. dri-ving and driven teeth are gathered apparently toonly driven gear teeth, which. have ideally th.earne figure and the arne amount of deviaticr s for

    CALCULATION X:PERIMENT

    mi.' lSOO",m1:~.100[JPllW. II-;!

    z

    1500 rpm

    100

    ""s' -'r1~~tlo ..,l . I J -"so . -I-1-::-'1- .. Tz"

    2000tpm

    """,~",so I .,. ., ...o .

    .S() _I. 'I '.":"I;r;I'-

    2000 rpm

    F4l. 7-Verification by experiments on the ,changing speed.every tooth in the gear. Therefore an teeth of thedriving gear have ideally no error for calculation.

    Per/ormo,ncediDgrams on a non-error pail'.The produced performance diagrams on a pairhaving no err-Of at each speed !,/inchanging froma low value ofO.2[ to a high value 0.98. The inter-val of vibration level between adjacent contourlines is a 0.025 vibration level. Generally, at ea.chspeed the vibration level becomes mall accord-ing to an increase in overlap contact ratio, exceptfor the 2nd resonance speed ~/!,j = 0.49) and thehigh speed region ..

    AI tow speed if;,lin

  • At high speed (0.7

  • alongthe line of contact of a helical gear and causevibration,

    Whe.11 the tooth. surface is crowned. vibrationin the range of .e1J~1.0 decreases in comparisonwith the pair with no error.

    The simulator can depict vibration levels andwaveform behavior precisely, The performance dia-grams depicted the .influence of deviation and oper-ating speed on the vibration level of a pair ill thecontact ratio domain. Using these diagrams, adesigner can select the be t dimen ions to lower thevibration of a newly designed gear 10 the lowestvibration or influence area by the 'Useof deviations.Also. when an engineer has to improve a noisy gear ..he can choose the most effective improvement bycrossing to the contour line of the diagrams.

    Bias ModUicationFinally, bias-in and bias-out modifications are

    discussed as they relate to shaft parallelism devia-tion with theuse of the simulator on a helical gearunit (Ref. 23).

    Among gear vibrarioas, rotational vibration isthe most important. It can be approximated with asingle-degree-of-freedom model. However, theeffect ofthethru t force from the helix angle of ahelical gear complicates the vibration of a gearunit. To farther reduce v.ibration, it is important toreveal the actual modal behaviors of the gearvibrations in every direction as wei] as the vibra-tions of the shafts.

    The vibration of a belicalgear unit as shown inFigure 10 with various gear ratio. has been investi-gated. The dynamic response of transverse, rot lion-al, tilting and axjalvibralions of helical gear aremeasured by acceleration pick-ups mounted on thegear blank, Modal behavior is interpreted based on amodulation scheme due to shaft rotation. The modes !of shafts and gean; are measured precisely vtith a i I

    jlaser Doppler velocimeter. Then the simulation on a Idynamic model, including transverse, rotational. lilt- !ing, and axial vibrations, i developed

    Modal Belunior. The locus of the transversemotion of the gears and gear shafts, measured with alaser Doppler velocimeter at resonance, are pre entedas q and Q in Figure I ~.Cilrde marks are the points ofinstantaneous displacement when the rotation of thegear is Ilell that the paration of the gears is thegreatest .along the line of action. Triangles are thespots of the opposite condition. Arrows indicate thedirection of motion. Additionally, tilting motion of thegear is pres.ented Ihrol.lgh the differentiation 0~tworneasurementsat both shouIde ( and V in figure13) of the gear body.

    Regardless ofihe ratio. the shaft of the biggergear vibrates with an S- baped mode. Each part

    whirls along a. thin, elliptic locus with the mesh fre-quency. The major axis of this ellipse is not parallel10 the line of action. Atlhe bearing position. wherethe motion should be interpolated from the resulu ofboth sides, a. low amplitude vibration exists, sug-gesting that the bearing positions are not con-trained as . imply upponed pivot. The modal

    behavior is also unique to an individual gear-shaft-bearing assembly regardless of driving/driven con-ditions. Di placement of the pinion snail. at tihe IiI'ring side bearing is a liittle larger than at other bear-ing positions. This might be an individual feature ofeach bearing. Althoughlhe shafts are vibrating in aninteresting manner, the gear itself is supposed 10move in the direction of the line of action if weassume the vibration of the gear center by interpo-lating with outer vibration.

    The simlliotor .0/ 12-degree-o/~freedom. To pre-dict the vibration behaviors of helical gears asshown in Figure ]4, the aulhor proposes a 12-degree-of-freedom dynamic model that includesrotationaltransverse, tilting, and axial motions. Agear is assumed to be a rigid body which can bevibrating ill six direction in terms of equivalent.sriffnessand effective masses including the dynam-ic properties of gear, shafts and bearings. Toothmeshing springs of two coupled gears are modeledas two parallel springs that vary temporally with acertain phase relationship due to the helix angle.

    ViblCalion ana~ysis..Figure 12 shows that trans-verse vibration can be expressed by dynamicbehaviors in the x and y directions. ROlationalvibration can be expressed in the (J_ direction.

    o.~~'",~

    M."O.~Ir>r/.-:7r > /~-0() .

    Bearin,g

    TIlLing vibration - --\

    I~ _ ..-~-

    !

    Fig. H-Modal representation of the gear sy tern b}' means of laser Dopplermeasurement, Gear ratio .3:4.

    JANUAJ\VIFeB~U"'RY 2000 23

  • Flg. 12-Vibratiol1. model of hel.ical gears.

    Simulation

    Fig. 13- The verifi.catlon of the developed 12DOF vibration simulator of ahelical gear sy tern by experiment. mod und r incn:asing 4:3, about .2460 Hz.

    Fig. 14--.Bias..(lutandi Bias-in modification.24 GEAR T.ECHNOLOGY

    Tilting vibration can be expre sed iII the OJ:and 9ydirections. and axial vibration can be expressed inthe z direction. In each direction. the equivalentstiffness and effective mas are determined by thegear, shaft,. and bearings ..

    An-,gu]ar displacement in me rotational direc-tion 9~is expre sed in 'term of tangential dis-placement .along the ba e circle as w = r/lt Angular displacementsin thetilting directions Oxand 6y are also expressed aIIong the base circle as.u = r89~, v= riJ~. The equations of motion canbe expressed in tile matrix equation

    Where 1,51 is a. vector of displacements as

    [m] is a.mass matrix, [D] is a damping malrix,and(k] is a stiffness matrix.

    To verifylh imulator with the u e of the pro-po ed formulation, experiments were performedfor different ratios. Tile results agreed with fhecalculations ( ee Figure 13). The mode at reso-nancepeed was found to be f~= 2460 Hz whenthe gear ratio i. 4:3.

    The perjomwI,ce of (J bias-modified helicalgear pair.. To decrease vibra.tion, bias modification isoften applied 10 the tooth surface, There are twomethods in bias modification, bias-in and bias-out(see Figure 14). II IS not clear which modification isbetter.

    Using the vibration simulator of a 12-degree~of-freedom helical gear unit. !he relationship betweenthe performance of vibration level and misalignmentis discussed on !he bias-in and We bias-out modifiedhelical gear pairs. These pairs nave a high tota] con-tact. ratioe = 3.81 [usually used in automobile trans-missions) to realize low vibration level, Thegea:rdata is: .zl and h'"52. m,,;;;;; 2.0, a=20 and ~o = 30,face w:idth 30 mm and load 133 N/mm..

    Misalignment is defined as positive when theaxis incline to the leading ide bearing. On thebias-out modification with misalignment from-lOjl to lOjlm. arnplitide factor contour mapshave been developed in which the abscissa is thedimen ionles modification length bi p, and theordinate is the bias modification hbLJ,lm] (seeFigure 14).

    The contour Lines in the maps show a ratio ofrotational vibration to that of a non-modified heli-cal gear pair at the resonance speed. The Lnfluenceof the amount ofbias-out modification and modi-fication length on vibration can be obtained using

  • the contour lines on each amplitude factor contourmap. The influence of misali:gnment on vibrationis realized by comparing the maps to each other.

    ConclusionThe propo ed classification of a parallel gear

    pair and contact ratio domain are verified to beuseful in the design of a quiet gear pair:

    Our re earch has shown that there is an asym-metrical relationship between vibration magni-tude and the direction of'each deviation (seeFigures 4 and 5). For further noise reduction, Illeeffects of shaft. bearing and gear-box on vibrationare of great importance,

    Finallythere is no new knowledge on how todesign a quiet parallel. gear. However, it is clearthat surface deviation, as well as the direction ofthat deviation, can affect the vibration level of agear pair. Gear engineers should. see thac theirproducts tum ill the right direction. They are verysimilar men who walk step by step' carefully thenarrow ridge between high mountains. 0

    Rereren.ces:I. Olsson, R.G. "Biegung der Rechteckplaue bei linear

    veranderlicber Biegung teifigkeit," Ingenieur-Archiv,Vol. 5, (l934}, pp.363-373.

    2. WalJ>:er,H. "Helical Gears;" The Engineer, (1946). July12,pp.24-26:.1uly 19, pp.46-48: July. 26. pp.71).71.

    3. Jaramillo. T.J. "Deflections and moments Due 10 aConcentrated Load on a, Cantilever Plate of InfiniteLength," Journal of Applied Mechanics, 1.1950),pp.67-72.

    4. Davis. A.W. "Marioe Reduction 'Gearing."The'Iwenty-eighth Thomas Lowe 'Gray Lecture.Engineering. Vol. 20.1. (1956), pp.477-498.

    5. Monck. E. Roy, A.K. "SpannungsoptischeUntersuchung eines schragverzahnten Stirnrades,'Konstmction.9, Hefl II (1957), pp.429-438.

    6. Trbojevic, M.D.. "Lo d Distribution on Helical GearTeeLb:' The Engineer, (1957), Aug. 9. ppW7-190;Aug. 16 pp.222-224.

    7. Wellauer. J., Seireg. A.G. "Bending Strength of GearTeeth 'by C~ti.[ever-Plate Theory," Tnmsac(oru ofthe ASME Journal of Engineering for Industry. PaperNo. 59-A-50, (1960), pp. 1-8.

    '8. Hayashi, K, "Load Distribution on the Contacu Line ofHelical Gear Teeth ![II Report. Ba icInvestiganon),"Trans. Jpn.Soc. Mech. Eng. (in Japanese), Vol. :!8, No,193, (1962). pp.I093/1101.

    9. Niemann. G. und Hosel, T. "Gerauschuntersuchungenan schragverzahnten Stirnradern Einffu (von Drehzahlund Belastung," Verz!!hnungsdaJ.en und Zahnfehiern,Konstruktion, 18, Heft 4, (I %6), pp, 129-141.

    10. Niemann, G. und Baethge, J. "Drehwegfeler,Zahnfederharte und GeJl!!.!schbel Snmradem," '1DE-Z112, Nr.!!, (1970), pp. 495-499.

    I L Houser, D.R. Seireg. A. "An ExperimentalInvestigation of Dynamic factors in Spur and ,-{elicalGears;" Transactions of the A.SME Journa! 0/Engineering lor Industry, (1970). pp.495-:503.

    12. Seireg, A.. Houser. DR "Evaulation of DynamicFactors for Spur and Helical Gears." Transactions oftne ASMEJoumai of Enginteringlor lnauslry.(1970),pp.504-SI5.

    13. Conry, T.F., Seireg, A. "A Mathematical ProgrammingMethod for De ign of Elastic Bodies in Contact."Transactions of the ASME Journal of AppliedMechanics (1971). pp.387-392.

    14. Conry, T.E, Seireg, A. "A Mathematical ProgrammingTechnique for the Evaluation of Load Distribution andOptimal Modifications 110r Gear Systems,"Transactions of the ASME Journal of Engineering forindustry, (1973). pp.111 :51122.

    15. Umezawa, K., et al, Trans Jpn. Soc. Meek. Eng. (inJapanese), Vo1.35.. 0.270. ([ 9692), pp.423/43 J.

    16. Umezawa, K.. "Deflections and Moments Due 10 aConcentrated Load on a Rack-Shaped Cantilever Platewith Finite Width for Gears," Bull. JSME, Vol.l5, No.79.(1972). pp.II6-130.

    17. Urnezawa, K. ''The Mestling Test on Helical Gearsunder Load Transmission (I" Report, The ApproximateFormula for Deflection of Gear Tooth)," Bull. JSM.f.,Vol. 15. No. 90, (1972), pp,1632-l639.

    18. Umezawa, K. "Deflection Due to Contact betweenGear Teeth with Finite Width," Bull. JSME. Vol. [6,No.97, (1973), pp.1085-1093.

    19. Umezawa, K. "The Meshing Test on Helical Gearsunder load Transmission (3'" Report, The SlaticBehaviors of Driven Gear)." Bull. JSME, VaLl 7..No.112. (1974-10), pp.IJ48-1355.

    20. Umezawa, K, Suzuki, T. Houjoh, H. and Sato, T."Vibration of Power Transmission HelicalGears (The effect of contact ratio on the vibration),"Bull. JSME, VoL 28, No. 238 (1984), pp, 694-700.

    21.. Umezawa, K. Suzuki. T. Houjoh. H. and Bagiasna, K."Influence of Misalignment on Vibration of HelicalGears," Proc. of 2nd World Congress 011 Gearing. Paris,France, Vol. I (.1985). pp. 615-626.

    22. Umezawa, K. "The Performance Diagrams for theVibration of HelicalGears," Proc. 011989 Tnt. PowerTrarumission and Gearing Co'!f.. Chicago, illinois,Vol. I, (1989). pp. 399-408.

    23. W!!IIg. S., Urnezawa, K., Houjoh, H. and Matsumura,S. "All Analytical Investigation of the DynamicBehavior of a Helical Gear System," Proc. 0/ 7'h Int.Power Transmission and Gearing' Carr!. San Diego.California. Vol. 88, ([996), pp, 169-176.

    24. Umezawa, K., Houjoh. H., Matsumura. S.. Wang, S.and Ohshima, S. "Bxpenmental Investigation onModal Behavior of Helical Gear Units with VariousRatio," Proc. of 7'" tm: Power Trorumi5siof! andGearing Conf. San Diego, California, Vol. 88 (1996),pp, 509-517.

    25. Umezawa, K. Wang, S., Houjoh, H., and Matsumura,S. "Investigation of the Dynamic Behavior of a. Hel lealGear System (4dl Report, Dynamics of Gear Pairs withBias Modification)," 17:ans.Jpn: Soc. Meek. Ellg. (inJapanese), Vol. 64. No. 620 (1998). pp. 1414-1420.

    A version ot Ihis anJele firs1appearedl as te.chnicllIpaper 98FT1M5at the 1998 AGIMA IFalil TechnicalMeeting. We'd Ilil'e toexp.ress our thanks to Dr.Haruo, IHoujoh. 01 the Tok~yoInstitute 'of lechnology.as weill as the Umezawa family. for thair ,assist.ance!in Ipreparing fllis ,anie'le.

    TeU Us What You TIIInk .. ,If you found this article of interest and/or useful,please circle 101.

    JANUARY/FEBRUARY 2000 2S

  • MILLENlNIUH DunDon "

    "There is definitely a shrinking oJdemand lor g.e8'S due to innove-tiens and substitutions to rep/acegears. There are new dri've tech-niques, for instance. You will seein a few years gear bobbingmachines whlclt manufacturegears but which do not have anvgears within the machines.Conventional hobbing machinesused to beve more than 150 gearsbetween the spindle drive of thecutter or t.he hob and the table,and today, if you count 5 to 10, thisis the maximum, and it goes thisway that one day there will bepmbably nons. It is happening inthe wilDie machine tool industry.Direct drives and the substitutioof gear reducers due to more flex-ible drive systems. "-Peter Kozma, President. LiebherrGear Technology, Inc.

    '891-Robert Hermann Pfauter invents thefirst gear machine capable of cuttinq roth spur and helical gears.This machine included a horizontalworkspindle on vsrtical ways, 8 hobswivel, and a hob carriage feedalong horizontal ways .along thebad of the machine. The hOD fBedwas .accomplished manualty with acrank on the end of a feed screw.

    1896-Invention

    of the FellowsGearShaper.

    1900-Invention of the

    paperclip.

    ~

    Gear ManufacturingPast, Present & Future

    Charles !MI. Cooper '& William R. St'oft

    m oughly 100 years ago, Cornelius J, Bra nan of Springfield, Ma achusens,i.~ven.te~ and.:r.ec~ive._dthe first U.. S. p~tent for~. paper clip. At about the.sametune, Ins fellow inventors were coming up WIth such marvels as the zipper,the safety razor and the typewriter.While these inventions seem mundane compared to the differential gearhobber or

    the gear shaping machine. sometimes it helps to put things in perspective, and the factis, these inventions came at around the same time. Gear manufacturing . like mostindustries, has seen more change in the 20th Century than it has in all our previous his-tory. But these changes didn't. take place in a vacuum, They've been affected, influ-

    enced and driven by industry, war, politics and consumer demand.Our Recent History

    "For sure, the biggest driver of change has been the mass production of automo-biles," says Peter Kozrnapresidem of Liebherr Gear Technology. Saline, MI. "Eachpart which goes into an automatic assembly line has to be exchangeable. Therefore,standard had to be developed, and standards such (hat every supplier could make thegears according to the standard and that they would fit into this mass production envi-ronment.' Is it any wonder, then, that only eight years after Henry Ford introduced hiModel T, the American Gear Manufacturers Association was formed?

    1908'-Max Maag d6V8lops the geometry ofnonstandard involute spur and helical

    gears using rack type cutters.

    1918-Maag grinding

    machines with saucershaped wheels areintroduced. "This

    invention was impor-tant .becausa it provided the first automaticcompensation for thewear of the grindingwheel, making it the

    first and most famousautomatic control sys

    tem in the macl1inetoof history. "- from

    Development of GearTechnol.oQY and Theory

    of Gearing,by Faydor Lirvin.

    !

    1916-AGMA Founded.

    1916-Gleason invents

    a process forgenerating spiral

    bevel gears.

    1906-Gould & Eberllardt produces

    its first gear hobbing machine.

    1!ID1-, Lees-Bradner

    produces its Ifirst success-

    fulgearmachine, theNo.5 GsarGenerator.

    '910-Berber Colmanships its first

    hobbing machine,e No. 12 model

    1908-Ford began producing the Model T using an assemblyline. "The introduction of the automobile had s far-reach-ing effect upon the machine tool industry and machinetoof design. The demand for high-grade materials capa-ble af withstanding shacks and stresses of highspeedcars, made it necessary 10 design machine rools capableof working the metals at ecomonical speeds and feeds.These demands. in tum, showed weaknesses inmachine tool design and construction Forexample, it showed that castirongears were entirely inadequateJ'n manv cases. " - Machinery,September 1975..2&

    '9'4-'918-Wor/dWarl.

  • Gary Kimmet, Vice Pre ident of Worldwide Sales for the Gleason Corporation,points to tlte [970s oil embargo as having a big effect 00 gear manufacturers. It forcedus to look at the fuell economy of our vehicles, and we saw a shift to smaller, ftoru-wheel. drive cars and away from rear-wheel :trivegas guzzle . For Gleason, thi m anta significant decrease in the demand for 1lU' spiral bevel gears that drive rear axle dif-ferential . But increased con umer demand far port utility and 4-wheel drive vehiclesreversed this trend in the early 1980s, Kimmet says.

    Ecoaomicfaetors have certainly played :II big role in ihe change the gear industry haseen, ln fact, the most important factor could be urnmed up in one word, says Bill

    Maple marketing manager for Star Cutter Company. "Globalization," Maples says,pointing [Q the number of international corporate :melllersand the number of major maa-ufacturing companie moving their production location. outside the United Slate .

    Joe Arvin. pre idem of Arrow Gear Company. agrees. "The U.S. used 10 be able tosell becau e omewhere in the world they would buy our products." But in th- 1970 ,he say, foreign competition, particularly from Japan, began to challenge the ability ofAmerican compa.nie to selJ their products not only abroad, but at home as well. "Theyused to laugh at the Japane e products. It wasn't until the 80s thal they realized whatwas going on," Arvin says.

    A big factor io today's gear industry is the concern for the environment. "Thechange . ill environmental requirement will .definitely have an impact on the gearindusoy,"ay Liebherr' Kozma, We're seeing an increased demand for alternativeene:lID' ourees, ueh as wind turbine he DjS. "Environment al 0 mean to eliminatewaste," Kozma ay. 'That means. to increase efficiency, and this will al 0 requiretran missions in a different quality etas ,"

    The demand for energy saving, higher efficiency and increased power density havebeen the driver of more and better gears as well a more economical way of manu-facturing them, says Dr. Hermann Stadtfeld, Vice President of Research andDevelopment at Gleason Corporation. The e demands have resulted in the

  • --"We are ready for the challenges ofthe 21st C,entllry, Peoole are sayingtllat tile old-timers are leaving andthe young upstarts don't know any-thing, and that's not true. Youdon 'Ihave to have the old school crafts-'lien with the comptUerized ma-chines. We're better equipped ill theU.S. than we were. The problem isbeing able to combat foreign com-petition, "-Joe Arvin, President. Arrow Gear

    "I tllink that aile of tile biggestthings that forced change ill theUnited States is the influence of theJapanese manufacturing culture asit was perceived here. Its not that itwas better. but it was truly per-ceived as being better. It revolution-ized tile "'inking in tile automobileindustry, and accelerated changesthrough improvements. "-Bill Maples, Marketing Manager,Star Cutter Co.

    '931-GleasonFormatemethod

    isinvented

    byJames

    Gleason.

    manual automobile transmission, and the 5-speed. automatic. he says.Another big influence on the gear industry has been the emergence of computers

    and computing technology. Computers have allowed the development of tooth contactanalysis. CNC controls, computer aided design and advanced metrology techniques,all of which continue to have a huge impact on the way gears are made.

    The 1\Jm of the MiUenniumToday's gear industry is clearly very different from the gear industry of any other

    time. Machining gears out of metal was dearly the most common method WO yearsago. Today, this method of choice is being challenged by a far wider choice of mate-rials-s-including, most notably, plastics and powder metals-and methods-.indudingcasting, forging, molding, grinding, EDM. stamping. sintering, fineblanking.laserandwaterjet cutting. This is to ay nothing of the choice we have today for improving agear after it's initially formed, induding the multitude of heat treating methods, coat-ings and finish machining processes.

    "I think the industry is reinventing itself to adapt to the changes in technology,"says Star Cutter's Bill Maples.

    All of today's choices require the gear expert to obtain more and more education. 'Thegear industry requires a lot of technical skills to do a good job," says Gary Kimmet ofGleason, "J:t demands an ever-increasing movement in those technical skills. There is a con-tinuing difficulty of having enough people who understand gears technically-how to design!hem so they are strong and quiet, and how to manufacturethem,"

    "\\'e don't. see an. overwhelming desire to go into the gear industry." Maples says.Parents would rather encourage their children to go into computers, medicine or law. hesays. A career in manufacturing is not seen as one with. promise. The AGMA has recent-ly produced. a video to promote the gear industry to young people deciding 011 a careerpath. The video is intended for high school and college guidance counselors, and accord-ing to Maples, it's the type of prom orion tile gear industry needs to do more of.

    On the shop floor, at least, some see increases in machine tool technology as a way

    t955-17W introduces rhe Spiroidgear drivs.

    7!151b -Powder metal is first

    used for gears,

    '950-Maag introduces spurand helical gear

    grinding bV planarcontact.

    1954-Dar/e

    DudleypublishesPractical

    GearDesign. 11156-

    6e8r Honingintroduced bv

    NationalBroach &Machine.

    '955-The first numerically

    controlled machine toolsare on displ8V at the

    National MachineTool Show

    {precursor to IMTSI.

    193!J.f945 -Wor/dWarf/.

    '.939-The firstdigital

    computer.

    '!IU-The first can

    trolled, self-sus-tained atomic

    reaction is con-ducted at theUniversity of

    ChiciJgo,

    I'938-du Pont researchers invent Nylon. Today,plBsticgears are one of the tastestgrowing segments of the market.

    '949-China

    establishedPeop/fJSRepublic,

    1947-Dr. fdwinH.

    Land introducesthe Polaroid

    camfJf8,

    '95'-UNIVAC. thefirst com-mercial

    computer. issold to theUs. Census

    Bureau.1951-

    Russians launchSputnik, the first ani-

    fieie/earthorbltingsatellite.

  • MILLENINIUM DUnOOHto offset the difficulty in finding expert gear makers. MalIY American workers are notas killed as their European counterparts, says Ron Scbomann, Vice President ofLMT-Fette. "Thi costs American industry in terms of lower quality and broken tools.Tile development of electronic centrols ha allowed America to catch up because CNCmachines are not as dependent on the operator to know as much as in the past.America has many unskilled people turning out good gears using this technology."

    Joe Arvin of Arrow Gear agrees that machine tool technology can make a big ,dif-ference. "PeopJeare saying that the old-umersare leaving and the young upstartsdon 'I know any tiling." However. a the machines get better. we depend less on tileskills of those old-timers, Arvin says. "You don't have to have old school craftsmenwith the computerized machine ."

    But the rapid pace of change in todaiy's technology requires an ever increasing need forcontinuing education. 'The education we provide today to the next generation of special-ists i the highest ever, and I believe that the learning phase in somebody's life willincrease, not shorten. People will stay longer in the leaming process," says Kozma.

    The Next 1000 Years"I cannot really tell YOII what sort of tran missions we will build twenty years from

    now," says Kozma. When you think what happened! in the last WO years, ifyou lookback in the hi tory books at. bow people were dressed and. the tools they were using100 years ago, and if you ask me to look forward [00 years from mow, or even 50 yearsfrom now, and ask me how [thlnk it will change, it's a very difficult question."

    Kozma sees concern over the environment as being a key issue in the years to.come. "In everything that we manufacture, we'll have (Q be focused on a higher envi-ronmental friendliness," Kozma says. "whether it's automobiles, whether it's masstransportation like airplanes ortrains, or whether it's a refrigerator, and we have toconsider when we're manufacturing it that there must be an environmental way of dis-posal, We cannot continue to make waste mountains, which have a, tremendous nega-tive impact on the environment"

    '96'-Development ofTooth ContactAnalysis by

    Meriwether Baxterand Ernst Wi/babe;

    at Gleason.

    t!164 -Oarle Dudley pulJ.

    lishes his GearHandbook.

    1968-Pfauter intro-

    duces carbidehoobing.

    t96i-S~mitomo

    introduces thecvcloidal gearreducer in theUnit,~ States.

    '963-Earle

    BuckinghampublishesAnalytical

    Meroanics ofGears.

    1963-John F. Kennedy

    assassinated. '968-Apollo 11astronauts

    land onthe moon.

    I. ,.*, 'II'

    '960'-Invention

    of thelaser. .,

    1961-General Electricintroduces cubic

    boron nitride (C8N).*

    "The gear industry requires if lot oftechnical skills to do a good iob. Itdemands aSlever-i',lcr8,asing move-ment in those technics! skiUs.Tbere is a continuing difficulty of

    IlRving enollgll people who wlder-stand gears leclmically-how todesign them so they are strong aridquiet, flow to macwfaclUre them.The shill sets IlecesSilry to do agood job are 110t thete. More trsin-illg, something. lias to be done to'encaumqe people to go ituo the;/I(1115try.Tile US is worse off t.hansome countries, tnn tile global trelldis for less skilled people. Ifs goingto lead us to havillg organizationsproviding those skills 011 all out-sOllrcing imsis. "

    -Gary Kimmet, VP WorldwideSales and Market;,,!}, ,Gleason

    '974-Pfaurer introduces firstNC hobbing machine,

    incorporating the"Electronic Gear Box."

    '976-KappCBNhob

    sharpening intro-duced to the u.s. (byAmerican Pfauteri.

    J913-Oil embargo.

    1916-Steve Wozniak' and Steve Jobs build their first .computef, theApple I. "liVhen my dad was writing the Manual of GearDesign. he calculated everything by hand from 15-place trigtables. He literally wore out an old handrun calculator.Nowadays, you'd Just do the whole thing I?II a compl!cer.

    - tllOC K. 8lJCkmgham;8Jlcerpted from a

    1997 interview.

    JANUARY/FEBRUARY 2QOO :291

  • ,.r-First CNC con-trolled combi-

    nationleadlinvalutegear checkersint/oduced to

    U.S. (AmericanPfaulerJ.

    '9IM-Gear Technologypublishes its

    first issue.rSlZ-

    KappCBNplaced wheel

    I

    pra.file g..rin. d-ing introducedto U.S. &Canada

    (AmericanPlautfir).

    JJBO'-Ti/l/coated~ear toolsmtroducedby.BarberColman.Star &fette.

    L

    J9BD-~First Spacs ..Shuttle. .

    '983-CompactOld:

    Debut.,_,-The begmning of the rise of tile sport utitlityvehicle. The greater demand for rear-axle dif-ferentials in 4X4 and SUV vehicles has a hugeimpact on the demand for spIral bevel gears;

    Gary Kimmet adds that the trend toward globalization and increased competitionwi1l inten 1fy. "I see consolidation of gear companie ," K:immet ays. "The impact ofglobalization requires some level of critical mas in order to compete in the globalmarket. That means trouble for some small. gear companies."

    Many predict tlUIl the automotive industry will continue to drive trends in gear manufac-turiQg. Eleclric vehicles and C\iT technologies will certainly have an impact in the decadesto come, allhoogh the exact nature of that impact is still uncertain Electric vehicles may elim-inate geared transmissions altogether by using direct drive teclmology. Continuously variabletransmissions will probably require more accurate, IOOre ,efficient gear ystems.

    "We foresee in the next years to come tremendous changes in consumer behav-ior," says Kozma, "There will be new products on the market which we don't eventhink of today. When YOII think about the changes only in the 101 t 20 years as far athe consumer market is concerned. the speed ingoing into different products willrequire from us that we stay ab olutely alert. to look forward, to en e in which direc-tion the next generation wiJl go."

    The con ensus seems '10 be that there will almo_ t certainly be gears in a diversityof products for many years to come. How they're made, and in what quantity and atwhat quality will be determined only by time.

    "I don't want to be negative," Kozma says, "but the demand for gears on a worldwidebasis will in quantity reduce, but has (Q improve in qua1ityand performance. All the prod-ucts coming in tlJe future will definitely require a higher class of quality. There will be sub-stitutions to the gears which havebecn traditionally mancfaemred. There will be gear mak-ing melhods which maybe limve not been invented. There will be technologies to come andtools which are not on the ID.ar1s:ettoday. But gears will be required in the future. But Ican-not tell you to what extem new technologies will eliminate gears."

    Bill Maples puts a. more positive pin on theindustry's potential. "We haven't. seenanything yet," he says. "I don't see why it's necessary to be anything but positive, Themain thing people have to realize is that it's going to change." 0

    '.'-Dpti-Gash Hobs areintroduced by Pfautar-Masg Cutting Iods.

    '9!15-HsrleYD~vidson begins g". inding transmis-sion gears to reduce nOise.

    ,m-U.S. del8fjation

    becames the secretariatto ISO TC..so. '996-,ulUnthaf

    DIEIGElIIINDU,STRY

    IHOME~AGE.

    1994-LieMe"

    introd/ICBSdry hohbing.

    1994-Carbide

    Hobs intro-duced byUebherr,PfauterMaag,Fette

    '!11-WaferHobsare intra'ducedby

    PfauterMsBgCutting Tools.

    '911- IThe First GearExpo is heldin Cincinnati;

    DH,

    '191-Gleason and

    Oerlikondebut drycuttilll} of

    spiro/bevelgears. '999---.....

    UIIIJ-Fallot the'Berlin Wall.

    1!1SO-Breakup

    of theSoviet Union.

    1919-Nelson Mandelselected presidentof South Africa.

  • - - --

    ------- --- - - MIL~ENNIUMIDUlLOOH

    JANUARV/FEBRUARY 2000 31

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

  • Reverse Engineering ofPure Involute CylindricalGears Using Conventional

    Measurement ToolsIsaias Reg,aladol & Rodrigo' Lopez,

    IntroductionDe igning a gear et implies a considerable

    effort in the determination of the geometry thatfulfills the requirements of lead capacity, reli-ability, durability. size. etc. When the objectiveis to design a new set of gears, there are manyalternatives for the design, and the designerhas the freedom to choose amongl.hem.Reverse engineering implies an even biggerchallenge to the designer. because the probleminvolves already manufactured gears whosegeometry is generally unknown. lln this case,the designer needs to know the exact geometryof the actual gears in order to have a referencefor the design.

    Nomencla.ture

    MOBN

    N.N,ODOM

    Pp- nR

    ~Rb

    RDRM

    Measurement over ballsTotal number of teethNumber of spaces in the span measurement

    Number of teeth in the measurement over ballsOutside diameter

    Outside measurementTransverse diametral pitchNormal diametral pitch

    Theoretical pitch radiusAuxiliary radius during measurerne lover ballsBase radiusRoot diameterRoot measurementRadius of the wire (ball for helical gears)Span measurementTran verse tooth thieknes at reference radius RTheoretical normal pres ure angle

    Auxiliary pressure angle during measurement over ballsTheoretical transverse pressureangle lit reference radius RTheoretical. helix angle at reference radius RBase helix angle

    U iog advanced measurement machines, theprofile of the tooth can be checked and comparedwith 11 reference surface; therefore, using a trial anderror scheme it is possible to approximate the actu-ail geometry of ihe gears. Unfortunately. thesemachines are expensive and seldom available to thedesigner, so the need for a melhod using conven-tional measurement tools i ju tified, especiallywhen the measurement has to be done in the field

    This article presents a methodology ba ed onmeasurement over wires, and span measurementto determine the geometry of a pure :involute gear.

    BackgroundFor the complete specificaeon of a cylindrical

    gear, it is necessary to know the following:

    Number of teethPres ure angle al a. reference diameterOutside diameterRoot diameterHelix angle at 3 reference diameterCircular tooth thickness at a reference diameterFace w:idth

    It is well known that the operating surface ofthe tooth is uniquely defined by the base radiu andthe base helix angle. This surface i limited by 'theoutside diameter, fOIDl diameter and face width.The tooth thickness is defined by the relative posi-tion of two symmetric tooth surfaces.

    In order to define thegeometry of a gear, ilt isuseful to divide its characteristics into threegroups,The first group include characteristics that can bedirectly measured with conventional tools. The sec-end group tis integrated by properties that requirespecial tools or procedures foriheir derermination.The third one is fanned by tho eproperties wlrichrequire some additional calculations for their deter-mination. Thi division is shown in Table 1..

  • The proposed method is based on the measure-ment of the four properties in Group ] and tWo inGroup II (measurement over balls and span mea-surement).

    The procedure to calculate m.easureme t overballs and span measurement is available in tile lit-erature (Refs. 1-3,).. Fig, 1 shows the transverseplane of a gear: from this figure. it may beob erved that given the transverse tooth thickness'T' of the gear at a given radius 'R', the measure-ment. over balls may be calculated as follows:

    MOB, = 2R.... + ~ )2-2COS (2~N,) mWlI.ere:

    And $2 Iscalculated from:

    .. Tin) R"" ItInv($2) = -- + v(I. + ---,r - --2R .~ N

    In the case of helical gears, the effect of thehelix angle has to be considered, and, Equation 3becomes:

    11: (4)NFrom Fig. 2, the span measurement for a

    given gear may be calculated by the equatioa:

    Again. in Equation 5, the base helix angle isincluded to compensate for the fact that in helicalgears the measurement is actually performed inthe normal plane. The number of teeth consiseredduring the measurement (N.) is limited by twoconditions-contact of the caliper with the root ofthe teeth and contact of the caliper wi.th. the lip ofthe teeth.

    Fig. 3 bows the limiting number 'of teeth fordifferent numbers of teeth and pressure angles instandard spur gears. A may be observed. mere isalways a range of teeth numbers to use for thedetermination of the span measurement.

    ToolsDuring the measurement precess the fol.ow-

    ing tools are required: A conventional calliper or micrometer of suitablesize for the gear to be measured, If a digitalcaliper is available, it is recommended, alth ughthi is not strictly neces ary. A et of pins for the measurement of gears. It isconvenient to remember that helical gears must

    Group] Group H(Directly Measured) ,(Requires Speci.aJ TooWP:rocedu..res)

    Groupm(Calculated)

    Number of teethOutside diameter

    Root diameterFace width

    Chordal thic.lcness & addendumMeasurement over balls

    Span measurement

    Pressure angleDiametraj pitch

    Helix angle

    Table l - Division of the geometrical ,characteristics .108 gear

    (2)

    ).~--n.'.._./... ...

    (3)

    R.

    Pig..1-Measureml1n' over balls I'n, a pur gear.

    Fig. 2-Span measurement in a spur gear.

    be measured with balls instead of pins. The rec-ommended "standard" ball diameter is defined as1.728IDiametra] Pitch or 1.68lDiametral Pitch. Ifa set of "standard" pins is, not available. a set ofsteel balls of nominal diameter close to the stan-dard! may be used instead, A set of disc calipers is desirable. although inmost of the cases this tool can be replaced withconventional caljpers, A calculator or a portable computer with the pro-gram for measurement. The computer is recom-mended only because the calculations can be donefaster, but the procedure can be easily done withthe calculator,

    Dr. lsalas Regaladois a gear designer andconsultant at CIATEQ A. c:(J research' and developmentinstitution providing techni-cal support to Mexicanindustry:

    Dr. Rodr:igol Lopezis the director of IheMechanical TransmlsssionsDepartment ai' ClATEQ' A.C.

    JANUARV/fEBRUARY 2000 33

  • Calculate I R P I pGiven. .c> $[ ljI nI

    I

    RbI

    ~ Sino! ( Sln(~) ) eos-I ( Tan(

  • Because of the fact that the tooth thickness isthe same for all the teeth, it is possible to. definea constant K2as:

    J( =..I.. + 2]nv( q, ).~ R 1_ SM) _ 2nN I- K N_ . SM2 _ 2nN.z- KI N

    Then from Equation 3:

    And from. Equation I.

    ~ _ -,.._M_0_8_,-_2_~~_

    2 - 2Cas ( 2-;f! )

    Then, from Equation 2:

    U' it is po sihle to measure with balls of differ-ent radius, the value of Rb would be the average ofthe individual values obtainedapplying EquatiensW-12 for each ball diameter.

    Using the definition for KI' it is possi le toobtain \jib by:

    'Vb = Cos" ( ..~ )

    ]t i well mown that it is possible to manufac-ture a gear with a given pressure angle at a refer-ence diameter using a hob with different pressureangle by properly pulling or pushing the hob dur-ing the manufacmring process. Based on this, it ispo sible to. assign an arbitrary value to anyone 'Ofthe following properties, and determine the rest ofthe parameters in the gear.

    Ijl, Normal pressure angle$t Transverse pre sure angle\JI Theoretical helix. angleR Theoretical pitch radiusPdn Normal diametral pitchPd, Transverse diametral pitch

    The equations relating these parameters mlly befound in References 2 & 3. Six cases arepos sible,and the equations for each of them are listed inTable 2. Once tile e parameters have beendefined, the tooththlckness may be calculated

    applying Equation 9 as:

    (9)

    ([ 1)

    (12)

    (a)

    fb)

    (13)Fig. 4-Oulside anti root measurement/or a gtarwith odd or missing' ,teeth.

    Biblio.graphyI Lynwander, Peter. "Gear Drive Systems,

    Design and Applications," Marcel Dekker.

    Inc. 1983.2 Dudley, Darle W. "Dudley's Gear

    Handbook," McGraw-Hi]], 1991.3 American Gear Manufacturers Association.

    "ANSUAGMA 2002-B88: Tooth ThicknessSpecification and Measurement," 1988.

    JANUAAYIFEBAU",AY 2000 35

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  • _____________ IMA!NAGEMIENT MATTERS _

    Shop Floor Safety-Things to Think About

    D I should be a point ofpride that the gearindustry is actuallysafer than most. othermetalworking industries.

    However, accidents do hap-pen ..A review of OSHA inspec-tion reports for the gear manu-facturing industry (SIC 3566)from January, 1990,throughNovember, .1.999, showed atotal of 247 violations forwhich OSHA sought fines,including one fatality. Theseviolations ranged. from hazardcommunication and control of

    hazardous energy-lockout/tagout procedures at the highend (36 and 30 violationsrespectively) down to electricaltraining and arc welding and

    outting procedures at the lowend (1 violation each),

    Because of the nature of

    the business. gear shopsattract a higher caliber ofskilled worker than, otherkinds of shops, and this goes a

    long way to creating a safeworkplace. "From the shopsthat I have seen, they are verywen setup," said JohnConiglio, vice president ofOSEA, the OccupationalSafety and EnvironmentalAssociation, Inc., an industri-

    al safety consulting firm. "Ifind them in good order, neatand clean, with good accidentrecords. If they have a prob-lem. you normally see handand finger injuries or eyeinjuries." These are thingsthat the proper use of machineguards, .Iockoulltagout proce-

    Charles M. Coo;per

    dures and personal protectiveequipment used as part of acompany-wide safdypro-

    gram can effectively preventA safety program can do

    other things for your businessas well, Such a program canimprove your bottom line bylowering the costs associatedwith health insurance andworker's compensation; byraising employee morale andproducl:ivi:y; and! by reducingthe scope and! occurrence ofregulatory fines and penalties.

    What elements go intosuch a program? Shop floorsafety aris es from a combina-tion of factorsvall of whichyou can control-environ-ment, equipment, training and

    supervision. When these fac-tors are in place and workingtogether properly, your shopfloor will be a safe and produc-tive place 10 work.

    Safety from the Top DownSafety in 'the workplace does

    Dot begin -wilh technology, butrather with the mindset, partici-

    pation and leadership of man-agement determined to makesafety part of their company'scorporate culture, This is impor-tant, because wilhout support

    from the Ieadership, no safetyinitiative will last.

    According to Coniglio,

    "Companies need to recognize,in a business sense, that safety is

    Ihey have good safety people,they do because the safety per-son is looking at the cost pethour and the cost of goodsimpact that safety and healthhave, The best resource theyhave is the people who work inthe plant, and that resourceneeds to be protected because ofthe return on investment."

    Coniglio then explained thatcompanies need people in safe-ty positions who can tell the

    board of directors what the costimpact is, not only in terms oflosses, but also in terms of pro-ductivity and product improve.ment. These factors all tietogether to improvelhe compa-ny's bottom line. 'The companythat has aneffective safety andhealth program," said Coniglio,"will absolutely be better offthan their competitors;"

    [tis the job of managementto develop the overall safetystrategy for the company and toprovide adequate training toboth workers and supervisors.This strategy should tellmanagement how and whento use engineering or admin-istrative controls to limitworker exposure to hazards.It should also tell workersand their supervisors where

    hazards exsist and how toimplement these safety direc-

    tives to abate them. The strat-egy should also include

    110 more o~ less important than audits and surveys to allow.anything else that they do. They management to track the sue-mm O\.It a quality product. They cess or failure of the programtum out a product that's safe. as well as a way for workers1hey need to recognize thai. if and supervisors to suggest

    changes and improvements,

    Environment, equipment,

    training and supervision arethe factors that corne togetheron the shop floor to create asafe work environment, andthe strategy ought to reflectthat. These broad categoriesinclude many obvious thingslike machine guarding, gog-

    gles and gloves, proper elec-trical maintenance, Clean anddry floors and air quality,Theya]so include obscurethings-temperature, ergon-omics, noise, the way storageareas are set up, stress, vio-lence-the list goes 01'1. [t is

    up to you to go through yourplant and try to see it as anOSHA inspector would. Try to

    JANUARY/FEBRUARY 2000 31

  • _-----------MANAGEMENTM'-ATTERS------------see what kinds of hazardsexist in your plant and figureout how to abate them.

    EnvironmentalSafety Issues

    This covers your facilityas a whole and includes airquality, temperature, noise,surface contamination, light-ing, and building structuressuch as floors and stairs, rail-ings, sprinkler systems anddoor signs. All of these fac-tors must be taken intoaccount, but a [at of it is justcommon sense. Floors mustbe kept clean and dry, walk-ways should be weU markedand clear, and places whereworkers could faU should beguarded in some fashion. Anyhazards in these areas shouldbe either guarded or fixed.These guards and fixes don'thave to be very complicated,either. It could be as simple asswapping out one kind offloor covering for another."Sometimes the best resultscome from the simplestfixes." Coniglio says.

    Other things to considerare that ladders should not beused where a permanent stair-

    38 GEAR TECHNOlOGY

    case would be appropriate,work areas should be well lit,sprinklers should function,exit doors should be wenmarked and open easily fromthe inside. Dealing with itemssuch as these, which are cov-ered under OSHA standards,would be a good start to anysafety program. However,there are three shop floorenvironmental issues thatshould be looked at closelysince they can have long termeffects on your employees-fluids, temperature and noise.

    Metalworking/MachiningFluids. Chemical contamina-tion is becoming a majorissue for American industryand labor. According toOSHA, millions of workersbuilding automobiles, farmequipment, aircraft, heavymachinery, and other equip-ment are exposed to machin-ing fluids, Studies haveshown that occupational ex-posure to these fluids hasresulted in cancers of theesophagus, stomach, pan-creas, colon, rectum and othersites; respiratory problemsranging from respiratory irri-tation and asthma to bronchi-tis, lipoid pneumonia andhypersensitivity pneumonitis;and skin problems includingirritation and dermatitis.There is evidence of impairedhealth at levels wen below thePermissible Exposure Limit(PEL) for oil mists (5 mgim3

    time weighted average(TWA)) and the "nuisancedust" exposure limits applica-ble to aLIother machining flu-ids (15 mg/m3 TWA for totalparticulate ).

    Because of this evidence,there are those in industrywho do not believe these stan-dards go far enough. "TheUnited Auto Workers areinvolved in looking at worker

    exposure to oil mist in theair," said Coniglio. The UAWeven had a hand in a I 992report caned "Health Effectsof Exposure to MachiningFluids." According to theauth ors of the report, "Resul tsfrom both the respiratorymorbidity study and the mor-tality study suggest associa-tions between machiningfluid exposure and respiratorydisease or cancer that are con-sistent with an interpretationof causality. Our initial dose-response analyses suggestthat an exposure level of 0.5mg/m" wouLd minimize anyadverse health effect of work-er exposure to machining flu-ids .." This study and othershave led to calls from bothlabor and business for a low-ering of PELs for metalwork-ing and machining fluids,

    Because of these acknowl-edged health dangers, .oSHAhas designated metalworkingand machining fluids to be apriority for comprehensiverulernaking, The agency is inthe process of working withbusinesses and labor to devel-op these rules. In the mean-time, some of the immediatesteps you can take today to[ower the risk associated withthese fluids include protectiveclothing and equipment,mechanical splash guards andenclosures, local exhaust ven-tilation, marking any handtools used in contaminatedareas to prevent chemicalcontamination from spread-ing, and a. good program ofpreventative maintenance.

    Ambient Noise. Noise inthe workplace is another envi-ronmental hazard that shouldbe addressed. In high-noiseenvironments, hearing candeteriorate over time, begin-ning in the higher frequencyranges and progressing down

    into the low frequencies todeafness. OSHA regulationsstate that in work areas wherethe noise level is 85 dB(A) orabove, hearing protectionmust be provided, but it is upto the worker to use it At 90dB(A) or higher, the use ofsuch protection is mandatory,

    Ambient noise issues callbe addressed administrativelyor mechanically, Administra-tive controls can includerestricting the amount of timea worker is exposed to thenoise and/or mandating theuse of personal protectiveequipment such as earplugsor muffs.

    These devices carry noisereduction ratings (NR)thatwere developed by ANSI. Thehigher the rating, the morenoise is muffled. Care shouldbe taken to get the right NRrating for your work environ-menlo For example, an NRrating of 6 or better is neededto cop