theioumalot gear manufactu'ringrecently begun pursuing a computer system to help us in our gear...
TRANSCRIPT
The Ioumalot Gear Manufactu'ringNOVEMBER/DECEMBER' 1987
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Uigh production cutting of identical gear shapes requires both speed and accuracy.But some fast. accurate machines incur maintenance and operator costs that eat up profits.With Kapp CBNform grinding, you don't give up productivity (Q maintain profitability.• Kapp CBN machines are faster than other grinding processes, with no heat checking orburning. Kapp CBN accuracy has proven itself on spur & helical involute forms, radial forms,near-net forgings, internal & external profiles, vane pump slots and constant velocity joints.• Kapp CBN machines are operator friendly. for fast recall of setups and accuracy time after time.• Kapp CBN machines use CBNwheels that incorporate the desired form right in the wheel withno need for dressing.Ifyou'd like to find out how Kapp CBN technology can improve your productivity, contactAmerican Pfauter, 925 Estes Ave.,ElkGrove Village,lL 60007. Phone (312) 640-7500.
Klingelnberg introdiuces the fastest ... most accuratecomplex worm and thread grinder available ... any-where in the world! The' eNG ccntrelled HNC-S5 storesdata for up to '960 'com;pl'exshapes, reducingl set-up'to, 10-15 minutes ... a fr:aotion of the time required! withmechanicaUy ,controlled grinders.The HNC-35 is versatUe,loo'. It perrorms ,creep-feedgrinding from the solid, eliminating U1eneed for pre-liminarY milliingl of worms, threadsand rotors. 111"S,twomachines in one .... with the high degree of accuracyyou'd expect from Klingelnberg'.
~ KIL'INGELNBERG
The C'Ne ,controlled HIN:C'·35Wo'rm and Thlre'ad Grlind,r
The HNC-35 is available w:ith a mechanical dresser oran optlonal CNC dresser, for speoiall forms and fl'ank5.Whether you produce, smalllQuantities or long produc-tion runs, U,e FAST sst-up .... FAST cycling ... HNC·35 will' Improve your worm and thread IproducUvity.:Foraddltional iinformation anda copy of our cataloq,contact: IKling:elnberg CorlPora.tion, 15200 FoltzIindustrial Parkway, CI'eveland. OH 44136,. Or, phone(216) 572·2100 for an extra FAST response.
EDITORIAL STAFFPUBLISHER &EDITOR-IN-CHIEFMichael GoldsteinASSOCIATE PUBLISHER &MANAGING EDITORPeg ShortPRODUCTION/ADVERTISINGPatricia FlamASSISTANT EDITORNancy BartelsEDITORIAL SECRETARYPamela NolanFREELANCE ARTISTCatherine Murphy
RANDALL PUBUSBING STAFFPRESIDENTMichael GoldsteinVICE PRESIDENTRichard GoldsteinGENERAL MANAGERPeg ShortART CONSULTANTMarsha Goldstein
COMPUTER AIDED DESIGN FOR GEAR SHAPER CUTTERSDonald S. Whitney
11
KHV PLANETARY GEARINGDavid Yu
21
FINISHING OF GEARS BY AUSFORMlNGMaurice F. AmateauRaymond A. Cellitti
32'
RANDALL PUBLISHING1401 Lunt Avenue
P.O. Box 1426Elk Grove. IL 60007
(312) 437-6604
SELECTION OF HOB BING nATAYefim Kotlyar
38
EDITORIAL 5
VIEWPOINT 6
TECHMCAL CALENDAR 9
SME GEAR CLINIC 9The Advanced Technology
ofLeonardo Da Vinci
1452-1519
COVERLeonerdo designed a great many
machines for use in the textile industry.The design on our cover is a shearingmachine for removing the llilP from woolendoth, a job previously done by hand withenOfT1J()USscissors. The doth was stretchedon a travelling frame which was pulledthrough the machine. A set af gear worksactivated the second blades of the scissorsdevices. Leonardo also designed a gig millfor raising woolen nap that was so effec-tive that when one of its successors wasincorporated into textile machines in theearly J9th century, widespread unemploJl'ment and rioting among textile workersresulted.
BACK TO BASICS ••• GOOD CEARS START WITH GOOD BLANKSWilford E. Maples
42
CLASSIFIED 41
November/December, ]981 Vol. 4, No.6
GEAR TECHNOLOGY, The Journal of Gu. Mam,r.d ..rI"lI USSN 0743-6858) ls published bimonthly by Randall Publ .. hin.ll.Co., Inc .• 1425 Lunt Avenue. P. O. Box 1426. Elk Grove VlIl"lle. It G0007. GEAR TECHNOLOGY. The Journal of GeaT Manufar·turi'll!.. is diSlribu.te..· d fT. e. of Chari!._.e to qualified individuals and firms in the lIear manuf .•cturi~$ industry. Su.bscrip.tinn Tates fo.I' non-qu"Med indi.vid.uab and firms are: 135.00 in the Unite<! States ..$55.00 for foreign countries. Second-Class pos\ajle paid al Arlil1ll!OnHeights, IL and at. additional mailiTll! ottic<!.Postmaster. Send ..ddr ess changes to GEAR TECHNOLOGY. The Journal of Gear M.nufacturinlil. 1425 L"nt Avenu . P. D. BoM1426. Elk Grove VilI"IIe. IL G0007.©Contents copyrighted by R.ANDALL PUBLISHING Co. .• INC. 1987. ArticJes appearing in GEAR n:CflNOLOGY may not bereproduced in whole or in part without the express permission of the publisher or the author,MANUSCRI.PTS: We are requesting technical: paperswith an educational emphasis fOT anyone having anything to do WIth thedesign. manufacture. testing or processing of gears. Subjects sollllht are solutions to ."""i1k problems. explanations of new: I£Ghnol.o!&.techniques. desil!n s, processes. and alternative manufacturing methods. These can range 'rom the ..How to ... " of geal' CU'Ul'll!(BACK TO IBASICS) to the most advanced technol<>!lll.AUman""ripts submitted will be cardull.y considered. 110....,""1', the l1'ublish£r.... umes no responsibility fOTthe safe~ Or return of mal1US(:ripts.Manuscripts m.at be accompanied by a self-addressed. s"Jr·.tampe<!
I....... ....JI :.3.;:.and be sent to GEAR n;CHNOLOCY. Th. Journal of Cear Manufacturing, P.o.. 80 •. 1426. Elk Grove. [I.. ,G<lOO7·,(312)
Operator ControlPanel for part load-Ing and machinesetup.,
Graphics Jprintercopies CRT.
Plotter deliversmulti-color hardcopy of graphicsand test -data.
CNCstatusmonitor providesstatus and posi-tional display ofmechanical systemand CNG ,controlfunctions.
one-time entry of partprint and tolerancedata. "Mouse" pet-mits use of CADtechniques.
Our Model 3000 'OC Gear Analyzer is a third generation CNCgear inspection system iin-corporating all of the comprehensive analytic-all tests and evaluation capabilities ofprevious M & M systems, such as our Model 2000" but with these added capabiUties:• Dramatically improved speed and aocuracy through new mechanical system d'esign
and advanced eNC oomrot teChnology .• ' Computer hardware and applications software are modular to aUow the user to buy
only the required capability., This makes the 3000 ac adaptabl'e to laboratory test,ingor production-line inspection.
• Integrated Statistical Process Control' with local' data base capability is an optionalfeature.,
• Networking wilth MAPS compatibiUty is available.• Robotic mtertaclnq for totany automatic load/test/unload operation can be
incorporated.For more information or applications assistance, write or call: M & M Precision Systems,300 Prog.ress Rd., West Carrollton, OH 45449,513/859-8273, TWX 810/450~2626,FAX 513/859~4452.
M&M PRECISIONSYSTEMS
AN ACME·CLEVELAND COMPANY
OIRClE A-6 ON READER REPLYCARD
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I~I)It'()IIIJ.U4
DONT SELL US S,HORTI
How is It that we woke up one day In the early 1980s[0 rind that apparently .American industry was suddenly in-efficient. our workforce unproduUlve and our managementinept7 Almost overnight Industry found its sales droppIngdramaocal'y, while for many companies foreign cornpeu-tion became excruclaongfy Intense ThiSsudden change inthe economic climate provedfatar for many companies andhas been nearly as hard on our conecnve morale. In a coun-try used to winning. we began to hear ourselves talked ofas losers.
Unfortunately. thiSgnm diagnoSISwas right In some cases.The tough times of the early 1980s were. perhaps, anecessary, if cruel. awakening for Amencan business. Butthese first assessmentswere only partial truths. and the postmortems. premature. As with Mark Twain's obituary, [hereports of the death of American manufactunng have beengreatly exaggerated.
While we had. perhaps, been careless and allowedourselves to be blindsided by Foreign competition. not allour troubles could be laId at the door of a soft, agingeconomy that had lost its edge. Industry was in a bind thatno amount of competitive edge or effort could entirelyovercome.
The early 1980swas a orne that the American dollar andinterest ratesrose to their highest levelsin many years. Pricesfor goods manufaaured for export suddenly increased interms of foreign currencies, while dollar prices of foreignproducts dropped. cutting off marketsand making Americanproducts uncompetltlve through no fault of our manufac-turers. Whlfe some American companies failed because ofcornoeeuve softnessor bad management. most others werevictims of economic CIrcumstancesover which they had nocontrol. Even the most astute ousnessoerson cannot over-come these kinds of economic conditions, or. for that mat-ter. a trade or fiscal policy on the part of the govemmentthat undercuts hIS or her best efforts.
But Amencan Industry has always responded well underpressure. HistoncaJly,It has been pragmatic and flexible. Ithas learned from its own mistakes and has taken advan-tage of good Ideasfrom everywhere. Itsattrtude In the early19805was no excepnon. In spire of the foreign exchangedisadvantages, a great many companies took the stepsnecessary to survtve They Invested in updated machines.processesand practices.They desIgnedbetter. more saleableproducts. and they developed a savvier approach to theirrole In the global economy. They took some of their com-petitors' best ideasand used them to their own advantage.At the same time, businesspeople and. hopefully. theirelected representatives, became more aware of the needfor sensibie government trade and economic policies.
All these hard-learned lessons are beginning to havean effect The recent "weaker dollar" is actually a more"competitive dollar." giving American business a fairer
shot at global markets. As a result, more and more foreigncompanies are finding It profitable to buy from Americansuppliers. American companies are again becomrng com-petitive in terms of price, quantity and delivery.
Just as Important, American quality is again becomInga standard by which products can be Judged Some ofour rouqhest competitors from overseas now buy partsfrom us, not because they're cheap or because It'Spolitically advantageous to do so, but because our prod-ucts are the best they can get. American IngenUity, re-sourcefulness and fleXibility are again making a differenceIn our competitive stance.
Of course, things will never be the same as they weretwo decades ago when American products dominatedevery market. That era ISover. probably never to rerum.We as a busmess community have had some seriousproblems. not all of which are yet solved. and all ourtroubles are not over. Because of our size. response timeto changes can seem painfully slow. and current globaleconomic realities will demand every bit of techmcal.manuFactunng and business expertise we can muster. Truscountry is unmatched in terms of human and physrca:resources and market size. HistOrically. we have alwaysbeen able to summon the will and the means to get anyjob done that we really wanted done. Times andeconomic conditions have changed. but Americanresourcefulness has not. In evaluating winners and losersin the economic arena over the next few years. we shouldnot sell ourselves short.
November/December 1987 5,
Dear Editor:
Thank you for the very good magazine on gears, It is veryinformational. contains a wealth of trade information. but stillmaintains a high level of papers. unfortunately not typical forother trade publications.
Eugene I, RivinProfessorWayne State University
Questions From the Industry
Dear Sirs:
We are interested in purchasing a computer program whichwould enable us to undertake the following:
J, Plot involute gear tooth profile forms.
2, Indicate the Interference patterns generated with pinioncutters,
3. Show the action of undercutting for varying numbers ofteeth; all produced from mathematical input data,
We shall be pleased to learn if you can be of help to us inthis respect
Uewellin's Machine Co. Ltd,M.S. Horlick15 Kings SquareBristol BS28JJEnglandr02721 424026/9
Gentlemen:
We have a smallJob shop type gear company. We haverecently begun pursuing a computer system to help us in ourgear calculations. Due to the time involved in figuring formulaspertaining to various gears on paper. we are looking for pro-grams to use on a computer system.
We are asking if you know of any computer program that
Letters for this column should be addressed toLetters to the Editor, GEAR TECHNOLOGY, P.O.Box 1426. Elk Grove Village, IL 60007. Letters sub-mitted to this column become the property ofGEAR TECHNOLOGY. Names will be withheldupon request; however, no anonymous letters willbe published. Opinions expressed by contributorsare not necessarily those of the editor orpublishing staff.
6, 'Gear Teohnology
may be available pertaining to gear formulas.Also, We have a Gould & Eberhardt 48H Gear Hobber and
we are interested in a computer program for changing gearcalculations for hobbing helical gears non-differenbalfy. Thisprocessisoften time consuming to do on paper; and we thinkthat somewhere, someone has a program to simplify rrusprocess,
Any help or suggestions you can offer would be greatlyappreciated,
Bethlehem Gear & Machine CompanyRobert A. Schrump.o, Box 157Moundsviffe. WV 26041(304) 845-9050
Gear Couplings
Rethe article of Mr. Stan Jakuba: "Give your Gears a Break-Selectthe Right Couplingl" MaylJune. '87 issueand the con-tributions In July/August. '87 issueby Mr. Michael M. Cahstratand Mr. Stan Jakuba.
The following comments of experts in the field of torsionalvibration calculation ITVe) will prove that the selection ofthe right torsionally soft coupling rrlght elasticity, springcharacteristic and damping) is not "black magic" anymore,but an easy task for an engineer having a highly sophisticatedcomputer program and the right input data for all componentsof the transmlsson. The right coupling for a geared dieselgenerator set can be selected in a few minutes. Provided thegovernor of the engine is stable in the system. the couplingwiJllast for ten or more years, A fluctuating torque monitor-ing device as developed by the signer can be helpful. especial-ly for larger sized transrnissions. as shown below even forrather complicated systemswith several branches, The Signerhas done the TV C, for 13 USNavy support vesselsWith highpowered diesel geared installations (300,()(X). HP total).
As a practical example. Fig, 1 shows a main and auxiliarydrive for a large sized shuttle tanker r125.()(x), tdwl. Thefollowing components are used. The main diesel two-stroke,slow-speed engine IMAN - B&W. 5 cylinder. 6526 kWat 102revj is driVing a propeller through a redUction gear. whichalso includes a PTO (Power Take Off) for a hydro powerpackage (5200 kW at 1200 rev) for discharging the crude all.Between the main engine and the reduction gear a very softcoupling is arranged. On the forward end of the engine agenerator drive (1200 f<W at 1800 rev] via a speed increas-ing gear is attached. and a turbine driven by the exhaust gas(550 kW at 1800 rev) is Incorporated, The generator IS runnngat constant speed even at variable engine speed using a RCFrRenkConstant Frequency) gearbox. For eight different modesof operation for this vessel. an optimized coupling has to be
TORSIONAL VI8~ATION SYSTEM
AUSl 111 SoP1'!OPflLER
I
KJ./S60/1200/550
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2'lpl " " I .r,1 .J3 19 37 36 35 33 _3041 COMPLETE SYSTEM [J
o priooipallocallOnS of 'forced vibrallon caleulauon I] TURSI£.rCS
I:' supplementary locanons 01 lorced vibration calculation 'O·'IFjj') .._1
1
• recommended IocallO('s lor torque measurement at sea mals.2 '3'
5
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DREHSCHwINGLI"IGSBER[CHNU GTORSIONAL VIBRATION CA.LCUl.AT]ON
fi . 1-~ of the torsiorWvibrillion system for it crude oil,shull~ tanker.
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POWER PACI,
(continued 01'1 page 48)
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Fig. 2- T.V.C formisfiring situation.Cylinder 1 has onlycompres ion. Mainengine is driving pro-peller and turbine. TheSth order and 1 l orderof engine are dominant.
selected. It beIng Impossible to shift all cnrical resonances outof the speed range.
Fig. 2 shows a typical example (or a mlsfinng sruaaon (onlycombustion). which ISdeFinrng [he worst situanon for the In-stallation. The first order dominant at misfirrng and the fifthorder dominant for this five cylinder enqme create fluctuat-ing torques which at certain modes of operation may exceedgiven permissible values for either resuent coupling rnarenator the gears. Twenty years of experience in T V C have builtup so much knowledge in selection of the right componentsfor transmisions in marine and industrial application that [hepoints discussed by Mr. Jakuba and Mr Cal,strat are nor aserious subject In my daily routine any more
Dr. Wilhelm SchaefferRenk Tacke GmbHAugsburg. West Germany
~ +---------~----_;r_-+--------~-+------~
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Novem'ber /Deoem'ber 198,' 1
Forget that (liMA. is one of the top gearhobbing machine producers in the world.Disregard the fact that you get superiorreliability and engineering from a companythat has been a gear cutter pioneer forover 40 years.
Remember that CIMAstarted in Italy.
That's where (1M>\.built Its legendarycommitment to customer satisfaction, And,until now, that's where you had to go for(IMA quality. No more. ClMA USA is nowheadquartered in Richmond, Virginia,Whichmeans your assembly takes place inAmerica and every (I'N\A machine is nowbuilt to the American standard . , . yourstandard.
Being in America,CIMA Saves You Money.
NOW, you buy direct from an Americanmanufacturer: CIMA.USA 501 lower costsfor you, plus better and faster (IMA. serviceand more accessible (INV\ gear productionconsultants.
You know that CIMA.can reduce yourlabor cost per job. Because (IMA'sadvanced computerized automations trimset up timet speed up tool changes andprovide grea,tercutting accuracy andflexibility.
Get Savings In Gear with CIMA.Better quality, lower costs. Nowt get it all
in gear with a call to CIMA~I.JSA.Give us awelcome call or circle us on the readercard to cut your cost now that CIMA:shere,
CIMA·USADivision of G,D. PM, Inc,501 Southlake Boulevard'Richmondt VA 23236(804) 79~9764
Robot LoadingSystem Telefax (804) 79~6187 • Telex684-4252
-~ ------
C,IRCLE A-10 ON READER REPLYCARD
Ctyourcosto i every gear.
wthatCIMA's here.
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Institutes and urnversmes will be Included. This meetIngIS sponsored by the Machine Design & Mechanisms In-stitution of the Chinese Mechanical Englneenng SooetyCo-sponsores are the International Federation for theTheory of Machines & Mecnarusrns. Japan SoCiety ofMechanical Engineers. Verin Deutscher lngenleure andASME/GRI For further Informacion. contact: Inter-Gear'88 Secretariat Zhengzhou Research Institute of Mechan-Ical Engineering, Zhongyuan Rd , Zhengzhou HenanChina. Tel: 47' 02, Cable: 3000, Telex 46033 HSTEC CN
- - -- ---------
TE'CHNICAL CALENDAR I
SME GEAR CUNIC & TABLETOPSH'Q'W IN SUBURBAN DETROIT
NOVEMBER 17-19SME GEAR PROCESSING &MANUFACTURING CLINICMichIgan Inn, Southfield. MI
Three days of presentanons and diSCUSSIOns,TopicS tobe covered Include gear manufacturing methods andmachines, hob deSign and selection. gear Inspection andchart evafuancn, gear finishing. contour gear hardening.gear grinding. cold orbital forming, coolants and CNCgear shaping, Tuesday evening. Nov. '7. will featuretabletop exhibits of the latest gearing products. For moreInformation about attendance or exniomon space. con-[act Joe Franchini at SME. 1313J271-1500. x394.
CAll FOR PAPERSINTERNATIONAl CONFERENCE ON GEARINGZhengzhou, CnmaNext year. Nov. 5-10, 1988 there Will be a three-dayconference which Will Include diSCUSSIonson theory oftooth form. gear strength and durability, gear materialsand heat treatment. dynamiCs of gear systems. vibrationand noise analYSIS.lubrication. non-cyhndncal and non-Involute gears, power transrmsaons and standards. Thedeadline for abstracts Ina more than 400 words] ofpapers to be presented is Nov. " 1987 The workinglanguage of the conference Will be English. A gearproducts exhibition and tours to local factories. research
November I' 7-19. 1987, S1V1Ewill present its Gear Proc-essmq and Manufactunng Clinic and Tabletop Exhibits atthe Michigan Inn. Southfield. MI.
Some of the papers [0 be presented include "Methodsand Machines of Gear Manufacturing." "Design andSelection of Hobs." ",BasICGear Design." "Gear inspec-nonand Chart Evaluation." "Selection of High-SpeedSteel for Gear Cutting Tools." "Orbital Forming in [heManufacture of Gears" and "Deburring ano FinishingGears With Power Brushes."
In addition to these presentations. there will be oppor-tunIty for attendees to meet and discuss the presenta-nons with Individual speakers on a one-an-one oasis.
The M'anufacturlng Engineering Certification Institute hasapproved this clinic ror 18 professional credits toward
CHANGE OF SCHEDULE - CALL FOR PAPERS
ASME's lntemanonal Power transmesion & GeanngConference Will be held Apnl 5-7. 1989. In ChIcago. IlPlease nore this change of date
The conference Will focus on major technical aspects ofpower transmission component deSign. manufacture andapplication. Including gear effiCiency, geometry, raCIng.lubricanon. noise, dynamrcs, chains, belts, drives. bear-ings, shafts, and clutches and brakes for heavy. off-roadequipment Industrial. autornonve. manne and otherappncanonsThe deadline for papers for rrus conference ISDECEMBER 31. 1987.
For further Information, contact: Donald L Borden.P.O. Box 502. Elm Grove. WI 53 I 22.
the SME Recertification Program.
Tuesday evening of the conference has been reservedfor an SME reception and for tabletop exhibits of someof the latest products available in the ,gear industry. Theexhibitors rnclude Gleason Works. ITW Illinois Tools{,ITWIIlitron. Dexter Gear & Spline. M&M Precsion Systems,Bourn & Koch Machine Tool and Abrasive Technology.
SouthfrelCl.MI. is a suburb of Detroit. The MIchIgan Innis located off U,S. 10 between Eight Mile and Nine MileRoads. approximately 30 mmutes from DetroIt'sMetropolitan Arrport.
For more information about the clinic and eXhIbit,contact Joe Franchini at SME headquarters.(313J 271-1500. x394.
Novem'ber/December 1,987 9
"ThM'Swby, n ... Dlckaonnle. ,Ex.....tlve Vice ,P,resldent andl ,GeneralManager of TIle GJ•• lon 'Woris,..... Just tillren _ 1bokI, ......... toprovide' gear.1IIaI'IIIftIcII wlltldIemostlldVanced and' aMbprehenslwe... .,. 01 gear rnet.rvIOgr praducal Indie WDrId." --
Together - two YtN!1I~ ,names Ingeirfng- ,Gleasonand Hofler, DIVIsionof carlZ:clssThe Gleason Works has signed an agreementwith Hofler to provide {omplere sales and
service ofHofler gearmetrologyproducts inthe U.S. and'other ceun-tnes. Thebenefit forcustomers isImmediate:even greaterSj&emS c:ap.TbUity fromGleason. and
the strengttl ofGleason's\NOl'ldIMde salesandservice organization for users of Hoflermetrology products.
leading, the wayIn the months ahead' \Ii.Ie'1i ron out a steadYstream of advances and breakthroughs espe-ciallydeveloped to meet the CfItical needs ofthe gear making industIy. IJ..then ,it comes togears, Gleason provides an int grated ap-proach to geartechnologyand gearmetrologylike no one else in the world. The GJeasonWorks, 1000 University Avenue. Rochester NY1469:2. [716)473-1000
GleasonThe Warldl at IGsllrln,-
CIRCLE A-24 ON ,REAIDER ,RE·PLYCA'RD
Computer Aided Design For'Gear Shaper Cutters
Computer programs have been devel-oped to completely design. spur andhelical gear shaper cutters starting fromthe specifications of 'the gear to be cutand the type of gear shaper to be used.The programs generate the workingdrawing of the cutter and, through theuse of a precision plotter, generateenlarged scaled layouts of the gear asproduced by that cuner and any otherlayouts needed for its manufacture.
The gear data which should appear onthe gear drawing to insure thatacuttercorrect for the part can be designed areshown.
Part information should include thefollowing items:
1. Number of teeth.2. Diametral pitch or module. (If
helical, speCify normal or trans-verse.)
1. Pressure angle (normal or trans-verse).
4 .. Outside or inside diameter. (In-dude limit if topping ..)
S. Tooth thickness (normal ortransverse at some given diameteror dimension over Of betweenspecified pins).
6. Helix angle and hand.
AlJfHOR:
DONALD S. WHlTNf:Y worked forFellows Corporation for 46 years until hisretirement in early .1987. He began with thecompany as:Q gear shaper cutler designer andthen specialized in computer programming,writil'lg va-,ious pr~grams for the design of gearshaper cu.tters and shaving tools. Mr. ltVhitneyis a member of the AGMA Gear 1l1Spectl'onHandbook Corl11l1itteeQJ1da .Life Member ofthe Society of Manufactun'ng Engineers.
Donald S. WhitneyFellows Corporation
Springfield, vr
7. Depth of cut. (Specify rootdiameter and tolerance.)
8. Ma.terialand hardness at time ofcutting.
9.. Lowest point of contact. (Spe-·cified as true involute formdiameter. Mating part and centerdistance information will answerthis requirement.)
10. Root fillet radius specification.11. Stock allowance for preshave,
pregrind, or roughing operations(amount and position of undercutif required).
U. Amount of chamfer measuredradially with limit angle ofchamfer if necessary.
13. AGM_A quality number.14. Type and serial number of
machine,A computer program works through
an. optimizing process to produce the bestcutter design possible for the part inquestion. A good program considers themany constraints and variables involvedand investigates many designs before itarrivesat the optimum one. Because ofthese many variables, i,t is not possibleto write a direct formula or algorithmthat wiU result ina cutter that will meetall of the requirements. For this reasonmany designs may be investigated. Thefollowing is a step by step description orhow such programs are arranged.
Fig. 1 illustrates the three basic cutterblanks that will be discussed here: disk,deep counterbore for internals and partswith interfering shoulders, and tapershank (usually for internals).
The type of blank is 01-" input. pa-rameter with the blank dimensions,thickness, facewidth, life, etc. being sup-
plied by program libraries o.fstandarddimensions for the pitch and cutter sizeinvolved. If special blank dimensions arerequired, they can be substituted for thestandard ones . The basic size of the cut-ter (number of teeth) win be computedto fit the machine being used if this isknown, or it may be input by the num-ber of teeth or pitch diameter wanted onthe cutter.
In addition to cutter blank dimensions,all other information required for the
Disc Cutl ...
\1hdJD•• p Count.rbora
-e--J -{£#}~ I-LII.
Taper S....n..
Fig. 1- Typical blank designs.
November/December 19'87 11
design, such as, clearance angles,tolerances, material, etc. is supplied bythe program libraries and need not beentered as input parameters, unlessspecial, non-standard values arerequired.
Once the cutter size (pitch diameter)has been fixed by one of these methods,
the program computes the cutter toothdimensions for the given part and thenchecks all of the following points, ascer-taining that it produces the part specifica-tions and meets the following good cut-ter design criteria;
1. Does the cutter have sufficient tipland?
ACllw. P, ••• ut. AngleLine
CUTTER WORK
a.••DI.mat.,
Fig..2 - Enlarged cutter - too little lip land.
CUTTER
.>:a•••_______ Dlem.t ...Actlv.P,.nul. Angl.
Line·
Fig. 3-.R.educed cutter - sulfident tip land.
12 Gear Technology
2. Will the true involute form (TIF)diameter be held1
3. Will the cutter have a suitable sizeradius on the tip comers?
4. Will the cutter modify the tips ofthe work teeth 7
5. Will the undercut produced by pro-tuberance be positioned correctly?
6. Will chamfer produced be to spe-cifications?
7. Will too much rough side rub bepresent on cutters for internal.work7 Will cutter have finish rub?Will it trim the tips of the workteeth?
8. Is the cutter barrel strong enoughon taper shank cutters] Does itneed flutes?
9. Will flank rub be present on inter-nal or external work?
Items 1, 2, 3,4, 5 and 7 are depend-ent on the active pressure angle (APA)between the cutter and work, so the pro-gram. must determine by tria] and errorthe best starting APA to produce bestresults when the cutter is new andthroughout its life. The APA of a cutterchanges as it is sharpened back, so wemust investigate what happens throughits whole life. The APA discussed hereoriginates from. a cutter that operates atthe transverse pressure angle of the work.When the cutter size (center distance) isincreased from this point, the APA in-creases on external work and decreaseswhen the size (center distance) is de-creased ..The active pressure angle changeis in the opposite direction on internals,but the effect of enlarging or reducing thecutter is similar to external work withrespect to cutter land and the true in-volute form (TIF) produced, This articlewill use the term "enlargement" or "reduc-tion" of the cutter to indicate that theAPA is being changed to satisfy re-quirements. The following examples wi.~1indicate situations that dictate this typeof change.
Each time the cutter size (enlargementor reduction) is changed to improve orsatisfy one of the above conditions, thenew design is completely computed. Eachfeature is then checked to be sure thatsome other design requirement has notbeen violated.
Fig. 2 shows a cutter with too littleland on the tips of the teeth. Fig ..3 is thesame cutter reduced to a point wheresatisfactory land is attained. This is an
external part; therefore, the APA isreduced with cutter size. Standards forthe minimum allowable land for goodcutter life are stored in the programlibraryand are dependant on pitch andpressure angle of the part.
Fig. 4 illustrates how cutter enlarge-ment affects the TIF produced. A reducedcutter will lower the trochoid height pro-duced. resulting in.a design that will holdthe required TIf.
Fig. 5shows a condition where the in-volute at the tip of the work tooth willbe modified because of contact below thebase diameter of the cutter. Shown onthis same figure is thecondition of cut-ter contact below the base circle of thework, resulting in "undercut", whichtakes away some 'of the involute near thebase diameter of the work.
Undercut is most likely to happen onpinions of 20 teeth or less, while t.ipmodification is more common on largegears and Internal gears. Enlarging thecutter will improve or eliminate both theundercut or modffication conditions ..
From the Ioregeing, it can be seen thatsome situations require cutter enlarge-ment, while others require reduction ofthe same cutter to remedy the problem.Obviously we cannot do both, so a com-promise must be made by the program.The final design will always be one thatat least has minimum land and producesthe specified true involute form.
Cutte,r Rub (Internal Gears.)This condition is almost always pre-
sent to' some degree when cutting inter-nal gears, All gear shaping machinesrelieve either the cutter or the work onthe return stroke to avoid scuffing thecutting edges. This r,elief is generally ac-complished by separating the cutter andwork by approximately ..010" (.25mm) to.032~(.81m:m), depending upon the makeand type .of machine. When cutting someinternal. parts, a wrapping effect of theinternal part around the cutter results,causing the cutter tointerfere or rub withthe internal teeth when it is pulled backto give cutting edge relief. Three typesof rub can occur and are described asfollows:
Rough Sid.e Rub. This interference, asshown in Fig .. 6, is caused by the hook-ing action of the cutter teeth relative tothe work profile as they enter on the un-cut side of the work near the inside
CUTTER' WORK CUTTEJI
Cutt", 0"' NotPrOduc. T~t.F~
Cfru. Involut. Form)DI.met.,
1lielM1.,To SI8ft 01
car~ Cutl ..
WOIIII
...... Cull •• R..... c...To Hold l'.I.F.
Fig. 4· - Effect '0£ cutter enlargement '011 true involute form,
Oulll<lo DI.m.t.,
~ CIIUI' Conlael.a.low I ••• DI.mat.rC... lnll Undercut
Involute Prollie 01 Work- Tooth Will a. Modlll.cI O"lolei.
01 Thl. Dlem.te,
Fig. 5 - Example of tip modification and undercut.
diameter. At this time, no generating ac-tion has taken place. Spaces producedare an image oJ the cutter teeth, requir-ing the cutter to be pulled back at anangle away from the hook side to pro-vide relief on the return stroke. Thedotted lines show the position of the cut-ting edges after the relieving motion hastaken place. In the example shown,cut-ter rub exists even though the cutter wasrelieved on an angle known as the hack-off angle. The amount of backoff angleis limited, as will be shown Later. Theconventional angle is normally about So,which is sometimes increased to as, much
as 10~12°to correct extreme rough side'rub conditions. A small amount of roughside rub [less than .OOZ' (.OSmmJ.l can betolerated and is usually present when CI..It~
ting small internals ..Excessive rough siderub will show up as an excessive burr onthe face of the gear and the insidediameter from the trailing side of the cut-terteeth, This problem causes excessivewear and/or load on the trailing s,idenear the tips of the cutter teeth, resultingin a deterioration of tool life. Aside froman increase in the backoff angle, withlimitations as shown later, the only wayto reduce this condition is,to decrease the
INovember IDeoemberl'98,7113
Uncut Sid.(Trailing)
Convnon ~~---"'-WOI'k C.nler Cutt.r Cenler
:II
~•i•Inlern.1 WorK
FlnI.".d Sid.(Leading)
Fig. 6-Rough side rub.
J
tI:D :;-o ~.. =:- -" 0ii :0
:0 2I Int.rnal WOI'k
Po.lllon Of Culler T •• IIIOn Ralu,n Sl,oke
Fig. 7-Finish side rub.
COI'_ 01 Work Tooth I.Tr_d Wldl. Cun.rI.aeln, F.d Into D.pth
Inl.rna' Work
Comnlont~_L-_~+" __Work C."I.r 'cutter Cent.r ("'
I
1'0."1cNo 01 C.tt .. T.alll ~'IAI ao_ I'Nt Durlnlllnf •• d t" .J
Par.llel To COIIIIIIon i.Or Line 01 In'.ad
Fig. 6 - Infeed trim.
14 Gear Technology
amount of backoff, usually to not lessthan .01'0" (.25m_m), reduce the numberof teeth in the cutter, increase the insidediameter of the part or use multiple cutsas described later.
Finish Side Rub. As shown in Fig. 7,finish side rub occurs when the cutt.er sizeis large relative to the work size, and itappears on a fully finished side of thework teeth. finish rub will show up inthe form o.f an excessive burr left at theinside diameter oJ the work teeth on theleading edges. The cutter will show ex-cessive wear near the tips of the teeth onthe corresponding side ..The direction ofbackoff angle is almost always taken asshown and is dictated by the require-ments of the rough side ..Decreasing thisangle would improve the finish side rub,but this usually cannot be done f.or thepreviously mentioned reasons, An in-crease in the operating pressure angle byreducing the cutter diameter and/orreducing the number of teeth in the cut-ter will decrease the amount of finishrub. This type of program win notallowany amount of .finish .rub to be presenton the final design.
lnieed Rub. This is rub on the leadingside of the teeth caused by the same con-ditions as finish side rub and occurringonly while the cutter is feeding intodepth. For this reason, the burr left at theinside diameter while infeed rub takesplace will be cut away when the cutterreaches full depth and cannot be seen onthe Hnished part. Excessive infeed rubwill show up as abnormal wear on theleading side of the cutter teeth. The sameremedies listed previously for improvingfinish side rub hold true for infeed rub.The multiple cut method, described later,will also reduce or eliminate infeed rub,
lnieed Trim. As shown in fig. 8, in-feed trim can exist regardless of theamount of backoff and occurs when thenumber of teeth in thecutter is too largein relation to the number of teeth inwork. The angle of backoff can affectthis trimming condition if it is ac-complished by offsetting the cutting headupright (which is common on some ofthe newer types of gear shapers) and notby the swiveling method ..lnfeed trim willshow up on the finished part as amodification or trimming at the insidediameter of one or more work teeth. Thistrimming is done by a cutting action, asopposed to rub, and thus does not harm
the cutting tool. This condition can bereduced or eliminated by increasing theoperating pressure angle of the cutter andwork by decreasing the outside diameterof the cutter or by decreasing the numberof teeth in the cutter.
Maximum Cutter Sizes (Internal Gears)Fig. 9' shows the relationship between
recommended teeth numbers in cuttersand work pieces for the more commonpressure angles. The data given here isto be used as a guideline in. the selectionof acutter that will not produce excessiverough side rub, infeed rub or any amountoJ finish side rub or infeed trim, Whenthe number of 'teeth in the work is lessthan the cross bars on the chart indicatefor the pressure angle involved, the in-side diameter should be increased byshortening the addendum. On such partsor on marginal ones, the amount of rubpresent should be checked by the com-puter program beforecut"ting. Variationsoccurring from machine to machine inthe amount and angle of backoff alsomake a precutting check desirable. Ofcourse, internal parts of fewer teeth thanshown on this chart can be cut suc-cessfully, but. ,they should be treated asindividual cases, The majority of partsin this category must be cut on machineswith reduced backoff. The programstores the equivalent of this chart, whichis used as a starting point to determinethe number of 'teeth in acutter for an in-ternal part. IT the starting number ofteeth results in excessive rub, this numberwill be reduced by the program until therub is eliminated,
fla.nk Rub (Extemam or Internal Gears)This type of rub can occur on the per-
tion of the cut~er ItoO'th below its base cir-cle on the trailing side of the cutter andwill show up as excessive wear at thispoint. Fig. 10 illustratesthis condition onan internal gear, If the previous cutleaves stock no greater than that shownby the dotted line, flank rub will not bepresent. For this reason, a commonmethod for eliminating flank rub is totake multiple cuts or use the multipassmethod described later. The amount tofeed in for each pass is determined bycomputer. Anything that can be done 'toincrease the distance from the cutter basediameter to the outside djameter, such as,cutter enlargement or an increase in the
number of teeth, will help eliminate thiscondition.
Multiple Cut Or MultipassCutting Method
Most modern gear shapers are equip-ped to take multiple cuts (3 or 4 cuts inthe normal manner) or to use themultipass (high rotary feed at low infeed
rates) to provide a way of ellminating orreducing rough side rub and infeed rubon internals. These techniques alsoeliminate flank rub on both internal andexternal parts, Fig. 10 shows how multi-ple cuts can eliminate flank rub on an in-ternal if the previous cut stock is asshown by the dotted line, This processcan also be used to elim:inate rough side
NILES 6£ARI6RlNDERMODEL~ ZSTZ 1630C3 It_STOCK!
SPECIFIICATIIONS:'Out. lei'. diameter, max •.•• lin.RooS elrc'le d amele,; m'ln .• lin.INum'ber ,01 teeth" max.. • • . . #INumber of teeth,. min.. • ... , #DlmaetraJI pitCh,. min ••..•• D'.P.Dlametral' pitch, max .•..•• D.P.
29.5,2
1!401,212.72.12
Maximum lhe'lliingle ..Stroke.ength , , • , ...••Double r__mstrokes
(llnflnltely var.) •.. , ••MaxCmumtabL Iload ••Table bore ..••.•• ,.,
deg. 45In. 8,'9
11/mln. 754,15Ibs. 880'In. 3.5,
lMiel'·West Office1665 Tonne IRoad
Elk Grove VlII'age, IL 60007Pho.ne (312) 36445301
WMW Machinery, Inc.570 Bradley Hm Roael
Blauvelt, INY 10913IPhone (9"4)358~3330
CIRCLE A-12 QN READER ,REPLYCARD
November/December 1987 15
-------------- -
.:!::t:Ii- ,WW·I-
30 I :s.~-I..--,,-;.:-+---:'-'-!-'-'iII:WIII
20 2---+~-+r-~~~~~~~~~~---~IZ
10
5
o 10 20 30 40 50 60 70 80 90100
fig. 9-Relationshlp between recommended teeth numbers in cutters andwork pieces. for common pressure angles.
.I
pARAun TO CoMMON to· --.
\RADIAL FLANk CUTTER
~'tE"
~
Figure A
0- F~~---E E·ijA ...
fig. 10- Flank rub diagram - internal work.
Un. P..... 1eI ToCommon ~
.. __ ~mount Of Relief......k~f1'Angl.~-j --
_ - -~ -- : If SPK- From Previous-, '. Cut Are Het'e. No RubSolid Line Is Poeition " Will ExistOf Cutter T.. th On '..,Cutting Stroke ':V\,.. I>epth Of
~ Previous CutDotted Line .. PoeItIonOf Cuttet' On RelUmStroke
lntern.1 WOrk
Fig. ll-lmptovement of beam strength by use offluted barrel design.Fiig. U-Multiple cui or multipass method of eliminating rub.
16 Gear Technology
Section AI.
rub on internal. gears. Fig. 11 shows thatif the stock where rub takes place isremoved by a previous cut, it will nolonger rub. In this example, possiblymore than one cut had to be taken to getto the "previous" depth, to attain thatdepth without rub, The amount of infeedbetween cuts for both flank rub andrough side rub elimination is determinedby the computer program.
Another important feature of the mul-tiplecut/multipass feature is to allow theuse of a taper shank cutter larger thannormal when cutting small internalsplines. Because of reduced rub, a cutterwith one or two teeth more may be used,resulting in a cutter with a stronger bar-rel which will be less apt to deflect.
Cutter Deflection of Small TaperShank Cutters
The long slim cutters necessary forsmall diameter, wide face width, internalsplines require special attention, A goodprogram computes the relative beamstrength of the barrel of the cutter, andif it comes below a previously deter-mined minimum, it should change thecutter to a fluted barrel design. Fig. 12illustrates the difference in the fluted andnonfluted design.
Finished Cutter DesignWhen the final optimized design has
been determined using the methodsoutlined above, computer and plottercreate a .fully detailed working drawingas shown on Fig. 13. In addition to. this,any enlarged layouts required for thefabrication of the cutter are plotted along
Figure 8
SAME CUTTER AS FIG..A WITH ·FLUTES·ADDED. BEAM STRENGTH INCREASED 50'-'
FORII,ASTERGIRINIDIIINIG WHE,EL 'P'R.O'IFIILEIR
EAS,Y T'O IINSTALL. - Because ,of Us,small size andl welglht, the FOFl,MAST,ERdoes not re-quire maJiormachine modifications and can be Instailledl on nearly any 'QI:rlnder.lnslallaUon, canusually be accomplished in ressthan a day.IEASY T'O' OPE,RATE -Two axis design simplifies proQlrammlng andl operation. You canchoose between four popular eontrots tnat f,eat.ulremenu and G·Code proglrammlng, graphicsimulation, autorna •.ic corner rounding, automatic d;liamond thickness, 'compensation, ,andmore.
MA'DE liN U.S.A.
Patent No..4,559',919
IMP':ROVES ACCURACY
IREIDUCES WHIEIELDRESSI,N:'G TIME
A'CCURATE- To within .:t .0001" of pr,ogrammed dimension, with repeat accuracy to within.00006"·, Extra prectslon roller bea.rlng ways, pre-loaded roller aerews and opUcal Uneareneoders, as well as superior des1ilgn,and construction. 'Olivethe IFOR'MASrEFIthe' abliltyt.,o holdInspecHon gage accuracy,PROIDUCTIIIVE - No templates or speclall diamond rolls are needed, so lea.d times and tool-ing Inventories are reduced. Most forms can be programmed and dressed In, r,eady to 'QlrllindIn30- to 45 minutes. Flefr'Bshllng•.he form between glrllnding passes Iisaccompilished In seconds.VERSATIIlE - Can be, used wlthsiing'le point diamonds or with optional rotary diamondwheel attachment Nearly any tenn can be dressed quickly, ,easily and ,a.ccura.tely..IDURA.BLE - Hard seals are close'liy HUed and are air purg:ed to' totally exctude contarntna-tlon ..Sealed servo motors, automatic Ilubrlcation and totaUy inclosed 'encoders miinlmize downtime, and ensure long servlce Ufe.
P•.10:. Ba'K 69Arden" NC 287'04,(7,04)684.,1002
P,.O. Bo')( .207Northville" Mil 4816,1'
(3,13) 349·2·644·ACCH~CUEA-li9 ON IREADERIREPl¥ CAJ~D
IEXAMPLEI I WOI. I .0, I NO 'WH J
'"00""10 0" i,:rcco 1.5,. C'L~t"LE 1,.00 fa
'l: fl /~I~'. I:' I i,,~ ~Duuii's.c ' ~ I' PIfCH ~'1~6 4.000 O'_...jl •.!
7 23..flfoo.--·-·----4.330D ..I--------ool ..
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NO IEIlH ~O, 0000,nCH D'.... .,.11000.... ,:n etA. OH ], .db92
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1
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PRECI$IO"! ,~WE, :p 0 lOX 3~1.SPRlKQFIElD. \IT, 05IY·OI501 us ..
\HT. OF FILLET~~\
Fig. 13- Sample working drawing.
~ HT. OF FILLET
T.I.F. I LIFE
RAD TO HT. OF FILLET UFE .51602
RAD TO HT. OF FILLET FRONT .51"00
FIg. 14-American National Standards Institute(ANSI) standard full fillet inlemal spline, 1.0module, 30" p.a,
13.0T.I.F.
18.9791
I, /1../rr-------------,T------------~
'--_'/3.01.-T
.000H
SoI.20s()
18 Gear fechnol:OQV
r-,.
CUiproftl.~ IFlnlsh4ld Profil .....
HT. OF FILLET HT. OF FILLEr
LIFEFRONT
RAD TO HT. OF FILLET LIFE 1.77818
RAD TO HT..OF FILLET FRONT 1.7lM!91
Fig. 15- Example ·0£ undercut for preshaving orpregrlmling, 10 d.p., 25" p.a,
Fig. 16- (left) Plottedinvolute chan of partshown in fig. 15. Notestock left at TIFdiameter.
Ij
J
RAD TO HT. OF FIL.LET L.IFE .73300RAD TO HT. OF FILLET FRONT .72781
HT. OF FILLETI
\\
,. MOD. DlA. L1F,E
AMOUNT MODIRED AT I.D•• 0001 AMOUNT MODIRED AT I.D .• 0032RAD TO HT. OF FlUET LIFE 5.3OH5AAD TO MOD/RCATION DIA LIFE 5.10066RAD TO HT. OF FILLET FRONT 5.29375RAD TO MODIFICATION DIA FRONT 5.07038'
...,MOD. DIAi FRONT j
I
1HT. OF FILLEr
FRONT
HT. OF FILLET
BASE DIA.LIFE
I-r tFig. IS-Extreme undercut, 10 d.p., 141'1,0 p.a,pinion.
Fig. 17-Tip mod~ication-6f8 d.p., 2.0°p.a, In-ternal gear. See also Fig. 5.
with a greatly enlarged layout from 10to 100 x size of the work tooth profile.Examples of these work layouts areshown in Figs 14-18.
NOTE: These layouts show twovalues of fillet height and modificationdiameters, one forUfTont" (new cutter).and one for the life position. This changeis due to the reduction of the outsidediameter of the cutter as it is sharpenedback, resulting in a change in the activepressure angle (APAt thus changing thefillet and modification diameters.
The computer programs also computeand print other important informationfor the designer and user, including thevariation in depth of CUlt throughou; thelife of the cutter, variation in chamferproduced by a chamfering cutter andvariation in the outside diameter pro-duced by a 'topping cutter ..
Each final cutter design. along with al.lof the input gear data, is stored in a database on the computer system and isavadable to any computer aided man-ufacturing (CAM) programs used in thefabrication of the cutter.
CondusionThe development of this type of soft-
ware greatly enhances the ability torapidly design a gear shaper cutter to dothe best job possible. The many criticalpoints that must be checked are done sowithout [ail, withappropriate action ineach case. The precise plctted layouts ofthe work are invaluable in communi-eating the exact profile that will be pro-duced on the workpiece.
Acl!n.owledge.ment:Reprinted courtesy of the Society of Manufac-
tun'ng Engineers, copyright 1986. /rom the GearProcessing Technology Clinic.
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HANSfOlI'[)DAVIS 'KEYSEATEIR
Hansford Manufactunng COrp.3111 Winton Road SouthRochester, New York 14623(710,) 427 -0660
CIRCLE 14.·15 'ON ,READER REPLY CARD
INovember/IDecember 1'987119
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Dla. (in) Pilch (D.P.) (lbsj
GA15CNC 5.917.9 6.35 10 8800GA25CNC 9.8 4 10 17600
Gear Hobbers GA40CNC 15.7 4 10 18700GA63CNC 24.8 1.8 20 24,200
SA25CNC 9.8 4 7..5 11,000Gear Sl1apers SA4QCNC 15.7 4 10 15,600
SA63CNC 25.6 32 24.7 21,100
Gear Shaver FA30CNC 12.2 a.z 7,5 11.500
, MITSUBISHI:~ HEAVY INDUSTRIES, LTD.
5·1, Marunouchl 2-chome, Chiyoda·ku, Tokyo, JapanCable Address: HISHIJU TOKYO
Mitsubishi Haavylndustries America, Inc.873 Supreme Drive, Bensenvule, JL 60106 Phone (312) 860-4220
Mitsubishi International Corporation873 Supreme Drive, Bensenville, JL 60106 Phone: (312) 860·4222
CIRCliE A-a ON READER !REPlYCARD,
KHV Planetary GearingDr. David Yu
M~C P"oouds Corporation.Skokie, 11
Abtrac;t:When ,evaluating mod'· m machinery, space and weight are often
indices as important as effidency. Planetary gearing may have manyo.f the desired characteristics: light weight, smaH size, large speedratio, high effidency, etc, The question is can a single type ofplanetary gearing possess all the above advantages combined. Inorder to give a correct answer, the basic Itypes of th - plan t~ry gear-ing will presented first; Ithen,. through comparison of different types.a r,elatively flew type of planetary gearing. ,the KHV planetary, willbe recommended. ln a. later .artide.an optimum programming forthe design of the KHV planetary gear wilI be introduced.
IntroductionTraditionally. a worm or a multi-stage gear box has been
used when a large speed ratio is required, However, suchboxes will become obsolete as size and efficiency become in-creasingly important considerations for a modern transmis-sion. The single-e..nveloped worm gear has a maximum speedratio of only 40 to 60. Its ,efficiency is only 30 to 60 per cent.The necessity of using bronze for the worm gear and grind-ing nitroaUoy steel. for the worm drives up material andmanufacturing costs. Large axial Iorces (that on the wormareequal to the tangential force on the worm gear) requirebulky bearings and shafts. Double-enveloped worm gearingcan obtain a higher ,efficiency, but the required technologyis complicated with no in I!erchange.ability. The maximumspeed ratio is about 5 to 7 for a single st.age gear box and25 Ito 50 for a double-stage. The multi-stage gear box is com-plex in structure with many gears. shafts, bearings, etc., andits efficiency decreases when power passes gears and bear-ings in each stage. There are many advantages to epicyclicor planetary gearing, such as, light weight, small size, largespeed ratio. high efficiency and the capability of providingat differentia) motion. However, each type of planetary gear-ing has its own particul ..ar fe.atuI'es, and whether or not thereisa type that can possess all the features and all the abovemerits combined is debatable.
Most methods for classifying epicyclic or planetary gear-ing are based on structure, but sometimes the 'structure alonecannot Jlepr6ent the other important Features. Hence, it is
AUTHOR:
DR. DAVID YU is ,Q gearing specialist for MPC Prod1ds Corpora-tion. Since 1982 he has been an Honorary Fellow of the Universityof Wisconsin at Madison. in the academic arena, he has served asthe Deputy Head of the Mechanical Engineering D.epartment, andas Professor of Machine Design at ,Q chin2se ul1ive.rsity. Pro/essar Yuis the author of numerous articles on gearing. H is &I member ofCMES, JSMEand ASMf Gear Research Institute.
suggested that not only structure, but also other .inmces (suchas, speed ratio, efficiency, etc.) be expressed in Ithe' classihca-tion, The classification and some strict definitions used in 'thisartide might be quite different from those in other books.For example, according to Gear Handbook. (11 the "singleepicyclic gear" has three Iypes:"planetary geat' (Fig. Ia), "stargear" (Fig. Ib) and "solar gear" (Fig. tc). The "compoundepi.cydic gear" also has three types: "compound planetarygear" (Fig. 2a)'. "compound star gear" (Fig. 2b) and "compoundsolar gear" (Fig. 2c). But in 'tMs articie, four of the six dJffer-ent categories aile considered one type, .2K-H (-),and the othertwo types might not be considered ,epicycliC gears at all, It
b c
-Ifig. 1- Thre types of "Single Epicyclic Gear"aClcording to Re erellCl· 1.
a b c
Fig. 2 - Three types of "Compound Epicyclic Geu" OI!;COrding 10 Rcle~ncrl.
!November IDecember 1987 .21
is better to use the term "gearing" instead of the above "gear,"since "gear" means only one gear, and "gearing" implies a pairof gears or a. gear train or a gear set. An epicyclic gearingmust have a planet gear which orbits a common central axiswhen it is revolving its own axis. The locus of any point ex-cept its center is an epicycloid orepitrochoid, which is wherethe term "epicyclic gearing" comes from. The "star gear" (Fig.Ib) or the "compound star gear" (Fig.. 2b) should not be con-sidered a type of "epicyclic gearing" because the carrier isfix.ed, and there is not any epicydeidal motion. Practically,it is only a conventional gear train.
In order to give a strict definitien, the author suggests usingthe term "moving-axis gearing." A moving-axis gearing con-sists of planets with moving axes and the other gears tha:directly mesh with the planets. Fer example, in Fig .. 3,. themoving-axis gearing includes a-H-p-b, where p is the planet,and H is the carrier supporting the planet. Both gear a andgear b are in direct mesh with the planet p. Either the axisof gear a or the axis of gear b coincides with the commoncentral axis 0-0; therefore, a and b are called central gear K.Neither gear c nor gear d has a moving axis nor does eitherone directly mesh with the planet, Therefore, they are netmembers of moving-axis gearing, and they form a conven-tional gearing. Since in conventional gearing, all the axes ofthe gears are fixed, they can be named fixed-axis gearing.
In a moving-axis gearing, as in Fig. 3, if gear b is fixed,we only need to knew the motion .of either H or a. Then
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IBeHeveit. HelicremenlalESCOFlER: maeblnes can do it-a!nd UiPllOI .iv,e'tim.es faster thanany other methodl
A.I - --
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CIRCLE A-130N READ.ERREPLYCARD
22' Gear Technology
.=-;p b,
.. cI'. -r-
0, a L 07""'" ~~
I
-!.. , --~ I
! I.- I
, ,;:..J .....I
dI
I
.Fig. 3 - Moving-axis gearing & fixed-axis gearing,
we can determine the other. In ether words, there is only oneconstraint or one degree of freedom. Since the motion of thiskind of gearing is something like the motion of the planetorbiting a fixed star, the author suggests using the term"planetary gearing," A planetary gearing isa type of moving-axis gearing that has only one degree of freedom.
In the planetary gearing, one of the main members (ex-cept the carrier) must be of zero angular velocity, Usually,zeraangular velocity implies fixed, but nat always ..Excep-tions will be explained later. The speed ratio of the planetarygearing is aconstantand can be determined by the relationof the numbers of teeth of the gears.
Another type of moving-axis gearing is differential gear-ing, which is defined as fellows: A differential gearing is amooing-axis gearing that has two degrees of freedom. Forexample, if in Fig.. 3, neither a, b nor H is fixed, two mo-tions of the three members should be given; then, the thirdcan be determined. Therefore, the speed ratio of the differen-tial may net be aconstant if the motion .of any of the threemembers is changed. Through a differential, two motions canbe composed into one motion (two input toone output), andvice versa, The term "fixed-differential" used in Reference 1will not be used in this article. Because this type of gearinghas only one degree of freedom, it is net a differential, buta planetary gear.
In order to have a dear comparison among different types,it is necessary to introduce the calculations for speed ratioand dficiency.
Speed RatioIn moving-axis gearing, the sign of a speed ratio should
be taken into account, and some definitions should be given,The angular speed ratio of two members, a and b, is de-
fined as
Cab - Na/Nb
where the subscript ab means From a to b, and N, and Nbare the angular velocities (or number of revolutions per time)of a and b.
If the speed ratio is from b to a, then
rba - Nb/Na =lIrab
If rab > O,a and b rotate i.n the same direction, and if rab< 0, in opposite directions.
If Ir. bl > 1, hum a to b is a speed reduction, and if Irabl< 1, from at to b is at speed increase.
A high speed ratiocan be obtained when either the ab-solute value of at reduction speed ratie is very large. or theabsolute value of an increase speed ratio is very small. Forexample, both Irabl - INa/Nbl - 100 and Irbal - INb/Nal- 0.01 are ccasidered high speed ratios. The lowest speedratio is Irl - 1.
n a speed ratio of two members is relative to a thirdmember or a relative speed ratio, a superscript is used. Forexample. the relative speed ratio of a and b to H is defined as
~b - (Na - Nh)/(Nb-Nh) - l/rGa (Ia)
In the same way,b . . ~ . b
rah - (Na - Nb)/(Nh - Nb) - l/rha (lb)
r~h - (Nb - N,)I(N" - Na) - 11 ~b (Ie)
Then we can obtain the following three basic 'equations:
~b + r~h - 1 (2a)
rCa + r~h - 1 (2b)b . a 1 (2-)rha + rhb -c
There is onJy one speed ratio (or its reciprocal) that canbe related to the size and can also provide some characteristicsof the planetary. It is the relative speed ratio to the carrierH and is named. the basic speed R".Ro - ~b (The reciprocal rta can also be used as analternative. )
The relative speed ratio of a and b to H is based on con-sidering the carrier Has relatively fixed. It,. therefore, canbe determined in the same manner as that for a fixed-axisgear train, and the relation of teeth or diameters can be used.
Then
Ro - r~b- (-ll(Zb Zb , .. )/(Za Z~ )(3)
where: Za' Z~. ' ..... are numbers of teeth of the driv-ing gears from a to b: Zb. Zb. . . . .. . . .. . are numbers ofteeth of the driven gears from a to b, and p is the numberof pairs of external grearing from a to b.
EfficiencyInput power Pill is defined as positive, and output power
Pout and frictional loss power Pr are negative, Convention-aUy, efficiency is used asa. positive value. therefore.sometimes a minus sign or an absolute sign should be addedas follows:
1/- -Pout/Pin - (Pin - IPEiJ!p., -1 - IPI1/P,,, (4a)
and
If the frictional loss power can. be evaluated, it is not dif-ficult to calculate the efficiency. The method for calculatingthe frictional. loss power is based on "latent power" Or "gear-ing power." Although the procedures of derivationare dif-furent.the resulting formulae are similar in References 2-7.
Frictional power is caused by fr.ictional force and relativesliding velocity and is a function of either force and relativevelocity or torque and relative angular velocity. Suppose thereare two systems. planetary gearing and its modified system.in which the carrier H is assumed to be relatively fixed,Torque is independent of motion, and the relative an:guJarvelocity of any two members remains unchanged whetherthe carrier is relatively fixed or not. Therefore, the twosystems have the same frictional loss power. Through themodified system. find out the frictional loss power, thencalculate the efficiency .of the planetary. We define
P~ - Ta (N~ - Nj\) (5a)
and
(5b)
T a and Tb are the torques. P~ and P~ are the latent powersof a and b. respectively, Since they are not real powers, buthave the same dimension as power, it is convenient 'to referto them as the latent powers.
In the modified system, if P~>O (P~<O), from Equa'ti.on4a. then
and
(6a)
(7a)
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The State of the Art ...HURTH CNC HARD OE---
The HUATH !hard finiishiin'gprecess is an entireliynew approach togear manufacture and finishingbecause it enables the manufacturer to aner thegeomehy of the teeth whUe smoothingl the tooth"lank surfacesot external and internal hardened'gears. This process can correct errors linIprofUe,spacing and 'lead, as weill as such parameters asradial runeut, pitch and cumulative pitch, Theend product is a more accurate, smoother,Qluieter~:running gear~
To accampltshthts, the tool flank and theworkgear flank beingl machined are positively ,guidedin such a way that the' workptece and tool arerigidlly Illinkedl durlngl machining wlith the too:I'
performing a pl!ungle-feed motion for stockremoval. AIIIIr,lght·handfla.niks are finished first.The maehlne then reverses andlfinishes Ileft-hand flanks. Thiis sing:I!g..flankcontact means nobroken-out tool teeth due to workpiece defectsand permits eerreetleri er "redesign" of theworkpiece, 'gear durilng finishing',
The tool, either Bora.zon®or ceramle, is condl-Uoned and profil'ed for the work gear g:eometryand desiredstock remova!1 by uSingl a coateddressing master. Dressingltalkes no longer thanthe time requlred to flinislh one workpiece andeach dressiing removes a. minilmal amount ofmaterial from the tool surfaces.
The hard finishing process gives the widest rangeof a,pplications ot a/l post-hardening gea', finishingmethods, Adjacent shoulders or col/ars rarely poseserious problems.
This illustration shows the tool finishing the work-piece gear and the exteme! masrer ge.srs engagedto control ;Ihe operation.
Other advantages of the process:• .AGMA Class 14 achtevable,• Deflinitely no grindingl burns.• Tool marks run diagonally to glear
diameter;• Permits machining, of gear teeth adlacent
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In the modified system, if P~<O (pg>o), from Equation4b, then
71ta - -P~/Pg - P~/(P~ +Pj) (eb)
and
The superscript h indicates that the carrier is relativelyfixed. Some feature of the modified system is similar to thatof a fixed-axis or conventional gearing. Therefore, the dataor formulae for calculating the ~ffidency of a conventionalgearing can be loaned to 'l~b or 'lCa'
In a planetary system, one of the basic members shouldbe of zero angular velocity. For example, Nb - 0, then Hand a will be the input and the output.
Let Sa - P~/Pa - Ta(Na - Nh)/(Ta Na) - 1- Nh/Na-
1 - l'ha (8)In the planetary, a is the input or driving member; i.e.,
Pin - Fa - T a Na > °If 5a>o, then P~>o. Using Equations 4a and 7a, obtain
'laJ, - -Ph/Pa - 1 - IPfl/Pa - 1 - (I -11~) P~/Fa -1 - (1 - 'l~b) (1 -rha) (9)
If Sa < 0, then P~<O. Using Equations 431 and 7b, obtain?lah = -Ph/Pa - 1 - IPfl/Pa - 1 - (1 - T]ga)IP~I/
(Pa tjGa) - 1 - 11 - fhal (1 -1jGa)I?lGa (10)
In the planetary, H is the input or driving member; i.e.,Pout = Pa - Ta. Nil < 0.
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CIRCLE A-17 ON READER REPLYCARD
.26, Gear Technology
(0) I b) Ie)
Fig. 4 - BaSICarrangements of 2K-H (-) type.
[f Sa < 0, then P~ > 0 .. Using Equations 4b and 7a,obtain'1ha. - -Pa/Ph - Pa/{Pa + Pf}
~ 111[1 + (1 - J1~b) 11 -s,n (11)[f Sa > O,then P~ < O. Using Equations 4b and 7b, obtain
%a - l1g.l(71ga + (1 - 1jga) (1 - rna)] (12)As mentioned before, there are different methods for classi-
fying the planetary. The classification suggested in this arti-cle can specify some important features of each type andmight be better than the others, Since the primary subjectof this article is not the classification system, only some basictypes will be introduced for a.comparison between the KHVand the others ..
2K~H (-} TYPE
2K means two central gears, H denotes one carrier, and(-) means that the basic speed ratio is negative; i.e., Ro <O. The basic arrangements of the 2K-H ( - ) are shown in F:i:g.4.
Speed RatioRo - r~b is the basic speed ratio which can be determined
by the numbers of teeth. For example, in Fig. 4a and 4c, Ra= ~b - -Zb/Za<O;and in Fig ..4b, Ra - r~b = -Zblg/(Za2f)<'0.
If b is fixed, 0'1' Nb = 0, then r~h - {Na - Nb)1(Nh - Nb) - Na/Nh - tah'
From Equation 2a, r~h - 1 - ~b - 1 - Ra,· thenraj, - Na/Nh- 1 -r~b - 1 + I~bl - 1 + IRoI (13)If, instead of the ring gear b. the sun geara is fixed, just
exchange the symbols a and b in Fig. 4, and fand g in Fig. 4b.
EfficiencySince raj, > 1, cha - lIcah < 1. From Equation 8, Sa - 1
~ rha > O. Therefore, if a is input, Equation 9 should beused, and if a is output, Equation 12 should be used ..For ex-ample, if Ro = r~b - -3, then fan - 1 + IRal - 1 + 3 -4. The effi.cienciesare listed in Table 1.
If 'I'j~bor 1jga is a constant, the relation between efficiencyand speed ratio is as in Table 2.
Important FeaturesSince 2K-H ( -) type has a Ro<O, as for cylindrical gears,
it must consist of one pair of internal gearing (+) and onepair of external gearing (-), S0' that (+)( -) - (-). For bevel
Table L Efficiency of a 2K-H (-) planetary withconstant speed ratio and different J7~ (or '7t.)
Reduction Speed Ratio rail - 4 Increase Speed Ratio Ih.. - 1 4
w ~ W ~~ ~~ W ~~~ %.~ % %.~80 85.00 80 84.21
Table 2. Efficiency of a 2K-H ,,-) planetary withrespect to the speed ratio .
Speed Reduction " ,fa., - 95% Speed increase " "t. - 95 %
95.1195.5095.10
710SO
gears, when H is relatively fixed, members a and b shouldhave opposite directions of rotation as in Fig, 4c.
Fmm Equation 13, r..h - Na/Nn - 1 + IReI. For exam-ple, if Ra- -ZbIZa' then fah - 1 +~/Za' It reveals thefact that the speed ratio of a planetary r..h is only one plusthe absolute value of the basic speed ratio, Ro, whichrepresents 'the speed ratio ·of a fixed-axis gearing or a con-ventional gearing. Usually, the larger the Rot the larger thediameter of th biggest gear, which determines the overallsize. Therefore, the 2K-H (-) type cannot be used for highspeed ratios, because its size will be too large. The maximumspeed ratio for the 2K-H (-) type is about 12. For example,the "ROSS" reducer wi.tha structure similar to, Fig. 4a hasa maximum speed ratio of only 9, (8], which sometimes canalso be obtained by a pair of conventional gears. When ahigh speed ratia is required, muhi-st~ge gearing should beused, which results in. a complicated structure with manygears, shafts and bearings.
Since rah > 0, the input and the output always have thesame direction of rotation. Since raJ,> 1, froma to H mustbe a speed reduction, and from H to a must be a speedincrease.
from Tables 1 and 2, we can observe that the change ofspeed ratio has liule effect on the efficiency, and the effiden-'cy of the 2K-H (-) is higher than the efficiency when H isrelatively fixed, This is a very important feature. For exam-ple, if the efficiency of a gearing transmitting 10,000 hp drops1%, this might be' a small relative amount. But 10,000>:::1%- 100 hp, which means an increase of 100 hp of power lossor the generation of a large amount of heat. Then thetemperature of the lubricant would increase and its viscositywould decrease, which might cause the failure of the gear-ing. Therefore, for the large power gearing, the efficiencyshould be kept as high as possible, and the 2K-H (-) isagood candidate.
2K-H {+ ) TypeThis lypea]so consists of two centra] gears and one car-
rier, but has a positive basic speed ratio Ro > O. Its basic
95.6895.4895.10
11711101150
arrangements are as shown in Fig. 5.If b is fixed, from Equation 2 and the fact that Ro > 0, w
find
fah - N./Nh - 1 - ~b - I -Ra - 1 - IRaI (14)
When Ro approaches 1, the rah approaches zero, whichmeans ran will become a very high speed increase ratio andits reverse rha will be a very high speed reduction ratio ..Forexample, in Fig. Sa .if Zit - 100, Zb- 101, Zg - 99, andZf - 100, then Ro - r~b - Zg Zb/(Z. 21)-99x101l(100xlOO) - 9999110000 >0, and rah - Na/Nh ,-1 - Ro -1110000 and rha - Nh/Na = 1000.
The mai:n features of 2K-H (+) type are as follows:Since Ra > 0, usually, the 2K-H (+) consists ,of two pair
of internal gears or two pairs of external gears .. A. for thebevel gearing, a and b should have the same direction of rota-tion when H is relatively fixed.
When R-o approaches 1, r ah approaches zero and CM ap--proaches infinity. Therefore, a very high speed ratio can beobtained and the size remains small.
When 0 < R, < 2, the.n Irahl < 1. This means from a toH is a speed increase. If Ro >2, then Irhal > 1. It means froma to H is a speed reduction. Usually. a large Ra requires a
( oj ( b) ( cl
:Fig. .5 - Basic arrangements of 2K-H (+) type.
INovember/Deoernber 198,7 .27
GEAR TRAINING PROGRAM
Gear S,ystems3601 WEST TOUHV AVENUE
UNCOLNWOOD, IILLINOIS 60645312-761-2100
1. BASIC FUNDAMENTALS1. o..r HI.tory
A. Cycloidal TeethB. Involute TeethC. Gear CUlling MachmeaD. Gear CUlling Tools
2. o..r TypeaA. Parallel AxisB. Intersecting AxisC. Skew Axis
3. a.. "-tIM•. Involute Gelll' Geometry
A. NomenclatureB. Involuntary - Contact Ratio, etc.C. Helical Gears - Lead - Helical Overlap
5. Our Toolh Sy.t8IMA Full DepthB. Full FilletC. Stub Depth
8. Genenil Formulae7. Malhemlltlc. - (I.T.W. Trig Book)
2. HI SPEED STEELSA. Common TypesB Special TypesC Heal Treatment - Metallurgy - ForgingsD. ControlsE. Surface TreatmentsF. Special Cases
3. CUTTING THE GEAR1. Forming
A. MillingB. BroachingC. Shear CUlling
2, GenemlngA. Shaping
a) Rack Typeb) Circular Typec) Machine Types and Manufacturers
d) Schematic - Principlese) Speeds - FeedsI) Machine Cutting Conditions
B. HObbinga) The liobbing Machineb) Types and ManufacturersC) Schematic - Differential and
Non·Dlfferentiaid) Speeds - Feedse) Climb Cut - Conventional CUiI) Shifting - Types
3. The Hob .. a Culling ToolA. How It CutsB. Tolerances and ClassesC. Multiple ThreadsD. Hob Sharpening and ControlE The Effect of Hob and Mounllng Errors
on the Gear•. The Shaper Cutter aa a Cutting Tool
A. Know Your Shaper CuttersB. Design limitationsC SharpeningD. The Effect of Cutler Mounting end
Errors on the GearE. Manufacturing MethodS
5. Tool Toleranee Va. Gear ToleranceA. Machining TolerancesB. Gear Blank Accuracy and DeSign
Limitations
4. FINISHING THE GEARI. Gear Flnllhlng- Before Herdenlng
A. Shavmga) The ShaVing Cutterb) Types of Shaving - Conventional,
Underpass. Diagonalc) Crown ShaVingdl ShaVing Cutter ModiflcalJOnse ClHlrdina\lng Tool Deslgn-
The Shaver and Pr'II·Shave Tool1) Ae·Sharpeningg) Machines
BRoiling2. Ge., Flnllhlng after Heat Tr•• t
A. HOningB LappingC. Grinding
a) Methods - Formed Wheel-Generallng - Threaded Wheel
b) Machine Types
5. GEAR INSPECTION1. Funcllotlal
A. Gear RollersB. Gear Chaners
a} Aeadlng the Chartb TOOlh.to',TOOlhComposite Errorc Tolal Composite Error
C Masler Gearse,l Tolerancesb Designsoj Special Types
2. AnalyticalA. Size - Tooth ThicknessB. RunoutC SpacingD. LeadE. Involute
3. Automltlc and Seml-AutomatlcA. How They WorkB. Whal Can Be CheckedC. How Fast
4. Chart Interpretation - Analytical and FunctionalA. Reading the ChartsB. Which Errors Affect Other ElementsC. How 10 Correct the Error the Chart Shows
6. INDIVIDUAL INSTRUCTIONAND SPECIFIC PROBLEMSOR PLANT TOURThis Program is flexible and changed to meet Iheneeds of each group.
The 4-day program consists of a coordinated series of lectures given by the Engineering,Production and Inspection staffs of Illinois Tool Works Inc. They represent over sixty years 01experience In gear and tool specialization.
The sessions are conducted with a technique and approach that. leads to intereslngdiscussion and participation. Starting with Ihe basic fundamentals. the program is directedinto those arees 01 greatest Inlerest and value 10 the people attending the particular session.The groups are kept small so that IhlS object is rea.dily accomplished.
As mentioned. the planned program lasts four days. One·half of the fourth day is for in-dividual discussion 01 specific problems In a detailed manner with members of the IllinoisTool Works' staff.
More than 4,000 individuals from hundreds of companies representing manufacturing,engineering, inspection and management. have come to Chicago lor these programs. Theyhave been conducted on a monlhly basis since 1958. Classes have also been conducted inEurope. We are certain that this well rounded program has helped all of them to a better joband also given them a beller understanding of engineering. manufacturing and inspection.
All those attending are assigned 10 the same hotel. This promotes friendly contact anddiSCUSSionof mutual problems and interests. Tuition for the course Includes transportationfrom the hotel to ITW and back, one group dinner, all continental breaklasts and all lunches.
We hope we may Include your company In one of our Training Programs.
CIRCLE A-4 ON READER REPLYCARD
1987 Monthly Four Day SemlnanlNovember.. !}.12 December 7·10
1988 Monthly Four Day Semina ...JanuaryFabrauryMarchAprilMavJune
18-2115-1814-17,,·,416·11113-16
JulyAugustSeptemberOcloberNovemberDeatmber
18-21.5-1826-2917·2014-,7
5-11
TUITION FEE' 5595 00
Add~'onaJ sludllnts.samecompany. same class $550 00
Includ" the Iransporllll'On fromthe hotel 10 ITWaM back, one group dinner. haspotalltymM"OII.
conl", ... 'a1 b<ellidulS. and llil lul'O('-.
FOI'addlf/olW InlOnM/IoII con_:ROIICRT H. MODEROW
M.nager. Training312..711·2100
large size, therefore, Ro > 2 is seldom used.When Ro < 1, then Tab > 0, which means that a and Hare
in the same direction of rotation. \!Vhen Ro> 1, then Cab <0, which means that a and H are rotating in oppositedirections.
When R.. lies between 0 and I, fan - I - R, - 1 to 0,therefore, 1ha - lIran > I and Sa - 1 - rha < O. If a is theinput, then Equation 10 is used for calculating 7)ah' If H isthe input, Equation 11 is used for 1'100"
When Ro is larger than 1then fah < 0; therefore, rha < 0,and Sa > O. U a is the input, Equation 9 is used for,calculating for 'lilll" If H is the input, Equa'tion 12 is used for'lha'
The efficiencies of Ro, - 64/6.3 and Ro - 11/12are listedin Table 3 as 'examples.
From the above, three important conclusions can be drawn:a). The 2K-H (+) has a very useful feature, the capability
of providing a high speed ratio with a small size. However,the larger the speed ratio, the lower the efficiency. For ex-
ample, the "ANDANTEX" reducer is similar to the one in Fig.Sa. When rha - 3.27, 'lha == 95%, but when lha - 67, I1ha,is only about 45 % .(91 Therefore, effort should be made Itoincrease the efficiency.
b). When the geari_ng is for speed mcrease, the ,efficiencymay become negative, which is called self-lock and is nor-maUy undesirable.
c). The efficiency is very sensitive to the ,change of l(j~ (er'lCa). Therefore, how to obtaina. high 'l~b is a crucialproblem for increasing the efficiency of the 2K-H (+) Itype.
KH.V TypeFrom the previous discussion, it is clear that the 2K~H (-)
type can obtaina high efficiency, but its maximum speed ratio,is small (not much larger than that of a pair of conventionalgears)', and 'the 2K-H (+ ) type can provide a high speed ratio,with a small size, but its efficiency is low. One feasible methodof overcoming these disadvantages is to combine these twotypes. The combinarion (which can provide a medium speed
Provides actual overball/pin measure-
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ratio with a medium efficiency') is named 3Ktype. Owingto space limit, the details of the 3K will not be discussed here,However, its structure must be meeecomplkated than a single2K-H (-) or 2K-H ,(+), and sometimes, the gain may be lessthan the loss. An interesting question may arise: whetherthere is a type that can obtain both high efficiency and highspeed ratio with a small size and a compact structure.
first, for a large speed ratio, it is better to choose .2K-H(+) type which is made up of two pairs of either internalgearing, (+) (+) - +, or-external gears ( -) (-) - +. Canwe just use one pair of intema] gears (+) Ito obtain a morecompact structure?
Secondly, for increasing efficiency when other conditionsare the same, the most important factor is '1~b (or '1Ca); i.e,the efficiency when the carrier is relatively fixed or the effi-ciency of a conventional gearing. (See Table 3.) This figurecan. be obtained from some empirical data (for example, 0.95to 0.98 for a pair of external gears and 0.97 to 0.99 forapair of internal gears) or from some formulae as in References5, 6 and 10. One of them for a pair of gears is as foUows:,
171Z - 1 - 3.14159 iJ' x, (22 ± Zl) 1 (2 Z2 Zl) (15)
where: 2z and Z1 are numbers of teeth, I! is coeffident offriction,"+" stands for external gearing, "-" for internal gear-ing: and K, is meshing ·coefficient.
K, has a relation to 'contact ratio and the position ofmeshing. I! bears relation to materials, surface finishing,lubrication.etc, Besides K, and u; the important Iactorsarethe numbers of teeth and arrangement. For example, in a pairof external gears where Z2 -100 and 21 - 99, the (Za +ZI) 1(2221) - 199/9900. In an internal gear pair. (Z2 -Z1)/(22Z1) - 119900. Therefore, internal. gearing is muchbetter than external, and the best arrangement is Za - 2]- 1.
Thirdly, ina planetary along the power flow, the fewerthe pairs of gears, the higher the ,effidency. If i.t consists ofonly one pair of gears, the power loss would be the smallest.
It is the KHV type that can satisfy the above requirements,Consisting of only a central gear (ring gear b) meshing withplanets (a), a carrier (H), and an equal angular velocitymechanism (V), the KHV (as shown in Figs. 6(7) is compactin structure, light in weight, and capable of providing bothlarge speed ratio and high efficiency. The speed ratio for a
b
Fig.6 The KHV type.
30 Gear Technology
Jig. 7 - The KHV reducer With H as input and V as, output.
single stage KHV is from 40 to 200. Its weight and size areabout one quarter those of a multi-stage conventional gearbox. Through optimum design, its ,efficiency can reach 92 %when the speed ratio is up to 200. .
The KHV has at basic speed ratio Ro - 2b/Z" > 0, whichis similar to the 2K-.H (+). Therefore, the KHV ·can providea high speed ratio. Since it consists of only one pair of inter-nal gears, it might be possible for the KHV to obtain a. highefficiency.
There are only three main members in the KHV: the ringgear b. the carrier H, and the planet a .. If one is fixed, theother two should be the input and the output.
If the ring gear b is fixed, or Nb - O,then
r~ - Na/Nh - 1 -Ro - 1 - r~b- 1 - Zb/Za - (Za -Zb)/Za (See Equation 2a.)
(16)
If the angular velocity of the planet is zero, or Na - 0,r6h - Nb INh - 1 - r1:a - 1 - 2a/Zb - (2b - Za)/Zb
(17)
The equal angular velocity mechanism V is used to transmitthe motion and power of the planet to a shaft whose axiscoincides with the central axis. Any ,coupling 'that cantransmit motion between two parallel shafts, such as, univer-sal joints or Oldham couplings, might be used as the V.However, these kinds of couplings are too large and heavy,which would tend to, nul[ifythe advantages of the KHV.Therefore, special designs for the V should be used. One ofthem is the plate shaft type, as shown in Fig.B. On the planetthere are several holes of the same diameter d2 equallyspaced ona circle of D. On the plate shaft there isa platehaving several pins of the same diameter d1 equally spacedon a cir-cle of D. Each pin fits into one hole. The dimensionsare so arranged ,that d2 - d1 - 2 0102, where Ol~ is thecenter distance of b and a. Then OlOzM N can form aparallelogram four-bar linkage, in which. the opposite barsalways have the same angular motion. Since M and .02, areon the plate, MOz can represent the plate shaft. Since Nand01 are on the planet, NOl can represent it.. MOz and N01
therefore, are opposite bars of the same angular motion. Asmentioned before, Na - 0 does not mean that the planet ais fixed, otherwise the KHV cannot work because it isjammed.
In Fig. 8, if :ring gear b is rotatable, and the plate shaft(M02) is fixed, the planet (NOl) can move when carrier H(DI02) rotates. Since (NO}) should have the same angularvelocity as the opposite bar (M02), the angular velocity ofthe planet (N01) is zero Na-O, and the movement isatranslation with no rotation. There are also other types ofthe V, such as floating plate type, zero teeth difference type,etc.
fig. 9 is a KHV for driving a five ton gantry. The plateshaft is fixed, the carrier is the input and the ring gear is theoutput. The speed ratio is +741. from outside only the 5.Shp motor can be seen. The old design used to be a bulky3-sta:ge gear box parallel tothe wheel. The KHV cuts downweight and size to the maximum ,extent, since there is no in-crease in weight and size for the KHV. Allthe parts of theKHV are built inside the wheel. In the same way, the KHVcan be built inside the drum of a winch, the pulley ofa con-veyor or the adapter of a gearmotor.
The KHV was first patented in Germany in 1925.lts toothform was epicydoid. In the 19'30's involute tooth form wasalso used for the KHV.. However, its development washindered for a long time by the problems of interference andefficiency. Having studied those problems for decades, thelapa.nese Sumitomo Company developed theCYCLOreducer .. Improved by using hardened rollers, high accuracyand modified epicycloid (or epitrochoid) tooth form, theCYCLO has reached an efficiency of 95% with speed ratioup to 8,-1mand has become a successful gearing in the worldmarket. Some businessmen predict that the CYCLO willreplace muln-stage'gear and worm boxes in the future,However, it is difficult for other companies to design andmake the particular gear cutting and grinding machines forthe m.odified epitrochoid teeth and to know how to modifythe form.
The basic speed ratio of the KHV is positive (+), similarto the 2K-H (+) type, which can provide a high speed ratio,but the higher the speed ratio, the lower the efficiency.
To avoid mterference, the minimum teeth difference be-tween the ring gear-and the pinion of an internal pair of gearsis usually limited to 10 or 12 for 20C pressure angle involutetooth form ..(12, 13) But the KHV cannot keep to this restric-tion. Since the 1960's KHVs with teeth differences of 2 to 6have also been used in China, Iapanand Russia.
However, the author suggests using the smallest teeth dif-ference: i.e .• 1, and a high speed ratio in order to bring theadvantages of the KHV into fun play. The question is howto avoid interference and increase efficiency. The interferencecalculation of internal gearing is very complicated and isseparate!,y introduced in another work by this author. (14)
From Equation 15 the speed ratio fha - -Z,/(Zb - Za)'therefore, 'the more teeth and the smaller the 'teeth difference,the higher the speed ratio. For example, if Zb - 50, whenteeth difference, Zel - Zb - Z.a - 1, fha --49/(50-49)--49', and when Zd - 6, rhil - -441(50'-44)- -7.3 the same result can also be provided by a pair of
Fig. 8- The plate shaft type equal angular velocity mechanism.
Fig. 9 - A KHV reducer built inside a wheel with H as input iIIId ring gearas output.
simpleconventicnal gears.The best arrangement for high speed ratio and compact
structure is Zd - 1. In Equation 15, because the term (Z2- Z1)/(Z2Z1) - Zd/(Z~O!), the mOJ1e teethand the smallerthe teeth difference, the smaller this term and the higher the1/~b(or TId,· which is an important Iacter determining ,effi-ciency of the KHV. The best arrangement is also Zd - 1and a large number of teeth or high speed ratio. Therefore,it might he possible for the KHV with Zd - 1 to obtainboth high efficiency and high speed ratio, Through optimumprogramming, the KHV can reachan efficiency of 92 % withspeed ratio up to 200.
The maximum speed ratio of a single stage CYCLO is 87,which might be limited by the table of the grinding machine
(continued on pll8,e48)
November/December 1987 31
Fe e hi f G b A- f ·InIS mg 0·. ·-·ears .y __usornungMaurice F.. Amateau, Pennsylvania State University and Raymond A. Cellitti,. R.C. Associates
GROUND & REFRIG.( -320 F )
I 0 GROUND AND NOTFEFR IG ( -3201 F l
Fig. I-Pitt:ing fatigue of 9310 steel carburized to 0.90% carbon,
Abstrad:A low temperature thennomechanical finishing process now under
development has the potential for producing longer gear life andstronger, more reliable and lower cost gears. This process ausformsthe carburized surface of gear teeth while in the metastable austeniticcondition during a gear rolling operation. A high degree of gearaccuracy is possible by the combined use of interactive forming,low temperature processing and precision gear rolling dies. Ther-momechanicalprocessing can eliminate the need for hard geargrinding, thus offering substantial reductions in. finishing costs aswell as improvements in pitting fatigue life.
IntroductionAlmost all machines or mechanical systems contain preci-
sion contact elements such as bearings, earns, gears, shafts,splines and rollers. These components have two importantcommon requirements: first. they must possess sufficientmechanical properties, such as, high hardness, fatigue strengthand wear resistance to maximize their performance and life;second, they must be finished to dose dimensional tolerances
32 Gear Technology
to minimize noise, vibration and fatigue loading. As theserequirements become more stringent, the cost of processingcan increase significan.tiy. The combination o.f mechanicalproperties and dimensional control is normally accomplishedby separate manufacturing steps, each of which may partiallynullify one or more of the desirable characteristics inducedin the prior operation. For example, highly loaded precisiongears are general1y earburizad to minimize plastic deforma-tion and wear. They are then ground to. achieve the necessarydimensional control, remove high temperafure transforma-tion products and improve surface finish. The optimummechanical properties are developed in the as-earburized con-dition; thus, the finish grinding operation, which is requiredfor achieving dimensional. requirements, precludes achievingmaximum strength and reliability. This point is illustrated byexamining the pitting fatigue behavior of carburized 9310 steelsubjected to various surface treatments.(1) (See Fig. 1.) Theunground.as-carburized finish results in the best fatigue per-formance compared to the as-ground surfaces, Maximumdimensional stability and resistance to plastic defo.rmation
areachieved when. the microstructure of the steel is totallymartensitic, Diffusional transformation products, such as fer-rite, lead to low hardness, as does untransformed austenite.The untransformed or "retained" austenite Isalso detrimen-tal 'to dimensional stability, as it can eventually transformunder mechanical stress to martensite. resulting in a volumechange. Cryogenic treatments after normal quenching areoften used to control the amount of retained austenite. as seen.in Fig. 1. Such treatments can also have a.detrimental effecton fati-gue life.
Improvements in performance, reliahility and manufactur-ing costs could be realized i.Esurface finishing and strength-ening were accomplished in a single process. Certain lowtemperature thermo mechanical treatments. such as aus-forming. have this potential. AusEorming treatment is appliedto the steel whil.e it is in the metastable austenitic conditionprior to quenching to martensite. The principal benefit of thistreatment is that i't can produce significant improvements instrength without degrading teughnessand ductility. In somesteels, toughness is adually improved simultaneously withstrength. The low temperature nature of this treatment pro-duces very Iiule thermal distortion. thus making it ideallysuited for precision finishing operations, The ausformlng pro-cess can he directly substituted for groups of ccnventionalfinishing processes, saving considerable cost while optimiz-ing mechanical performance. Fig. 2 compares the processingsteps for finishing gears by conventional methods with thoserequired for ausfonning. Ausform finishing can eliminategrinding. shaving, shot peening. honing and cryogenic treat-ments. The import.ance of eliminating grinding for optimizedrolling conta t fatigue l:ife is illustrated in Fig. 3. Removal.by grinding of more than 1 mil of surface material from 8620steel carburized 'to. 1.2e can. severely reduce fatigue strength.This phenomenon can originate from two sources. First. thefatjgue resistant compressive layers of carburized material areremoved, and, second, incipient grinding damage in the formof micrecracksand transformation products is generated.
AlffHORS:
DR. MAURICE F. AMATEAU.is Head of tIle Engineering MaterialsDept .. Applied Research Lab. tmd Prof. of Engineering Science &Mechtmics, Pennsyl'vtmw State University. Prior to his work at PerinState. Dr. Amateau held research positions at Batt.elle Memon'alln-stiMe «rid TRW ll1c .• 1711(:1· was Director of Materials fngineeriPlg ,at1»temmio,utl Harvester Co. He lIas sertied on various committees ofthe National Research Coundllmd is cummtly an advisor to the Com-miltee· on Recommendations for U. S. Army Basic Scientific Research.He is the author of numerous technical papers on fatigue, fracture.wear and tribjology of .structural materials and composites. He holds" masters degree from Ohio State University and a Ph.D. inmetallurgy from Case Western Rese.roe University.
RAYMOND A. CELlrrn is president of R. C. Associates, a11
engineering and' manufacturins cOrlSulting firm. He has 34 yearsu.-perienawitll Intmrati01U1JHlH'Vester Co. in applied mechanics. fatiguJ!testing. process control. metalworking and materials. engineering. Heis the author of numerous technical papers and co-author of'~Bihliography on Residual Stresses," SAf Fatigue Design Handbook.He was awarded the patent Or! the ausTolling process that fO",115thebasis for tllis article He holds a masters degree in physics from LoyolaUniversity. Chicago. and one in'metallurgialJ engineerir:Jgfrom Illinois1l15titute of Technology.
In addition to. ausfonnirtg, other low temperature ther-momechanical treatments for precision finishing are p-ssi-ble. low temperature deformation during the decompositionof metastable austenite to bainite, known as .isoforming, willresult in significantly different toughness and strengthcharacteristies than ausfcrmiag, Numerous other lowtemperature treatments are also possible. providing a largerange of processing options and resulting effects.
Cu:rre.nl Status of Ithe TechnologyThe strengtheningeffect of ausfermingisanributed to the
inheritance of-much of the dislocation structure and carbide
tlN>'[NTItx..At fiNISHING
Fig. 2: - Comparison of manufacturing steps - conventional versus ausfonn-ing fLnishJng of precision gears.
401. 2 "loC, REHfAf
20•
10 -
5
,---
0.5 1 1.S 3 5o 10
DEPTH BElOW SURFACE, MilS
Fig. 3-Fatigue life as a function of the amount of rnaterial removed. 8620teel carburized 10 1.2%C and reheat treated from 15S06F. All test5 al347 ksi.
NovemberjDeoem'ber l,987 33
DID
izlllll-am
I1«11
~ 1100 ' (0'06-11· 2lmm>-
1600
15000 2S
«l'025-Q'05Imm
75 100
DEAJlMAnON BY ROlliNG IfoI
FIg. 4 - Effect of amoWit of deformation al S10~C on the yield ~trength ofa O.32C-3.0Cr-l.SNi-1Si -a,SMa steel, A range of martensite plate sizes (inbrackets) was investigated at each deformation .IS)
~150
IIIIII
II
cr 1C3m-
7500--
10-
Cl 60
Fig. 5 - Carbide and hardness chang by allSforming.'I>'
distribution generated in the metastable austenite duringdeformation to the final, martensite after quenching~2J A finedispersion of carbides occurs during the working of austenite,stabilizing not only the grain size, but 'the subgrain size aswell. (3) Ausfonning results in a very high dislocation densi-'ty in the final martensite. The dislocation network producedis not the normal one where the dislocations are concentratedat the cell walls; rather, they are more uniformly dispersed,Larger scale microstructure effects also play an impostant rolein the strengthening process. The low working temperatures(in the range from room temperature to ll00°F, dependingon alloy composition) tend to restrict austerute grain growthand, ultimately, the martensite plate size.(4-5)These effectscombine to result in an increase in yield strength with increas-ing amounts of plastic deformation. The effect of the plasticdeformation of metastable austenite on resulting martensiticplate size and strength for 0.32C-3.OCr-l.SNi-l.SSi.~0.5Mosteel is shown in Fig. 4~SJEachpart"icular steel. compositionhas a saturation limit above which very little furtherstrengthening occurs. for a high-carbon, high-chromium cold-worked die steel (02 tool steel). this saturation effect is
34 Gear Technology
IG
1100
AUSTENHE• C~RB IOE
l ISECrtiDS M!NU!J[
IIIJUI
ID~¥ 1110£ n:oc SCAlEI
Fig. 6 - Schematic illustration depicting ausrolling time-temperatur regimequench from austenitizing temperature,
associated witha.change in carbide composition. (6) Thechange in hardness and carbide form over the range betweeno to 60% de.fonnationisseen in Fig. 5.
The two principal requirements fora. steel to respond ef-fectively to the .ausforming treatment are the presence of somecarbide forming elements and the persistence ofthe austenitein the metastable form -that is, the existence of a deepaustenite bay region in the isothermal time-temperature-trans-formation (T -T -T) curve - fora sufficient period of time topermit the required amount of deformation. Fig. 6 is theT-T-T curve for a 1.0C-1.2Cr-3.ZSNi-O.13Mo steel (carbur-ized 9310) exhibiting such 3. bay region. This steel has beensuccessfully surfaceausfcrmed. Numerous highly alloyedsteels are potentially ausformable; however, for low alloysteels, alloy modification or careful selection may be required.Some existing through-hardened steels that may prove to besatisfactory are 51870, 4370 and 1580. There are also, severallow-alloy steels specifically developed for ausforming, oneof which is the Si-Mn-Mo- V-Cu steel developed at RARDEover ten years ago. ('7)
At the present time, it is not dear that thennomechanicalForming near the martensite start 'temperature (Ms) isdetrimental to the final properties. For conventional ausfor-ming, working dose to the M, is not common practice sincedeformation can raise the effectiv,e martensitetransformationtemperature and promote the transformation reaction. In thiscase, a considerable volume of strong and brittle martenslticmaterial would undergo deformation. [f ausforming is con-fined to only the superficial layers, the formation of somemartensite may be tolerated; and, i.ndeed, may even bedesirable.
Surface ausforming of carburized steel has been alreadydemonstrated. Similar success may be possible for other sur-race conditions such as nitriding and carbonltriding. Thereis no experience available to suggest the effect of surface com-position, case thickness or gradient on the properties of ter-momechanically treated surfaces.
Ausfonning can have a significant impact on the temper-ing response of steel. These effects could be utilized advan-tageously to minimize processing operations and maximizemechanical properties, Two consequences of ausf,orming arethe low carbon content and low degree of tetragonality ofthe subsequent martensite. These result from the precipita-
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temperature thermomechanicaltreatments only to the sur-face ·of parts overcomes both of these limitations, renderingauslorming an idea] processing method for precision machineelements ..
Auslorming significantly improves the rolling contact pit-ting fatigue strength of EX15 steel. Fig. 7 shows the Weibulldistribution of rolling contact fatigue failures at a. constantcontact stress of 450 ksi for both ausformed and convention-ally quenched and tempered steel. A significant imp.rovementin fa.tigue lile can. be seen.
The principal features of the apparatus for precision ausfor-ming of gears are interactive forming utiliz.ing dosed-loopcontrol aad a high accuracy forming die. A schematicdiagram of this system is shown in Fig. 8. In this apparatus,the gear rolling die is driven by a hydraulic raotor. and theworkpiece gear is engaged and driven by the die. A speciallead profile is generated on the die gear to produce a swagg-ing action on the workpiece as it is being fed Into the die.This geometry, illustrated in Fig. 9, shows a crown sectionon the bottom half of the lead and is used in the final finishingoperation.
The control architecture allows for control signals for thevertical. and horizontal feed. to be either independent or depen-dent on each other. Command signals can be dynamicallymodified based on feedback signals from each of the fourtransducers. The current system is supervised through a 9600baud serial link to the external microprocessor, The systemis under actual position control at all times, but is in virtualload control during the deformation operation by use of theexternal microprocessor which supervises the generation ofthe command signal. The surface austenidzation is ac-complished with a 10 KHz AF induction system. Thermalmonitoring is performed with a noncontacting fiber optic lRsensing pyrometer. This system is capable of measuringtemperature over the range from 600 to 1800°F using a zincsulfide detector. The system response 'time is one millisecond,permitting continuous reading of the temperature over gear
10 10 10CYCLES TO FAILURE
fig. 7-Rolling contact fatigue of EX15 steelat 450.000 psi contact stress.
tion of carbides during working. Ausforming steels of car-bon contents above .3% can eliminate Stage I tempering,which would occur during the tempering of conventionallyquenched martensite; thus, auto tempering appeal'S to be pro-meted by ausforming. For surface ausforming, optimumtempering treatments are most likely not those used for con-ventionally developed martensite.
At the present time, low temperature thermom.ec:hanicaltreatm.ents have very few industria] applications. The reasonis that substantial amounts of plastic deformation are re-quired; thus, making it difficult to achieve uniform defor-rnation in complex parts and requiring high forging presuresand considerable energy expenditure. Applying low
ERROR S'lGNAl
COM/oM.ND I SYSTEM 10·- COOTRCI.
I
SIGNAL~ GOOATCII
POSITION FEEDBACK. , CONDITI<HRl()!'D FEEDBACK I AND SEUCTOA
,
I SERVOI COOROlUR
COMMAND
'SYSTEM 10 CONTA!NS:MUlTIP.U:XER,AIO ANDOJA CONVE!RSION,SI'GNALCOND ITIONERS, + 5 V TTLOOTPlJlI, ! 10 II ANALOGOUTPUli
fig. 8-Control system for interactive gear forming.
36 'GecTTechnology
GWIEN,"'V
TAPEREDLEADFOR SWAGGING,
STRAIGHTSECTION
IHOUDWSECTION
Rg. 9 - Special lead design for swagging and crowning.
'tooth profile. A 0-10 volt analogoutput is used as a controlinput for real time process control,
Preliminary results on the finishing of gears by rolling inthe metastable austenitic condition have indicated. a poten-Hal for substantial improvements in gear accuracy. Process-ing has been performed on a hobbed gear with an initial gearquality of approximately AGMA 8. The microstructural ex-amination of the finished gear indicated that approximatelyV2 to lit mil of material wasseverely worked by the treat-ment. Considerable improvements in surface finish have alsoresulted. An average starting surface roughness of 43.2microinches eLA has been transformed to an averageroughness of 11.7 microinches after processing. The retalnedaustenite at the surface of an ausf.ormed gear is about 7%,which is similar to that achieved by conventional finishingthat includes both c:ryoggnic treatment and shot peening. Thehardness profile of the surface ausformed gear tooth was iden-tical to the conventionally treated gear below the depth ofaasfomung.
The ini'tial experiments provided great insight into thepotential economic advantages of thermomechanlcalfinishing. The .ausforming gear rolling operation takes 51seconds to complete, during, which time ill crown eentour canalso be developed on each tooth. This 'compares teapprox-imately 38 minutes of grinding time to finish this same gearwithout the crown. If crown grinding were petfcrmed, thefinishing time would be closer ,to one hour. Since significantdeformation can be achieved by thermo mechanical, working,
additional cost savings can be realized by the elimination ,ofshaving operations or by requiring less, dimensional, control.during rough cutting or hobbing operations. In the case ofgear finishing by rolling, a significant cost savings may berealized in the inspection phase by eliminating the need fO.l"match setting of gears.
ConclusionLow temperature thermomechanical processing has con-
siderable potential for the finishing of precision machineelements to net shape. The fe.asibiHty of applying aus orm-ing, one such process, to the finishing of spur gears hasalready been demonstrated. In this process, the final dimen-sions and finish quality are achieved by thennomechanicallyworking the carburized cases of gear teeth while they are stillin the metastable austenitic condition prior to qu nching tomartensite, The results of such processing methods are (1)the elimination of several manufacturing steps including grin-ding and. hard finishing, (2) the generation and retention ofsurface compressive residual stresses.and (3,) the achievementof ausfonn strengthening in the surface layers subjected tothe high operating stresses. The following benefits are d rivedfrom these eHects: sign:ificantly lower manufacturing costs,greater yield strength, improved fracture resistance, greaterpitting and bending .fatigue strength and greater productrelia bility.
The encouraging results from previous studies justify ad-ditional research and development to refineand implementthe technology and to extend it to the other machine elementssuch as bearings, splines, cams, rollers, dutch 'surfaces andshafts.
RefeI·ences1. lAMATHE. R.M., ZAGAESKJ, T. F., CELUrn, R. A. ,Ik
CARTER, C; "Effect of "f:est Variallleson Rollil1~ ContactFatigue of Al51 9310 and Vasco X-2 Steels:' Intern lional Sym-posiumon Rolling Contact Fatigue of Bearing Steels, Phoenix,AZ. May 12-14, 1981.
2. SKARET, J., HABROVEC, F., KOUNICHY, J., ,Ik RYS, P.,"Inheritance of Defects by Mart nsite in Ihe Process of Aus-forming," 1. Iron and Steel lnst. 205, 3 March, 1967, 330-331.
3. COX, A. R. and JONES, P., "The Fr c::ture of AusformedSteels," t. Mater So. 4 1969, 890-894.
4. SHYNE, J. c., ZACKAY, V.F. &: SCHMATZ, D. J., "TheStrengths of Martensite Formed from Cold~Worlc.edAustinite,"Trans. ASM 52. 196(1,346-361.
5. ZACKAY, V. r. Nati.onal Physical Laboratory Symposium, No.15, HMSO, 1963
,6. DAS, A. K. and GUPTA, P. K., "How Ausfonning StrengthensHigh·Carbon, High-ChIomium Steel," Metals and Maten'als.November IDecember, 1974, 49.2-4:94.
7. OXLEE, C. H., 'The Development of_ Low Alloy SteelAmenable to Ausforming." Prot: Int. Cont. on Sci. b Tech.of IrOIl and Steel, Section 6. Tokye, Japan. 1912, 1025-10.29.
AcknowlHlge!nent:Reprinted courtesy of the SocWty of Manufacturing ~ Copyright. 1986,from the GeQr Processing Teclll101ogy Clinic.
November /December 1987 :3.1
combination, and in case of ill non~hunting ratio. thenumber of starts should be reduced until ill hunting condl-tion is reached ..For AGMA quality less than 11. the number of starts canequal 2. even in the case of non-hunting ratiocombinations .For AGMA quality greater than 10, the number of startsshould flat exceed 3. (See Table 2.)Selection of number of hob gashes. The more numbers of
gashes, the more cutting edges are engaged. resulting in lesscutter load and wear ..Greater numbers of gashes also increasethe number of enveloping cuts, which make the involutesmoother. This is especially important when cutting gearswith small numbers of teeth. Table 3 shows minimum recom-mended number of gashes depending on number of hobstarts.
Selection of hob diameter. Smaller hob diameter usuaJ]yresults in less cutting time sincegreater hob RPM 'can beachieved. Limiting factors for reducing further hob diameterare usually minimum number of gashes and lead angle. Max-imum lead angle for hobs with straight gashes is usuallywithin 6 to 8 degrees. Sometimes for high production, hobdiameter has to be increased to enable utilization ,of a longerhob, since very high length over diameter ratio may under-mine the system rigidity.
Hob accuracy class selection .. Hob accuracy selection isbased on AGMA gear quality, stage of manufacturing andnumber of starts. Class accuracy should be equal or bett,erthan the accuracies shown in Tables 4; and 5...
Selection .of the Machinin,g Da.taThe selection of the number of cuts is influenced by pitch,
number of gear teeth, stage of manufacturing, surface finishand gear quality. A two-cut cycle can be selected for gears.wi.th a module greater than 4.5. For small numbers of teeth(less than 12) and a module greater than 4, a. two-cut cydeshould also be selected. The number of cuts for finish hob.bing can be selected from Fig. L
Hob speed is usuaUy selected based on cutt,er material. andcoating as well as workpiece material, hardness and pitch.Fig .. 2 can be used to determine machinabili,ty in referenceto workpiece material and Brinell hardness, assuming the cut-ting tool is made of M35 or the equivalent,
Based on machlnabilityand module, one can determinehob surface speed from Fig. 3.
Ye6m KotlyarAmerican Pfauter, Ltd.Elk. Grove Village, IL
IntroductionThe art of gear hobbing has advanced dramaticaUy since
the development and introduction of unique machine and toolfeatures such a no backlash, super rigidity, automatic loadingof cutting tools, CNC contJlols,additi.onal machine powerand improved cutter materials and coatings. It is essential toutilize all these features to run the machine economically,
The Following guideline is an attemp! to systemize themodern knowledge of hobbing and to assist gear processengineers in selection and detennination of various unknownsfor cutting, gears most efficiently ...obviously, it is an impos-sible task to take int.o consideration all the variables influ-encing machine, cutter. speed and feed selection. There arealso differences of opinion regarding the best ways to hobgears ..Nevertheless, this guideline can serve as a starting pointfor a large variety of applications and sizes. The :recommen-dations are based on the assumption of using adequate hob-bing machines, rigid fixtures and TiN coated hobs made ofM35 or similar material.
Cutter SelectionSelection of number of starts. The number of starts of the
hob depends on pitch, number of teeth, stage of manufac-turing, gear quality and divisibility with number of teeth ofthe gear. GenercaUy, the productivity increases when hobswith greater number of starts are employed,
Table 1shows multi-start hobbing limitations dependingon pitch and number of teeth ...
Additional limitations can beset for finish hobbing inreferenee to AGMA quality.
In the case of non-hunting ratio combinationsbetween thenumber of teeth of the gear and number of starts of the hob,the maximum number of starts should not exceed two.
Additional limitations for pre-shave hobbing,The number of starts should be tested for hunting ratio
AUfHOR:
MR. YEFII'WIKOTl YAR has been an applications engineer withAmerican· Pfauter, Ltd. since 1979, where he is responsible for com-puterized·.analysis of gear geometry and gear technologies . He earnedflis MS in mechanical e'lgineering from Odessa Marine Institute,Odessa, USSR. After graduation Mr. Kotlyar worked in design andmanufac!'uring of agricultural machinery at Tashkent MachineInstitute, USSR.
38 Gear Technology
No of Hob Starts
biog limUa:ti.ons.
LIMITATIONS
(NDP) Min. No. of Teeth
) 13) 17) 206) 25
on to AGMAquality levell..
9 8 7 8
2 2 3 3I
fetation till' hob starts.
3 4 5•13-17 17-19 17-21
I
-acy vs. hob, starts.
Selection lor 3 to II Hob
Finish Pre-Shave
Class C 3 44 55 6
Class B 6 7I
Class A 7 88 9
1011
INovember!IDecembe. 1987 3'9'
Table 1- Multi-start hob
12 11
Max. Module
2345
5.5 (4.614.5 (5.643.0 (8.462.5 (10.1
Table :z - Number of starts· in relati
1 1
N?MA Quaity level 10
Max. No. of Starts 1
Tahl J - Minimum g~hes, in
tUnber of Starts 2
MIn. No. of Gashes
1
12-139-12
Table4--S-AGMA class ac,rur
SelICIIan .. 1 81' 2 Start Hob
Finish Pre-ShaveClass C 3 4
4 55 6
Class B 6 77 8
Class A 8 99 10
10 11
Class AA 11 1212
40 Gear Technology
12
11
10
MMA(uBty 9
8
1
2 3 4 5 6 7 8 9Module
fig. 1- Finish hob cut selection chart.
757065I:
f~25201510
!I I
,
I ' I I II 11/ -If\:' '-.' ! I I I I IV il -e-. J I I I
,
i ::><' --, b.. !"">; I:-.. !; , I
V, I / ...., .... ~ I'- I I I Tf"?/ fl\...... C\ K· "- .7 ..
I [ r"S ~ t-.;I " '-I+- I I I
I,!' f..(! .... -i'{, t-. ..§, ,
I 1'1 ...... , !~ .'-': ~.... ~g-1r---u, I
I
! ,''';: ~ ..... --. :,-!-I
I II! ....i i~
!,I
I , II . I , ,
f404S! 55 til 65 j 75 :vi !II !IIi .1IJ;l1lli 110 1151 P1!51kl135f 140 14S~T".strength kp/rym'.. '150 '2lD 's ':iJo '3 [I) 400BRNU HARDNESS HB
'lllllltl F' t' ."II If .....(AISI 0eIIgr1ltlons)
1 C8rbon SIIII8 11)0(, l1xx, 12xx. 15xx2. Law allay c:hmmHIII:tGeI stIeIs3 ttillRIeIB _ 26xx ... QIromH1IckeISMeIs5. fIIh *t dInImIHicIaII steels, 31¥X, 33xx, 303xx SIIiiIIII ....8. ~um SIIII6 43Kx. 47xx. 8&cx. 87xx. 93loc. 98loc,1~"_48xx"'~alllls41lcx... 0I0me .... S1xx. 511lCX, 521xx. 514xx. 5t5xx
• Qnn_ VllIIdUIi 8lBIIIBS1xx.11 ~ SIIeIs 92lcx12. DucIIa lnIn
Fig. 2,-MachinahiJity in reference 10 workpiece material.
III
2D
10
10 2D
K
13
1.2
11
10
1
234
:11
ag
10
40machlOabI y 11%
50 60 10
70 I
I r,
/itV/1
~ ./V'/I..- Z V/i
V/ V..-·L1
I »: v/ // /'I /'V/ "/ /L /'
~ V/V ""/ /~ ~/ c....-: // /' »:
~ i/::/V V......../' / /'--:::::-::: ~ v--: v..........,/' ~ »:
...-::::::. ~ :::::-:::V..........~ r;:...---: V .,/'
-~~ ~ ::::::::::: :::-:::::~ v.........~.-~
::.- -::::: r-::::.I----""1
Fl,g.3-Hob urface speed in relation to module and machinability.
50
FIg.4-Multiplier K chan.
F£f.D RATE IN I CH/REV.3SECOND CUT
..!.!W'l:_S-START
HOB4"START
HOB........... ~"""" .."'- .... 2
...--,-
-25
)'STAm_I:IOB__ .15
2·S1ART_JiO!._
I·STAATHOB
FU:D SEI!EC-fIONI CHART
-.-.,...........-~......--...•..•..•..••.-..
4 6 8 WNORM,6;L MODULE
12 14
Fig. 5 - Roughing cui f-J rate: chan.
For TiN coated hobs, the speed can be increased depend-ing on the machinability for all materials (except ductile iron)according to, the multiplier Kselected from Fig. 4(K-multip1ier) .
Feed SelectionFeed rate for roughing cut can be selected according to Fig.
5. The selected rate should be multipli d by the machinabili-ty factor eland the factor C2 for small number of gear teeth.
ci _( Mach~oability ).4Gear teeth Iactor should apply only if number ,of teeth is
less than 2S.Gear teeth factor
C2 _ (Numbe~Of teeth ).3Feed rate for finish cut shouldbe limited by allowed feed
scallop depth. Maxlmumallowed feed rate for fLnisncut canbe calculated with formula:
Feed rate - co~ • .J.o '. 4 .• DADSIN )..
(3 - helix angleo - allowed feed scallop depth
DAG - hob diameter)., - pressure angle,
For pre-shave cut, the feed scallop depth should not ex-ceed .0008,". It approach feed control rate is available. it canbe set to roughing feed rate.
Where
I .1I I
~1 ..--- II ~ I
! 1...,..".- 1I """"'-1 II ~ J
November /IDecember 1987 41
may warp or distort unevenly during heat treatment. A wellproportioned blank with the adequate locating area anduniform cross section compared toa poor blank design isshown in Fig. 2. The poor design has very little supportmaterial behind the gear teeth and a thin web cross section.This blank is an extreme example that would be difficult tolocate accurately for hobbing and shaving. It would also bedistorted considerably during hardening.
Good Gears Start With Good BlanksWm'd E M- I.. mor . __0 ap es
Star Cutter CompanyFannington Hills, MI
Fig. 1
IntroductionThe quality of the finished gear is influenced by the very
first machining operations on the blank. Since the gear toothgeometry is generated on a continuously rotating blank inhobbing or shaping. it is important that the timed relation-ship between the cutter and workpiece is correct. If this rela-tionship is disturbed by eccentricities of the blank to itsoperating centerline, the generated gear teeth will not be ofthe correct geometry. During the blanking operations, thegears centerline and locating surfaces are established and mustbe maintained as the same through the following operationsthat generate the gear teeth. This 'centerline oE the manufac~turing operations must also be the same as the operatingcenterline of the gear as it is used. (See fig. 1.)
Gear Blank DesignThe gear design engineer can assist in assuring good quality
finished parts by designing gear 'teeth on well proportionedblanks. The configuration of the blank should be one thatallows the workpiece to be supported just inside the rootdiameter of the gear teeth during cutting operations. Anotherconsideration in the blank is to avoid thin cross section areasbetween the gear teeth and the operating bearingarea that
AUTHOR:
WILFORD E. MAPLES is marketing manager at Star Culter.Farmington Hills, MI. He has thirty years' e;;r;periencein engineeringand sales at Hydro-Mafic Division of General Motors. ITW and atStar Cutter. He earned his:Bachelors of Industrial Engineering 'it theGeneral Motors ltJ5tiMe in Flin«, MJ. Maples is Q member of SME.
42 Gear Technology
Gear Blank InspectionDuring the blanking operation, adequate gaging must be
done to insure that the locating surfaces of the blank are main-tained perpendicular and concentric to the centerline of thegear. It is good manufacturing practice to do finish turningand facing operations on the blank prior to (cutting the gearteeth. In the case of a hole type gear, the blank should befinish cut on the locating Iace or faces. and the bore finishcut perpendicular to the face and concentric to 'the outsidediameter, Typical tolerances for an automotive blank 25 mmthick and 100 mm outside diameter would be:
1. Locating face squareness to bore 0.01 mm to 0.02 mm.2. Outside diameter concentricity to bore 0.12 mm
maximum.3. Bore size tolerance for 2S mm bore 0.01 mm to 0.02
mm.4. Bore size taper tolerance for 2S mm bore 0.005 mm to
0.008 mm.
Fig. 2
labl'e 4-1-Typica:1 Gea,r Bllank: Toleran,ces'--- - ---...... ,.. fWI H. H. 0.0.DIa • ..~ IIu '''' R.1IftdMu 0.0. RunlulI.. I.. I.. 1•• /111. 111.-11 .. IlL-II ... In.
Up 10 I. 0.0003· 0.0003· 0.0002· 0.0002· O.OOl 0.003l-in, Tlllck 0.0005 0.0006 0.0003 0.0003
11104. up10 1-", OOOlM· 0.0005· 0.11002· 00003 0.005 o OOSThICk 0.0001 0.D111 0.0003 000051101 00006· 0.0001- 00002· 00004· 0.005 0001
I0.0012 0.0012 0.0003 00006
110 12 0001· 0001· 00002· 0.0005· 0005 0.0080.002 0.0015 0.0003 0.0001 ,
'Tolerances lor Speclllc:,G ill Sh 'Illd be Self tIed mil.ccordance "",InQuality'ReQUlrements.
Fig. 3
S.AMP,lE IPINION GEAR BlANK 'CttECK
i~hI:t D03
l1- Ben So t DOO5-I
Fig. 4
Fig. 3 is a table of differenl gear blank tolerances. Fig. 4is a sample pinion gear blank. while fig. 5 is a sample inter-nal gear blank.
The blank tolerances should be specified by the manufac-turing engineer separately from the finished part print'toleranoe. Gaging fixtuJleswith precision indicators shouldbe supplied for the machine operator's use to ch ckalignments, concentricities and perpendicular accuracies oflocating surfaces to the centerline of the blank. The gagingfixtures should be placed at each finish turning machine forconstant use by the machine operator.
Fig. 6 illustrates basic arbor for checking pinion blanks,while fig. 7 is a photograph of a fixture to check face runoutand 0.0. runout.
The bores or bearing journals should he inspected at theirfinish machining stages using air gages or precise indicatorgages. It is important to check both the size of 'the bore orbearing journal and its configuration. A tapered or out-of-round condition win result in poor workholding efficiencyif the blank is driven by damping in the bore or on the bear-ing journal during the gear generating process. Fig. 8illustrates various bore configurations to check.
When production rates are high, automatic gaging is usedto check each blank for size, concentricity and perpendicularlocating surfaces. The automatic gaging of each blank is themost precise method of gear blank gaging, The operator's in-fluence is removed from the gaging operation and. all deci-
,INTERNAL GEAR ,BLANK:SA_MPLE.CHECK
1-------""'. D Stt•• .QQ.02-1
fig. 5
BASIC ARBOR FOR CHECKING PINIDNI BLANK
Fig. 6
SET-UPSTAKE
SEC'Q'N'DS* ,IN'TERNAL-EXTERNALSPU,R'& HEUCAl GEARSto .20 INCHES DI'AMETER
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OIRCLE Awn ON READBR REPtY CARD'
November (December 1987 43
sions are made by the instrument. There is also the advan-tage with automatic gaging that all elements are checked bythe gage at a high rate of speed.
Metal1urgjcal ConsiderationsVarious types of materials and metal preparation are used
for gear blanks; specifically, forgings, castings, cold form-ing or basic bar stock, In the case of cold forming, sometimesan in-process heat treatment may be necessary to improvepart machinability, Also, if a part has been turned on veryhigh speed equipment, work hardening may be experienced,and again, in-process heat treatment may be required. Thereare various other examples, such as making a blank readilymachinable for hole broaching, but having poor tool lifewhen the gear teeth are generated. Each individual processwill have to be experimented with, and experience willultimately determine if either metallurgical change is calledfor or an in-process heat treatment should be employed.
Gear Blank Related Errors,The errors caused by gear blank inaccuracies can be illus-
trated by assuming that a perfectly aligned hobbing machinewith accurate tooling is used to cut gears from randomblanks. The gear blanks are simple hole type flat gears thatare damped in the bore and located on the faces. Presentinga gear blank to the precision hobbing machine with the boreaccurate for size and shape, but the locating faces not perpen-dicular to the bore centerline, will result in the gear blank
I~JJ'J}J~:\ f10 DF. IPoulbl,\!,.
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OTHER' MACHrWeSBevel geal' gffler-alc IS spjra,1 & stralg hiCuHlt gt ndef6 !ihi.OiNi1.shavu~ & I"toIJCyclo d gear millersGear gnndeni 'Straight • eerucal, ifller,"a_
tyc~oldat & "'wO-fm- whee"Gear hobbet5 1 Inen ~o -'0 root d~ame'IBrGear homng mactuneiGear norse lesll~g macnJnesGear 'snaverSHypo1a genera.t(lrs. lappers & leSle1$Bad< $1\_($Sp)ne S1'I3'1 m ~ng machln.esTOOlh chamrermg: mac;nnes,WOfm wheel ho'bbeirs/US£R REFERENCES AVA!l.ABLE/
$,PIECIFICA,IIOH!IMalll:,,,"um 'O,.aJ dLameter 20·Ma.Jlmum face W1dlh S-Ma. mum poldi 40PIncl1.id.. (50) d1ange gears
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44 Gear Technology
Fig., 7
VARIOUS BORE CONDIIIIONS
omI , .
,', I I , ,, I ,. I
,, I _ I
- I
Taporld I 0 801 Mouth II 0
mC-I.O.
I
1- Fig. 8
wobbling during the hobbing operation. The inaccuracy ofthe locating faces causes the centerline of the bore to beskewed from the generating centerline of the hobbingmachine. The resulting lead inspection would produce a chartthat shows high lead variation. If tooling, specifically the hob,is improperly mounted to an extreme runout condition, a partwith excessive involute error could be produced, as illustratedin Fig. 9.
Presenting a gear blank to the hobbing machine with ex-cessive concentricity error between the outside diameter andthe bore centerline will result in uneven cutting load aroundthe blank. The resulting gear teeth will then show a like con-centricity error when a red line check is performed on theteeth: that is, when the teeth are checked from the centerlineof the bore and/or rolled with a master gear.
Presenting a blank to the hobbing machine with an over-size bore will result in poor damping in the bore. The blankwill then have a tendency to slip on the arbor, resulting inmutilated or off lead gear teeth as shown in Fig. 10.
In the case where the blank is centralized on the bore anddamped on its faces, the blank centerline will be shifted offthe centerline of the hobbing machine. The subsequent con-centricity check of the gear teeth to the centerline of the borewill show excessive concentricity error.
In the high volume production of gears, such as in theautomotive industry, diHerent locating areas are used,specifically in pinion hobbing. Here the fixture holds the piece
'.GEAR "A"
",.••..•
'....•'.', -,
A.S. i.s.INVOLUTE
CENTER OF BLANK
Fig. 9
GEA_R "0" .002' , •-- ...' ~.
...
..'......,. .. :..• •!Wi - ~ :-·~-~III ".MT- . ~
.' . ~ ·":'1• ..1-." I• I!' • '."~' ~ ~':~~.~.'.~~-~""I , ":_.~~.. .I.' ,ii'.!
..,
0-LEAD
Fig. 10
AUTOMOTrVE ILOCATlNG IPDIN"TS
Fig. n
,CONVENTIONAL LOCATING IPOINTS
lJ.~_~ng_,
Fig, 12
EXAMPLE OFINTIERNAI. GEAR: :I.OCATING, IPOIN'TS
AooI !)qI hMml!!OHr
Th ... """" CoIucI..._1-Fig. 13
GEAR IDEIBURRINGGri'ndingl • Brushingl • Mi!IHng
:S"n --Ie ,D. lM'u'lf~1-- :Stali:::: nLgi !O!l JP e _0Efiminate Tedious Hand Deburringl,A Modestnvestment With A IFiastIRetum
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November/December 1987 45
LOCAT[NGSHAFf &\ ~ARCOMElINATlON
Fig. 14
LoCk-up nut Is not square to holding plale.Therefore, arbor Is bent. -
fig. 15
-'--. --==:ANOUT~----~ .Oversize blank I. O. Therefor,e, part will have gear runout.
Fig, 16
BlllJ1ks not'squarely mounted. ResullS inlead, involute and concentIicit)/ errors.
Fig, 17a.
'Benl arbor results In lead, involule' and,concentricity errors.
Fig. 17b
46 Gear Technology
• ta--=- - \~
IFig. 19
EXAMPLE OF CHAMFERS TOMINIMIZE ,uAT,ERIAI. HANDLING, DAiMAGE
all
Fig. 16
EXAMPLE O.FBLANK OUNTEI) ONDIRIiY ARBOR AND'/OR FIXTURE
., 1- 011 Po'pt1I(!leylllAmounl..
part in the bore only and does not locate on the face area.(See Fig. 11.) The conventional method is to locate the piecepart on the bore as well as the lower face, as illustrated inFig, 12. Locating points for internal gears are shown in Fig. 13,while locating points for shaft and gear combination areshown in Fig. ]4.
Several examples of improperly mounted gear blanks areillustrated in Figs. 15 through 17.
Another point that must be considered is material handlingabuse. The gear blanks should be designed with adequatechamfers at the outside diameter edges and locating surfacecomers. (See fig. 18.) Nicks, burrs, dirt and any other foreignmaterial on the locating and damping surfaces will cause thepart centerline to skew, resulting in lead variations and ex-cessive concentricity errors. (See Fig. ]9.)
SummaryThe quality of the finished gear is affected by the quality
of the blank on which the gear teeth are cut. The operatingcenterline is the centerline from which the gear is designedto run: therefore, once a manufacturing centerline is estab-lished, it must remain the same as the operating centerline.
Good gear practice by the design engineer is helpful 10 themanufacturing engineer in producing high quality gears atlower manufacturing costs. The manufacturing engineer mustremember that all errors in the locating surfaces and clamp-ing surfaces of the blank are reflected in the quality of thefinished gear. Good inspection and quality control procedureswill result in early detection of bad blanks. The poor blankscan then be removed from the system before subsequent ex-pensive operations are performed on them.
Reprinted cOllrtey of the Society of Manufactun""g Engllleers, Copyn"ghl1986. from tile Gear Processing Technology Clinic.
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• Gear Hobbing MachineSetup
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There's stll! time ..•,ard'er ,ol'osing date, foraclassified ad in the Jan./Feb.issue lis Nov. 10th.
November/December 1987' 41
KHV PLANETARY GEARING .•.(continued from page 31)
and the strength of the equal velocity mechanism. Mostmaterials for the CYCLO are high carbon chrominum steelwith high hardness, which requires an elaborate heat treat-ment and an accurate grinding. The KHV has involute teethwith a concave to convex contact (internal gear contacts ex-ternal gear), which results in. a high contact strength. Theinternal. gear has a. very strong bending strength, and theexternal gear is modified, which increases the bendingstrength. Therefore. the KHV can use conventional gearmaterials and common accuracy. Usually, the ring gear iscarbon steel without grinding, and 'the planet is either car-bon or alloy steel, All the gears of the KHV can be generatedby standard gear cutters and conventional equipment.
Compared to the CYCLO, the KHV is easier to manufac-ture and less expensive .. Therefore, it is a very promisinggearing.
M~}'!ythanks to Proiessor Ali A. Seireg of the University of Florida andthe Ul1iversity of Wiscon5ip! for his review of this article.References1. DUDLEY, D. W., et a1. Gear Handbook, McGraw-HiU Co.. 1962.
2. MACM1LLAN, R.H. "Epicyclic GeM Efficiencies". Tile .Engineer, Dec.23. 1949, pp. 727-728.
3. MACMILLAN, R.H. "Power FI.ow and Loss in DiH, rentialMechanisms", Journal of Mechanical Engineer:ing Science. Vol. 3, No.1, 1961, pp 37-41.
4. MOROZUMO, MUNEHARU. 'The Efficiency and the Design ofModified Internal Gearing", Mechanical Researches (Iapanese), No.5.1970, pp.720-'716.
5. KUDLYAVTZEV, V.H., "Planetary Geanng" (Russian). M chineBuilding Publishing House, 1966.
6. YU, DAVID. "Problems Arising in the Calculation of Gearing Effic-iency", Liaoning Machine (Chinese), No.2, 1980, pp. 33-42.
7. YU, DAVID and N. BEACHLEY. "On the Mechanicall Efficiencyo{ Dif-ferential Gearing", Transaction of the ASME, Journal of.Mechal1lsms,Trc:msmissiol'ls. and Automalion il1 Design, Vol. 107, Mar. 1985, pp.61-67.
8. Catalog of Equadyne Planelary Speed Reducers, Ross Industries. 1985.9. CIl/Rlog of Andante:c Reducers & Differentials, Andantex USA., Inc.
1983.10. TUPUN, W. A., Gear Design, American Edition, The Industrial Press,
1962.11. Catal'og of CM-Cycle, Su:mitomo Machinery Corp. of America. 1987.12. SPOTTS, M.E Design of Machine Elements. 6th edition, Prentic- Hall,
lnc., 1985. -13. OBERY, ERlI<, et al, Machinery's Handbook. 22nd edition •. Interns-
tional Press, Inc., 1984.14.. Yl.l, DAVID. "On the Interference of Internal Gearing". Proceedings
Second World Congress on Gearing, Paris, MM., 1986, pp. 317~326.
VIEWPOWNT(continued from page 7)
In the note in Table B.l the symbollG/in should read ,Ib/ln.
ERRATAEditors Note: We apologize that several errors appearedIn recent Issuesof GEAR TECHNOLOGY. We regret any in-convenience these errors may have caused.
In the article "lo.ngftudlnal load DistributionFactor for Straddle- an'd Ove.rhang-M'ountedGeaa" by Toshlml Tobe. et al. appearrng in our JuJlAugIssue. the following errors occurred:
Equation 17 should read
k " !Pn Ib/I[wl + Wz + vvP]maxk - K -o96[k1_H/l KHtl
Equation 19 was ommitted. It should read.When both tooth surfacesjust come into contact at 11 -
'I! *, the position 7J" is obtained from
dSoll'/J -0dfj 11-"'*
as follows:
In Equation 20. the figure ez d should read ez dThe letter f in Figs. 9 and J Sb should read ~
The first equation in the footnote on the bottom of pager 6 should read KFtl - KH~
48, Gear Technology
In the caption for Fig. 14. the last equation should readc,/b! - 0.5, e~ - 2 O~m.
In the last tvvo paragraphs on page 46. Fig. B. I ,isincor-rectly labelled A. I.
In the Sept/Oct issue, on page 50 of Stan Jakoba's "51Unlts:- Me surementl and Equlval neles" thefigures 1 kg-m under "Moment afforce ... " I kg/dm under"Specific force of gravity" and I kg-mlrad under' 'Spring rate:torsional" all refer to kg force, a symbol sometimes writtenas kp.
In this same issue, page 47 was incorrectly laid out. Thetable of terms at the top of the page and Equations 3 and11 immediately below it both are part of the article, "Selec-tlon ,of a P,lIOper,Ball Size" " ." by Van Gerpen andReece. coonnuec from page 34.
Equation 3 should read:PACB
I BTN ]~.+ K*lnV(PACPJ]Cos /BHA) *BDI _
+ PACP/ (3)
The remainder of the equations on page 47 [Nos. 12-19)belong to Paul Dean's article, "Inter,r,elatfonshl,p ,ofTooth,Thlckn IS Mea...:sur.ments as IEvaJuat dl byVarious Measurlngl if: chnlq1ues,:' continued frompage 23.
Higlh Iintensity,Muliti-!Freq,uency Scanne'rs
RED'UCiEHEAT TREATIIINGICQ,STS, up to 41010/0A. recen,tlUCCO development, Hig'h,IInt.ens,ityInduction Hardening I(HUH!)rM, reduces heattreating costs substantia11ly"lina variety ,of,appli-cations. HIIIH has been used successfully withapptications on automotive and off-hig:hwayengine, and drive train components, as well asspecialized gear applications. The HIIH scan-ning process, with present technology, canbe adapted to parts up to 15" diameterandlengths to 120".,Parts that preViiouslywere flame hardened in abatch process, can now Ibe indluction hardened,in-Une,with greaterflex,ibility, rnors preclslon,lindividua' 'quality monitorlingl, and at lower costHigh Intensity Iinduction Hardening is indeed,a process of "The Future" ..
Cross section 'of ,camshaft lobe dernonsirates uniformity ot hardening.Multi-frequency,lhigl1 intenSity hardening, ,01'gears produoes a highha~dness c-haracterislic lor improvedl surface contacl 'Ialigue Ufe.High resid ual compreSSive' stress in the roct area lis also achievedfor improved lOOlh strength.
For tile fatest state-of-the-art heat treating technology,contact your TOCCO representative, or call: TOCOO,tnc; 30100 Stephenson Highway. Madison: Hls., MI,48071. Phone; 3"13-399·8607 or 1-800'-4'68-4932(outside Michigan).
A .unit ,of Park Ohio, Industries, Inc.
I"IEIErERYTHINB rIll'"IAY8I"llAB'",P"OICIIIISE"IThe production: of parallel'-axls -spur ,and helfcall - gears: has JUstundergone sucb a major change rhaI:'most macr,',nery In usetod~y Isobsolete.Gleason CNC Systems compatible hob-bing machines have written a wholenew set of rules on how to produce spurand helical gears profitably, The GleasonCNC nobbers offer h,ighest volume,highest degrees of flexibility and fastestonangeover. Whafs more you can geEautomatic hob and fIXtUre.change plusautcmanc pan load/unload.That's why auto transmission plantsthroughout the wor,ld are equipped withGleason hobbers.And' that's whyGleason's production hobbingl capabilityis rapidly becomingl the 'IIVOrld standardfor gear production.
The real Gleason plus is the worldWidenetwork of service and applicationengineering support that Greason pre-v,ides. The result conststenny lis this:maximum ,eqUipment reliability. maxi-mum uptime and highest quality gearoutputCall now to learn more about the paral-lel'-axis gear production of today - andtomorrow. The' Gleason Works, 1000Unfve,rsily Avenue, IRochester.NY 1469.2,
GleasonTh., Warl'd af Im•• rlng
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