thejournal of gear man'ufacturing of gear man'ufacturing january ifebruary 1985 ... •...
TRANSCRIPT
The Journal of Gear Man'ufacturingJANUARY IFEBRUARY 1985
'Guesswhobuilds.ore'
-I • •mU'I-axl'SCNCI ho! bing.achines f'orl
a'UI ',o.oIive-size gears?
Americanl Plauter.of co rse'. -For example, our new PE150 represents the bestof high production capability plus flexibility forhabbing gears up to 6-in. Because of hig'h dynamicrigidity, it's capable of using the latest in TiN andcarbide tool technology. Setup times are reducedas much as 85% because change gears andmechanical gear trains have been replaced withtrouble-free electronic controls.Simple CNC operation is assured with a variety ofavailable software. Dialogue programming coversall operational sequences, walks the operatorthrough data entry and alerts him to conflictingor illogical data . .A diaqnostic program simplifiesmaintenance procedures by detecting anddisplaying errors dilmctly on the CRT.Flexible automation is a reality with the PE150'sintegral workhandling system which combinesunsurpassed speed' and versatility-,even wheremedium or small production lots dictate frequentretooling during one shift.
Faster 1001change is accomplished with the quickhob change system which saves more than 90% oftool changing time while assuring hob concentridtyilndependent of operator skill. A tool magazine withautomatic changer is also available.
Shorter machining times. Shorter changeovertimes. Faster tool change. Reduced idle times.Lower operating costs. All at a price no higher thanconventional hobbing machines. For additional,information, contact American P1auter Ltd., 925East Estes Avenue, Elk Grove Village, IL 60007U.S.A. (312-640-7500).
~ t(\J]fi]~ ~tn-Q]~ OJ][Jffi[Ji]]])World-class gearmaking technology In hobblng• grinding· shaping· hard gear flnlshlngl •ilnspectlon • gear ,cells and systems
CIRCLE A-l ON READE,RREPLYCARD
DUring a recent business trip to our Rockford. Illinoisheadquarters to discuss Gear Manufactunng and DesignProblems, I had an opportunity to scan your magazineand was very much impressed.
Here In our Denver, Colorado facility. we are theprimary manufacturing source for most of the individualparts that are used in the Aerospace products that Sund-strand supplies to customers worldwide. These productsinclude electrical generating units. commonly known asConstand Speed Drives, auxiliary power units, wingactuators, rudder speed brakes for Space shuttle, and thelist goes on and on, All of these products use gears, andalmost all of our gears are precision ground. Suffice it [0say, we In Denver, are very much involved in Gears,
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LeHen for this columnlshould be ad'dressed to Let·ten lathe Editor, GEARTECHNO~OGY..P.O'.Box1,426, Elk Grave Village, IL 60007. Letters sub-mitted to this column ,became the prope,rty IOfGEAR TECHNOL:OGY.Names will be w.lthheldupon request; how vel', no anonymous I'ettenwill be published. 'OpinIons eXPlJlessd by con-tr,lbutors are not necessarily those 0' the editoror publishing stall.
Dear Edlto,rlYour new Journal IS a most attractive. informative pub-
lication. I'm certam that you and' the rest of the GEARTECHNOLOGY publication staff labored long and hard toproduce such, an excellent professionally-renderedproduct.
Your journal is also unique; there is none other like itin print. It appears that you have set out to serve animportant previously neglected area of technology, Thisaction is commendable. and will be a definite service togear designers, manufacturers, and users,
Please accept my congratulations on this newendeavor
Ken G. Merkel. Ph.D .. EditorThe Journal of Engineering Technology
The first two issues of your very fine journal deal ex-tensively with baSICS.I have found the ordinary gear-manother than an engineer does not comprehend what isSImple to the engineer.
The "Gear Ratio" article Isecond issue) was particularyinteresting: I have made a program for that but hadthought it was impossible for the computer to find thefactors. Now I know how to achieve the "impossible",Thank you for that. Best of success with your ambitiousendeavor,
Robert P. Ellenberger, Engr.Federal Gear, Inc.
In our country. the lack of reference sources andresults-of-research Information make keeping up to date inour job an extremely difficult enterprise. This publicationwill fill a sorely needed gap.
Alexander H, Danon G.General ManagerPedro MeusnierJuarez. MexiCO
Your Oct.JNov. issue arnde on Austempered DuctileIron by Dale Breen was reviewed with great Interest. Weare currently involved in a test program with one of ourcustomers on gears made from this material. The conte-uof the artide was quite helpful. Keep up the good work.
B. A. SchalerAllrson G.3S Turbine Opera£lOns
Peter F. Palko, Section Mgr.Sundstrand Aviation Operations
Your magazine GEAR TECHNOLOGY IS a tImely assetto me. We are just starting to hob our own gears inhouse. We have little actual gear cutting experience andany information we can get our hands on is a greathelp.
Keep up the fine articles espeCially the "Back [0 Basics"Series. Alan R. Ayotee
Process Engineer
I would like to compliment you on your Joumal. Therehas been a need for a publication of this kind for a longtime, I have passed the number on to my colleague con-cerned with the CAD of Gears, and , am sure he willgreatly appreciate the publication.
Professor S, A, TobiasUniversity of Birmingham, England
As a Manager of Special PrOjects leading companydevelopment in certain areas including non srand.3rdgearing. I have found your Gear Technology Journal VoLI NO.3 to be an excellent reference source.
I would like to receive it regularly.Also, if possible. I would like to receive Vol. 1, No. 1
and Vol. l. NO.2.Valentin G. BarbaSpecial Projects ManagerPlessey Dynamics Corp.
Editors note: ThISletter is typical of many that we havebeen tecevmq. Because of the extra time and expense In-volved' in sending individual back issues: we must advisethai there is a charge for back issues, S 7,00 for theUmted States, S 15.00 for Foreign Subscribers. There isalso only a limited number of these issues available, Ifyou Wish to purchase any back issue. msuyou: checkand indicate the issue you are requesting to:GEAR TECHNOLOGYP.D. Bo» 1426Elk Grove Village. IL 60001.
Jclnucry/februcry 1985 1
ANALYZ,ING ,GEAR TOOTH AS A FUNCTION OFTOOTH ,CON-rACT ,PATTERN' SHAP,E AND POSITIONLowell Wdcox-Gleason Works
,COMPUTER' A1D,ED' DESIGN ICAD~ OF FORGING ANDEXTRUSION' DIES: FOR IIHE PRODUCTION 'OF GEARS IB,YFORMJNGDavid Kuhlmann. P.5. Raghupathl-BatteIJ 'sCOlumbus Division. Gal)' Horvat-Eaton CorporatIOn.and Donald Ostberg-U.S. Army Tank Automonve Command
THE EFFECT OF LUBRfCA_NT TRACTI'ON ONWORMGEAR' EFFJCJ~NCYW. R. Murphy. V. M. Cheng. A. Jackson. J. Plumen.M. Rochette-Mobil Research & Development Corporation
HIGH POWER TRANSMISSION' WITH CASE-HARDENEDGEARS AND INTERNAl. POWER IBRA'NCHING,J. Thelssen-A Friedr. Flender GmbH u. Co. KG
,16
VIEW-,pCINTNOTES IF,ROM THE EDITOR'S, D,ESK
GUES:r IEDITORIAL. BY DON McVITl'iIE,BJKKTO BASICS ,... DEFINlT,fQNSOF GEAR
EL~M~NTS-,FELLOWS CORPOR'AJIION
CLASSIFIED
57
42
January/February 1985 Vol. 2. No. I
SUBSORtPTION liN FORMATION; GEAR TECHNOLOGY I~ dtSUltMed free at charge [0 qualified Indlvl(ll.l Is and /IrmiIn ttle gear manulacrunng InduSlJ'y To conllnU!! recelVJ/19your subiCflpllOI'1. (om~ and rna"!tIe apploGlII()n card fOlJTldelsewhere In !hIS magazme Paid subscnpllon rates In the US are S5 00 pef ISlOe ... 5 I 75 lor poiIagt> &. handling orS30 00 per year. 5bO 00 per year, Me.xICo and Canada', S10 00 per ~ar all OItler rOft'lQrl countne's Sub!C!'IJXlOf1 requests[0 RII,ND ....LL PUBLISHING CO. INC. PO ,BOX 1426 Elk Grove. IL 60007MANUSCRIPTS: We are requesung technICal papers 01 every sort from manufactured 01 gear makIng maChinery andrel.Red equipment. unlvers
NOW you can assure non Qualitybefore cutting your first gear
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The Hob Check™ 2000 is turnkey software whichworks in conjunction with our ac 2000-4 gear inspec-tion system. It directs completion of hob testing pro-cedures, and, test results can be stored, then analyzedthrough software procedures. Computer analysis oftest results to different standards (such as US andEuropean) makes this system cost effective and flexible.
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For Hob Check™ 2000 specifications and ourModel2Q00-4 ac System brochure loaded with informa-tion and applications on true universal gear inspection,write or call M & M Precision Systems, 300 ProgressRoad, West Carrollton, Ohio 45449, 513/859-8273.CIRCLe A-3 ON READERREPLYCARD
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AN ACME·CLEVELAND COMPANY
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January/February 1985 5
I,N-LINE-TRA,NSFER
Better blind splinebroac:hing, withl easi:ertoo II maintenanceApex's newest in-Iline-transfer blind sp.linebroaching machine lis now out there cuttingteeth into automotive sun gears ..It's dOing themtwo at a time, 190 per hour, without operatorassistance. When an operator is needed, tochange tooling, one of the major advantages ofthis maohine is realized: all tooliing is fullyaccessible, situated only inches from the edgeof the table.
Progress.ive broach toolling is mounted on areciprocating tabl'e. A pair of parts isautomaticaUy loaded onto expanding arborsunder a single vertical ram. The parts arepushed lntothe 8 sets of tooling lin quicksuccession, and the table rapid-returns forautomatic part removal.
Make deeper cuts, o~higher quality, withIionger tool life, on your blind splines, holes, orkeyways., Just call APEX. We can show you howto do it
BROACHING liS OUR ONtY BUS.INESS
External blind splines are broached to with'nO.DOOS-in.concentricity to fnternal bore.
1. Parts loaded under ram. 2. Parts in auto-loader.3. Titanium-nitride hard-coated tooling.
Designed for water-basehydraulics, the machine neea is-ton, B·in. stroke rammounted on a bridge overthe sliding tool tabie. Pick-and-place unit straddlestable at right.
APEX BROACH 8: MACHINIE CO..6401 E. Seven Mile Rd., Detroit, MI48234
~~~I~~~8:S°~DBUILDERS OF St.AN.'. DARDAND' A' ,SP,ECIAL IBROACHING MACHINES .AND'HYDRAULIC PRESSES/BROACH TOOLiNGIFIX'JIURES/HOLDERSlPUlliRSlSIY\RPENERSI APEXCUSTOM AND PROTOTYPE BROACHING ---' ~/:OAC!fNACH:\
CIRCLE A-4 ON READER REPLYCARD
GEAR RESEARCH, THE STATE OF THE ART
Gear research seems to be thnvlng Between Sep-10th and October 17th. 120 papers about gears
were presented, at three conferences In Milwaukee.Boston, and WashIngton. to a total audience of about~ The authors were from nine countries. SlIghtly morethan half of the papers were prepared by authors whOhve outside the US and Canada
Why ISIt then, that gear desIgners, manufacturers, andstandards writers seem uncertam about the performanceof ther products? Why do prototypes undergo extensivetestrng before release for volume manufacture? Why didthe total audience at the three conferences. WIth duplrcate attendees and authors eliminated. probably not ex-ceed 200?
Let's look at the papers whIch attracted this aucnenceiThey might be diVided into four groups;
• Many papers could have been subtitled "What I OldWith My Computer" More than one thIrd of themwould fIt Into trus group.
• Other papers mIght have been named "Here ISaProduct or Process I'd Like You To Buy" About onefifth of them Fit into thIS group.
• Some covered new ways to do old tncks calculatingthe AGMA geometry factors, layIng out tooth formsand constructing rano tables.
MR. DON McVITTIL author of the Guest Edltoflal.ned The Gear Works-Seattle. Inc as Executive Vice
'President In 1969. The Gear Works speostees In thenusual. particularly small lot prcduaion of coarse pucn.'found gears, planetary drives and custom oesiqnea
reducers and maeesers. He IS also the Presaern of GearEngineers. Inc He has been an saive psmopem In thevvneocen Gear Manufacturers ASSOCiation since 1972 HIS
aln Interest has been the tecnmcst D,V,SIon. where he'has served on many commmees including the Gearr?atlng Committee. the ManufactUring Committee and theMetnc Resource and AdVISOry Committee. He IS cheumsn'of secoon I of the TechnICal DIVISIOn. compnsmq nomen-clature, metncaClOn. lubflcaeion. and metallurgy. and IS ai'mI"Inhi¥ of the Techmcal DIVISIOn Exeanive Commutee~ IS the asrem PreSIdent of AGMA Mr. McV/me IS aLk:ensed ProfeSSJonal Engineer In Washington. and afnember of ASME, SNAME. and SAE
• The rest of the papers. which were rne mosr valuableto me. and I thmk most engineers covered a vanetyof suQjects. includIng mteresnnq rnsronca, rnechamsms,new methods of analYSISWith test results for vennca-non, Investigation of the fundamental mechanisms offaIlure and real test reSUltson real gears.
Few, If any. of [he research projects reported on thsubjects wtnch are of the greatest concern In geardeSign'
• Transverse load distribution, particularly for gears Withlarge InItial mlsaltgnments or large elasrlc defleclronunder toad
• Internal oynarruc factor. the effe(( of rransrmsson rroron tooth load We sorely need an analYSISmethodwhich gives good results for most gears uSing thenormal qualIty measurements as Input. WIthout theuse of a mainframe computer for the analYSIS
• External oynamk factor or apphcanon factor We usedto caU It service factor It relates the performance ofgears under steady state laboratory conditions to therrperformance under (he fluctuating loads [hey usuallysee In the field. What IS It about some loads thatmakes them so hard on dnves?
• What rnarenal quality factors make the most differenceIn the allowable stress numbers for gears? What arereasonable frmlts on material and process for each leverof allowable stress?
{ConClnued on pa
These little understood areas of gear deSign account formost of the failures In Industrial gear drives OUf present
January/February 1985 7
'THE ,UNB,EATAB,LE GH C~.OWAPPEARI!N~G AT BENSENVI:LLE
IMit'su'bishi':s fullll CINC Gealr' Hobbingl M:achiiin,e, GH,400N'CBased Oil iits 25 year history of manufa.cturinggear nobbinglmachines, Mitsubishi nas oompleted its fu n,eN C 5-axis gear hob-betme GH400NC.Now field proven in the domestic market in Japan, the GH400NCmakes its debut herein the U.S.A. The machine will be displayedat the Mitsubishi show room at Bensenville. Mitsubishi has oper»ed it's new offioe here.
'.Large diameter master worm wheeland high accuracyball screws results to high accuracy gear products.
• Heavy duty construction and high power motor enablesto generate gears up to module '10 'tDP 2.5),
• Preset tapered hob arbor makes hob chang,ingl fasterwith ease.
BRllEFSiPECillFICATIONSFEATURES,
Ma)(imum workpiece diameterMaximum moduleMinimum number of teethMaximum number of teethRadial travel XAxial travel ZHob shift VHob head swivel angle AMaximum table rotation CHob speed range
400mm (40~)10 IDP 2.5),6120'250mm (101-)300mm (12-)1'50mm (6W
)
±45°27rpm80-350npm
.Set-up time reduced to 1/101h oompared to conven-tionaltype machines,
.Simple programming', Computer memory stores up to100 different kinds of p.rograms ..
.Capable ,of tapered gear nobbingl and crowning underCINC. No templates required,
For more details please wl'lte llS to tlheadcWess below or call'(312) 860-4220
J.. !!!T"D¥s".IHl5-1, Ma",,mouchl 2-chome. Ch~¥odl·ku. Tokvo. Jlpan
Cobl. Add,. .. HISHIJU TO~VO
Mitsubishli Heavy Industries America. Inc.873 Supreme Drive. IBensenvllle. ,IL 60106, Phone: (312) fI6O.4220
Analyzing Gear Tooth Stressas a Function of Tooth Contact
Pattern 'Shape and Positionby
Lowell Wil.r:oxThe Gleason Works
Rochester, New York
AbstractThe development of a new gear strength computer program based
upon th finite element method, provides a better way to calculatestresses in bevel and hypoid gear teeth. The program incorporatestooth surface geometry and axle deflection data to establish a directrelationship between fillet bending stress, subsurface shear stress,and applied gear torque. Using existing software links to other gearanalysis programs allows the gear engineer to evaluate the strengthperformance of existing and new gear designs as a function of toothcontact pattern shape, position and axle deflection characteristics.This approach provides a better understanding of how gears reactunder load to subtle changes in the appearance of the no load toothcontact pattern.
IntroductionThe Fatigue life of bevel and hypoid gear designs has long
been known to be a function of the length, width and posi-tion of the "no load" tooth contact pattern. For example,careful positioning of the tooth contact pattern relative tothe gear member can produce dramatic increases in bendingfatigue life ..Fig. 1shows a. two-fold increase in bending fatiguelife obtained by positioning the tooth contact pattern towardthe toe of the gear tooth rather than at a central position.
Based on the results shown in Fig. I, a gear designer mightbe tempted to conclude that a central 'toe position of toothcontact pattern should always be used to obtain maximumfatigue life. However, the relationship between gear fatigueI.ifeand the position of tooth contact pattern is complicatedby additional considerations that must be made. For exam-ple, what position of tooth contact pattern produces the bestsound qualities? What combination of the adjustabiHty of thegear design and the stiffness of the axle housing permit the
AUTHOR:
LOWEll MlCOX is Senior Staff Research Engineer incharge of the Controls Research and Computer Aided DesignGroup' at The Gleason Works.. Dr. Wilcox earned his BSME,M5Mf and Ph.D degrees from the University of Rochester:Since 1970 he has been active in the development of finite ele-ment based software for use in analyzing stresses in bevel gearteeth. Pr:esentJ'y the author is conducting research that willextend the capabilities of the finite element based software to'include a wider range of stress induced gear failures than canbe handled by preS2l1t theories.
optimum position of tooth contact pattern to be obtained,and what will the mode of fatigue failure be? Clearly, it wouldbe desirable if the relationship b tween fatigue life and toothcontact pattern parameters could b determin d by analyticalmethods rather than relying on experimental data only.
In September of 1981 the author(l)] presented a paperoutlining a new method of gear stress analysis based on thefinite element method used in conjunction with the methodof Tooth Contact Analysis TeA. This method or analysisincorporates adjustabiHty and axle deflection data along withfinite element modeling of the gear and pinion members tocalculate root fillet and surface stresses as the gear and piniondeflect under load. In the sections of this paper that follow,the new method of stress analysis will be used to analyze therelationship between length, width and position of tooth con-tact pattern and the stresses that result in fatigue failure. Theexamples given will demonstrate that stress levels in gear teethcan be related quantitatively to the parameters describingtooth contact, thereby, improving the gear designer's abilityto predict the fatigue performanc-e of bevel and hypoid gears.
Stress Analysis Model.The stress model us d to analyze fillet and surface stresses
in gear 'teeth is based on the combination of three well known
&'E-'II'$i....S..II
i.u"e"Iii:
Fig.. 1- Bending Fatigue Live Vs. P.osition of No Load Center of Contact(1' 1 Relative to Gear Member
JonuolY IFebru.olY 1985 9
Point on Pinion0' Gear T,ooth
z
Rp (or Lg)
Pinion AJC~$
IP,olnl,onTooth Surface
y
x
Point In A,~lalViewfL. - R' Co-o,dlnalesj
z
Fig, 2 - Method of Ceneratlng Points on Tooth Surface based on Co-ordinatesin Axial Section
analytical approaches; TeA. the finite element method andthe flexibility matrix method, A detailed discussion of howthese separate approaches are blended to form a stress modelsuitable for use in gearing is found in references (1) and (2).What follows is a brief overview of the essential features ofthe stress model.
TCA is used to define the geometry of the gear and piniontooth forms and to define the lines of contact that existbetween gear and pinion teeth as they rotate through mesh.Fig. 2 shows, for the pinion member, how TCA is used todefine the co-ordinate 1Jp based on given values of the axialco-ordinates r" and Rp- The axial plane co-ordiantes Lp andRp can readily be determined from ordinary algebraic equa-tions using blank dimensions as input. Once Lp and Rp arespecified at a point on the gear surface, TCA is used tocalculate (by computer interation techniques) the third dimen-sion 1Jp• In other words, TCA is used as a "black box" todevelop a point by point description of the tooth surface. Theresulting point by point description of the tooth surface iseasily converted into a three dimensional Finite elementmodel. Fig..3 shows a typical finite element model of the gearmember.
1. Numbers in parentheses refer to similarly numberedreferences in bibliography at end of paper.
2. TeA is an accepted method of vector and matrix opera-tions used to describe the Forrnand Kinematics of gearteeth.
10 Gear Technology
Heel
fig. 3 - Five tooth segment of gear showing relative location of HEX 20 FiniteElement Model
fig. 4 - Location of instant lines of contact on gear tooth model
Fig. 4 shows three lines of contact ala particular point ofgear and pinion rotation as defined by TCA. The lines ofcontact represent the theorectical location of the possible con-tact points that can occur as load is applied to the teeth. Eachof the three lines shown in Fig. 4 is discretized into a seriesof modes that can be analyzed using the flexibility matrixmethod.
The fundamental principal of the Ilexibility matrix ap-proach (3) is that the tooth stiffness, interface load and toothsurface defied ion can be related by an equation of the form
Ci) is the combined gear/pinion/axle compliance matrixand represents the load-deflection characteristics of each nodealong the lines of contact. By specifying the nodal deflection0'; in a manner consistent with normal gearing constraintsthe interface load distribution Pi' Fig. 5, can be directly ob-tained from equation L Once the interface Ioads Pi,aredetermined, the finite element method can be used to relatefillet and surface stresses to the interface loads Pi'
Fig. 5- Calculated load pressure distribution lor all contact 11n~ ill givenposition 01 rotation
The process discu sed above provides a complete descrip-tion of the gear and pinion stresses at a particular point ofgear and pinion retatlon as shown by the instant lin s in Fig.4. In ,a straight forward manner. any point of rotatloncanbe specified thus giving a complete picture of the variationin 'stress as gear and pinion rotate through me h. Further-m re. the maximum stresses, both bending and surface. arecalculated directly as a function of the TCA input parameters,and more importantly, as functions of the length, width andposition of the tooth contact pattern relative to the gearmember. Additionally, as axle housing deflecnon enter intothe compliance matrix ell (Equation 1). the stresses alsorellect the influ nee of the axle housing compliance.
In summary. it should be mentioned that all of the abovesteps required to cal ulate gear stresses have been integratedinto' a series of computer programs that are essentially drivenby the TCA pr gram. In other words, the logic and deci-ions necessary 10 per: OJ:m the above steps are automatical1y
carried out by th computer and are, therefore. tran parentto the gear design r. It is possible, therefore. to generate acomplete stress picture corresponding Itoany devel .ped TCA.
Selection of Gear De ignTable I lists the parameters defining the gear d -s.igns
analyzed by the finite element stress program. D ign A,Band C are typical of a low ratio, double reduction truckaxle. The nominal pressure angle and spiral angle for e chdesign are 22.5° and 35 respectively and the diametral pitchequals 3.161.
Designs Band C are variations of Design A in thai the cut-ter radius has been decreased from 4.5 inches to 3.75 and3.0 inches respectively. Designs A. Band C represent threedifferent designs from the point of vi w of th if adjustabililY.Other parameters such as point widths, dd ndums, deden-dums, etc., were calculated according 1'0 the CI.eason spiralbevel dimension sheet program.
The axle deflections were measured in a Glea on T6R·I1Tester. Fig. 6 hows the magnitud and directi n of llE. llP,.llC and £. corresponding to a pinion input of 36,500 lb-in,It should be noted that the direction of the 4G e .mponentof deflection is opposite to that normally shown in bothGleason and AGMA literature. This is because th finite ele-ment gear strength program holds the gear member fixed andapplies aU flotlsing related deflections to the pinion member.Therefore. aG becomes the pinion motion relativ I rh gearmember, or in keeping with the original defini.tion of aGobecomes minu the gear deflection.
D finition of Tooth Contact Patt~rn.In order '10 systematically study the inAuence of tooth con-
tact pattern parameters on gear and pinion 'fatigue tress, threedifferent combinations of length. width and position wereanalyzed. The .first combination isolated the influence of toothcontact pattern position. I. by holding th no 10 d contactpattern length equal to O.5F, where F is the gear toothIfacewidth and holding width equal to o.sh, where hI i thegear tooth whole depth. Three separate p sitions of toothcontact pattern (2:) were used in the analysis.
Fig. 7 illustrates these positions relative 'to Ithe g; ar number.A non-dimensional coordiante ystem was selected uch 'thatthe position of the center of the contact pattern. I, is zero
TABLE IGEAR DESIGN PA'RAM,ETERS USED' IN STRESS ANALYSIS
OF SP,IRAL B'EVEL TRUCK AXLE
INo. TeethDiametral, PitchFace WidthPressure .AngleAddendumDedendumCutter :RadiusCUller Edge :RadiusPilch AnsleMean Spiral An Ie
DESIGN A DESIGN B DESIG CPinion Gear Pinion Gear Pinion Gear
17 29 17 29' 17 293.161 3.161 3.161,
IS' 1.5" I.S" IS' IS' 1.5,"22.5" 22.S" 22.S"0.347" 0.188" 0.331" '0.178" 0.307" 0.164"0.246" 0.4[)4" 0.236" 0.388" 0.221" 0.365"4.496" 4.500" 3.743" 3.750" 2.999" ),(101)"
'(1.055" 0.1)95" O.OSS" 0.095" 0.055" 0.095"30.379" 59.,621" 30.379" 59'.621"
I30.379" 59.6,21°
35.0" 35.'1:1,0 35,.0" 35.0" 35.0" 35.0"
January / February 19851.'
Pinion IDI.placementAlong Gtlr ,Axil
(.10) .0033"
L - O.75'F IL : g"sl'
pot •• )All' 0 '0.25
pot. b)M-G'
o-- I
l I -~II -.... ~
-I pot. c)
_' All': ·0.2,5, ~~--...f!:'==F==l
I 2 Gear Technology
[jg.9- Equivalent alternating bending fatigue stress derived from tensil andcompressive stress components using a modified Goodman diagram
at the center of the gear face width, -0.25 hallway towardthe toe end and 0.25 halfway toward the heel end. The toothcontact patterns were positioned at three differentlocati.onsalong the face of the gear, corresponding to 2; = .025. 0,and -0.250. The extreme values of X = .025, -D.2S corres-pond tocentacts that ius] touch the ends of the gear tooth(in the case of O.SF length) to slightly overlapping the endsof the tooth (in the case of O.7SF length).
Th second combination of tooth contact patternparameters varied I in the warne way as shown in Fig. 7,holding the width equal to 0.5 ht, while length was set equalto O.SF and O.7SF.
The third combination of tooth contact pattern parametersagain repeated the z: variation of Fig. 7, but held length equalto O.SF, while width was set equal to O.Shl or O.7Shl.
Presentation an.d Discussio.n ofStress Ana1y is Re u1ts
Generally. three distinct types .of stress pattern occur ingear teeth in response to laods applied to the gear teeth; bend-ing stresses in the fillet regions, contact stresses on the sur-face of the tooth profiles (including friction) and subsurfaceshear stresses in the case region. The results of the stressanalysis in this paper pertain onlytothe bending stresses inthe fmet and subsurface shear stresses in the case region ofthe teeth,
Fig. 8 illustrates the locations and components .of the bend-ing and subsurface shear stresses. The bending stresses in the
fillet region are principal stresses Ithat lie on the surface ofthe fillets. As the gear and pinion rotate through mesh, theprincipal stresses range from. maximum tensile values at a par-ticular point to minimum compressive values. In rd r tosimp.lify the handl'ing of both ,tensile and compressive stresses,a modified Goodman diagram is employed to, reduct! the t n-sile and compressive stresses to an equivalent ahernanng stresswhose mean value is equal, Ito zero, Fig. 9a shows a typi altensile/compressi.ve stress pattern, for either gear or pini n,calculated from Ithe finite elemen'tgear strength program. Thmaximum tensile stress a the gear and pinion rotate throughmesh is 0'141' while the minimum ab elute value ofcompres-sive stress is uKC' The mean stress is um~an = (UK! - uKc)/2.Fig. 9b shows the alternating str S5 pattern equivaJ nt to thatshown in Fig. 9.a, but with zero mean stress, The stress pat-tern shown in Fig. 9b can be determined from the modifiedGoodman diagram shown in Fig. 9c o.r a.ltematively Irom thefonowing formula.
(21
Equation 2 is derived from Fig. 9c with ,(1'1.111, the ultimat-stress of the case hardened gear structure, equal to. 330,000PSI. By resorting to an equivalent altemating stress a singlestress life curve can be used to compare diff,efientgear d' igns,
In the case of subsurface shear (4, S, 6) there are actually
January/February 1985 1]
two such components as is shown in Fig. 8. The deepestpenetrating shear is the '45 shear. The 1'45 shear results infatigue cracks that usually occur at the case-core interfacesuch as in heavy spalling. The other component oJ subsur-face shear is the reversing orthogonal component of shearwhich occurs at 64% of the depth of the T45 shear. The or-thogonal component of shear, To, is reversing in that as thecontact zone moves across the tooth profile a point beneaththe surface of the tooth, sees both a plus and minus valueof T". The T45 shear, on the other hand, does not changesign as it lies along the centerline of tooth contact. It will beassumed in the ensuing discussions that although themagnitude of the ill component is less than the '45 compo-nent the 1'0 component is in fact the critical component formost gear failures because the fully reversed stress amplitudeof the To component results in a worse state of stress thandoes the single direction 1'45 amplitude.
Influence of Pcsltlon of Tooth Contact Patternand Cutter Radius on Fatigue Stress
Fig. 10 shows the influences of tooth contact pattern posi-tion and cutter radius on bending stress and subsurface shearstress .. Gear bending stress, 0':, and pinion bending stress,(1~,are shown on the left hand side of Fig. 10, while or-thogonal shear stress, Ttl. is shown on the right hand side ..The abscissa (l,;) of Fig. 10 represents the "no load" positionof the center of contact along the gear face while the ordinaterepresents equivalent alternating stress measured in KPSI.Non-dimensional contact pattern lengths and widths are eachset equal to 0.5 for the stress curves shown in Fig. 10.
The influences of tooth contact pattern position and cut-ter radius on fatigue stress can be generalized as follows. Asthe center of the tooth contact pattern is positioned towardthe toe of the gear tooth, both gear bending and subsurfaceshear stress increase. At the same time, pinion bending stressdecreases. As cutter radius is decreased from 9.0 inches to6.0 inches, gear bending and subsurface shear increase whilepinion bending stress decrease.
Bonding S....1DO
110
10 10
St.,tlS, Sir",(OPSll (KPS!) .'.10 10
50
:;0
D~ 0., 0' -03 0.3 o.~ 0.1 0 -0.' -0.2 -0.3Hee:I T.,. ...." TOIl'
I I
Fig. 10 - Variation of ,O'~, ,(J'~ and T~ with tooth contact pattern positionl: 11. = O.SF, W = 0.5\1 .
14 Gear Technology
Bending'oo~----.-----.----, 100,-----,-----,-----,
IIO~----+_----+_--~
·10 1-----+-----+---""""1
~~~--~-+--~~~0.1, D.'I 0.'"OIl
l1li -O..1! -0,,2 -0.3E Too........ 1 Too
fig. 11- Vaxiiltioo of J~, 0 ~ al\d ,~ with tooth contact pattern positionI ( L = O.SF)
(·-·-----L = O.7SF)
The percentage figures shown with each of the curves inFig. 10 indicate the mag:nitudeso£ change found in the stresscomponents for each case. The gear bending stress increasefrom between 6.9 and 17.2 percent as the contact pattern ispositioned towards the 'toe. Subsurface shear increases frombetween 5.6 and 11.2 percent while the pinion bending stressdecreases from between -19.0 and - 20 percent.
The corresponding changes due to the influence of cutterradius are smaller. At the center position of tooth contactposition (1: = 0l. the gear stress increase is 10.9 % as cutterradius decreases from 9.0 inches to 6.0 inches ..The subsur-face shear stress increases very slightly, by 3.8% while pinionstress decreases by-B.O percent.
Summarizing, both tooth contact pattern position and cut-ter radius have significant influences on fatigue stress. Basedon the author's experience with fatigue tests conducted onthe designs shown in Table 1, the results above tend to sup-port the observation that building the contact pattern centertoe and using smaller cutter radii (better adjustability) doesresult in improved fatigue life.
Influence of Tooth Contac,tPattern Length on Fatigue Stress
Fig. 11 shows the influence of the length of the contact pat-tern on fatigue stress as the contact pattern length is increasedfrom O.SF to O.75F. The solid lines correspond to a 0.5F lengthwhile the dashed lines correpsond to a 0,75F length.
The primary influence of increasing contact pattern lengthis to rotate the stress posit.ion curves about the 2; = 0 value.The basic trends of stress versus l,; and cutter radius remainthe same as outlined by the rotation of the stress curves ..
When the detrimental effects of lengthening the tooth con-tact pattern are examined, it is apparent that the pinion bend-ing stresses in Fig. 11 are increased from between 5 ..7 and8.0 percent when the tooth contact pattern is positionedtoward the toe of the gear tooth. The gear stress on the otherhand decreases from between -2.8 and -4.9 percent. At
100B.n<!I~ 'Shelf
100,
!IQ !IO
10 10
Sb'eNi SII'tuCIIPSII IKP$lI
70 70
~+--4--+--+--+--+-40.3 D.2 O.'I D ~.1' -0.2 -0.3
Too
Fig. 12- Vanation of (J~, (J~ and T~ with tooth contact pattern position
:!( L .~ O.5F h,)(--L = O.7SFhtl
the same time, subsurface shear stresses decrease frombetween -1.7 and -2.2. percent. If the position of tooth con-tact pattern is moved in the opposite direction, toward theheel of the gear tooth, the 'trends given above are reversedby about the same magnitudes.
Summarizing, when Fig. 10 and 11 are compared, it is seenthat the importance of contact pattern length changes onfatigue strength are approximately one half those experiencedwith position change and approximately the same as thoseattributed to cutter radius changes.
Influence of Contact Pattern Wid'thon Fatigue Stress
Fig .. 12 shows the influence of contact pattern width onfatigue stress when the contact pattern width is changed from0.5h, to 0.75hl, where h, is 'the gear tooth mean whaledepth. The dashed lines represent the 0.75hl width while thesolid .lines represent the O.5ht width.
It is apparent from Fig. 12 that the change in contact pat-item width from 0.5hl to. 0.75h, has almost no effect at allon bending stress and only a very small eHect on shear stress,The pinion bending stress decreases by less than one percentat the! = .0 position of tooth contact pattern. Gear bend-ing stress decreases by -1.9 percent or less and shear stressdecreases by -1.4 percent or less,
Summarizing, the width of the contact pattern has the leastInfluence of all on bending and shear stresses. Changes infatigue life due to changes in bending and shear stress of lessthan two percent would be diHicult to detect experimentally.
Comments on Experimental Validity of Stress Dalta
In the preceding sections of this paper, analytical stress datawere presented relating changes in fatigue stress to changesin the tooth contact pattern parameter length, width, ~ andto cutter radius. At present 'there is very little 'experimentaldata collected relative to two af theseparameters: k and cut-ter radius."') Furthermore, a portion of the data concerning
Rc was obtained from simulated gear tooth shapes ratherthan from actual bevel gearsl81. The influence of ~heparameters length and width have not been experimentallyverified.
Although the results presented in Section 5 are encourag-ing, it must be stated that these results are largely theoreticalpredictions at this point in time. Hopefully, more experimen-tal data will be available in the future to improve confidencein the results of Section 5.
Conclusions and Future PlansThe main objective of this paper has been to show thai!
fatigue stress can be quantitatively related to. tooth contactpattern parameters and to. cutter radius. To that end, resultshave been presented showing the percentage changes in bend-ing stress and subsurface shear stress as contact patternparameters and cutter radii were changed in a systematic way.
The results presented in Figs. ]0 thru 12 show that [atiguestress does change in a predictable manner as tooth contactpatter parameters are varied for each of the three toothdesigns employing different cutter radii. Generally, thechanges in fatigue stress vary from 10 to 20 percent in thecase of position and cutter radius variations dawn to onlya few percent in the case of tooth contact pattern width.
(Continued 0/1. page 23)
Gear Hobbingl Ma.chinesare stiU built -with the sametime~honOlledlSwiss Precision',
SlKfwn:Model 82, the Seml-Allto-matlc High Precision Ge!!rIHobblng MaChine· for·spur; helical, bevel geanl,worms, I!J!d worm wheels.Max. gear dla S" (6.89')Max.l\obbing lenglh 4'110"NQ's of !«Jelh 2·800Max. D.P. ..•....• nNet Weight. 3300 Il>s.
ERIC R. BACHMANN COMPDY. DlC_I) J200 Easl90th Street, New y"ork, New York 10128. (212) 722·8699 - II,
" . .Quality mach'Me t·ools •. /Jac.Iu;J6.t~ __ -_
CIRCLE A-5 ON READER REPLYCAIRD
Jonuorv/Fecruary 1985 15
'Computer Aided Design (CAD) of Forging and ExtrusionDies for the Production of Gears by Forming
byDavid I. Kuhlmann
P. S.. Raghupathi(Battelle's Columbus Division)
Gary L. Horvat(Eaton Corporation)
Donald Ostberg(U. S. Army Tank Automotive Command)
Material losses and long production times are two areasof conventional spur and helical gear manufacturing in whichimprovements can be made. Metalforming processes havebeen considered for manufacturing spur and helical gears, butthese are costly due to the development times necessary foreach new part design. Through a project funded by the U.S.Army Tank - Automotive Command, Battelle's ColumbusDivision has developed a technique for designing spur andhelical gear forging and extrusion dies using computer aidedtechniques.
Gear Forming MethodologyGear manufacturing processes are highly specialized due
to the complex geometry and high accuracy requirements ofthe gear teeth. Precision forming methods for gears offer con-siderable advantages including the reduction of material andenergy losses during finish machining. However, to establishprecision forming as an economical production technique re-quires' the capability to design and manufacture dies withprecise and reproducible dimensions with long life and at anacceptable cost.
The traditional method of forging and extrusion die designand manufacture is based on experience and trial and error.A preliminary die is made and a few parts are formed. Meas-urements are taken of the finished part and the die is adjustedaccordingly. A second series of trials is conducted, and soon, until the final die geometry is obtained. Such a develop-ment program is required for every new design which makesthe precision forming process economically less attractive,especially when complex and precise geometries are involved,as with spur and helical gears. Therefore, methods need tobe developed to apply advanced computer aided design andmanufacturing (CAD/CAM) technologies (finite element,metal forming and heat transfer analyses) to gear formingdie design and manufacture. This approach benefits from thecapabilities of the computer in computation time and infor-mation storage and allows the die designer to try variouschanges in the die design and the forming conditions, withouttrying out each new change on the shop floor.
CAD / CAM Applied to Forging and ExtrusionIn recent years, CAD / CAM techniques have been applied
AUTHORS:
MR. DAVID J. KUHLMANN is currently.a Researcher inthe Metalworking Section of Battelle's Columbus Division, Forthe past two years he has been developing interactive, graphicsoriented computer programs for metal forming processes andhas authored/ co-authored four publications. Mr. Kuhlmannreceived his B. and M.S. degrees in Mechanical Engineeringfrom the Ohio State University and is currently an AssociateMember of the American Society of Mechanical Engineers andan Engineer-in- Training in the State of Ohio.
DR. P. S. RAGHUPATHI'5 experience is in the area of coldextrusion, dosed die forging, deep drawing, metal formingmachine tools and computer aided design and manufacturing.He is currently the Associate Manager, Metalworking Section,of Battelle's Columbus Division. In addition to being theauthor I co-author of more than 20 publications, he is also aco-editor of a Metal Forming Handbook which is soon to bepublished. Dr. Ragl1upatl1i holds a BE, University of Madras,India, ME from the Indian Institute of Science, and a Dr.Ing. from the University of Stuttgart, W. Germany. As a
16 Gear Technology
member of the International Cold Forging Group based inEurope. he maintains close contact with European Universities,research laboratories and companies active in manufacturingtechnology.
MR. GARY L. HOR1lA T has been employed at Eaton Cor-poration since 1977..His work in Forging and Forging Develop-ment at various Eaton Divisions has given him a uniquebackground in the precision forging of gears. Currently, Mr.Horvat is a Manufacturing Development Engineer. He at-tended Cleveland State University, graduating with a.B. andM.S. Industrial Engineering. He isa member of AmericanSociety for Metals, Society of Man.ufacturing Engineering,CASA, Computer and Automated Systems. He is .aRegisteredProfessional Engineer in the State of Ohio.
MR.. DONALD OSTBERG is currently a Materials Engineerfor the United States Army Tank-Automotive Command.He has been at 'L4COM since June 1977. During this time hehas been involved in the manujacturing technology efforts.Mr. Ostberg studied at Cleveland State University and holdsa B.A. in Chemical Engineering.
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to various forging processes. The experience gained in ali ofthese applications implies a certain overall methodology forCAD / CAM of dies for precision and I or near-net shapeforming. This computerized approach is also applicable toprecision cold and hot forming of spur and helical gears, asseen in Fig. 1.. The procedure uses as input: (a) the processvariables and (b) the part (gear) geometry. The former con-sist of:
forming (forging and/or extrusion) a set of spur gearsand a set of helical gears.
The Phase Iwork and the Phase n spur gear extrusion trialshave been completed. A simplified flow diagram for the com-puter aided design and manufacturing of forging and extru-sion dies for spur and helical gears is shown in Fig. 2. Usingthe overall outlines of Figs. 1 and 2, the die design effort wasdividied into four tasks:
1. Definition of gear and gear tooth geometries.2. Prediction of forming load, pressure and stresses.3. Estimation of tool deflections, shrinkage and corrections.4. Development of an interactive, graphics based computer
program for performing Tasks 1 through 3.
(1) data on billet material under forming conditions (billetand die temperatures, rate and amount of deformation),
(2) the friction coefficient to quantify the friction shear stressat the material and die interface, and
(c) forming conditions, such as temperatures, deformationrates, suggested number of forming operations.
Using the process variables and the part geometry. apreliminary design of the finish forming die can be made.Next, stresses necessary to finish form the part andtemperatures in the material. and the dies are calculated. Theelastic die deflections due to temperatures and stresses canbe estimated and used to predict the small correctionsnecessary on the finish die geometry. Knowledge of the fonn-ing stresses also allows the prediction of forming load andenergy, The estimation of die geometry corrections isnecessary for obtaining dose tolerance formed parts and formachining the finish dies to exact dimensions. The correctedfinish die geometry is used toestimate the necessary vol-ume, and the volume distri-bution in the billet or thepreform. Ideally, a simula-tion of the metal flow shouldbe conducted for each diedesign. This is a computer-ized prediction of metal flowat each instant during form-ing. This simulation is math-ematically quite complex andcan only be performed at thistime for relatively simpleparts ..In more complex appli-cations, die design can bedetermined by computerizeduse of experience-basedformulas.
Two Phase ApproachThe present study is still in
progress and is being con-ducted in two phases asfollows:
" Phase IComputer Aided Design(CAD) of fanning dies.
• Phase IIComputer Aided Manu-facturing (CAM) of theforming dies and demon-stration of the effective-ness of CAD I CAM by Fig. 1-Descriptive Computer Aided Design Procedure for Finish Forging Dies
Generating the Gear Tooth GeometryTo define the tooth geometry, certain gear and/or cutting
tool parameters must be specified. Some additional data per-taining to the mating gear mayalso be required in certaininstances. All the data required for the computations can beobtained from a "summary sheet" developed by gear designers(Fig. 3) and also the geometry of the cutting tool (Fig. 4).With this data, standard gear equations are used to calculatethe X and Y coordinates of the points describing the gear toothprofile.
The basic geometry of a spurgear tooth is seen in Fig. S,with the .following majordefinitions (1):
• addendum-the radial distance be-tween the top land andthe pitch circle
• backlash-the amount by which thewidth of a tooth spaceexceeds the thickness ofthe engaging tooth onthe pitch circles
• circular pitch-the distance, measuredon the pitchcirde, froma point on one tooth toa corresponding point 'onan. adjacent tooth
• clearance-the amOUJ1tby which thededendum of a. gear ex-ceeds the addendum ofits mating gear
• dedendum-the radial distance fromthe bottom land to thepitch circle
• d.iametral pitch-number of teeth on thegear per inch of pitchdiameter
JanuaryjFebruaryl,985 17
DESCRIBE GEAR GEOMETRY INDIGITAL FORM FOR USE IN COMPUTER 1-0-----,
MODI FrCAT.IONS
CORRECTIO'lS
INSPECT THE GEARS ANDEVALUATE FORMING PROCEDURE
UPDATE COMPUTER PROGRAMSAND REF INE CAD/CAM'METHODS FO~ DIES
Fig. 2-Genera.l Procedure for the Design of Gear Forming Dies
• pitch diameter- diameter of the theoretical pitch circlewhich is tangent to the correspondingpitch circle on a. mating gear
The majority of the gears produced by conventional cut-ting methods are either hobbed or cut using a shaper cutter(2). In this study, for defining the tooth geometry, standardequations were used to simulate the gear cutting process (3-7).These equations are included into a computer program, canedGEARDl, as discussed later.
Forming Load PredictionTo determine the elastic deflection of the forming dies,
stresses acting on the die during the forming processes must
18 'Gear Jechnology
be known. This stress analysis is necessary to obtain not onlythe elastic deflection, but also to calculate the formingpressure and load.
ExtrusionThe extrusion process is seen schematically in Fig. 6. The
punch load required to extrude a spur or helical gear isdetermined by estimating the following forces:
• the ideal deformation force,'. the force due to internal shear at the die entrance and exit,.' the friction Iorce along the die walls and the punch.
Using the slab method of analysis, the equations for thepunch force were determined and programmed.
DATA
061DATA=;;===
011DATA
DRAWliNG INIFORMATION FOR:A DRIVEN COUNTER SHIAIFT
IDENTIIFICATION NUMBERSET NUM'BER . . . . . .NUMBER OF TEETHI. . . .NORMAL DIAMETRAL PITCH IMODULIEINORMAL IPRESSUREANGLEHELIX ANGLEHAND, OF HEUX. .. . . .LEAD .TIR'ANSVERSEDIAMETRAL PITCH (MODULE)TRANSVEIRSE PRESSUREANGLE
MAXIMUM' OUTER: OIIAMIETER. . .MINIMUM OUTER DIAMETER . . .MAXIMUM' TIP CHAMFER: DIAMETERMINIMUM' TIP CHAMFER' DIAMETERTHEORETICAL PITCH DIIAMETERMINIMUM ROOT D'IAMETER
BALL/PIN OIAMETER FOR (MOPI .MAX. MEAS. OVER PINS (MOP).MIIN. MEA.S.OVER PINS (MOP). .MIN. CAUPER MEAS. (41 TEETI--I .MAX. CALIPEIR MEAS. (4i1 TEETH .
MEAN FACE WmUIL .. . . .MIN. NORM lOPLAND IMAX. 0.0. WID CHAM]MIN. THEO. NORM. CIRe. TOOTH THICKNESSTOOTH THIICKNESS@HALF OF WHOLE DEPTHCASE DEPTH .MAX. PITCH DIAMETER RUNOUT (TIAI . . ..
@ MAX. OUTER RADIUS . . . .@MAX. ENIDOF ACTIVE PROFILE@ MAX. HIGH CONITACT POIINT@OPER. PITCH POINT. . . . .@ MIN. LOW CONTACT POINT . [email protected] OF ACTIVE PROFILE@STARTOF INVOLUTE CHECK@ BASE RADIUS. . .
MAX. LEAD VARIATION. . .MAX. LEAD RANGE. . . . .CROWNING IN MIDDLE 80% OF TOOTH
MAX. RUNOUT n.I.R.' . . . . . .MAX. TOOTH TO TOOTH COMPOSITE VAR.MAX. TOTAL COMPOSITE VARIATION.MAX. PITCH VAIRIATION .MAX. PITCH RANGE. . .. . . . . .
ENGL.ISH METRIC(liNCH) (MIMI
81.0220 81.0220810.0123 810.0123
32. 32.10.0000 2.5401'9.0000 19.00031.5739 31.574
LEFT19.2000 487.6808.5197 2.981
22.0064 22.006
4.079 103.604.069 103.354.049 102.844.039 102.593.7560 95.4023.'511 89.18
0.2160 5.4864.1716 105.9584.1681 105.8701.1056 28.0821.1071 28.121
0.875 22.230.029 0.740.1626 4.1300.1764 4.481
.023/.033 0.59/0.830.0025 0.063
ROLL ANG. IRADIUS RADIUS:;;;;11:;;::==: ===== ;;;;~ .. :::r:::=== ;;;;:;;;==;ra.
34.95 2.0395, 51.80333.99 2.0245, 51.42230.30 1.9697 50.03025.02 1.9000 48.26022.42 1.8697 47.49117.45 1.8202 46.23316,.72 1.8138 46.0700.00 1.7412 44.226
0.0004 0.0100.0008 0.020
.00000/.00050 .0001.012
0.0025 0.0630.0008 0.0200.0032 0.0810.0004 0.0100.0029 01.073
Fig. .3 - Example of A Typical Gear Manufacturer Summary Sheer DefiningGear Geometry
JamJolIV/February 1985 19
LI
IT•• T o. c.l"_AiH'IIIIOAC" "'OD, .. DUM
TOOT... '''0111 L.Io. "'--~ _'.'.1.1II1II1 AP4CLI
..... !,..A1II9'0 v.,W 01 :J9. TOO"~
c."..t.y or abulc hob
OUTSIDEANGL!'
fig. 4 - Geometry of A Hob and A Shaper Cutter
fig. 5-Gear Terminology
ForgingA typical tool setup for forging of gears is shown
schematically in Fig. 7. The punch force necessary to fill thetooth cavity by radial metal flow was also calculated usingthe slab method of analysis and empirical equations. Addi-tionally, the forging load was estimated using a Finite ElementMethod (FEM) based program in order to verify the calcula-tions made by the slab method and empirical equations. The
.20 Gear Technology
results of the FEM analysis correlated closely with theempirical analysis.
Estimation of Die CorrectionsThe geometry of the forming die is different from that of
the formed gear because,
• The die insert is normally shrink fitted into the die holdercausing a contraction of the die surfaces.
• In warm I hot forming, the dies may be heated prior toforming and further heated by the hot billet during form-ing. This causes the die insert to expand.
• During forming, due to forming stresses, the die surfacedeforms elastically.
• After forming, the gear shrinks during cooling from form-ing temperature to room temperature.
To obtain the desirable accuracy in the formed gears, eachof the geometrical variations listed above was estimated andthe die geometry corrected accordingly ..Referring to Fig. 8,the original pitch radius is represented by R. Shrink fittingof the die causes the gear profile to shrink. hence the die mustbe increased by a corresponding amount, S.. Similarly, in-creased die temperatures and forging pressures cause the dieto expand. These two factors are compensated by theamounts Hand E. Finally, a. warm I hot formed gear willshrink during cooling; therefore, the die must be enlarged bythe amount C. The results of the die correction analyses wereused to alter the coordinates of the gear tooth profile toachieve the appropriate die geometry.
Cutting the DieA common method of die manufacture is called electrical
discharge machining (EDM). The process uses an electrode,usually made of graphite or brass, which is the negative of
I Punch2 Top Insert:3 Conical or Stream-
lined Insert4 Gear Insert
5 Support Insert6 Reinlorcing Ring7 BilletB E~trusion
Before Extrusion Aller Extrusion
Fig. 6 - Schematic of the Extrusion Process
e
~
&OTTOW GUIO[IILOC.ctlUUDI PUNCH.aTTOW [JECTO"
Fig. 7- Typical Tool Setup for Forging Spur or Helical Gear5,
the die geometry. The electrode is brought dose ,to. but notin 'contact with. the die material. An electrical current isallowed to arc across the gap which "burns" away the diematerial. Another form of this method of manufacture iscalled wire EDM. Current is passed through a straight wireIthat moves in two dimensions, burning the die geometry asit goes. Helical gear dies must be made by lIsing a solid dec-trode but spur gear dies c-an be cut using either a solid elec-trode ,or a wire EDM process. In either case. a eorreeted 'setof gear tooth profile coordinates is needed. This new set ofcoordinates is computed by applying a correction factor tothe' radius vector from 'the center of the gear to each pointon the gear tooth profile. The correction factor is a functionof the values for S, H, E, and C as shown in Fig. 8 ..
As previously mentioned, the geometry of the die is dif-ferent from the final gear geometry ...When ,cutting the geardie using 3-" electrode, it may be desirable Ito manufacturethe electrode using a hob or shaper cutter ~pecifically designedIto cut the electrode geometry. The computer program,8,GEARm: allows the user ,to design this new ,cutting tool.
Computer Program "GEARDI'"Using the equations developed in Phase l, a graphics
oriented computer program called GEARD] was d veloped,The main functions of GEARDl are:
'. define the exact tooth form of a spur or helical gear,
• compute the forming load required to produce the CUI-
rent gear design,• compute the coordinates of the corrected gear geometry
necessary for machining the EDMelectrooes by taking intoaccount the change in the die geometry du to temperaturedifferentials, load stresses and shrink fitting, and •
•' determine the specifications 'of a 1.'001 which can cut thealtered tooth geometry on a conventional hobbing orshaper cutter machine.This program enables the user to design spur and helical
gears, predict tooling loads and pressures, estimate meta] flowfor forming the gear, and define the geometry required tomanufacture the tooling using conventional or wire (;DM.Several examples of gears, currently being forged in industry.were tested in the GEARDI computer program. The predictedforging loads were within 10 percent of the actual loadsmeasured during production runs.
GEARDI is an interactive, graphics-oriented programwhich runs on Digital Equipment Corporation VAX 111780.111750. and PDP-lll44 computers. h isa menu driven pro-gram that allows the user to select various options from apre-defined list. F.ig. 9.is a simpli1ied flow diagram of the pro-gram depictingth various menu oplionsa.vailable to the user.One 'convenient feature, the ~COMPAR]SON DISPLAY" op-tion, allows the user to superimpose two gear profile draw-ings on the computer and determine the maximum differencebetween the two profiles. Fig. 10 shows th superposition ofan original spur gear ,tooth profile and the corrected g~metrywhich was determin d by the program ;for a specific set offorming conditions.
The GEARDI program has powerful applicationpossibilities, not only in the area of metallorming, but alsoin the area of gear and gear train design. with its ability to
Fig. ,8-Correction 10 Gear Qoometry (Symbols Expl ined 10 Text]
Jonuary IFebruary 1985 21
GEARDI INPUT/CHECK - RElURN TO "" I II HENU
READ INI GEOMETRY FROM F I L E
, - KEY IN &EOMETRY
- COMJ!U1t PROF ILE
- ORAl;! GEAR lOOTH
IJIAW £NTIREGEAR
ECHO DATI
CHANGE DATAAl1tR FILLET
HEl!P
--..,_- RETURN TO KO.!N MEIIU
!TE INPUT DATA
WRITE FORMING ANALYSIS fILE
ANALYSIS ---,,..-- RETUR TO ""IN MENU
INPUT FORMING: DATACHECk FORMING DATARU fORMING ANALYSIS
COMPARlSOfI DISPlAY
CREATE TOOL
- HELP
-EXIT
F,ig.9 - Flow Diagram for the Computer Program GEARDI
I l.Q Inch I
fig. lO-Compl.Iler Program Display of the Original Gear Tooth and theCorrected Gear Tooth Geometry
design hobs and shaper cutters and to modify the fillet froma trochoidal shape to a circular shape.
Spur Gear Extrusion lHalsFig. 11 shows a picture of the tool setup for the spur gear
,22 Gear Technology
Fig. ]I - Tool Setup for Spur Gear Extrusion Trials
extrusion trials, conducted at Battelle's Columbus Divisionusing a 7~ton hyd:rauHc press. The gears were extrudedusing a "push-through" concept. Each gear is first partiallyformed and left in the die while the punch is retracted. Asecond biUet is placed on Ilop of the partially formed gearand the press is cycled again. During this cycle, the partially
Fig. 12- Sequence of Parts for Extruding Spur Cears. Billet is on Top, Par-tially Formed Gear is in the Middle, and Complete Extruded Gear is on theBottom.
Fig. 13 - Extruded and Shot-Blasted Spur Gear
formed gear is finish formed and pushed through the die,dropping out the bottom of the die. Fig. 12 shows thesequence of parts in the toollng. Once formed, the teeth onthe gear are not machined further. A fixture which holds thegear on 'the pitch line of the teeth is used to finish machinethe inside and ends of the gear, The spur gear formed in thesetrials was designed to be an AGMA quality class 8 gear ..Measurements taken on the extruded gears indicated a gearof between AGMA quality 7 and 8. An 'extruded gear whichhas been shot-blasted is shown in Fig. 13.
Refe.reJ1loes,
1. GEAR. HANDBOOK. 1st ed., Darle W. Dudley, McGraw-HillBook Co., New York (1962).
2. "GEARMANUF~CTURrNG METHODS AND MACHINES,A REVIEW OF MODERN PRACT[CES,· J. Richard Newman,Proceedings of the National Conference on Power Transmis-sion, Vol 5. Fifth Annual Meeting.
3. ANAL ¥TICAL MECHAN1CS OF GEARS, E. Buckingham,Dover Publications, lnc., New York (1949).
4. MODERN METHODS OF GEAR MANUFACTURE, 4th ed.,National Broach and Machine DIvision / Lear Seigler, Inc,Publication, Detroit. MI (1972).
5. KINEMATIC ANALYSIS OF MECHANISMS, 2nd ed., J. E.Shigley, McGraw-Hill, Book Co., New York (1969).
6. DESIGN OF I'v1ACHINEELENfENTS, 5th. ed., M. F. Spotts,Prentice-Hall, lnc., Englewood Cliffs, NJ (1978).
7 ,"KNOW YOUR SHAFER CUITERS,· Illinois / Eclipse publica-tion (1977).
Tills, paper is based on work conducted by CI team of engineers. The authorsgratefully a,JrnoUJ/edge the (cmtribulion of Dr. T. Allan, Battelle Colum-bus Div.lsion. and Messrs. A So.bro/f and J. .R. Douglas. from EatonCorporation.
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THERE'SSTILL TIME..CLOSING IDATE IFOR ACLASSIFIIEID AID liN THEMARCH/APFUL II'SSUE IS
dANUA.FlY 25th.
A~ALYZENG GEAR TOOTH STRESS •••(continued from page 15)
Having established that stress levels vary in a predictableand quantitive way, work has begun on correlating the stressdata obtained from the finite element stress program tosources of experimental data. Two parallel programs are nowunderway Itoprovide such correlation, The first program willanalyze several hundred fatigue test data points from full scaleaxle tests ana four square fatigue tester. The purpose of thjsprogram is Ito establish a reliable S-N curve for each of themodes .of fatigue failure; e.g., bending fatiguea.nd subsur-Face shear ..The second program will involve Iatigue data ob-tained from simulated gear tooth specimens using a closedloop hydraulic tester. The test data obtained from thesimulated gear tooth specimens will be used to augment thedata obtained f.rom the .ful1scale axle tests thus providing ill
relationship between S~N curves for various materials andheat treatments to the S-N curve obtained from full scaletesting. The successful completion of this final step shouldresult in establishing the finite element gear strength programas a powerful gear analyzing program for the design of beveland hypoid gears.
Refe.rences1. L. W]lCOx. ~An Exact A_Ralytical Method for Calculating
Stresses in Bevel and Hypoid Gea.rTeeth," JSME Conference,Tokyo, Japan, September '7, 1981.
2. L. WILCOX and .R. AUBLE, "Three Dimensional Stress Analysisof Meshing Gear Teeth: World Congr'- .5 on Ge.aring, Paris,France, 1977.
3. A. FRANCAVILLA and O. ZIENKJEWlCZ, "A Note onNumerical Computation of Elastic Contact Problems," Inter-national .Joumal for Numerical Methods in Engineering, Vo!'9, Pl'. 913-924, 1975.
4. S. TlMOSHENKO and J. N. GOODIER. "Theory of Elastici-ty,N Second Edition, Chapter 13, pps. 377-382. (McGraw-HiliBook Company), 1951. . -
5. J H. RUMBARGER and L LEONARD', ~Deri.vation of aFatigue LifeModel for Gears." USAAMRDL Technical Report72-14, Eustis Directorate, US Army Air Mobility Research andDevelopment Laboratory, Fort Eustis, Virginia, May, 1972.
6. E. SANDBERG, "A Calculation Method for SubsurfaceFatigue,", Paper No. 8-30, Vol. 1, JSME Ccnlerence, Tokyo,Japan, 1981.
7. L WILCOX,. 'Unpublished Gleason Works EngineeringReport"8. L. HOOGENBOOM, "Experimental Stress .Analysisof Hypoid
Gear Tooth Models." Mechanical Technology R,epo.rtMTJ-66TR58, November lB. 1966.
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Is, next to diamond, the.. Iva known and has extremely
____ strength compared to diamond..!CQ_IfUIC8N technique demands a stiff,rigjd machine tool and Intensive coolantflooding of the grinding zone. The StarBorazone Hob Sharpener meets both theseconditions due to its precise, rugged design
ture ofetlmlnatN aU manual except forloading and unloading the hob. The machineis also very quiet (72 dba In cycle withapproximately 68 dba background noise).
A number of CNC Borazon" Hob Sharpenershave been operating in automotive plants forsome time with outstanding results. We offerfast delivery. Our machines are competi-tively priced. Service and engineering assis-tance is included. If interested, please writeor phone for details.
Operators console has a grinding spindleload meter, a CRTscreen and a keyboard forentering hob diameter, number of flutes,stock removal per rough and finish pass andnumberof passes,feed rate and right and leftstroke limits. A CNC programmable con-troller is employed for sequence logic,feeding the grinding spindle slide, and posi-tioning the hob spindle.
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The Effect of Lubricant TractionOn Wormgear Efficiency
byW. R. Murphy, V. M. Cheng,
A..Jackson, J. Plumed ,& M. RocheteeMobil Research &; Development Corporation
LABORATORY TEST A
30:1 RATIO .. 1.65 HP WORMGEAR
201510
5
CYL. OIL SVN G SVN S
Fig. 1- Improvement Over Conventional 5 IP Mineral Based Oil
AbstractThe effed of various lubricant factors on
wonngearefficiency has been evaluated usinga variety of gear types and conditions, In par-ticular, the significant efficiency improve-ments afforded by certain types of syntheticlubricants have been investigated to determinethe cause of these improvements, This paperdescribes broad wormgear testing, both in thelaboratory and in service, and describes the'extent to which. 'efficiency can be affected bychanges in the lubricant; the effects of vis-cosity, viscosity index improvers and, finally,synthetic lubricants are discussed. The workconcludes that lubricant tractional propertiescan playa significant role in determining gearelficiency characteristics.
26 Gear Technology
IntroductionOver the past ten years, the trends to
hotter-running industrial. gears has pro-vided the authors' company with the op-portunity to evaluate synthetic industrialoils developed with the superior ther-mal/oxidative performance. In severalinstances, it was noted that not only wasoil life improved by using synthetic pro-ducts, hut that the equipment ran coolerthan with the mineral-based productsOriginally used, This behavior has beenreported.(l) The simnl t exl nati - f--~_ _ pes _ p_arLa ._on orcooler-running is a reduction inhorsepower loss; i.e, an improvement inpower transmission efficiency.
These findings, in part, resulted in a
significant effort to evaluate industrialgear efficiency characteristics of differentlubricants, including the syntheticproducts.
Laboratory Evaluations ofWormgear Effidency
Results of wormgear tests available inthe authors' laboratories in Europe andthe U.S. appear in Figs. 1 through 4.
Equilibrium operating temperaturedata obtained with Wormgear Aoperated at 1500 rpm and 100% nominalload are shown in Fig. 1. Both syntheticsshow signiflcant temperature decreases.A conventional steam cylinder oil(AGMA 7 Comp.) is also shown forcomparison against the reference, whichis a conventional AGMA 7 EP mineral-based oil. The viscosity grades (see Table1) for Syn S and Syn 'G were chosen fromtheir respective product families to besimilar to that of the reference oilat theapproximate 100°C operating tempera-ture of the tests,
Data in Fig. Z compares both efficiencyand temperature rise differentials usinga second manufacturer's gearbox,Worm-gear B. Similar temperature decreaseswere found for the synthetic products,but the steam cylinder oil ran slightlyhotter than the reference conventionalSIP mineral oil. These results are re-Bected in the efficiency data for these 'oilswhich show 2-3 % benefit for the syn-thetics anda directional worsening forthe cylinder oil, Efficiency measurementsin this test were made by means of straingauges on the input and output of thegearbox which was run at 1760 rpm in-put and reached about 100°C at equil-ibrium. Loading was achieved hydraul-ically as part of a four-square 'testarrangement,
Fig. 3 data shows benefits in efficiencyfor both synthetic products and thesteam cylinder oil versus the' referencemineral EP oil. using Wormgear C (30:1reduction ratio). This test is run at 1500rpm and at 96 and 117% thermalloadcapacity. Fig. 4 shows similar data forWormgear D, a 50:1 ratio worm gearoperated at 1680 rpm input at 100 and200% Class 1 mechanical. rating ..This lat-ter test is run with the oil sump therm-ostatted at 95°c' Both tests C and D
measure efficiency via input and outputshah torque strain gauges with dyna-mometer loading.
The data 'of Figs .. 1 through 4 dearlyshow the correlation of improved effi-ciency and temperature control forlubricants Syn Sand Syn G comparedwith the mineral sulfur/phosphorus oilreference. Steam cylinder oil, also, showsa general benefit for both measurements,but with significantly smal1er degree ofimprovement.
These data are summarized in Table 2.Also shown are results of gear manufac-turer tests with Syn S compared withreference mineral oils of either the com-pounded steam cylinder type or theAGMA EP type, The degree of efficiencybenefit recorded in these latter testsdepended on the operating conditions ofthe tests, and Table 2 lists the averagebenefits recorded. The gear manufacturertests also indicated benefits in tern-perature control for Syn S.
The gear efficiency benefits for Syn Sin tests B through G show a wide rangeof numerical results. These data arerationalized in Fig. 5which shows a goodcorrelation of efficiency benefit asa func-tion of increasing gear reduction ratio.Based on the measured and catalog effi-ciencies for these gears (using conven-tional oil) the rule-of-thumb effect of SynS is to reduce the gearbox il1ejfkiency by20-25%,
Practical Appllcatlons for ImprovedWormgear Efficiency
Benefits other than the cooler runningcharacteristics initially found for thesesynthetic products are apparent:
One gear manufacturer, Hub CityD:ivision of Safeguard Power T ransrnis-sian Co., has applied the benefits of SynS to increase wormgear horsepower rat-ings. Catalog thermal input horsepowerratings have been increased 10 to 15%when the recommended synthetic oil (aSyn S rebrand) is used. This representsa new design application for this prod-uct which already is used in sealed-for-life wormgear units based on its extremeoperating temperature capability.
A second application for increasedtransmission efficiency is to reduceequipment power requirements, thereby,
LABORATORV TEST B10.:1 RAno
3.0 HP WORMGEAR (100% RATED LOAD)
4.0
3.0
2.0
1.0
CYL I NDER SVN G SVN SOIL
20
15
10
5
CVLlNDER SVN G SVN SOIL
Fig. 2-lmprovement Over Conventional SIP Mineral Based Oil
Fig. 3 -Improvement Over ConventionalSIP Mineral Based Oil
reducing utility costs, Field measure-ments of power draw of various in-dustrial. equipment in customer plantshas now been demonstrated Ior Syn Sand is currently being evaluated forproduct Syn G.
(continued on next page)
AUTHORS:
DR. W. R. MURPHY is a ResearchAssociate at Mobil Research and Devel-opment Corp. in Paulsboro, N.}. He hasa B. Tech. in Chemistry and a Ph. D. inPhysical Chemistry from the Universityof Bradford. England. Prior to workingat Mobil, he did Post Dodra! work atRice University in Houston.
DR.. V. M. CHENG studied Physics atPrinceton University and has a B.S.,M,A, and Ph. D, in this field. He is cur-rently an Associate at Mobile. Formerlyhe worked in the Space Division ofGeneral Electric. Dr. Cheng has beenlisted in Whos Who in American Science.
DR. A. JACKSON is a ResearchAssociate at Mobile Research andDevelopment Corporation in Princeton,NJ He has a B.S. and Ph. D. inMechanical Engineering from ImperialCollege, London, England,
LABORATORY TEST C30:1 RATIOJ 3.3 HP WOR~~EAR
8.0
6.04.0
2.0
C S CYLINDER OILS = SYN SG = SVN G
MR. J.. PlUMEID has been employedat Mobil Research & Development Cor-poration for the past five years. He hastwo degrees in Chemical Engineering, aB.S. from Layfette Col1ege and a M.S.from Princeton University. Mr. Plumeriis a member of ASLE, and NSP£.
MR. M. ROCHETTE is the Leader ofMechanical Testing Group, Research andTechnical Service Division, Mobil OilFrancaise, ND de Gravenchon, France.He studied Chemical Engineering at EcoleNationole Supede~lre des IndustriesChimiques, in France and has a B.S. fromthat University.
January/february 1985 .27
Syn S field results in Table 2 showmeasured average electrical power re-quirements for both worm and steel gearindustrial transmissions. Efficiencymeasurements in field applications can bemore difficult than in the laboratorybecause operating conditions are not asprecisely controlled. A statistical ap-proach is often necessary. This was thecase in the second steel. mill test in whichthe combined power requirements of themotor drives of a series of five worm-gears were measured by means of arecording wattmeter. Two basic opera-tions were evaluated in this corrugatedsteel pipe drive: a regular drive cycle anda cut cycle. Data for the two cycles areshown as normal distributions in Figs. 6and 7.
The Syn S results show lower mean(50 %) power draw for both cycles: thenon-overlap of the 90% confidence limitsfor each distribution comparison in-dicatesa greater than 99% confidencethat the benefits measured were real. andnot the result of chance. The averagebenefits measured for the two cycles were5.8 and 5.9%.
A different approach was taken in thepower consumption test at the food proc-essing company shown in Table 2. In thiscase, two food aerator units were operat-ing in parallel. In this test the mineral oilin the gear drive o·f only one of the unitswas replaced with synthetic product andthe other was maintained as a control.Fig .. 8 demonstrates the relatively con-stant current draw Eor blower 2 (oil un-changedrcompared with the second unitwhich had a measurable (6 % lreductionwhen the mineral oil was replaced bySyn S.
The efficiency/power benefits for SynS in laboratory, gear builder andcustomer evaluations are summarized inFig. 9
Correlation of WormgeaJ Efficiencywith Lubricant Traction
The mechanism by which syntheticlubricant products, Syn S and Syn G,improve wormgear efficiency has beeninvestigated in the authors' laboratories.The wide accepta:nce of steam cylinderlubricants which employ relatively largepercentages of fatty additives has beenattributed to their ability to produce lowfriction films on the surface of the gearteeth. The present work generally sup-
28 Gear Techno'iogy
ports the low friction/improved effici-ency characteristics of the steam cylinderoils, and it was the surjace Trictionmechanism which was first investigatedas a possible explanation for the greaterbenefits shown by the synthetic lubri-cants ..
in one comparison using WonngearD, Syn S additives blended in the refer-ence oil mineral base versus the mineralreference oil additives in the synthesized
hydrocarbon base oil, dearly demon-strafed the efficiency benefits to be re-tained not by the Syn S additives, butwith the synthetic basestock. This in-dicated the efficiency benefits I~O beassociated with the nature of the syn-thetic basestoek, and not to result froma change in the frictional properties at thegear surfaces.
Operating viscosity was also con-sidered as a possible explanation even
Spiral Bevel ~arsup to 100" DIameter
AM'ARlLtO GEAR COMPANYA Division of the Marmon Group, Inc.
(806) 622-12.73 Cable: Amadrive TWX910-898-41.28·P.O.Box 1789, Amarillo, Texas 79105
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TABLE 1
TEST LUBRICANT INSPECTION PROPERTIES
TEST LUBRICANT5 P Miner.l
R~ferenc Syn 5 Syn C
SynthesizedBase Oil Type Mineral Hydrocarbon Polyglycol
ViscosityACMA VI!iCGrad 7 6S 5cSI @ 40 C 437 383 225cSI @ 05 C 35 -It! 35cSI @ 100 30.2 9.0 297Viscosity lndex 05 145 164Pour Point. F +20 -40 -15Flash Point. F 450 sao HO
Cli'L. SVN G SVN SOIL
C'I'L. SVN G SVN SOil
fig. 4 -Improvement Over Conventtonal SIP Mineral Based Oil
10 -
Ell iciencyGain n '. ,. 4 ~I"
~2
o~----~----~------~----~----~--~a 10 20 30 40 50Gearbox Reduction Ratio
III Relative to Mineral- Based Gear Oil
Fig" 5-Energy Efncient Gear lubricants Benefits For Syn S
though, as discussed earlier, the testswere designed to exclude this possibility.N vertheless, ancillary experiments withWormgear D evaluating the effect ofchanging the viscosity of the ,referenoe oil,were undertaken and app ar in Table 3.Compared with ACMA 7 EP referenceoil. no significant difference is seen ineither increasing or decreasing viscosity.This insensitivity to viscosity has al 0
been verified in workw:ith Syn S visco -i'ty variation,
Table 3 also shows the results obtainedwith viscosity index-improved products ..In this work. oil formulation wereprepared with the normal reference oilfuncHonaladditives. using AGMA 5viscosity base oil. but with VI-improvers.X and Y, added to bring the final vis-cosity to the AGMA 7 lev L In this waya quasi multigrad industrial oil was pro-duced, but in n ither case was a' ignifi-cant efficiency benefttobtained, with VIimproper Y giving a nega.tive effect. Anexplanation for thi may be the poorshear stability found for Y in viscositymeasurements under high shear condi-tions; X was found Ito be highly shearstable,
Finally, fluid tractional properties wereconsidered as a possible explanation ofefficiency effects. Traction here is definedas unit fluid friction in the high-pressuremesh of the gear, and is distinct fromboth viscous churning losses and gearsurface metal/metal frictional ,effects.
The tractional propertie of test fluidswere measured using a roller discmachine. This equipment employs a pairof 3,265" diametercylindricaJ test ringsmounted on hydrostatic bearings whichcan be load -d a.gain.st each other bymeans o.r a hydraulic piston. Each ringcan be driven independently in eitherdirection by induction drive units withelectronic feedback control. The tracti nforce between the discs is measured bystrain gauges mounted in each disc drivemechanism. The absence of disc surfacefrictional effects is ensured by polishingdisc surfaces to b Iter than 2 micl'oinchfinish. E1astohydrodynamic calculatlonsverified high specific film thickness andabsence of metal contact during the tests.
Operating conditi n for th roller discmachine tracHon measurements areshown in Table 4. Materials and surfaceloading were chosen to simulate the con-ditions of Wonngear Test D operating at:1:00% Gas, I load,
January/February 1985 29
TABLE 2
EffiCIENCY BENEFI!TS MEASURED fOR SYNTHETIC INDUSTRIAL GEAR 0115COMPARED WITH CONVENTIONAL MINERAL~BA5EDPRODUCTS
Oper.atingHorsepower
Ave.ra.ge EfficiencyBenefit, %
GearManufacturer
ReductionRatio
Syn S Syn G
Authors' Labora!tory Tests
A - Mobil Oil Francaise Lechner 30:1 1.65 * *Boston 10:1 3.,0 2.2 ,3,0
Durand 30:1 3.213.9 5.6 4.0
Cone Drive 50:1 3.10/6.0 7.7 7.1
B - Mobil R&D Corp.
C - Mobil. Oil Prancaise
D - Mobil R&D Corp.
Gear Manufactur,ers'Evaluations
Hub CityE - Hub City DivisionSafeguard PowerTransmission Co.
15:1 1.55/2.0 3.8
F - Ex-Cell-O Corp.,Power TransmissionDivision
Cone Drive 25:1 6.5/8.1 4.4
G - Winsmith Divisionof UMC Industries,Inc.
Winsmith 0.5-1.1050:1 8,g
Equipment Users'Evaluations
Steel Mill B&K 15:1 6
Steel Mill IMWIndustries
39:1 75 5.8
Phil adelphiaGear
Food Processing Company 3:1(a) 6
-(b)Textile Company 2
"Temperature Rise Measurements onl.y; differentialcompan!~d with reference mineral oils: Syn 5, -17°F; Syn G, -15DF.
(a) Helical gear.(b) Spur gear/chain dr:ivecombination.
30 GearTechnol'ogy
TABLE 3
VISCOSHY EFFECTS ON WORMGEAR EffiCIENCY(TEST 0)
Percent Efficiency Change'AGMA Viscosily Grade Relative to Reference
8 EP
7 EP
6 EP
5 EP
517 EP(V.L Improver Xl
517 EP(V.L Improver Yl
"Test repeatability ~ 1.0 %
+0.1
Ref
-0.5
-0.4
+0.7
-3 ..3
TABLE 4
Disc Material:
ROllER msc MACHINE OPERATING CONDITIONS
Disc Speeds, U:
Bulk OilTemperature:
Disc Load
Hertzian SurfaceStress:
A - AISI 4150 ResulfurlzedSteel, ......54 Rc (3/4" face width)
B - SAE 65 Bronze, 80 BrinellHardness (1" face width)
A - 400-1600 rpm
B - + 120-1400 rpm
ISO F
400 Ib
48,600 psi
TABLE 5
ROLLm DISC MACHINE TRACTIONCOEFFICIENT RESULTS
Traction Coefficientl11 Estimated Gear121
Lubricant @ 720 Ipm fr.iction, f
Syn S 0.012 0.015
Syn G 0.013 0.015
EP Mineral Oil 0.018 0.021
Syn T 0.030
(1) Slide/Roll Ratio = UA - UB = 2 ("Pure" sliding)112 (UA + UBI
(2) Wormgear Test D results using equation:Efficiency = 1 - f Ian X
1 + f cot t..
where f = friction coeff ..A= lead angle (Reference 2)
0.000011 Of A_NliNCH RUNI OUT ACCUR_ACY FOR 'GRINDING,MACHINING OR INSPECTION WIl'M IHDT HIIi'DRAULIC
EXcPANSIONI ARBORS AND CHIJCKS ~~"[email protected]_;~'.", .-,' ,_' ,,':Cus'lorn btul, '10 fil )lour won. from IA Inch C!I ,Ii1CI' up , , ""'~Y'lfon stop prevenl.l over expansion. EXpl1't8t(1nis U:i"lll'orm ov .... ,ntne -clamping: ilurllOS, no elcntlll9-S:!JpotrlQt uMlzBd IXitisIfUCfWI'i. no ufill :to 'ukMu!mum holding rcree ot 725{) pllfor maximumcuuJI"Ig power EI('p!!in'~Qn!Up 10 3 percen.t of holding
dlamete,l HardrU!!S5 R.;6O jodi-ron graph shQw:lesu, "'..11!'-1,jJ12 0fII! WRHI fOP!'~ CA1ALOQ. ~1.I1QCUrwq'.
CIRCLE A-9 ONI READER REPLV CARDJanuary/February 1985 31
ICONFIDENCE ILInITS 90
" MINERALPIIWDUCT
o
F~, ,6-Corrugated Steel Tube Drive Test
ICONFIDENCE LIMnS 90
PRODUCT
32 Gear Technology Fig. 7-Corrugated Steel Tube Drive Test
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'GEA.RTIECHNO'LOG'l
TELL MIEMORE!I
Based on the disc speeds chosen, re-sults are calculated in terms 'of tractioncoefficient as a function ,of slide-to-rollratio and relative sliding speed. Data forthe condition of pure sliding at a speedof 720 fpm are shown. in Table 5, in-dicating a signiEic.ant reduction in 'trac-tion coefficient ,for the synthetic oils, Forcomparison, an estimate of gear frictionbased on a, thecretical relationshiplZl forwormgear efficiency is also shown inTable 5. Despite the simplicity of therelationship, good ·correlation is obtainedbetween the traction and friction data asa function of lubricant type. Note alsothat the traction co-efficients for the syn-thetic products are reduced about 30%compared with mineral oil - a reason-able agreement with the geaJ inefficiencyreduction discussed previously. Thecalculated gear friction results aresomewhat higher" which may be ex-plained in terms of the other lossmechanisms outside the gear mesh; e.g.,churning, bearing and seal losses,
This strong correlation was recentlyverified by evaluating a,commercial syn-the tic 'traction fluid in Wonngear Test D,The manufacturer's information in-dicated the traction coefficient of 'thisfluid, designated SynT, to be about 50%greater than that of a mineral oil. Basedon this, a significant detriment to effici-ency in the wormgearwas predicted,Due to the low viscosity of Syn T, thereference mineral oil viscosity was. re-duced to an AGMA 2 EP oil. and thetests were run at 12S"F where both oilshave viscosities 'equal to that of the usualreference oilal 19SoP, the normaltemperature of the test.
This work showed Syn T approxim-ately 10% less efficient than the referencemineral oilat 100% loading. At 200%loading, the efficiency with Syn Twasso poor that the cooling water to thegearbox was unable to maintain theoperating temperature at 125"f and thetest was terminated to avoid damage tothe gears. These results strongly supportthe influence of fluid traction in determ-ining wormgear efficiency.
Work is now underway to measure thetraction coefficient o.f Syn T in the rollerdisc machine for inclusion with Table 5results. Substitution of the gear .efficiencyresult for Syn T in the gear friction equa-
tlon yields a value approximately 50%greater than that for mineral oil - ingood agreement with the manufacturer'sreported finding for traction coefficient
An important aspect of the work withSyn T is that not all synthetic lubricantspossess low tractional characteristics, Itis most likely tha.t lubricant molecularstructure is the key to tractional proper-ties and that structures can be syn-thesized to give either high or low trac-tion depending on the needs of theapplication.
Co.ndusionsand fUJither Wo.r.k
1, The cooler running characteristics oftwo synthetic industrial lubricants :ingear applications have been cer-related with wormgear efficiency.
2. 'Gear effiCiency improvements, ha.vebeen shown. to result in lower powerrequirements in industrial applica-'tions,
3. The improvedefEiciency afford dworm gears by these synthetic oilshas been used to increase wormgearthermal horsepower rating.
NA'YO.~-RCUT!
No matter how you cut It;. keyway, slot, serration. ispecial form ...anyinternal con,figuration ...no one has a I~eyseater IIkel Mitts & Menill. With90 years lof e~perlenc9 behind every piece of precision machinery, ourengIneers ,,'an recommend the right Keyseater that will give you bOthecollomy,and II'ongservic~lIfe. Cut it with the best.
MANVFAC7UI'IED 8YCARTIIAGE MACHTflECOMPANY, INC.
Dept. G1i-9. P,O, IBox 151, Carthage, NY 13619 (515) 493-2380 Telex 937-378
CIRCLE A-l10 ON READER R,EP,l Y CARD, JanlJQIY/FebruOryl1985 33,
250 I·'"wIll:IIJIi.
~ 240
I-ffi 230 -et:et:::lu
220
BLOWER tH GEARBOX CHANGED TO S~N S I -.: tl i. I, . t .. 'i .. ! "'-'r .; . i -'. '-!!--1~r-'-- -~T-,~, I' ~.. I :----;- -: --_.- ' ·t--
I I : . :~""; • BL'OWER #1.. I - "1 .-- 0 BLOWER 112 I -
, I. .
;. J' i-, ;!--+,--"'~ --~--.-:'--) -'~I
, 'j.~ _ ~---LL __ ,.L.. ~l"" '/V[, I _I __ :_.J __.! I
" I I ,4, i !"I i I. "'i . J . 1- I i- - i~;-!-- I -
I - -j - -1- I i :- T -------I: 1"- -I'__ .'I---L -..J...-..L..-.I---l-_1_---'_--'_--"'_---i_--'_-'
o 10 20 30 40 50'
DAYS ON TEST
Fig. 8 - Food Processor Power Consumption Test
Fig. '9-Average Efficiency Benefits' Demonstrated for Syn 5
4. Lubricant tractional properties havebeen shown to be a significant Iac-tor in determining wormgearefficiency.
5. Future work win focus on the effi-ciencycharacteristics, particuladywith respect to synthetic lubricants,oJ non-worm industrial gearing andwill evaluate lubricant tractionalproperties at the higher pressuresoperating in steel gearing.
The authors gratefully acknowledgethe permission granted by the gearmanufacturers to publish their results.
Referenoesr. L. E, TEDROW, 'Synthesized Hydrocar-
bon Lubricants Solve High Temperature,High Load Problems." Machine Design.Vol 17, p. 30. Sept. 4. 1978.
.2. H. E. MERRITI, "Gear Engineering." P.351. J. Wiley & Sons.
This paper was published pTl!lJiousiy by TheAmeriC4n Gear Manufacturers Assod"tian 1981.IP2s4.3J, and by Otgrmi Di Tn:msmissiofJe (Italy)1962.
12
10
8
GearboxEfficiency 6Gain. %
4
.2
n
• Relative to Mineral- Based sear Oills,
.34 Gecr Techno'iogyIE-3 ON R.£AIDERREPL'r(CARD
High Power Transmissionwith Case-hardened Gears
and IntemalPower BranchingBy
Dr. lng. J. TheissenA. Friedr .. Render GmbH u. Co KG
Bocholt, West Ge.rmany
1000Nlmnf
BOO
G'v ,600Ft t 400
200
!b~ 0
IatreductienIn the field of large power transmission gear units for heavy
machine industry, the following two development trends havebeen highly influential: use of case hardened gears and abranching of the power flow through two or more ways. The
~- -I,
I-- --- I-- - --
f-- 1--- - --~ -~
7~ ""- ,..,~
---~ ---- r-I
I--- \-_.- -- t-- I
t---~
I
I-- -1---. I
0 1 2 3 4 mm 5.--.. X
:Fig. 1 a) Contact of two tooth flanks. pl. p2 - radii of curvature at the contact point of unloaded flanks;Fn- tooth normal force. 25= flattening width under load;dH ~ maximum Hertzian contact stress at the tooth flank surface.
b) Dependence of equivalent stress dv on the depth x, module = 25 mm.
AUTHOR:
DR. ING. JOSEf THEliSSEN received his Bachelors degreein engineering from the Techniscne Hocnschule Aad1en, andhis Doctorate 1'/1 engineering from the Ruhr-UniversityBochum . From 1977 through 1980, he was chief-engineer atthe Institute for Machine-Elements and Gearing-Technics atRuhr-University Bochum. Since 1981 he has been working asmanager of the design department of planetary and high speedgear drives for A. Friedr.Fiender GMBH and' Co. Kg, a gearmanufactureri" Bacnolt, West Germany and in Elgin,USA IFlender Corporation.
maximum possible torque of large gear units is limited bythe machine capacity since the gear cutting machines can onlymanufacture gear wheels up to a maximum diameter. Thehighest possible output torque of gear units with casehardened gears and power branching is about ten times higherthan conventional gear units with through hardened gearsand without power branching.
The advantages of case hardened gears lie in Itheir highertooth flank load carrying capacity. The variation in the sub-surface strength matches ideally the sub-surface stre sdistribution. By optimising the gear geometry to balance theflank capacity to the root strength, the torque carryingcapacity of case hardened gears can be four 'times higher thanthat of through hardened gears having the same diameter.
Power branching leads to .3 further increase in the torquecarrying capacity, Such gear units have one input and oneoutput shaft, Within the gear unit, the power at the gear ,ofthe input shaft is branched out and flows together at the out-
Janu.aryIFebruary 19853,5
put shaft. To achieve equal power distribution in each branchspecial design featuresare requjred.
Firstl.y, the advantages of case hardened gears are shown ..Then, the dependence of output torque on the gear unit sizeand weight i;demonstrated. Also the efficiency of differentpower branching gear stages and simple gear stages are com-pared with one another. Lastly, the design of three la,fge gearunits, as given below, are presented:
• Rolling Mill gear unit with two way power distribution• Tube Mill central gear unit withthree and six way power
distribution• Planetary gear unit for ball m:iD drive with three way
power distribution.
GeM MaterialsThe load capacity oJ gear teeth increases with a decrease
in diametral pitch, i.e. decrease in number of teeth. The toothflank load capacity is the decisive parameter for the dimen-sioning of a gear pair that has a minimum number of pinionteeth without underc-utting.
The loading of a tooth flank along the common line of con-tact is calculated as the pressure load between two cylinderswith contact lines haVing the same lengths and radii of cur-vature as the unloaded tooth flanks. The load on the toothflanks is obtained approximately from the maximum Hert-zian contact stress assuming that the materia] properties ailethe same ..
The Hertzian contact stress alone, does not determine theload conliguration. In the contact zone an elasto-hydrodynamic oil HIm pressure is developed, dependant onthe roiling velocity, which varies from that of the Hertzian
1000Nlmm2
BOO
U 600
t 400HEA i
TREA TEDCORE 200
..a) b) 0
surface stress distribution. The tooth flanks slide and r,oUonone another and as a result a frictional force in the tangen-tial direction is created. In addition, there exist residualstresses on and below the tooth flank surface. However, themaximum effective Hertzian contact stress has proved to bea useful theoretical criterium.
Stresses below the surface of tooth flanks, with due con-sideration to the above mentioned influences, can be com-puted. (1.2). They can. be treated as an equivalent stress ac-cording to maximum distortion energy theory. Fig..1 showsthe relation between calculated equivalent stress at the innersingle contact p<>int of pinion and the depth ·x~ from. "the toothsurface. The maximum equivalent stressu vmax ::::::0.56 a Rlies apprcximatelya] a depth x R: 0.68 s whereby (f H is themaximum Hertzian contact stress and 2 sthe flattening width.
A sub-surface fatigue strength distribution that has a formclosely matching that of the stress distribution below the sur-face, is obtained with gears of case hardening steel. of lowcarbon content. Bycar:burizing the tooth surface and harden-ing, a hardened case of martensite is obtained while the coreof the tooth remains soft and ductile. Correct heat treatmentand a proper depth of hardness increases the root fatiguestrength ..Finally, grindin-& the tooth flanks gives a good toothquality. There will be no strength reducing notch effect wheng:rindingthe tooth root, if the teeth or the gears areprotuberance-hobbed before carburizing and hardening. Cll
F~g. 2 shows the Vicker.s hardness, curve and the relatedfatigue strength 11 :sch for repeated load cydesbelow the toothsurface ofa gear manufactured from 1'7CrNiMo 6 steel. Dueto the hardened casing the equivalent stress at any depth "x."is less than the fatigue strength for repeated (non-alternating)loads i.e, 11 v < IT sch-
v- I ~ r-,r-, GSch
"~-!-- (j "<,£ .~V,/ "- ~ r-.~., -- ..... ~.... ...
....." . :HV"- ...
...1 "
I "-1--- --I
HV
o
800700600500400300
4 mm 5
t1 2 3
-0004.... X
Fig. Z a) Cross section through a tooth of case hardened gear, schematicbl 'Dependence of Vickers-hardness HV (measured). d sch ... endurance strength under repeated load and dv ... equivalent stress. at the depth x for acase hardened gear from 17 CrNiMo 6, module - 25 mm.
36 Gear Jechnolog.,r
ITt I'~ III::;
'1
A B, IC
Gear units with case hardened and ground gears from case-hardening steel have the fallawing advantages ever gear unitswith heat treated steel and manufactured by cuttingtools:
.• more compact in size and lighter in wei.ght thus reducingmanufacturing costs
• higher wear-resistance and a lower susceptibility to shock• higher operating reliabil'ity through higher and more bal-
anced capacity of the tooth root and the tooth flank• lower rolling velocities and a lower tooth meshing
frequency,. lower internal dynamic additional forces and a reduced
noise level due to better tooth quality• increased efficienc:yat part and full load operating
conditions.
Case hardening and grind:ing ,of tooth flanks to increasethe tooth flank capacity of gears has proved its usefulness.and has been successfully applied Eor several decades on smallgears in Automobile lndustriesand for the last years on largegears far mdustrialgear units ..Camputation according to DIN
3990 or ISO I DP 3663,. based on the experimentaID andtheoretical investigations of isa safe method, pre-calculationof the capacity of case hardened gears.
Size, Weight Lnd Efficiency.Fig.. 3 shows schematically, gear units with and without
power branching. The diameter ratio of th gears corresponds't.o an. overall transmission ratio of 7. Shafts 1 and 2 are respee-Hv.el.ythe high and low speed shafts ..The gear units A, BandC have parallel shafts and gear units D, E,. F and G coaxialshafts.
Gear units A and B, respectively. are a single stage anda. two stage unit. Neither has power branching.
Gear units C. D. E, F and G all have twa stages and powerbranching. The gears on the intermediate shaft of the gearuni.ts C and D have d:iHerent diameters .• however, the in-termediate gears on one intermediate shaft ,of E, f and G havebeen reduced to a single gear, hence, the latter are treatedas single stage units.
Gear unit C has two way power branching. Equal power
I _
.1 O,OClO3 \\ ,
~\~
\ \. -"\:\. \.
\. \ \I \ \I \ \.
1\ \ \. 1 'II
'\ 1\ \ ,I
N~\ -, , C1\1\ ~ r-~
~ ~~E r-,I I ,
'\. ".... - "- r-,
'- I lF-, B-I 'AI l I
2 4 6, 8 10 ',2 14 16
Fig. 4 - Dependence of relative (to size) torque of gear units according toFig. 3 on the transmission ratio i. T2 ... torque of shah 2 in Nm: D ,- designlength or diameter in m; BL = load value in N I mm2
distribution is achieved by the herringbone gears of the highspeed stage and the axial positioning of shaft 1.
In the case of gear unit D,. the power of the high speedstage isequaJly distributed 'to three intermediate gears by theradial positioning of the small central gear on shaft 1. Thepower in the low speed stage is equally distributed throughthe three herringbone gears by the axial positioning of thethree intermediate shafts.
To achieve equal power distribution on the three in-termediate gears in the case of E, F and G, the small centralgear on the shaft 1 of large units should be radiallypositionable.
The large outer gear is an internal gear and is connectedto shaft 2, in the case of E,and to the gear unit casing inthe case or F and G respectively, Gear units F and G bothhave the planet carrier and shaft 2 forming one unit.
The intermediate gears rotate about the central axis asplanets. Herringbone gears and axial positioning of the in-termediate gears give an equal power distribution throughsix branches in the case of gear unit G.
Power branching influences the size and weight ofa gearunit. Figs. 4 and 5 show these relationships as CIt. function ofthe total transmission ratio
ruru (1)
nl and n2 aee the rotational speeds of shafts 1 and 2respectively.
38 Gear Technology
110,
,
" ,
1
\\'i ,
K\ , I11\ I\\. ~
'\ ~ l\.. I
~ 1"01 '- " 0
r-, "- """"'" c-, "'- I1""1>.: ~ , ....
IGI <, I ""I'... <, "" B
I i A <, ~F
I E,
I
1
I1
I
I I
1
60
l,()
~Ii;
.20
6
4
2
12'
Fig. S-Dependence o] relative (to weight) torque ·of gear units accordingto Fig. 3 on the transmission ratio i. Tz ~ torque of shaft 2 in Nm; G -gear unit weight in kg; BL - load value in N I mm2
Figs. 4 and 5 have plotted T21 D3BL and T 21 GBL againstthe transmission ratio iwhereby Tz = torque of low speedshaft 2, D = gear unit size, G = gear unit weight and BL= load value. BL is calculated .fromthe following'equation. (4)
(2)with Fu = tangenital force, d = diameter of pinion and b= Iacewidth.
Equation (3) gives the allowable load value BCapproximately.
BL* fw B__ 0
KA
KA is the application factor and fw is the load factor. Withrepeated load on the gears fw ... 1and with alternating loadfw = 0.7.
Gear units E, F and G have intermediate gears with an alter-nating load. For gear units dimensioned for an infinite fatiguelile the val ue of Bo is approximately 4 .. .. . 5 N 1mm2 forcase hardened gears and 1 ... 1.3 N I mmz for throughhardened gears. Gear size D and gear weight G can be ap-proximately determined for known values ,of torque TZ withthe help of Figs. 4 and 5 and equations (2) and (3).
The gear weight G includes the weight of solid gears, shafts
and case. The gear case forms shown schematically in Fig.3, wall thicknesses = 0.02 D and the density of steel are thebasis for the weight calculation,
Gear units G and F have the largest relative torques forlow transmission ratios and, therefore, are preferred. Atransmission ratio limit of i ~8 is obtained with tw= 0.7for gear units 'Gand F.
The relative torque of units G and F can be favourable evenfor higher 'transmission ratios when two gear units are con-nected in series. For example,two F ty~ gear units havingtransmission ratios i1 = i2 = 4a:nd are connected in series.The total transmission ratio is i = h • h = 16. The totalweight of these two units is about 1.8 times less than a singleD type gear unit with i = 16.
Fig. 6 shows 'the relation between the efficiency n of gearunits according to Fig. 3, and the transmission ratio iaccord-ing to equation (1). Only gear tooth meshing losses are con-sidered since this [ass is significantly larger than all the otherlosses for gear units under full loading.
!For the one stage gear unit, A the effiCiency correspondsto the efficiency n z of one gear mesh:ing,i.e.
n = nz. (4)But in the case ,of B, C, D and E the total efficiency is theproduct of the slow and high speed stage efficiencies, Le,
n = nzl nzl. (5)
Gear units F and G transmit part of the power directlywithout any loss. Here, the efficiency with shaft 1 35 the in-put shaft is
n =~ {1 + (i - 1) nzl nz2}. (6)1
The tooth meshing iffficiency nz of a gear pair i.sobtainedfrom the following equation
nz = 1- fz JI. z- (7)
The geometrical factor fz is calculated(S) from equation (8)with the numbers of teeth 'Zl and Zz respectively of pinion1 and gear 2
(.8)
Z2 is negative fol' internal. gears ..The values for El and E2are given bypartial transverse contact ratios (;1 and f2 ofpinion 1and gear 2 respectively,
E 1,2 ,= 0.5 - ,fI,l + ,e 1,2 for 0 <: fl,2 <:: 1 (9)
E 1.2= €1,2 - 0.5 (10)
E 1,2 = 0.5 - fl,2 (11)
The equations (9)1 to (11) derived for spur gearing in(6'arealso approximately valid fer helical gearing.
It is assumed that the tooth flank 'coefficient of frictioniUz= 0.06 for all the tooth meashings of the gear units in !Fig.3. Internal gears enhance the formation of a good elastohy-
drodynamic oil film due to the complementary profiles ofthe meshing flanks.
However, the sliding properties of internal gearings arepoorer due to higher tooth flank roughness and, thus, theassumption of the same' coefficient of friction Eor external andinternal gearing approximately holds good. The gearinggeometry for Fig. 6 is according to DIN 3960 for gears hav-Lng no addendum modification and number of teeth of thepinionzl== 17 for all the gear meshings.
Gear unit A with a single stage has the best efficiency, seeFig. 6. Since there are two gear meshings in gear units B, C,D, E, F and G, the ef.fi.ciency curves lie below that of caseA.. In. the case of gear units E, F and G, the internal. gear pro-vides a faveurable geometrical factor fz, thua abetter ,effi-ciencycompared to gear units B, C and D which have onlyexternal gearings. The power eomponen! transmitted without1.055 for gear units F and G gives a further improvement inefficiency.
Planetary gear units F and G, in view of their size, weightand efficiency, are the most favourablechoice. Consideringthe high manufacturing cost 'to obtain at good tooth surla.cefinish on internal gears, planetary gear units have a reducedadvantage over gear units with power bral1ching and exter-nal gears only,
Design .of Large Gear UnnsThree laxge gear uni~s with power bz;~nching, which have
proved to be useful in practice, are dealt with here. The roil-ing mill drive shown in Fig. 7 has a. two way power branchsimilar to gear unit C of Fig. 3. It has four stages to attain
11,000I
III ,
~..---F.G...-- -
/ V ~ E I
I /V r-- IIB,e,D
II
1 I I
0,995
0.990
0..985'1.
I f 0;980
0,970
01965-. - 2 12 14 16
Fig. Ii- Dependence of effkiem;y '1 on the transmission ratio i Iforgear unltaccording to Fig. 3.
January/February 1985 3,9
fig. 7-Rolling mill gear unit with two way power branching (see scheme in Fig. B). Power P = 1350 kW; shaft speeds nl = 980 min-I. n2 = 24.5 rnin-'.Total weight including flange disk G = 82 t. (Flender-Kienast-Conception)
the high transmission ratio, whereby, the second stage is abevel gear stage as the output shaft is in the vertical posi-tion. Fig. 8 shows the gearing system.
The input shaft 1 is connected to an axially free hollowshaft 2 via an axially moveable coupling made of steellamellas ..Herringbone gear 4, on the hollow shaft, branchesthe power equally due to its axial positioning. Bevel gears5 and 6, with cyclo-palloid-spiral teeth and longitudinallycrowned flanks, are case hardened and are cut after heat treat-ment "HighPower Gear-teeth" (HPG), The power is transmit-ted onward to the output shaft via the helical gears 7, 8, 9and 10. All the helical gears are case hardened, and the toothflanks are ground. A stub shaft, with coupling teeth at theshaft end,connects the output gear with the flange disk,shown in Fig. 7.
Hydrostatically lubricated axial sliding bearings with tilitingsegments carry the large forces from the millingoperationand the weight of the output shaft, flange disk and mill pan(not shown) and transmits the same to a. strongly designedgear case. Each sliding bearing segment has a temperaturefeeler gauge to monitor bearing load. No inspection duringoperation is necessary due to an adequate oil. supply.
Fig. 9 shows the central gear unit of a tube mill. The gearunit has, in the first stage, no power branching and has twoinput shafts. One of the two input shafts serves as an aux-iliary drive, and is driven at a greatly reduced speed via anoverrunning dutch and auxiliary gear unit (not shown).When the main input shaft is driving ata higher speed, theauxiliary drive will be disengaged due to the overrunning
40 Gear Technology
dutch. Both the main stages of the gear unit in Fig. 9 distributethe power similar to gear unit D in Fig. 3. The first.main stagewith spur gearing branches the power three ways. Equalpower branching is achieved by the radial. positioning of acentral pinion on a shaft designed for elastic deflection. Thesecond main stage, with the herringbone gear, branches outthe power six times. Theeccentric intermediate shaft has axi-al freedom ensuring theirequal loading.
The large intermediate gears belonging to the first mainstage are mounted onto the intermediate shaft by oil hydraulicshrink fitting. Thus, an exact alignment of the gearing of the
4
2
3
Fig. 8 - Gearing scheme of rolling mill gear drive shown in Fig. 7. 1 =itnputshaft; 2 = hollow shaft; 3 = steel lamella disk coupling; 4 ~ herringbonegear; 5, 6 = bevel gear pair; 7, 8. 9 = spur gears; 10 = gear on output shaft
...* ..,,=11'11, , I.. -.......,., ..-
..... H"~ ....... I... _-"!II ". .. JIll, _ 'In
I 't l I
'-iii Li::LWUII I___ ~..-!ol _
'-IlL
IiIi!r_liiiliii!liliI ... ~ ... _
two main stages during assembly is possible .requiring onlya small radial displacement ofthe central pinjon of the firstmain stage. Measurements have shown that the radialldispla.cement is not more than 0.2 m:m and the variation oJtorque distribution is 4% maximum.(7)
All the gears ,of the gear unit,. shown in Fig. 9', are casehardened and ground. It is worth noting that the resultantradlal forces on !theoutput shaft are theoretically non-existant.thus, the output :shaft hasr;ela'tively smaJl roller bearings.
A lwo--stage planetary geM unit fur a ball mill drive isshown in !Fig.lO.Each stage has spur gearing and three waypower branching and correspends to the gear unit IFof FJ.8.3 with the intema), gear fixed to the gear case.
A uniform force distribution on the three planet gears isa.chieved by the free pivoting (lonfiguration of the central pin-ionoE each or the two planet stages. The sun, gear centersitself in such a way that the three radial meshing forces ofthe planets are equal, thus. ensurin-& an equal 'transmissionof the tangentia~ forces.,
'IJ '....'I'!!Rliill!l!iiill _
/-
/
Due to the equilibrium conditions, Ithe three meshing pointsoJ the planet gears with thearLnuJ:us also have lequal tan-8enm
tial and centering fcrces, The sun gear which is ccentelledbythe planet wheel teeth hasradial freedom due to the bac:klashof the teeth and the double jointed clutch in each stag! . Thering gears of both the stages are 0.£ quenched and 'temperedsteel. They are hobbed or eceandseess relieved after ,thef· all ......::.. : ....m- mauww'6 pr~cess.
'SummaryGear units, with case hardened gears and in~erna1 power
branching, are relativel.y small. in size and weight. This typeis particularly suited for large gear units to Itransmit highpowers. Case hardened and ground gears. due to their higherflank wear resistance and strength, giv'e a higher ~oad carry-ing capadty than through hardened gears. The strengthcharacteristic below the tooth flank surfaceofa case hMdened.gear matches weU with the stress characteristic.
(cof1hf1uedorl page 48)
Januarv/lfebruclrVJ985 41'
--
11.t\"(~K'1'(),
D'EFINITIO'NS OF GEAR- -
ELEMENTSB,y
FeUows Corpo.rationEmhart Machinery Group
Springfield, Vt
As a means of identification, thevarious elements of gears and gear teethhave been given 'certain names whichserve to classify and explain them . Whilesome of the tenns used are more 'or lessself-explanatory, othercSare not. There isalso some confusion in connection withthe application 'of certain terms, TheAmerican Gear Manufacturers Associa-
Addendum - is the height by which a tooth pro-jects beyond the pitch circle or pitch line; also,the radial distance 'between 'the pitch drdeandthe addendum circle. (1).
AJ1tkndum, Chordal - is the height from the topof the tooth to the chord subtendi.n the cir-cUlar thickness arc. (14).
Addl1l1dum, Normal Chordal - is the chordal ad-dendum in the plane normai rome helix,orthe tooth curve at ,the center ·ofthe tooth ..(31).
Angle, Axial Pressure - is the pressure angle inthe axial plane of a helical tooth. (30).
Angle, Base Helix- is, the helix angle on the basecylinder of involute helical teeth. (32).
Angle. Base Lead - is the lead angle on the basecylinder. (33).
Ap!gle. Helix - is the angle between any helix andan element of its cylinder ..In helical gears andworms, it is at the pitc:ll diameter, unless other-wise specified. (28).
Angle. Lead - is the angle between any helix anda plane of rotation. It is the complement ofthe helix angle, and is used for convenienceon worms. It is understood to be at the pitchdiameter unless otherwise specified. (28).
Ang/e. Norma/Pressure - is the pressure angle inthe normal plane of a helical tooth. (30).
Angle. Outside Helix - is ehe helix angle on theoutside cylinder, (32).
Ang/e, Outside Lead - is the lead angle on the out-side cylinder. (33),
Angl'e. Pitch Helix- is the helix angle on the pitchcylinder. (32).
Angle, Pitch Lead - is the lead angle on the pitchcylinder. (33l',
42 GearTechnology
tion have adopted standard terms anddefinitions. This list, as it appliesex-elusively to involute gearing, is here ar-ranged in alphabetical order. Most ofthese terms are also graphically presentedin Figs ..1 and 2..The numbers in paren-theses indicate the location of the identi-Eying illustrations.
Angle, Pressure - is the angle between a tooth pro-file and the radial line at its pitch point, orthe anglebetween the line of actionand theline tangent to the pitch circle. StandardPressure Angles are established. in connectionwith s.tandard gear-tooth proportions. A givenpair of involute profiles will transmit smoothmotion at the same velocity ratio even when.the center distance is changed. Changes in.center distance', however, in-gear design andmanufactl.lriI1g operations are accompanied bychanges in.pitch diameter, pitch and pressureangle. Different values of pitch diameter andpressure angle, therefore, may occur in thesame gear under different conditions. Usual-ly in -gear design, and unless otherwisespecified, the pressure angle is the strmtLard'pressure angle at the standard pitch diameter,and is standard for the cutter used to generatethe teeth. The Operating Pressure Angle isdetermined by the center distance at which apair of gears operates .. The Generatin.gPressure Angle is the angle al the pitchdiameter in effect when the gear is generated.Other pressure angles may be considered ingear calculations. In gear-cutting tools. thepressure angle indicates the direction .of 'thecutting edge as referred to some particulardirection. In helical gears, the pressure angle,may be specified in the transverse, normal oraxial planes. For spur gears in which only onedirection of cross section needs to be con-sidered, 'the general term Pressure Angle maybe used without qualification. (5).
Ang/e, Transverse Pressure -is the pressure anglein the transverse plane, or plane of rotation.(5). Fig. 1- Diagram :Identifying VariousElern
----
III\.SICS . '..- -
-
AA _ 10
_~:r~~.P-f~~-~ARC lor I'IPfROAOHI ®
of Involute Spur and Helical Gea15.
EQUAl. ADDENDUM 1.0NG.PlSI-IOR'T~A~~M;E:*~~~ISTUB TEETH FUU.-.rr~~2_--_2-_ -
F!IlLET ~
-
- -~-ID"
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1 rACE IGEARS I@
Fig. 2 - Dlagam Identifying Various Elements of Involute Spur and, Helical Gears.
Jcnllarv/February 1985, 43
Arc of Action - is the arc of the pilch circle'through which a tooth profile moves fromthe beginning to 'the end of contact with a.mating profile, (6).
Arc of Approach - is the arc of the pitch circlethrough which a tooth profile moves Fromits beginning of contact until the point of con-tact arrives at the pitch point. -(6).
Arc of Recess - is the arc of t.he pitch circlethrough which a tooth profile moves fromcontact at the pitch point until contact ends.(6).
Backlash - is theamount by which the width ofa tooth space exceeds the thickness of theengaging tooth on the pitch circles -as ac-tually indicated by measuring devices,backlash maybe determined variously in thetransverse, normal. or axial plan.es,andeither in the pitch circles, or on the line ofaction. Such measurements should be cor-rected to corresponding values on transversepitch circles for general comparisons. (21).
Bottom Land - is the surface at the bottom of thetooth space adjoining 'the fillet. (13).
Center DistanCl!- is the distance between parallelaxes of spur gears, and parallel axes helicalgears, or the crossed axes of crossed helicalgears and worm gears. Also it is the distancebetween the pitch circles. (4).
Circle, Addendum - is the circle which coincidewith the tops of the teeth in a cross section ..(5).
Circle. Base - is the circle from whichinvolutetooth profiles are derived. (2).
Circle. Pitch - is the curve of intersectlon of apitch surface of revolution and a plane ofrotation. According to theory it is- the im-a.ginary circle that rolls without slipping witha pitch circle of a mating gear. (2).
Circle. Root - is the circle that is tangent to thebo ttoms of the tooth spaces in across sec-tion. (S).
Clearance - is the amount by which the deden-dum in a given gear exceeds. the addendumof its mating gear. m.
Contlict. Point - is any point at which two toothprofiles touch each other. (20).
Contact. Zone - is that portion of the line ofac-tion bounded by ,the "natural" interferencepoints,
Cylinder. Base - is the cylinder which cor-responds to the base circle, and is the cylinderfrom which involute tooth surfaces, eitherstraight Of helical are derived. (10).
Cylinder, Inside - is the surface that coincides thetops of the teeth of an internal cylindricalgear. (23).
Cylinder. Outsl'de - is the surface that coincidesthe tops of the teeth of an external cylindricalgear. (8).
Cylinder, Pilch - is the imaginary cylinder in agear that rolls without slipping on a pitchcylinder or pitch plane of another gear or arack. (9).
Cylinder. Root- is the imaginary cylinder tangent10 the bottoms of the 'tooth spaces in a cylin-drical gear. (8). .
Dedendum - is the depth of a. tooth spa.ce below
44 Gear Techno'iogy
the pitch circle or pitch line; also the radialdistance between the pitch circle and the rootcircle .. {ll.
Depth, Whole- is the total depth of a toothspace, equal to addendum plus dedsndum:also equal to working depth plus clearance.(1).
Depth. Working - i~the depth ·of engagement oftwo mating gears-that is. the sum of theiraddendums, (1).
Diameter, Base - is the diameter of the basecylinder of an involute gear. (3).
Diameter, .Internal - is the diameter of the ad-dendum circle of an internal gear. (23).
Diameter, Outside - is the diameter of the ad-dendum (outside) circle. (3).
Diameter, Pitch - is the diameter of the pitch cir-de. In parallel-shaft gears, the pitch diametercan be determined directly from the centerdistanceand the number of teeth by propor-tionality. Operating Pitch Diameter is thepitch diameter at which the gears operate.Generating Pitch DIameter is the pitchdiameter at which 'the gear is generated. (3),
Diameter, Root - is the diameter of the root cir-cle. (3).
face Advance - is the distance on a pitch circleof a helical gear tooth, or pitch line of ahelical rack tooth through which a toothmoves from the position at which contactbegins alone end of the tooth curve 10 theposition when contact ceases. at the other end,(29).
face Width - is the length of the teeth in an axialplane. (25}.
Face Width, Effective - is the portion that mayactually come in contact with mating teeth,as occasionally one member of a pair of gearsmay have a greater face width than the other.(25).
Face Width. TorRI - is the actual dimension ofa gear blank Ihat exceeds the eUective facewidth, or as in double helical (herringbone)gears where the total face width includes anydistance separating risht- and left-handhelices. (25).
fillet Curve- is the concave portion of the toothprofile where it joins the bottom of the toothspace. (12).
Fillet Radiu.s - is the radius of the fillet curve althe base of the gear tooth; this radius is anapproximate radius of curvature, (11).
Fillet, Full Radius - is the arc of a circle at thebottom of a tooth space, the' center of whicharc is on the 'center line of the tooth space.(22).
Groove Depth - is the depth of the clearancegroove between helices in double helical (her-ringbone) gears. (25).
Groove Width - is the width of the clearancegroove between helices in double helical (her-ringbone) gears. (25).
Helix, Base - of a helical involute gear or wormis the intersection ofthe looth surface withits base cylinder, (34).
Helix, Normal - is a helix on the pitch cylindernormal to the pitch helix. (36).
Helix, Outside - ,or an involute helical gear orworm is the intersec!"ion of a tooth surfaceand the outside cylinder. (34).
Helix, Pitch - is the curve of intersection of atooth surfaceand its pitch cylinder in a helicalgear. (34).
interference - is contact between mating teeth atsome other point than along the line 'of ac-tion. (20).
Interference, Fillet - is contact of mating teeth atsome other point Ithan on the line of actioninside the zone of contact. (20).
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Interference. Involute - is contact of mating teethat some other point than on the line of ac-tion outside the zone of contact. (20).
I..c2ad - is the axial advance of a helix for one com-plete tum. as in. the threads of cylindricalworms and teethof helical gears, (l8).
Length oiActian > is the distance on an involuteline of action thrcugh which the point of con-tact moves during theaction of the tooth pro-files. (5).
Line .of Action - is the path of contact in involutegears. It is a straight line passing through the
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pitch point and tangent to the base circles.(5). .
Line of Centers - is the line which connects thecenters of the pitch circles of two engaginggears, it is also the common perpendicularof the axes in crossed helical gears. When oneof the geal'S is a rack, the line of centers isperpendicular to its pitch line. (4),
Line of Contact - is the line or curve aJong whichtwo. tooth surfaces are tangent to each other.(19).
Module (inches) - is the ratio of the pitch diameterin inches to the number of teeth. It is thereciprocal of the diarnetral pitch.
Module (mill-imeters) - is the ratio. of the pitchdiameter in millimeters to the number ofteeth.
Offset - is the perpendicular distance between theaxes of offset face gears. (24). '
Pitch - is the distance between similar. equally-spaced tooth surfaces, in a given directionalong a.given line or curve. The single word"Pitch" without qualification has been usedto designate circular pitch, axial pitch anddiametral pitch, but such confusing usageshould be avoided. (4).
Pitch Lin.e- corresponds in the CTOSSsection ofa rack to the pitch circle in the' cross sectionof a gear. (4f,
Pitch Line Element - is aline curved or 'strail',htformed by the Intersectionof the pitch sur-face and the tooth surface. (16),
Pitch Point - is the point of tangency of two pitchcircles (ora pitch circle and a pitch line) andis on. the line 'of centers. The pitch point 0.£a tooth profile is at its Intersection with thepitch circle. (4).
Pitch. Axial - is the circular pitch in the axialplane and in the pitch surface between cor-responding sides of adjacent teeth in helicalgears. The termaxial pitch is preferred to theterm linear pitch , (29),
Pitch. Axial Base - is the base pitch of helical in-volutetooth surfaces in an axial plane. (30).
Pitch. Base - in an involute gear is the pitch onthe' base circle or along the line of actio.n.Corresponding sides of involute gear teeth areparallel curves, and the base pitch is the con-slant and fundamental distance between themalong a common. normal in a plane of rota-'lion. (2).
Pitch. Circular- is the distance along the pitchcircle or pitch line between correspondingprofiles of adjacent teeth, (2),
Pitch, Diametral - is the ratio of the number ofteeth to the number of inches in the pit,chdiameter, There is a fixed relatienship bet-ween diametral pitchandcircular piich,
Pitch. Normal Base - in an involute helical gearis the base pitch in the nonnal plane. It is thenormal distance between parallel helical in-volute surfaces on the line of action in thenormal plane. or is the length of arc on thenormal base helix. It is a constant distancein any helical involute gear. (30).
Pitch. Normal Circular - is the circular pitch inthe normal plane. and also the length of thearc along the normal helix between helicalteeth or threads. (35).
Pitch, Normal DiQmetrQI - is the diametral pitchas calculated in the normal plane.
Pitch, Transverse Circular - is t:..hecircular pilchin the transverse plane. or plane of rotation.(29,)
Plane of Action - is the surface ef actlon in In-volute parallel-axis gears with either straightor helical teeth. It is tangent to the basecylinders, (19.)
Plane of rototion - is any plane perpendicular toa. gear axis. (26).
Plane, Axial - of a pair of gears is the plane thatcontains the two' axes ..Ina single gear. an ax-ial plane may be any planecontaining theaxis and a given point. (26,)
Reference Planes - are: pitch plane. axial plane',and transverse plane. all intersecHng at apoint and mutuallyperpendicular. (26). (27).
Plane. Normal - is normal to the tooth surfaceat a point: of contact, and perpendicula.r 10the pitch plane. (27).
Plane, Pitch - of a pair ,cf gears is the planeperpendicular to the axial plane and tangemto the pitch. surfaces. A pitch plane in an in-dividual gear may be any plane tangent toits pitch su.rface. The pttch plane of a rackor crown gear is the pitch surface. (26).
Plane, Tangent - is tangent to the tooth surfacesat a point or line of contact. (27).
Plane. Tra115VerSe- is perpendicular to the axialplane and to. the pitch plane. In gears withparallel axes, the tnmsverse plane andp\aneof rotation coincide. (26). .
Radius. Base - is the radius of the base circle ofinvolute profiles, (7).
Radius, Equivalent Pitch - is the radius of thepitch circle in across section of gear Iteeth inany plane other than the plane of 1'0taHon.It is properly the radius of curvature ,of thepitch surface in. the glven cross, section. Anexample is the normal section of helical teeth.(31).
Radius, Outside - is the radius of the addendumcircle of an external gear. (7).
Radius, Pitch - is the radiuso! the pit.th circle, (7).Radius. Curoaturie or Profill! - is the radius of
curvature of a tooth profile. usually ilt' thepitch point Of a point of contact. (11).
Radius. Root - is the radlusof the root circle. (7) .Ratio. Axial' Contact - Is the ratio of the face'
width to the axial pitch in helical gears.Ratio. Cont·ac;t - is the ratio of the arc ofacelon
to the circular pit,C::h. and sometimes isthought of as an average number of teeth incontact.Por involute gears. the contact ratiois obtained most directly as the ratio. of thelength of action to. the base pilch.
Ratio, Face Contact - is the ratl.o ·of the face ad-vance to the circular pilch, usually havingthe same value as a'Xlal contact ratle.
Ratio. Gear - is, the ratio o] the larger to thesmaller number of teeth in a pair of gears,
R'atio. Normal Contact - is the contact ratio inthe normal section.
Ratio. Tota! Contllct - is the slim of the transvtr5l!contact ratio and axial contact ratio' whichmay be thought of as the average lotalnumber of teeth in contact in parallel helicalgears.
Ratio. Transverse - is the' contact ratio :in thetransverse plane. or plane of rotation.
Space Bottom - is a nne joining two fillets of ad-jacent toothproHles in 'the same plane. (1).
January/February 1985 45
Surface of Action - is tile imaginary surface madeup 0.£ all positions of the lines of contact ofa given tooth surface, (19').
Sur/aces, Pitch-are the imaginary planes orcylinders that roll together without slipping,For a constant velociry ratio, the pitchcylinders are circular. Sometimes, however.the velocity ratio may be variable, in whichcase djffe~en! forms of pitch surfaces may oc-cur, as for instance elliptical surfaces, (IB),(27).
Teeth. Equal-Addendum - are those in which 'twoengaging gears have the sameaddendums.(22).
Teeth, Equivalent Number of - is the number ofteeth contained in the whole circumferenceof a pitCh ci rde corresponding Ito anequivalent pitch radius.
Teeth, Ful/-Depth - are those in which the work-ing depth equals: . 2.000 inch (22).
diametral pitchTeeth, lnuolute - of 'spur gears. helical gears, and
worms, are those in which the active portionof the' profile in the transverse plane. is theinvolute of a circle.
Teeth. Left-Hand - are helical gear teeth or wormthreads in which the teeth twist counter-clockwise as they recede from the observerlooking al'ong the axis, (25).
7:eeth, Long and Short Addendum - are those inwhich the addendums of two engaging gearsare unequal. (22). . .
Teeth, Matched - are double helical (herringbone)gear teeth. the pitch line elements of whichInrersector' would intersect at the center ofthe groove if prolonged. (25).
Teeth. Number of (or Threads) - is the numberof t'eeth contained in the whole circumferenceof the pitch circle,
Teeth. Right-Hand - are helical gear teeth orworm threads in which the teeth twistclockwise as they recede from the observerlooking along the axis. (25).
Teeth, Staggered - all' double helical (herr-inghone) gear teeth, tile pitch line elementsof which do not intersect or would not in-tersect at the center of the groove, if prolong-ed, (25).
Teeth. Stub - are those in which the workingdepth is less than: . 2.000 inc~ (22).
diametral pitchTip Relief - is an arbitrary modification of a toolh
profile whereby a small amount of materialis removed near the tip of the gar tooth, (11).
Tooth Bearing - is that portion of the tooth sur-face which actually comes in contact with a.mating tooth surface. (17).
Tooth Chr:lmfl!r - is the beveled edge between theend of a tooth and the tooth surface to breakthe sharp edge. (17).
Tooth Face - is the surface between the pitch lineelement and the top of the tooth. '(13) and(15).
Tooth Fillet - is the curved line joining the toothflank and the bottom of the tooth space, (15).
Tooth Flank - is the surface between the pitchline element and the bottom land - it includesthe fillet. (13) and (15).
Tooth, Normal Profile - is the outline formed bythe intersection of a tooth surface and a planeperpendicular to the pitch line element. (35).
Tooth Profile - is one side of a tooth in cross sec-tion. Usually a profile is the curve of intersec-tion of a tooth surface and a plane or sur-
46, Gear Technolog,y
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face normal to the pitch surface, such as thetransverse. normal or axial plane. (12).
Tooth Surfllce - forms the side of a gear tooth,(16).
Tooth Top - is a line joining the outer ends oftwo adjacent tooth profiles in the same plane.In internal gearing it applies to the inner endsof the teeth. (13).
Tooth. Axial Thickness- in helical gears is thetooth thickness in the axial cross section atthe pitch line, (35).
Tooth, Base Circular Thickness - in involute teethis the length of arc on the base circle betweenthe two involute curves forming the profilesof a tooth. (14).
Tooth. Circular Thickness - is the length of an:between two sides of a gear tooth on the pitchcircle. unless otherwise specified. (14).
Tooth. Chordal Thickness - is the length of thechord subtending a circular-thickness arc.(14),
Tooth, Normal Chordal Thickness - is the chor-da! thickness in the plane normal to the pitchhelix, or the tooth curve at the center of thetooth (31).
Tooth. Normal Circular Thickness - is the cir-cular thickness in the normal plane. In helicalgears. it is an arc of the normal helix. (31).
Tooth, Tra.15uerse Circular Thickness - is the cir-cular thickness in the tranverseplane, orplane of rotation. See Circular Thickness,(14).
Top Land - is the surface of the top of the 'tooth,(D).
UndercuJ - is a condition in generated gear teethwhen any part of the fillet curve lies insideof a line drawn tangent to the working pro-file at its Iowest point. Undercut may bedeliberately introduced to facilitate finishingoperations, (I2).
Reprinted with permission of Fellows Cor-poration, Emhart Machinery Group, Box 851.Springfield, VT 05156-0851 "'Copyright 1955Fellows Corporation.
IE-S ON ,RE.AIDER REPLY CARD
G::_est Editor,. •(Continued from page 7)
design methods don't prediCl:all failures, so we tend tobe conservative in gear design or in instiMing gearstandards to cover all of (he unknowns. Certainly weover design and over specify most of our products tocover those cases where our analyses or our materialsfall down.
None of these problems will be easy to solve. but isn'tit time 'that we redirected our research if we are going tosolve them?' A good research job requires real exper,imen·tal data and data acquisitIOn is expensive, No single com-pany. nor single institution. pnvate or public. has thefunds today. It's tragic that the fUnds we do have are frit-cered away on peripheral projects, without attacKing theareas of real need.
Kettering'S famous quotation bears another repetition."Secrecy in induSUial research keeps out rnoreqood infor-mation than it keeps in."
Most gear manufacturers. and many large users, havedata in their own fields of experience. which if analyzedand correlated' withl that of Others. would provide abroader basis than we now have. The initiative mustcome from the industry; where the data. the judgement
and the need all reside. We must find a wa'y rortrosecompanies which have this data to snare it to their ownadvantage.
It's time for the users of gears. gear manufaoturers, andgear speCifiersto show some leadership ,in gear research.The direction must come from those who will use tileresults. but there must be direct: feedback of field ex-perience which is pertinent '[0 the research, When didyou last talk to a mechanical engineering professo~, amechanical engineering graduate student or an englneer-ing class about gear research? How can: [hey know tileneed if we don't tell them?
It's time to snare our information with tile universitiesand research institutions, and to make al united effort tofund the work: required' to lrnprove our solutions to meseproblems.
fj.•iHt!~Don McVittiePresident AGMA
NOTE.' The opinions expressed herein are mine. notthose of AGMA or any other organization.
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Cla.lng dlt,: Ads must be recaived Iby 'the25th of ths, month, two months, prior 10publication. Accepta.nce:. Publisher reserve,the righl 'to,accap! or rajed classified , dver-tisemenl I his discrelion.
fig. 10'- Two stage planetary gear will for ball mill drive with 'three wily power brallching pel" stage. TrlLnsmission power P- 4050 kW: shaft speeds n1 - 485 min_I; n2 - 13.8 min~l; gear unit weight G - 72 t
High Power Taansmissices(Continued from page 41)
A comparison of size and weight relative to output torqueshows that among the power branching gear units planetarygear units are favouraMe and better especially for smallertransmission ratios of single planet stages. The relative tor-que decreases with increasing transmission ratio. Fortransmission ratios above i= B the power branching gearunits having: external gearing only are preferred. Their relative~orque decreases at a lower rate with increasing transmissionratio, However, 'two or more planetary gears, coupled oneafter another, may still be more advantageous for highertransmission ratios above i ,= IS.
The efficiency of planetary gear units is comparatively bet-ter than that of other power branching gear units. However,for higher transmission ratios, one must couple moreplanetary gear units ORe after another and Lhis, advantage maybe lost.
Re~nences .1. WINTER, H. und P. OSTER Be.anspruchung der Zahnflanken
unter EHD-Bedingungen. Konstruktion 33 (1981) H. 11,. S.421-434
2. BORNECKE, K.: Beansprucnungsgerecilte Wiinnebehandlungvon einsattgenarteten Zylinderradem, Diss, RwrH Aachen(1976)
3. HEBENSTREIT, H.; Pl"otube.ranzgefraste einsatgeharteteundgescliliffene Zahnrader, Antriebstechnik 1-2 (1980)
4. NIEMANN, G.: Maschinenelemente, 2. Baad, Be.rlin,Heidelberg, New-York: Springer ..Verlag 1965
s. MUllER, H. W.: Di Umlaufgetriebe, Berlin, Heidelbe.rg, NewYork, Springer-Verlag 1971
6. DUDA, M.: Der geometrische Verlustbe:iwert und dieVerl.ustsymmetrie bei geradverzahnten Stimradgetrieben.Forschung im Ingenieurwesen 37 (1971), H. 1, VDlNerlag
7. HEYER, E. C.: Leistungsverzweigte ZaihnIadgetriebe mitAussenverza1mung, VDI-Berichte 332, :zahnradgetrtebe,;Tagung1979 in MUnchen, VDI- Ve.rlag Dusseldorf
This article was .roprin.ted from A'GMA paper no. 429.05, FaIl Irck"iad Con-ference 7982.
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