Computer Aided Design For'Gear Shaper Cutters

Computer programs have been devel-oped to completely design. spur andhelical gear shaper cutters starting fromthe specifications of 'the gear to be cutand the type of gear shaper to be used.The programs generate the workingdrawing of the cutter and, through theuse of a precision plotter, generateenlarged scaled layouts of the gear asproduced by that cuner and any otherlayouts needed for its manufacture.

The gear data which should appear onthe gear drawing to insure thatacuttercorrect for the part can be designed areshown.

Part information should include thefollowing items:

1. Number of teeth.2. Diametral pitch or module. (If

helical, speCify normal or trans-verse.)

1. Pressure angle (normal or trans-verse).

4 .. Outside or inside diameter. (In-dude limit if topping ..)

S. Tooth thickness (normal ortransverse at some given diameteror dimension over Of betweenspecified pins).

6. Helix angle and hand.

AlJfHOR:

DONALD S. WHlTNf:Y worked forFellows Corporation for 46 years until hisretirement in early .1987. He began with thecompany as:Q gear shaper cutler designer andthen specialized in computer programming,writil'lg va-,ious pr~grams for the design of gearshaper cu.tters and shaving tools. Mr. ltVhitneyis a member of the AGMA Gear 1l1Spectl'onHandbook Corl11l1itteeQJ1da .Life Member ofthe Society of Manufactun'ng Engineers.

Donald S. WhitneyFellows Corporation

Springfield, vr

7. Depth of cut. (Specify rootdiameter and tolerance.)

8. Ma.terialand hardness at time ofcutting.

9.. Lowest point of contact. (Spe-·cified as true involute formdiameter. Mating part and centerdistance information will answerthis requirement.)

10. Root fillet radius specification.11. Stock allowance for preshave,

pregrind, or roughing operations(amount and position of undercutif required).

U. Amount of chamfer measuredradially with limit angle ofchamfer if necessary.

13. AGM_A quality number.14. Type and serial number of

machine,A computer program works through

an. optimizing process to produce the bestcutter design possible for the part inquestion. A good program considers themany constraints and variables involvedand investigates many designs before itarrivesat the optimum one. Because ofthese many variables, i,t is not possibleto write a direct formula or algorithmthat wiU result ina cutter that will meetall of the requirements. For this reasonmany designs may be investigated. Thefollowing is a step by step description orhow such programs are arranged.

Fig. 1 illustrates the three basic cutterblanks that will be discussed here: disk,deep counterbore for internals and partswith interfering shoulders, and tapershank (usually for internals).

The type of blank is 01-" input. pa-rameter with the blank dimensions,thickness, facewidth, life, etc. being sup-

plied by program libraries o.fstandarddimensions for the pitch and cutter sizeinvolved. If special blank dimensions arerequired, they can be substituted for thestandard ones . The basic size of the cut-ter (number of teeth) win be computedto fit the machine being used if this isknown, or it may be input by the num-ber of teeth or pitch diameter wanted onthe cutter.

In addition to cutter blank dimensions,all other information required for the

Disc Cutl ...

\1hdJD•• p Count.rbora

-e--J -{£#}~ I-LII.

Taper S....n..

Fig. 1- Typical blank designs.

November/December 19'87 11

design, such as, clearance angles,tolerances, material, etc. is supplied bythe program libraries and need not beentered as input parameters, unlessspecial, non-standard values arerequired.

Once the cutter size (pitch diameter)has been fixed by one of these methods,

the program computes the cutter toothdimensions for the given part and thenchecks all of the following points, ascer-taining that it produces the part specifica-tions and meets the following good cut-ter design criteria;

1. Does the cutter have sufficient tipland?

ACllw. P, ••• ut. AngleLine

CUTTER WORK

a.••DI.mat.,

Fig..2 - Enlarged cutter - too little lip land.

CUTTER

.>:a•••_______ Dlem.t ...Actlv.P,.nul. Angl.

Line·

Fig. 3-.R.educed cutter - sulfident tip land.

12 Gear Technology

2. Will the true involute form (TIF)diameter be held1

3. Will the cutter have a suitable sizeradius on the tip comers?

4. Will the cutter modify the tips ofthe work teeth 7

5. Will the undercut produced by pro-tuberance be positioned correctly?

6. Will chamfer produced be to spe-cifications?

7. Will too much rough side rub bepresent on cutters for internal.work7 Will cutter have finish rub?Will it trim the tips of the workteeth?

8. Is the cutter barrel strong enoughon taper shank cutters] Does itneed flutes?

9. Will flank rub be present on inter-nal or external work?

Items 1, 2, 3,4, 5 and 7 are depend-ent on the active pressure angle (APA)between the cutter and work, so the pro-gram. must determine by tria] and errorthe best starting APA to produce bestresults when the cutter is new andthroughout its life. The APA of a cutterchanges as it is sharpened back, so wemust investigate what happens throughits whole life. The APA discussed hereoriginates from. a cutter that operates atthe transverse pressure angle of the work.When the cutter size (center distance) isincreased from this point, the APA in-creases on external work and decreaseswhen the size (center distance) is de-creased ..The active pressure angle changeis in the opposite direction on internals,but the effect of enlarging or reducing thecutter is similar to external work withrespect to cutter land and the true in-volute form (TIF) produced, This articlewill use the term "enlargement" or "reduc-tion" of the cutter to indicate that theAPA is being changed to satisfy re-quirements. The following examples wi.~1indicate situations that dictate this typeof change.

Each time the cutter size (enlargementor reduction) is changed to improve orsatisfy one of the above conditions, thenew design is completely computed. Eachfeature is then checked to be sure thatsome other design requirement has notbeen violated.

Fig. 2 shows a cutter with too littleland on the tips of the teeth. Fig ..3 is thesame cutter reduced to a point wheresatisfactory land is attained. This is an

external part; therefore, the APA isreduced with cutter size. Standards forthe minimum allowable land for goodcutter life are stored in the programlibraryand are dependant on pitch andpressure angle of the part.

Fig. 4 illustrates how cutter enlarge-ment affects the TIF produced. A reducedcutter will lower the trochoid height pro-duced. resulting in.a design that will holdthe required TIf.

Fig. 5shows a condition where the in-volute at the tip of the work tooth willbe modified because of contact below thebase diameter of the cutter. Shown onthis same figure is thecondition of cut-ter contact below the base circle of thework, resulting in "undercut", whichtakes away some 'of the involute near thebase diameter of the work.

Undercut is most likely to happen onpinions of 20 teeth or less, while t.ipmodification is more common on largegears and Internal gears. Enlarging thecutter will improve or eliminate both theundercut or modffication conditions ..

From the Ioregeing, it can be seen thatsome situations require cutter enlarge-ment, while others require reduction ofthe same cutter to remedy the problem.Obviously we cannot do both, so a com-promise must be made by the program.The final design will always be one thatat least has minimum land and producesthe specified true involute form.

Cutte,r Rub (Internal Gears.)This condition is almost always pre-

sent to' some degree when cutting inter-nal gears, All gear shaping machinesrelieve either the cutter or the work onthe return stroke to avoid scuffing thecutting edges. This r,elief is generally ac-complished by separating the cutter andwork by approximately ..010" (.25mm) to.032~(.81m:m), depending upon the makeand type .of machine. When cutting someinternal. parts, a wrapping effect of theinternal part around the cutter results,causing the cutter tointerfere or rub withthe internal teeth when it is pulled backto give cutting edge relief. Three typesof rub can occur and are described asfollows:

Rough Sid.e Rub. This interference, asshown in Fig .. 6, is caused by the hook-ing action of the cutter teeth relative tothe work profile as they enter on the un-cut side of the work near the inside

CUTTER' WORK CUTTEJI

Cutt", 0"' NotPrOduc. T~t.F~

Cfru. Involut. Form)DI.met.,

1lielM1.,To SI8ft 01

car~ Cutl ..

WOIIII

...... Cull •• R..... c...To Hold l'.I.F.

Fig. 4· - Effect '0£ cutter enlargement '011 true involute form,

Oulll<lo DI.m.t.,

~ CIIUI' Conlael.a.low I ••• DI.mat.rC... lnll Undercut

Involute Prollie 01 Work- Tooth Will a. Modlll.cI O"lolei.

01 Thl. Dlem.te,

Fig. 5 - Example of tip modification and undercut.

diameter. At this time, no generating ac-tion has taken place. Spaces producedare an image oJ the cutter teeth, requir-ing the cutter to be pulled back at anangle away from the hook side to pro-vide relief on the return stroke. Thedotted lines show the position of the cut-ting edges after the relieving motion hastaken place. In the example shown,cut-ter rub exists even though the cutter wasrelieved on an angle known as the hack-off angle. The amount of backoff angleis limited, as will be shown Later. Theconventional angle is normally about So,which is sometimes increased to as, much

as 10~12°to correct extreme rough side'rub conditions. A small amount of roughside rub [less than .OOZ' (.OSmmJ.l can betolerated and is usually present when CI..It~

ting small internals ..Excessive rough siderub will show up as an excessive burr onthe face of the gear and the insidediameter from the trailing side of the cut-terteeth, This problem causes excessivewear and/or load on the trailing s,idenear the tips of the cutter teeth, resultingin a deterioration of tool life. Aside froman increase in the backoff angle, withlimitations as shown later, the only wayto reduce this condition is,to decrease the

INovember IDeoemberl'98,7113

Uncut Sid.(Trailing)

Convnon ~~---"'-WOI'k C.nler Cutt.r Cenler

:II

~•i•Inlern.1 WorK

FlnI.".d Sid.(Leading)

Fig. 6-Rough side rub.

J

tI:D :;-o ~.. =:- -" 0ii :0

:0 2I Int.rnal WOI'k

Po.lllon Of Culler T •• IIIOn Ralu,n Sl,oke

Fig. 7-Finish side rub.

COI'_ 01 Work Tooth I.Tr_d Wldl. Cun.rI.aeln, F.d Into D.pth

Inl.rna' Work

Comnlont~_L-_~+" __Work C."I.r 'cutter Cent.r ("'

I

1'0."1cNo 01 C.tt .. T.alll ~'IAI ao_ I'Nt Durlnlllnf •• d t" .J

Par.llel To COIIIIIIon i.Or Line 01 In'.ad

Fig. 6 - Infeed trim.

14 Gear Technology

amount of backoff, usually to not lessthan .01'0" (.25m_m), reduce the numberof teeth in the cutter, increase the insidediameter of the part or use multiple cutsas described later.

Finish Side Rub. As shown in Fig. 7,finish side rub occurs when the cutt.er sizeis large relative to the work size, and itappears on a fully finished side of thework teeth. finish rub will show up inthe form o.f an excessive burr left at theinside diameter oJ the work teeth on theleading edges. The cutter will show ex-cessive wear near the tips of the teeth onthe corresponding side ..The direction ofbackoff angle is almost always taken asshown and is dictated by the require-ments of the rough side ..Decreasing thisangle would improve the finish side rub,but this usually cannot be done f.or thepreviously mentioned reasons, An in-crease in the operating pressure angle byreducing the cutter diameter and/orreducing the number of teeth in the cut-ter will decrease the amount of finishrub. This type of program win notallowany amount of .finish .rub to be presenton the final design.

lnieed Rub. This is rub on the leadingside of the teeth caused by the same con-ditions as finish side rub and occurringonly while the cutter is feeding intodepth. For this reason, the burr left at theinside diameter while infeed rub takesplace will be cut away when the cutterreaches full depth and cannot be seen onthe Hnished part. Excessive infeed rubwill show up as abnormal wear on theleading side of the cutter teeth. The sameremedies listed previously for improvingfinish side rub hold true for infeed rub.The multiple cut method, described later,will also reduce or eliminate infeed rub,

lnieed Trim. As shown in fig. 8, in-feed trim can exist regardless of theamount of backoff and occurs when thenumber of teeth in thecutter is too largein relation to the number of teeth inwork. The angle of backoff can affectthis trimming condition if it is ac-complished by offsetting the cutting headupright (which is common on some ofthe newer types of gear shapers) and notby the swiveling method ..lnfeed trim willshow up on the finished part as amodification or trimming at the insidediameter of one or more work teeth. Thistrimming is done by a cutting action, asopposed to rub, and thus does not harm

the cutting tool. This condition can bereduced or eliminated by increasing theoperating pressure angle of the cutter andwork by decreasing the outside diameterof the cutter or by decreasing the numberof teeth in the cutter.

Maximum Cutter Sizes (Internal Gears)Fig. 9' shows the relationship between

recommended teeth numbers in cuttersand work pieces for the more commonpressure angles. The data given here isto be used as a guideline in. the selectionof acutter that will not produce excessiverough side rub, infeed rub or any amountoJ finish side rub or infeed trim, Whenthe number of 'teeth in the work is lessthan the cross bars on the chart indicatefor the pressure angle involved, the in-side diameter should be increased byshortening the addendum. On such partsor on marginal ones, the amount of rubpresent should be checked by the com-puter program beforecut"ting. Variationsoccurring from machine to machine inthe amount and angle of backoff alsomake a precutting check desirable. Ofcourse, internal parts of fewer teeth thanshown on this chart can be cut suc-cessfully, but. ,they should be treated asindividual cases, The majority of partsin this category must be cut on machineswith reduced backoff. The programstores the equivalent of this chart, whichis used as a starting point to determinethe number of 'teeth in acutter for an in-ternal part. IT the starting number ofteeth results in excessive rub, this numberwill be reduced by the program until therub is eliminated,

fla.nk Rub (Extemam or Internal Gears)This type of rub can occur on the per-

tion of the cut~er ItoO'th below its base cir-cle on the trailing side of the cutter andwill show up as excessive wear at thispoint. Fig. 10 illustratesthis condition onan internal gear, If the previous cutleaves stock no greater than that shownby the dotted line, flank rub will not bepresent. For this reason, a commonmethod for eliminating flank rub is totake multiple cuts or use the multipassmethod described later. The amount tofeed in for each pass is determined bycomputer. Anything that can be done 'toincrease the distance from the cutter basediameter to the outside djameter, such as,cutter enlargement or an increase in the

number of teeth, will help eliminate thiscondition.

Multiple Cut Or MultipassCutting Method

Most modern gear shapers are equip-ped to take multiple cuts (3 or 4 cuts inthe normal manner) or to use themultipass (high rotary feed at low infeed

rates) to provide a way of ellminating orreducing rough side rub and infeed rubon internals. These techniques alsoeliminate flank rub on both internal andexternal parts, Fig. 10 shows how multi-ple cuts can eliminate flank rub on an in-ternal if the previous cut stock is asshown by the dotted line, This processcan also be used to elim:inate rough side

NILES 6£ARI6RlNDERMODEL~ ZSTZ 1630C3 It_STOCK!

SPECIFIICATIIONS:'Out. lei'. diameter, max •.•• lin.RooS elrc'le d amele,; m'ln .• lin.INum'ber ,01 teeth" max.. • • . . #INumber of teeth,. min.. • ... , #DlmaetraJI pitCh,. min ••..•• D'.P.Dlametral' pitch, max .•..•• D.P.

29.5,2

1!401,212.72.12

Maximum lhe'lliingle ..Stroke.ength , , • , ...••Double r__mstrokes

(llnflnltely var.) •.. , ••MaxCmumtabL Iload ••Table bore ..••.•• ,.,

deg. 45In. 8,'9

11/mln. 754,15Ibs. 880'In. 3.5,

lMiel'·West Office1665 Tonne IRoad

Elk Grove VlII'age, IL 60007Pho.ne (312) 36445301

WMW Machinery, Inc.570 Bradley Hm Roael

Blauvelt, INY 10913IPhone (9"4)358~3330

CIRCLE A-12 QN READER ,REPLYCARD

November/December 1987 15

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

.:!::t:Ii- ,WW·I-

30 I :s.~-I..--,,-;.:-+---:'-'-!-'-'iII:WIII

20 2---+~-+r-~~~~~~~~~~---~IZ

10

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o 10 20 30 40 50 60 70 80 90100

fig. 9-Relationshlp between recommended teeth numbers in cutters andwork pieces. for common pressure angles.

.I

pARAun TO CoMMON to· --.

\RADIAL FLANk CUTTER

~'tE"

~

Figure A

0- F~~---E E·ijA ...

fig. 10- Flank rub diagram - internal work.

Un. P..... 1eI ToCommon ~

.. __ ~mount Of Relief......k~f1'Angl.~-j --

_ - -~ -- : If SPK- From Previous-, '. Cut Are Het'e. No RubSolid Line Is Poeition " Will ExistOf Cutter T.. th On '..,Cutting Stroke ':V\,.. I>epth Of

~ Previous CutDotted Line .. PoeItIonOf Cuttet' On RelUmStroke

lntern.1 WOrk

Fig. ll-lmptovement of beam strength by use offluted barrel design.Fiig. U-Multiple cui or multipass method of eliminating rub.

16 Gear Technology

Section AI.

rub on internal. gears. Fig. 11 shows thatif the stock where rub takes place isremoved by a previous cut, it will nolonger rub. In this example, possiblymore than one cut had to be taken to getto the "previous" depth, to attain thatdepth without rub, The amount of infeedbetween cuts for both flank rub andrough side rub elimination is determinedby the computer program.

Another important feature of the mul-tiplecut/multipass feature is to allow theuse of a taper shank cutter larger thannormal when cutting small internalsplines. Because of reduced rub, a cutterwith one or two teeth more may be used,resulting in a cutter with a stronger bar-rel which will be less apt to deflect.

Cutter Deflection of Small TaperShank Cutters

The long slim cutters necessary forsmall diameter, wide face width, internalsplines require special attention, A goodprogram computes the relative beamstrength of the barrel of the cutter, andif it comes below a previously deter-mined minimum, it should change thecutter to a fluted barrel design. Fig. 12illustrates the difference in the fluted andnonfluted design.

Finished Cutter DesignWhen the final optimized design has

been determined using the methodsoutlined above, computer and plottercreate a .fully detailed working drawingas shown on Fig. 13. In addition to. this,any enlarged layouts required for thefabrication of the cutter are plotted along

Figure 8

SAME CUTTER AS FIG..A WITH ·FLUTES·ADDED. BEAM STRENGTH INCREASED 50'-'

FORII,ASTERGIRINIDIIINIG WHE,EL 'P'R.O'IFIILEIR

EAS,Y T'O IINSTALL. - Because ,of Us,small size andl welglht, the FOFl,MAST,ERdoes not re-quire maJiormachine modifications and can be Instailledl on nearly any 'QI:rlnder.lnslallaUon, canusually be accomplished in ressthan a day.IEASY T'O' OPE,RATE -Two axis design simplifies proQlrammlng andl operation. You canchoose between four popular eontrots tnat f,eat.ulremenu and G·Code proglrammlng, graphicsimulation, autorna •.ic corner rounding, automatic d;liamond thickness, 'compensation, ,andmore.

MA'DE liN U.S.A.

Patent No..4,559',919

IMP':ROVES ACCURACY

IREIDUCES WHIEIELDRESSI,N:'G TIME

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P,.O. Bo')( .207Northville" Mil 4816,1'

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'"00""10 0" i,:rcco 1.5,. C'L~t"LE 1,.00 fa

'l: fl /~I~'. I:' I i,,~ ~Duuii's.c ' ~ I' PIfCH ~'1~6 4.000 O'_...jl •.!

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PRECI$IO"! ,~WE, :p 0 lOX 3~1.SPRlKQFIElD. \IT, 05IY·OI501 us ..

\HT. OF FILLET~~\

Fig. 13- Sample working drawing.

~ HT. OF FILLET

T.I.F. I LIFE

RAD TO HT. OF FILLET UFE .51602

RAD TO HT. OF FILLET FRONT .51"00

FIg. 14-American National Standards Institute(ANSI) standard full fillet inlemal spline, 1.0module, 30" p.a,

13.0T.I.F.

18.9791

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CUiproftl.~ IFlnlsh4ld Profil .....

HT. OF FILLET HT. OF FILLEr

LIFEFRONT

RAD TO HT. OF FILLET LIFE 1.77818

RAD TO HT..OF FILLET FRONT 1.7lM!91

Fig. 15- Example ·0£ undercut for preshaving orpregrlmling, 10 d.p., 25" p.a,

Fig. 16- (left) Plottedinvolute chan of partshown in fig. 15. Notestock left at TIFdiameter.

Ij

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RAD TO HT. OF FIL.LET L.IFE .73300RAD TO HT. OF FILLET FRONT .72781

HT. OF FILLETI

\\

,. MOD. DlA. L1F,E

AMOUNT MODIRED AT I.D•• 0001 AMOUNT MODIRED AT I.D .• 0032RAD TO HT. OF FlUET LIFE 5.3OH5AAD TO MOD/RCATION DIA LIFE 5.10066RAD TO HT. OF FILLET FRONT 5.29375RAD TO MODIFICATION DIA FRONT 5.07038'

...,MOD. DIAi FRONT j

I

1HT. OF FILLEr

FRONT

HT. OF FILLET

BASE DIA.LIFE

I-r tFig. IS-Extreme undercut, 10 d.p., 141'1,0 p.a,pinion.

Fig. 17-Tip mod~ication-6f8 d.p., 2.0°p.a, In-ternal gear. See also Fig. 5.

with a greatly enlarged layout from 10to 100 x size of the work tooth profile.Examples of these work layouts areshown in Figs 14-18.

NOTE: These layouts show twovalues of fillet height and modificationdiameters, one forUfTont" (new cutter).and one for the life position. This changeis due to the reduction of the outsidediameter of the cutter as it is sharpenedback, resulting in a change in the activepressure angle (APAt thus changing thefillet and modification diameters.

The computer programs also computeand print other important informationfor the designer and user, including thevariation in depth of CUlt throughou; thelife of the cutter, variation in chamferproduced by a chamfering cutter andvariation in the outside diameter pro-duced by a 'topping cutter ..

Each final cutter design. along with al.lof the input gear data, is stored in a database on the computer system and isavadable to any computer aided man-ufacturing (CAM) programs used in thefabrication of the cutter.

CondusionThe development of this type of soft-

ware greatly enhances the ability torapidly design a gear shaper cutter to dothe best job possible. The many criticalpoints that must be checked are done sowithout [ail, withappropriate action ineach case. The precise plctted layouts ofthe work are invaluable in communi-eating the exact profile that will be pro-duced on the workpiece.

Acl!n.owledge.ment:Reprinted courtesy of the Society of Manufac-

tun'ng Engineers, copyright 1986. /rom the GearProcessing Technology Clinic.

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Hansford Manufactunng COrp.3111 Winton Road SouthRochester, New York 14623(710,) 427 -0660

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INovember/IDecember 1'987119