Grinding of Spur andHelical Gears

Dr. Sur,en B. RaoNaUonal Sc!ience Foundation

Washinglt1on. D,.IC:.

Grinding is a technique of finish-machining,utilizing an abrasive wheel. The rotating abra-sive wheel, which is generally of special shapeor form, when made to bear against a cyhndrical-shaped workpiece, under a set of specific geo-metrical relationships, will produce a precisionspur or helical gear. In most instances the work-piece win already have gear teeth cut on it by aprimary process, such as bobbing or shaping.There are essentially two techniques for grind-ing gears: form and generation. The basic prin-ciples of these techniques, with their advantagesand disadvantages, are presented in this section.

A general. introduction to the basic prin-ciples of the grinding process, however, pre-cedes the discussion of gear grinding tech-niques, This is based on the belief that thediscussion of the grinding process, in combi-nation with the description of the gear grind-ing techniques, would constitute a more com-

ABRASIVE GRAIN

BOND

V;: CUrrrNG VELOCITY VECTiOR

y;: NEGA nVE RAKE ANGLE

ex ex. ;: CLEARANCE ANGLE

Fig..I - Grinding process schematic showing negative rake aogZe.

20 GEAR TECHNOLOGY

plete treatise on gear grinding.Reasons For 'Grinding

There aretwo primary reasons for grindinggears. In spite of severalertemprs to the contrary,it still remains one of the most viable techniquesof machining gears once they are in a hardenedstate (50 Rc and above). Also, the process, incombination with highly accurate machines, iscapable of gear manufacturing accuracy un-matched by other manufacturing techniques.AGMA gear quality 12 and 13 are common, andAGMA gear quality 14 and 15 are not unusual,With the advent of cubic boron nitride (CBN),grinding bas been tried. with some success, as aprimary operation on hardened material insteadof bobbing or shaping before heat treatment(sometimes referred to as "direct grinding"),Obviously this is of greatest consequence only ifa gear is being made from through-hardenedmaterial, a process that is not very common. It ismuch more common for gears to be made ofcase-hardened material where the economics ofgrinding from the solid are not as beneficial.

Gear grinding is an expensive operation andhas to be justified on the basis of required gearquality in the hardened condition, The basicprinciples of grinding are now presented.

IGrind.ing Process Mechanicsand Process Parameters

'Grinding is a metal cutting process not un-like single- or multi-point machining. such asturning, milling, bobbing, etc., but with somemajor dissimilarities. Grinding is characterizedby the fact that the cutting tool, in this case thegrinding wheel, consists of a very large numberof randomly oriented cutting edges machiningsmall amounts of material, thus resulting in

extremely fine chip thicknesses. While chip th ick-nesses of20 urn (0.0008") or more are commonin operation Like turning. and chip thicknessesof8 um (0.0003") we common in operations likemilling, chip thicknesses of less than 1 urn(0.00004") are the norm in grinding.

work piece error will remain after the first turn-ing pass. In grinding. however. since R is ex-tremely large compared with K, values of 0 '"0.95 are not uncommon ..This signifies that ingrinding almost 95% of the initial work: pieceerror may remain after the first grinding pass. It

Though the abrasive particlesin the grinding is obvious from this discussion that careful ex-wheel ave randomly oriented, by virtue of theirshape .•they generally present a large negativerake angle to the cutting velocity vector as seenin Fig. 1. Negative rake angles always result inhigher cutting forces than do positive rake angles.Also. small chip thicknesses result in higherspecific caning forces, where specific cuttingforce is defined as the force required to cut a unitarea of chip cross section (kgf/mm2 or Ibf.lin2).

The combination of negative rake and low chipthickness gives rise to high specific power re-quirements in grinding. Specific power is de-fined as power required to machine unit quantityof material in unit time (hp/m:m3/m:in or hplin.3Jmin). This is 110t only indicative of the lowefficiency of the grinding process, but also itshigh susceptibility to burning damage. as all thepower consumed by the operationis convertedinto heat. The small chip thickness, however.also enables the generation of a high-qualitysurface and tight dimensional tolerances thatmake this process critical to the manufacture ofhigh-precision gears and components.

The combiaetionoflarge negative rake angleon the abrasive grain and small. chip thicknessalso results in cutting process stiffnesses in grind-ing that are almost several times the cuttingprocess stiffnesses in other machining processes •.SIlCh. at turning and milling. CHtting processstiffness here is defined as the force per unit chipthickness and is generally expressed inkgf/mm2

(]bflin.2) of chip thickness. Since the rate ofreproducibility of error due to a machining pro-cess is given by the formula:

0= _Jl'_I+Jl

where 0 is the rate of reproducibility and Jl isexpressed by the formula:

Jl",RK

where K is the stiffness of the machine tool andR is the cutting process stiffness.

In a typical turning operation Kis severaltimes R. and 0 typically computes to less than0.25 ..This signifies that only 25% of the initial

ecution of all previous processes to ens LIre agood pre ground gear is essential. to an economicand successful grinding operation.

Wear of the grinding wheel is an essentialpart of the process. As the sharp cutting edges ofthe abrasives wear out. cutting forces on thatparticular abrasive increase until either the grainfractures reveal new sharp cutting edges or theabrasive is pulled out of the bond and a. newabrasive grain is exposed. In essence, if theprocess were in perfect harmony, the grindingwheel wouldbe self-sharpening. But even thoughwheel wear is an accepted phenomenon, the rateat which it occurs is critical. For wheel wearresults, not only in wheel replacementbur alsoin oilier nonproducti ve wheel preparatory opera-tions, such as trueing, dressing, and profH:ing.Therefore. the ratio of work:materi al removed tovolume of wheel lost, also called the 0 ratio. isa measure of grinding efficiency. 0 ratios canrange from less than one to several hundred,depending 011 the e variables.

One other distinguishing feature ofthe grind-ing proces is the fractional amount of time theabrasive grain is actually creating a chip, incomparison with the total time this grain is incontact with the work piece material. Threedistinct phenomena have been recognized asoccurring as the abrasive grain comes in 'contactwith and leaves contact with the work surface.These three regions have been defined as rub-bing, plowing. and cutting, and the actual cuttingor chip formation may be occurring for onlyabout 30% of the time the abrasiveend the work-piece are in contact. The force at which thetransition occurs from rubbingand plowing tocutting is called the threshold force. When themechanisms holding the grinding wheel and thework exert a force in excess of this thresholdforce, grinding and metal removal will occur.

Finally, here is a word about spark-out. As a.grinding process proceeds with the rotating grind.ing wheel being fed into the work material.cutting force are generated. These cutting forcescause the electromechanical structure that holds

..

Ur. Suren B. IRaois currently the Directorof the ManufacturingMachines and EquipmentProgram in tile Divisionof Design and Manufac·turing Systemsat the Na-tlonal Science Founda-tion. He has a doctoratefrom the University ofWi~coII~in. He also stud-ied at McMaster Univer-sity and 01Bangalore Uni-versity. India.

JULY/AU(lUST Ig;2 211

•

the grinding wheel and the workpiece [0 deflectaway from each other. AI. a certain in tant in theprocess, the infeed of the wheel a:ndJorlhe work-piece is stopped, resulting in a reduction of theclJtt.ing force . T.his cause the strain energystored in the structure to overcome the deflectionand return the system to a state of equilibrium.A this happens, the wheel and workpiece moveinto each other and continue to grind as Lheforces decay to the threshold force level, afterwhich no more grinding occur. This part of the

-----

1000

12.0r;; 8000ll-

-00

vi 6000InUlZ0 4000 -t:::t:0:(l:0Ct! 2000 -ui

9.0

6,0

3.01

200 400 600 800TEMPERATURE, DC

0,006" 0,002"WEAR FLAT WEAR FLAT

of aluminum old de and euble boron nitride.

u,It.CI'l

~ 2000;:Jf0-al

~1600

:>.... 1200fo-u~Cl 800'z0U..J 400-(

~w:=fo-

350

300

200

100

W/M/K 29 40 50 400 113002000fJTUlfT·soF 4.6 6.4 8.0 64.0 20.8 32.0'

Fig. 4- Compares ive thermal condllctivit11 of abrasives and other materials.

22 GEAR TECHNOLO(lV

grinding process, where no infeed occurs butgrinding continues, is called spark-out. The timetaken to complete spark-outi a measure of' thestiffne s of the tructure of tile machine tool-teol-workpiece system. In general, some amountof perk-out in a grind cycle will improve workpiece qlHtlity.

AbrasivesThough aluminum oxide (A120), silicon

carbide (SiC), diamond (C),and cubic boronnitride (CBN) are generally considered in thecategory of abrasives where grinding is con-cerned; only aluminum oxide and cubic boronnitride are discu sed further. This is because ingear grinding we are usuaUy dealing with :fer-rnus alloys, and diamond and silicon carbidetend to perform poorly when grinding steel ..High wear rates ofthe diamond or silicon car-bide abrasive when grinding may be due to

interatomic di ffusion of the carbon atoms presentin these two abrasives. since steel is character-ized a "carbon hungry" at the elevated tempera-tures that are encountered during grinding.

The characteristic of aluminum oxide andcubic boron nitride that impact their perfor-mancea .abrasives are now presented in a com-parative manner. It is obvious from the follow-ing that cubic boron nitride is a considerablysuperior abrasive, though more expensive thanaluminum oxide.

Hardness. Fig. 2 shows a comparative plotof diamond, cubic boron nitride. silicon carbide,and aluminum oxide hardness at elevated tem-peratures. Iti obviou that cubic boron nitride isseveral times harder that aluminum. oxide andeven harder than diamond at temperatures higherthan 1472°f (800°C). The chemical inertness ofcubic boronaimde is also of significance, sinceany chemical affinity to jron would result inincrea ed wear rate .

Grain Shape ..When comparing grain shapesof aluminum oxide and cubic boron nitride. theformer i known to have a more pronouncedspherical form. while the Inter has a block form.For a given amount of crystal wear, a sphericalform exhibits a larger wear area than does ablock form (Fig. 3). Tendency to burning hasbeen related to wear flat area, indicating thathigher degree. of burning and surface damageare po sible with alumiaum oxide than withcubic boron nitride.

Thermal Conductivity. Fig. 4 shows a com-

par-ison of thermal conductivity of the variousabra ive and some common metals. Thoughdiamond hasthe highest thermal conducti ity,cubic boron nitride i not far behind and con id-erably higher thaaaluminum oxide ..The highthermal conductivity of cubic boron nitride al-lows more of the heat generated at the abrasive-work. material interface to flow into the abrasiveand into the wheel than into the work piece,resulting in reduced tendency for surface dam-age. It must be remembered, however, that it ispossible to produce thermal damage with cubicboron nitride ..The combination of high thermalconductivity and lower wear flat area owing to

grain hape allows for much higher metal re-moval rates to be achieved and higher spindlepowers to be utilized before thermal damage canoccur. The impact of a grinding abrasive on thework piece will generally induce a compre sivestress on (he work surface. However, the local-ized heating and ub equent cooling t.hat is morepredominant when grinding with aluminum ox-ide overcomes the compressi ve stress due tomechanical impact, and the residual stresses inthe uppermost layers ohhe work piece are highlytensile. The absence of this heating when grind-ing with cubic boron nitride re ults in residualstress that is a compressive on the work surface.Fig. 5 show typical residual tress profiles pro-duced by plunge grinding with the ItwOabra-sives ..Since ten ile stres esare accompanied bylowered fatigue life, clearly grinding with CBNoffer distinctive advantages. The only draw-backs to the application of cubic boron nitrideare its co ts and the need for tiffer, bigher-powered machine tools to funy utilize the advan-tages that cubic boron nitride ha to offer.

Grinding WheelsGrinding wheels and their properties are

only briefly discussed here, a a con iderabJeamount of literature i in existence. especiallyfrom. wheel manufacturers that covers this indetail. All grinding wheels. except electroplatedwheel, consist of an abra ive held ill a bond.The physical size of (he abrasive is a majordetermining factor in abrasive grain concentra-tion and in the number of' cutting edges engagedin the proce ofgrinding at any given instant tiltime; Ithat is, the larger tile abra iveize, thefewer the number of abrasi ve and cutting edges,and vice ver a. This in tum impacts the chipthicknesses grinding proceeds and, consequently,

160.

Z hiD0til 1.20zUll-

100Vi:.:: 80viI;IlI.I.l 60p,::;I-r:n..J 40<0(::i

ZC 20en 0Ul Vi0:: r:n 0IIIg:

~. -200u

.A I_BoRko :'CBN! 17eAl I ~ 1 I

If \,I--AI203

'I,

III

I

1\ ~ _J\ I J

\ I'\

1 I - I: Lj J

tL

00 (iRIT

-40o 0.0020.004 0:006 0.008 o.to

Fig..S - Comparathevalues of restdaalstre s distribution.

the surface finish that is obtainable. In general.coar e abrasi ve grain sizes, also called grit sizes,result in rougher ground surfaces and filler gritsizes in lower surface roughness values. Surfaceroughness values of O.41lm (16 uin.) are gener-ally po sible with 60 grit size abrasives, andvalues better than 0.1 l,Un (4 !lin.) are possiblewilh abrasives of 200 grit size or finer.

Wheel hardness is another important charac-teristic of the wheeland is relasedro the amountof bond used in the manufacture of the wheel. Ahard wheel has more bond, resulting in a greaterabrasive retention abili ty. The abrasi ve will haveto become considerably dull, in regard to itscuUing edges, before sufficient forces are gener-atedto tear it away. On the other hand, a oftwheel has les bond and consequently will loseits abra ive grain more readily. In general, softwheels are used with hardened materials be-cause the abrasive grain is known to dun rapidlywhen machining the hard materials, and fresh,sharp abrasives will be required to continuegTinding without the occurrence of high tem-peratures and surface damage. On the otherhand. hard wheels are generally used with softmaterials, since the abrasive is expected to lastlonger, and abrasive grain retentionis a propertythat is de ired froman economic point of view.

Wheel structure is another important charuc-teri tic. An open structure allows greater chipclearance and is preferable in roughing opera-tions where large quantities of material. may beremoved. Lack of suffieient space for chips

JULY/AUGust 1Sg2 23

24, G E ... R TEe H N 0 LOG Y

would result in the loading of the wheel. withsubsequent burning of the work surface. How-ever, open-structure wheels are also softer, be-cause of the reduced amount of bond material.

Abrasive grain size is specified by the wiremesh size that will allow the abrasive to passthrough. The smaller the number, the larger isthe grain size, It must be remembered that themesh size specified only indicates that grainslarger than the specified value do not exist in thewheel, but smaller abrasive grain sizes do. Wngeneral. the grain size distribution can be as-sumed to follow a normal distribution. Wheelhardness or wheel. grade is specified with aletter,with A being the softest and Z the hardest. Wheelstructure is generally specified with a number.with I representing a dose structure and 10representing a very open structure.

it must. be remembered that there are noabsolute relationships between work piece andwheel characteristics ..The aforementioned factsare only guidehnes,and the exact choice ofawheel for a particular work material-grindingoperation combination has to be arrived at 0111 thebasis of trial and experience.

Wheel Preparation. In most grinding op-erations where a dressable whee] is used,four distinct operations may be present, sin-gly or in combination: 1) wheel trueing, 2)

wheel dressing, 3) wheel. profiling, and 4)wheel crushing. The purpose and procedurefor these foureperations are now discussed.The mechanism for accomplishing these op-erations is described later.

Wheel Trueing. In this operation wheel. ma-terial is removed to eliminate wheelnonuniformiries of shape and geometry due towheel manufacture and mounting. The grindingwheel is mounted on its whee] holder, balanced,and then mounted on the machine spindle ..Trueing is then carried out by the motion of adiamond too] in a direction along the axis ofwheel rotation as the wheel is spinning at speedsclose to 0[ at grinding speeds. After all thenonuniformity is eliminated. the grinding wheelwill need to be balanced again, Wheel trueing isgenerally necessary only when the wheel ismounted for the first time unless nonuniformwheel wear has occurred during the grindingoperation. Trueing will reduce forced vibrationproblems due to nonuniform wheel shape andgeometry, resulting in improved surface finish.

Wheel Dressing. This is required to eliminatethe uppermost layer of dulled abrasive grainsand expose the sharp, next layer of abrasivegrains in the wheel to obtain efficient cutting. Ona new wheel it becomes necessary to do thiswhen the wheel is very bard and the bond mate-ria] completely encloses the abrasive grain. Forsofter wheels the trueing operation is generallyable to expose abrasive grains, and the firstwheel contact with the work piece is sufficient tobreak down any bond material that may still becovering the abrasive. On harder wheels thebond material. may need to be pushed back witha stick of silicon carbide or naturally occurringabrasives. such as corundum. etc. Too muchbond removal is, however, detrimental, asabra-sive grains would be unsupported and conse-quent1y lost easily, leading to lossofthe wheel

Dressing also clears the chip-loaded surfaceof the wheel, which may cause burning of thiswork piece. A loaded wheel, in. combinationwith dull abrasive grains, will have a smooth,glazed surface ..After dressing, the wheel surfacewill be rougher to the touch.

Wh.ee.lProfiling. In this operation the wheelis shaped to a specific profile in order to generatethe required geometry on the work piece. This isof special significance in gear grinding,as thewheel is either representing a rack in somegenerating-grinding operations or the norma]space between two adjacent teeth in form-grind-ing operations, Wheel trueing. dressing, andprofiling can, however, be combined into oneoperation on a machine, especially if a mediumor soft wheel is used. For hard wheels trueingand profiling can be combined. while initialdressing to push back the bond material is car-ried out. as a separate operation.

Wheel Crushing. This is a technique used forrapidly removing wheel material to profile awheel, A crushing roll, generally made of high-speed sreel, with the required proflle machinedon it, is brought into 'contact under pressure withthe grinding wheel, with no relative tangentialvelocity. Wheel speeds are generally reducedduring this process to about one-fifth to one-tenth the actual grinding speeds.

Bxeept for crushing and dressing of veryhard wheels, all other wheel preparation opera-tions are combined on most grinding machines.Profiling, trueing, and dressing can be done witha single-point diamond traversing the wheel

surface in a specific relation hip to generate therequired profile. Where profile accuracy is in-fluenced by the wear of the diamond point, arotating diamond d:isk that represents many dia-mond points will improve results, since the dia-mond wear is distributed over many points ..However, the di k should run true in axial andradial directions in order to maintain profilingaccuracy. For much faster profiling, in combina-tion with dressing and trueing, formed diamondrolls can be used. These rolls are, however.expensive, and sufficient part volume may benecessary tojustify the investment With a formeddiamond roll, intermittent dressing when thegrinding wheel is out of the cut or continuousdressing during the grinding operation are pos-sible. Continuous dressing is especiallyeffec-tive for high-speed, creep-feed grinding, whichis discussed later.

Grinding ProcessesThere are two distinct grinding processes

used in gear grinding, as in mo t grinding opera-tions. They aI1eas follows:

Conventional Grinding ..Fig. 6 illustrates thebasic properties of this process, which ischarac-terized by a wheel rotating at surface speeds ofabout 30 mJ (6,000 ftlmin), infeeds of 0.01 to0.050 mm (0.0004 to 0.'0002 in.) and work ve-Ioclties of 1.25m/min to 10m/min (50 to 400 in.!min). The chips generated are short, due to thesmall. arc of contact between an abrasive grainand workpiece in this process, and are easilydisposed of. Wheel wear rate .are generally highin this process, resulting in low to medium Gratios. This is because of repeated impacts be-tween the edge of the work piece and the wheel.due to the to-and-fro escillatlons of the work-piece, for which reason this process is alsosometimes referred to as pendulum grinding. Fig. ,6- Conventional or pendulum grindling.Researchers have also found that in this mode ofgrinding, the average force per abrasive grain ishigh. further contributing to rapid wheel break-down. Coolant is generally used, though drygrinding can be done if the amount of infeed is inthe 0.0005-mm (0.0002-in") range when grind-ing hardened teel. This is due to the fact thatmetal removal rates are very small, with a smallfraction ofthe wheel surface cutting at any giveninstant, with low power consumption and conse-quently low amounts of heat generation.

Creep-feed Grinding. Fig. 7 illustrates thebasic properties of this processthatare charac-

terized by large infeeds into the work in excessof 0.5 mm (0.0125") and up to 10 mm (0.4"),depending on machine power and stiffness; butaccompanied by much lower work velocities,which could be a low as 50 ram/rain (2 in.!min)and seldom exceeding 500 rnm/min (20 in.lmin).Work velocity is inver ely proportional to theinfeed. Work velocities exceeding 250 mm/min(10 in.lmin) are generally accompanied by spe-cial dressing processes, such as continuous dress-ing, which enable the maintenance of a harp,unclogged grinding wheel.

Since the infeeds are large, arc of contactbetween wheel and work is extremely large incomparison to conventional grinding. This re-suits in each abrasive grain cutting a long chip.The wheel consequently has to have a very openstructure to accommodate long chips.

The large arc of contact, which resultsin alarge number of grains in simultaneous cuttingaction, requires high . pindle power, which intum results in large cutting forces and the gen-eration of greater quanitites of heat than withconventional grinding. The machine tool has tohave the necessary power and stiffnes to with-stand the larger force . and a copious supply of

41om MMFEED

2 MM STOCK REMOVAL "'- -'

Flig., • Creep-feed grinding.

JULY/AUGUST 1992 25

process, with the grinding wheel being continu- kinematically illustrated in Fig. 8. The simHari-~--------------~------ ties of the mechanics of this technique to gearhobbing are very obvious, with the threadedgrinding wheel replacing the hob. The ratio ofwork speed and wheel speed when grinding spurgears is a simple ratio of number of teeth on thegear and number of starts on the wheel. Forhelical gears this has compensated (differentialindexed) for the traverse of the grinding wheelalong the face width ofthe gear.

Tn order to be able to carry out the grindingprocess, the threaded grinding wheel, unlike thehob, has to' achieve surface speed in excess O'f25m/s (5000 ft/min). The indexing mechanism hasto be considerably more accurate in order to

achieve tbe gear quality required in grinding. Inthe past, complex gear arrangements were nor-mally used to' obtain the simple and differential.indexing requirements between the grindingwheel and work piece. However,.electronic gearboxes (EGBs) are now commercially availableto maintain the kinematic relationship. Fig. 9shows a typical machine with an EGB for gener-ating grinding.

The quality of the gear being ground is alsosignificantly affected by the rack-type profile ofthe grinding wheel.lt mu t first be introduced onacylindrical wheel and then maintained throughthe grinding process as the wheel. breaks downdue to wear.

Introduction of the rack-type profile on acylindrical wheel is done in two steps. A rough

well-directed coolant to' carry away the heatgenerated in the process,

In spite of the larger power requirement,creep-feed grinding generally enjoys a higher Gratio than does conventional grinding when grind-ing similar materials ..The lowered wheel wear isattributed to lower forces per abrasive in creep-feed grinding and also to the fact that in conven-tional grinding many wheel-work piece impactsare present as the work piece oscillates from sideto side about the wheel.

Any means of eliminating the long chipsproduced in creep-feed grinding from loadingthe wheel will only improve the efficiency of theprocess. The use of high-pressure coolants to'flush the wheel has been one techniques allow-ing higher work velocities. Another techniquehas been continuou dressing, Here the dressingroll, which may have the required form, is con-tinuously fed into the wheel during the grinding

F.ig.8 - Kinematic representation ofthreaded wheel method,

Fig. 9'- Electronic threaded wheel-type gear grinder.

26 GEAR TECHNOLOGY

ously fed into the work to compensate for reduc-tion in wheel size. This continuous dressingkeeps the wheel clean and sharp, allowing higherwork velocities during creep-feed grinding. Ex-perimental work where work velocities were inthe Im/mm (40 in.lmin) range and higher havebeen reponed.

With this introduction to the various a pectsof the grinding process, it is now possible to

discuss gear grinding as practiced by the indus-try. The two most common techniques are formgrinding and generating grinding. The techniquesare now discussed in detail.

Generating GdndingThere are several basic techniques of gener-

ating grinding; each technique is associated witha pecific machine-tool manufacturer. Thesedistinct techniques are now presented.

Threaded Wheel Method. The basic machinemotions that generate the gear ill this method are

rack-type profile i cru hed into the wheel usinga steel crushing roll. Thiscan then be fini hed bya variety of techniques using diamond tool ,such a a single-point dresser or coated dre ingdisk. Profile modifications are introduced in thissecond step as required. With Ingle-point dre -ing tool , profile modidifications are made usingspecial cams. If coated disk are being used, themodifications are lapped into the disk by themachine manufacturer ..

Saucer Wheels Met/lad. This is another gen-erating technique where two saucer-shapedwheels are u ed as ihewn in Fig. 10. The grind-ing surfaces ohlle two,wheels represent the rack.and the involute profile i. .generated by the gearrolling relative to and in contact with. the twogrinding wheels. The wheel may be set parallel.to each other or at an angle up to 100

. The workpiece is reciprocated in the axial direction toprovide the feed motion as two flanks of twodifferent. teeth are ground in one pass, At the endof the pas the entire gear j indexed lIsingmechanical index head' 0 that two flanks of twoor more teeth are them ground by the wheel. Thedepth of cut i determined by the infeed of thetwo grinding wheels toward each other,

For spur gears, the axes of the grindingwheels are perpendicular to the axis of the gearand onl.y imple motion, to imulate the rolfingof the gear on the rack repre ented by the grind-ing wheel. i needed to generate the involute.Thi generating motion i produced by steeltapes fixed to a stationarytap stand, the otherendof which is wound over a rolling block that isgenerally the same diameter as the base-circlediameter of the pmflie being ground. This isillustrated in Fig. 1.1.When grinding a helicalgear, the rolling motion lhat is necessary 10

generate the involute has to be compensated forthe helix. angle a the grinding wheels movealong the face width of the gear. Tlii is accorn-plished by a helix guide rnechani m attached 10

the tape stand that is u ed to generate the rollingmotion. The helix guide is et to the base helixangle, and, a the gear moves along its axis,additional motion i imparted to ittoproduce thehelix along with the involute.

On older machine of thi type, changeoverfrom one gear to another required the change ofthe rolling block for each change in base-circlediameter. On modern machine. mechanismshave been developed that allow a range of ba e-

STA DARDROLLIG

GENERATINGHEADS

Fig. 11 • Typical. saucer wheel grinder showing basle eornponents,circle diameters that can be ground with thearne rolling block.

The contact between the saucer-shaped wheeland the tooth flank is generally restricted to avery small area at.any given time. Thi generallymake this technique of gear grinding time con-suming and slow. However, it also,enables point-by-point profile and lead modification along theflank of the tooth technique, termed topologicalmodification .. Consequently, the profile of thegear tooth can be different along the entire facewidth of the gear, a feature that none of the othergear grinding technique . form or generation.can duplicate. Use of computer to contrel thistopological grinding feature allow, an infinitevariety of tooth forms to be ground. It must beremembered, however. that this feature is at theprice of slower cycle time. and tradeoffs have tobe examined before a decision is made to use thistechnique, Also, at the present time, apart f:rom

JULY/AUGUST '8112 21'

28 GEAR TECHNOLOGY

11 few gear tool application , no other applica-tions of topological grinding have been applied ..

Vitrified aluminum oxide wheels are mostcommonly u ed in this method of gear grinding,and the grinding process is generally do lie "dry."Dressing is carried out with whee] cornpen 3-

tion, u ing single-point diamond. The purpo eof dressing i to en ure that the rotating urfaceof the wheel represents a straight loath of a.generating rack. Single-layer, cubic boron ni-tride-plated wheels have also been tried, as theyeliminate the need for dre sing, and wheel life ishigh for reason already explained in the text

Conical Wheel Grinder. This is another ver-sion of generating grinding using a grinding

Fig. 12 - Basic concept of a conical wheel grinder.

Fig. 13 - Conical wheel gllinder finishing a double-helical gear' ,in oae setup.

GRINDINGPROFILE ONLY

Fig. 14 - Basic concept oHllrDl gear grinding ..

wheel that represents a ingle tooth of the rack,as shown in Fig. 12. The sides of the wheelcorrespond to the pressure angle of the gearbeing ground ..The work. gear rotate and trans-lates linearly to generate the rolling action re-quired to generate the involute profile.

The simultaneous rolling and linear motioni generally obtained by having a rna ter gearwith the same number of teeth mounted on thework spindle rolling on a stationary masterrack. The master gear and rack must corre-spond to the gear being ground in terms ofnumber of teeth. pressure angle, diametral pitch.etc. Electronic means of varying the base rolldiameter to correspond to the gear being pro-cessed are, however, now available. In thisproce ,as with thepreviously di eus ed . au-cer wheels method, two flanks oftwo differentteeth are finished before the gear is indexed togrind two more flanks of two more teeth.

Helical gear canal 0 be generated by thistechnique. though helical master gears and racksare required. If the wheel needs to be dressed,diamond point operating at the specific pres-sure angle are required. Since simple traightline forms need to be eire sed, the dre ing mecha-nism is relatively simple. Tooth profile modifi-cations are produced by the modified grindingwheel. For lead modifications the tool slide withthe grinding wheel is radially advanced in syn-chroni rn with the stroking motion of the grind-ing slide, controlled through a tracer roll fellow-ing the lope of the template. A moderate-sizedconical wheel grinder, grinding a double helicalgear i shown in Fig. 13.

Form GrindingIn this technique.the abrasive grinding wheel

is profiled to repre ent the space between twoadjacent teeth on a gear. The wheel is thenpassed through the space while grinding occursOJil the two adjacent teeth flanks and the root, ifrequired. a hown in Fig. [4. This i one of theprimary advantages of form grinding in thatvarious simple and compound root form can beproduced. Form grinding al 0 enables the grind-ing of internal gear and external gearsposr-tinned against a boulder.

When a spur gear is being ground. the wheelis simply moved along the axisof the gear. Whena helical gear i required, the axial motion oHllewheel is combin d with a motion of the gearabout its axis in order to produce the lead. The

various axes of motion required to manufacturea gear on a horizontal axis grinder are illus-trated in Fig. i5. The A axis provides the tooth-to-tooth index and, when interpolated with theX axis generates the lead. The Y axis providessize control and, in combination with the Xaxis, provides lead modifications. The B axisallows the wheel to be set to the helix angle ofthe part. On a horizontal axis machine, twomore axes are generally required to dress theprofile on the grinding wheel. These are markedas the V and Waxes.

An analysis of current gear grinding equip-ment indicate that form grinders are ahead ofthe generating machine in the application ofcomputer control to gear grinding. In most gen- Fig. IS • Axes of motion for fiormgrinding.erating machines it was found that only someaspects of the process were under computercontrol, while other aspects used mechanicalcontrol devices such as index plates, sine bars. orcams. However, contemporary form grindersappear to have completely abandoned mechani-cal devices in favor of computer control andappear to be doing as well or better than the olderform-grinding machines, Also, computer con-trot enables these form grinders to be moreflexible and require le setup time than theirgenerating counterparts,

Since the wheel profile is constant, modify-ing the lead by Y axis motion. which results inachange in center distance between the grindingwheel and the gear, will re ult in slight di tor-rions to the profile. Lead modifications throughchange in the interpolation relationships be-tween the A and X axes are also possible.

his also important to note that, when grind-inga helical gear. the normal tooth pace that isrepresented by the grinding wheel has to bemodified to account for the interference thatoccurs between the wheel and the helical groovecommonly termed heel-toe action. This heel-toeaction is a. function of the wheel diameter. Con-sequently, this has to be compensated for wheeldiameter reduction during dressing to avoid er-rors in profiles.

In the past, mechanical devices such a sinebars, index plates, and cams were used to gener-ate the helix, index, and profile, respectively. Onmodern computer-controlled machines. such asthe one shown in Fig. 16, software generate andcontrols the relationship. Con equently, com-pensating for the involute as the wheel diameter

+Y

-s c.!J +B

J+X .y

-v

Fig. 16· CNC form gear grinder.changes due to dressing can be done just aseasily as speeding up the spindle is carried outfor changes in wheel diameter in order to main-tain constant wheel urface speeds. Tile onlynecessity is that the machine constitute a set ofnecessary accurate linear and rotary axes.

Wheeling trueing. profiling. and dressingareaccompli hed by the dre ing mechanism. Adiamond disk or single-point diamonds can beused. If production volumes can juslifJl it,adiamond preformed dressing roll can be used toreduce dressing times and increase productivity,Alternatively, electroplated preformed cubicboron nitride wheels can be used. and dressingtimes can be completely eliminated (keeping inmind that preformed wheels may cost up 10 ]00time the cost of a dressable aluminum oxidewheel). Vitrified. dressable cubic boron nitridewheels can also be used, These need to bedre sed,

JULY/AUGUST 199229

30 GEA.R TECHNOLOGY

but not as often a aluminum oxide wheel ,andare generally cheaper or about the same cost asa plated wheel.

The coordinates de cribing the profile that iII ed to control the dressing device are alsogenerated by oftware. wo basic approacheare evident. Onei .a more fundamental approachbased on solid geometry, where thegrindingwheel and work piece are considered as twocylinders intersecting each other at a presentdistance and angle between the two axes. Theshape of the inter ecting surface on one of thecylinders, that i . the workpiece, is defined bythe specified profile. Consequently the hape ofthe wheel surface can be computed. The profilemay be an involute with modifications or anoninvolute if required. The other ba ic ap-proach is heuristic or data- based in which profilecoordinates corresponding to different pressureangles, module (diarnetral pitch), base-circlediameters, and heli.x angles at P. D. are stored.Interpolated values of coordi nates for other pro-file can then be obtained. This approach is morelimited in scope and may need a few trials toarrive at the right profile.

The ability of form grinding to producenoninvolute forms cannot be overstressed. Gen-erating grinding is limited ill this area as the gearprofile is due to the rolling action of the workagainstthe wheel. Form grinding is. on the otherhand, limited only by the Iype of forms that canbe generated on the wheel.

Since the accuracy of profile obtained inform grinding is directly impacted .by wheelwear, any technique that could reduce wheelwear is obviou 1)'of benefitto the economic ofthe operation. Platedcubic boron nitride wheels,where wear of the wheel i almo t nonexistent.represent one approach. providing it can becost-justified. Creep-feed grinding. with its ac-compallying reductions in wheel wear, is an-other. In orderto accommodal.e the creep-feedgrinding process, current machines have beendesigned and built with high spindle power andhigh static, tiffness to utilize the power. lowtable speeds, and large coolant flows. All the efeatures have enabled the app.lication of ad-vanced proce ses to the technique of form geargrinding,

Cycle Tim.c E timatesThese are e seutial in job hop for quoring

purposes before a job of grinding a gear can be

started. Keeping in mind the variety of geargrinding techniques available and the variety, ofgrinding processes that could be utilized, devel-opment of. pecific formulae to suit each proceand technique was considered futile. Instead. amore general approach is now pre. ented: anapproach that can be modified to suit each tech-nique or process a nece sary.

The total time required to grind a gear isgiven by the expression:

Total time .. grind cycle time + work han-dling lime +etup Lime per gear.

Since the work handling time and. etup timeper gear are functions of sophistication and typeof work-handling equipment and machine tooland the skill ofthe operator, furtherdi cussion isrestrained to' the grind cycle time only.

The grind cycle time is given by the general-ized expression:Grind cycle lime .. grind lime ....index time +w.heel dre time ....re et time.

Further, grind time i .given by the expres-sion:Grind time = gear face width ....overtravel x

work traverse velocity

number of traverses x number of gear teeth.

Oear face width and number of leeth can beobtained from a part print; the amount. ofovertravel is a value nece ary to dear the partfor the purposes of indexing; and the work. tra-ver e velocity is a parameter that is dependenton a variety of factors. including the process andthe type of machine tool being utilized. Thenumber of traverses required for grinding isgiven by the formula

umber of traverse

semifinish stock + finish stock +emifinish infeed finish weed

number of park-out traverse .

All these aforementioned parameters are part-and pr . ess-dependent variables. The numberof spark-out traverse i al 0 dependent on tileincoming quality of the gear. the requiredoutgoing quality, and the stiffness of the ma-chine tool being utilized. If the work traver evelocity Jn the expression for grincl timechanges during the rough. semifrnish, finish,and spark-out, different grind times have to be

calculated for each pan. of theprocess andsummed to get the total gnnd time ..

The index time, which does not exist in thecase of generating grinding with a threadedwheel, is given by the expression:

The index time::: time per index x number ofgear teeth x number of index. traverses.

The time per index, usually a few second ,:isdependent on the type of machine tool and thenumber of teeth and isa pan-dependent param-eter. The number of index traverses is based onthe processe and can be computed from theexpression:

Number of index traverses :::

number of rough traverses +number of traverses/index

number of semifinish traverses + ...number of traverses/index

This combination is due to the possibilityof a number of traverse with grinding infeedon the arne tooth before indexing, a tech-nique that i u ed occasionally while rough-ing on a form grinder or generating grinderusing saucer-shaped or conical grindingwheels. If the grinding process being usedrequires indexing after every traverse, thenthe number of index traverses is the same asthe number of traverses.

Tile dress time igiven by the expression:DIe time = time per dress +number of dresses per gear.

In some types of generating grinding a num-ber of gears may be finished between dressesand so a fractional value will have to be used forthe parameter "number of dresses per gear."Also, the time per dress during roughing maybe different from the time per dress duringsemifinishing, fini bing, or spark-out, in whichca e the formula may have to be expanded toaccount for all these variables. Since a certainamount of time is usually required to bring thedressing mechanism into action at the start ofeach dressing cycle. this time should be addedfor a more accurate e timate of dress time.

The gear being ground, in almostall in-stances .. i held between two elements on themachine during the grinding process, for ex-ample, a headstock and a tailstock for an ex-ternal gear. Of the two, one is general thestiffer member, and consequently, it is prefer-able to grind against this member in what is

generally characterized as unidirection grind-ing. (This is not to ay that bidirectional grind-ing cannot be done. though this is restricted toroughing passes only.) The reset time is the idletime lost to reset the machine to do unidirec-tional grinding and given by the formula:

Reset time e face wIdth + overtrave] x- - wheel return speed

number of traverses x

number of gear teeth.

The wheel return speed is generally therapid traverse rate on the machine, thoughdepending on tile amount of travel, the tableof the machine may never reach that speed. Alower rate should generally be used to accountfor acceleration and deceleration. If a combi-nation of bidirectional and unidirectionalgrinding is used, the formulae have to bemodified to suit the requirements.

As stated earlier, only the general approachto estimation of cycle 'time is presented here.These have to be modified to suit the grind-ing technique and precess selected, Aboveall, process parameters, such as feed ratesand infeeds, have to be valid because thequality of the cycle time estimate is vitallydependent on them. I.References1. Boothroyd, G. Fundamentals of Metal Ma-chining and Machine Tools, McGraw-Hili. NewYork, 1975.2, Dodd, H. and Kumar, D,V. "Technological Fun-

damentals of CBN Bevel Gear Finish Grinding,"Gear Technology, Vol. 2, No.6, November-De-cember, 1985.

3. Dudley, D. W. Gear Handbook, Isted .., McGraw-Hill. New York, 1962.

4. Schwartz, R. W. and Rao, S. B, "A Wheel Selec-lion Technique for Form Gear Grinding," AGMAPaper No. 85FTM7, .1985.

5. Technology of Machine Tools, VoL 3 MachineTool Mechanics, UCRL-52960-3 LLL, Livermore,California, 1980.6. Tlusty, J. and Koenig, berger, F. "Specificationsand Tests ofMetal-Culting Machine Tools," UMIST,Manchester, England, 1970.

Acknowledgement: From Dudley's Geclr Hfllld-

~ 2nd. ed., Dennis P. Townsend, ed.. ©J991 byMcGraw-Hill. Reprinted by permission of McGraw-Hill Publishing Co,

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