32 G EIlR T ECHIo!OLOG 'f

AGMA quality level has a lot more to do withmeeting the rating requirements of the gearsthan it does with aspects of function such asnoise and tran mi sian error.

2. Diagnostic purposes. These inspectionsare done for the purposes of solving machin-ing problems and controlling noise and trans-mission error. Many time these will requiresome nontradnional methods of evaluation,

In this article, more time win be spent o.nthe nontraditional diagnostic techniques thanon the traditional A'GMA level characteristics.AGMA 2000-A88 has much more detail andbetter definitions for the inspection of gearsthan AGMA 390.03. Anyone involved in gearspecification and inspectlen should have acopy of AGMA 2000-ASS and become veryfamiliar with the measuring methods andinterpretations described within.

Good Dahl. on PurposeIt is very easy to get bad data and not bow

it. In order to have confidence in the data tbatone takes, it is imperative to develop goodtechniques. This section win deal wi.th someof the problemsthat may be encountered withvarious measuring methods.

Runout Control. Runout anywhere in themanufacturing or inspection process is one ofthe most damaging factors affecting gear qual-ity, h win have an impact on anything elsethat one want to do or measure. Factorsaffecting runout include:

Blank Quality ..Quality blanks are the foun-dation upon which a good gear is built. n doesno good to expect gear characreristies such aslead, profile and spacing to come out within afew ten-thou andths of an inch when oneallows the bore tolerance to vary one or several

Quality GearInspection Part I

IRobert IE. SmiithR. E. Smith & Co.• Ilinc.

Rochest'er. NIY

IntroductionQuality gear inspection means doing the

"right" in pections "right." A lot of time andmoney can be spent doing the wrong type . ofinspection related to function and doing themincorrectly. As, we will eli cover later, suchthings as runout can creep into the manufac-turing and inspection process and completelyruin any piece of data that is taken ..This is oneof the most important problem 10 control forquality inspection.

There are two main reasons for performingany gear Inspection;

I..Meeting print specificetions ..The specifi-cation. uch as AGMA 390.03 or 2000-A88criteria, ma.y be included on the print, Theyalso may be spelled OUI independently forsuch things as profile, leadvpitchvetc, ThegoaJ of such an inspection is making the partsmeet the expectations of the user. Meeting an

thousandths of an inch. Certainly, it is easierfor an operator to control the size of a simplecircle than it is to control that of many gearteeth with. a complex form such as an involute.Even a perfect machine can't make a goodgear out of a bad blank, Even if it did, the gearwouldn't work in the application, nor wouldthe inspection come out right unless themounting were duplicated.

Tooling Quality. Good tooling in machin-ing and inspection is a necessity for the manu-facture and inspection of quality gears. If agear is put on a solid arbor, there must besome clearance between the bore and arbor, Ifthere is clearance, there will be some eccen-tricity, which will result in runout; therefore, itis best to use some kind of expanding arbor ..This can fill up the clearance and! center theblank on the axis of rotation. Some types ofexpanding arbors are shown in Figs. 1 and 2.They can consist of expanding collets,hydraulic expsnsiontypes, interference ballsleeves or precision expanding jaw arbors thatcan control runout [0 .000[ or .10002....

Proofspots. Proofs pots are reference bands(axial and radial) that are machined true withthe actual bore. journals and shoulders of gearblanks (see Fig. 3). These can be checkedwhile mounted on the machine that finishesthe teeth, while mounted on the inspectionmachine or while mounted in the final applica-tion. For even more accurate work, theprcofspots are checked and marked for theamount and location of the high point ofrunout, This high point and amount are dupli-cated at every step in the process to control thevery highest quality gears.

Centers in shafts and their relation to teeth,and Journals. Unfortunately, most inspectionmachines for cylindrical. gears use centers forthe mounting of gears. This is most conve-nient, but not very accurate. "Murphy's Law"says that even though the journals and teeth aremachined from centers, they will never runtrue again. 'Gears are rarely run on centers intheirapplications, They are mounted from thejournals, and the teeth should be inspectedfrom the journals. At the very least, the journalshould be checked on the inspection machinebefore the teeth. Some new CNC machineswill check teeth relative to tile journals, eventhough they may mount the pan. from centers.

Balls are held in steelcage. Sleeve assembliescan be made with ballsthat are +.001", t.002" etc,to adapt same arbor todifferent bore sizes.

Diameter across balls is .0006" to.0012"largerthan gear bore.--~.....

Fig. 2 - Ball sleeve arbnr, -

Axial (proofspot)!Reference Surface

Fig.3 - Proofspots (reference surfaces],

Remember, if runout exists in the inspectionoperation, it will influence anything else mea-sured about the gear, such as profile, lead andpitch variation.

Spacirlg. The term spacing is used as a gen-eral term to refer to the accuracy with whichteeth are positioned around a gear. Spacing hasno numerical value and refers only toa groupof numerically valued tooth position mea ure-meats such as pitch or index. Many of theterms used to describe spacing are very confus-ing a.nd often misused. For that reason it isimportant to be careful about what someone isde cribing. Symbols a.re very usefulin order tokeep terms straight. Spacing issues to beaddressed in inspection include:

Tooth-to-tooth spacing. This is probablyone of the most misunderstood terms. It wasused in older versions of AGMA 390 and wasan unfortunate choice of words, Many people

iRoben E. Smithis the principal ill thegear consulting firm a/R. E.. Smith & Co., Inc.He is also olle o/GearTechnology's technicaleditors. He is active instandards developmentfor AGMA and is liteauthor of IlIImerous

hooks and papers ongearillg subjects.

SEPTEMBERIOCTOBER !9~4 33,

Dil. BetweenAllj. Pitches

Spac!l1~VanallDlI

A 0 ORal,B +2 +2 +2

C +2 +2

D .4 }s .2 +4}·2 .e -2 6

f 0 4, _2 0

G -2 ·2 -2

A 0 +2

Total IndexVanation

Influence of Flank Form Irregularities all the Single Pitch Readings

\1io. I rut 0' V11I8110" I, ,

II'r, Ii'$.', I

- 8~ Bi I I. . ~ L!.~ '[71 -, 1.5 .~,~t-,~ ~4 " .11:\ F>- .J --tJ!VI. J ~ ~ L.., , cD :~/,ICI f' I

Fli"-1 I

I AI I I I'''I I ,

t$'Wh<II. I I

Cucumfarence I , , <,

oIIMG .. r ,iii ~ , . ' Ind.)! Vaoatlon Pklt ir-' IC s

, ' ~t= -j II-f: I

~I-- ~ r--,' , ." !-- I--1.-"- A :5 - ""~ I

", . r-I

I. - : ,~

cI -s» => .~ -,'I---- B ~ , i ....... L.I,""

" I

!Fig, 5 - Determination of cumulative pilch variation curves (index variationlon the basis of single or span pitch measurements,

34 GEAR TECHNOLOGY

(probably most) visualize it as the errorbetween one tooth and the next (involves twoteeth), Inreality, i.t isnot, It j the differencebetween one pitch and the adjacent pitch(involves three teeth). A better choice of wordswould have been adjacent pitch difference.AGMA 2000-A8S no longer uses the termtooth-ro-tooth pacing. [I is now defined asspacing variation, v, The iso symbol is fUibut an earlier proposal, 111;). was more descrip-

tive, This parameter has no useful purpose andis not toleranced in AGMA or ISO standards.

Pitch Yariation. Pitch variation i the alge-braic plus or minus (±) difference in the tran -verse plane between the true position pitch andan actual pitch mea uremenl. Thi is the cor-rect measure of the placement of a tooth rela-tive to its adjacent tooth. This factor is mostimportant for evaluating the po itional aecura-cy of a gear andthe resulting influence ontooth stresses. The AGMA ymbol is Vp andthe [SO symbol is fp. This is the measure ofspacing that is toleraneed in the AGMA andmso tandards.

Index Yariatio». Index variation is the dis-placement of ~my tooth from its theoreticalposition relative to a datum tooth. This istheactual local ion of any ~ooth around a gear. h is110t toleraneed, but other values relative to'pacing, such as pitch variation and accumulat-ed pitch variation, can be easily interpretedfrom this data.

I',..ob,lems Witll Spacing Measurement.Spacing is usually measured by one of rwo sys-tems-the two-probe system and the single-probelindex system. The two-probe system imore likely to produce bad data than the sin-gle-probe/index system because of the influ-ence of surface finish (irregularhies) all theaccuracy of data, The influence is greater oncalculation of accumulated pitch variation thanit is on pilCh variation. Fig. 4 is an illustrationfrom Section '9 of AGMA 2000-A88_ It showsthe correlation bel ween a single-probe/indexmeasurement and a two-probe measurement ofthe same gear. In this ca e, the gear is a theo-retical one and bas perfect finish. As one canee, in columns A, G, B and F. the results are

the same for either measuring method.However .. in reality, the results will never be!he same, andthe worse the fini 11,the worsethe correlation.

More realistic results are evident. in the datashown in Fig . .5. This is from Appendix E ofAGMA 2000-A88. The upper pan of the figureshows what happens beca:u e of surface irregu-larities to the span distance between twoprobes placed at slightly different locations onthe 'teeth. The bottom part of the figure showsthe numerical results of measuring a gear threetimes withthe probes located in different posi-tions. Because of surface irregularities. there

will bea greater scatter in the results from thetwo-probe method. The difference is caused by

the accumulation of surface measuring errorsas well as pitch errors in the calculationprocess of the two-probe system. This calcula-tion is not necessary in the single-probe sys-tem. The reading for each tooth is direct. andsurface errors affect only that one reading.

Measuring 'the gear several limes with theprobe in a slightly different position and thenaveraging the results wi.ll give a more accurateanswer for the true pitch and accumulated pitchvalues ..This would be true for either system.

Another advantage of the single-probe datais that it give a direct visual picture of theplacement of each tooth around II gear. Pitchvariation is the distance between any two adja-cent reading , andaccumulated pitch variationis the total distance between the highest andlowest reading. When using the two-probe sys-tem, it is necessary to calculate the averagemeasured pitch, subtract this from each readingto obtain pitch variation valoes, and then accu-mulate the pitch variation readings to obtainthe accumulated pitch.

Problems With Size Measurement. Thespecified size of gear teeth, thelr circular 100lhthickness, is not measured directly. It is usuallymeasured by one of four other means: verniertooth calipers (chordal tooth thickness), overpins or wires, span measurement (base tooththickness) or by double-flank composite meth-ods, which measure functional tooth thickne s(see Fig. 6).

The first three of these methodsalso havethe limitation that the measuring device onl.ytouches a few points on one or a few teeth.Therefore, they may not findl the largest toothsize around the gear. They also measure thetooth size independent of the rotational axis ofthe gear. Even if the tooth size is correct,runout win vary the functional tooth thickness.Some teeth will be functionally larger than oth-ers if they are at the high point of runout, It isnecessary to make allowances for other varia-tions in tooth shape and position (involute,lead, runout, etc ..) in relation to gear qualitylevel. (see Fig. 7). If this is not done, the gearmay run out. of backlash with its mate.

The double-flank composite method willfind the largest functional tooth thickness any-where around the gear" His probably the best

iI

/\ /\i

Span M'easurement

Tooth 'Thickness M'easurement,Gear Toolh Caliper M'elholl

Tooth ThicknessInspection,

IMecasuremenl.Over Pins Compos1te Action Test M"easufBm.ent

of Tooth Ihic'kness

Fig. 6 - Method 01size measurement.

Maximum Effective:Tooth Thickness, linn _

MaximumMaterial ,

COl1dition••.•, ..J(Mating 'Gear) C·c _ -(

I 1 \ ~I, \ Greatest Backlash For· I:\, Tightest Centers*

\ "\ \ M" "\\ irumum\. \ Backlash, Bmin\ \

\ \ -"\ \ • ...,..' c I I-l.: ......-MInimum I I

" " Matenal ........l ", c' Cd" 7 I, .. on c IlIOn I,.

\ " '/c,v >, I,,-)...,LJ-

... Specified MaximumTooth Thickness

Maximum.MaterialCondition

(Subject Gearl

Minimum IEffectiveTooth Thickness _

MinimumMaterial!Condition

Specified MinimumTooth Thickness, tmin

Specification iBand,Elemental Measurement

Specification 'Band,CompositeAction 1,est

"Tlnis figure isdrawn atthe position of tightest center distance;if center distance is increased, backlash will increase,

Fi!l_ 7 - looth thickness. transverse plane.

SEPTEMBER/OCTOBER 1994 35

:Index ('itch and Accumulated IPitch)M'ellsuramants

I

Iinvolute Measurements

Probe iPosition ingfor Tooth,Alignmant I(nspection

Tooth Thickness Inspection,Mellsurement lOver Pins

Runout ICheck" Over P,in,Ball Pr,ebe

IFig. 8 - Elemental measurements.

Schematic of :Composite Action Test Device

..... __ 1 RevolutiOil (360°) of Work Gear ---.....,. . '.. [" '. ,..')= :-~--~--------- ------/_____ 14

~~ :::::~:;~;;~;;~::~~~::::::~ Tolal .-~ "\.- 't-= Compo'ite- M.!--- nt'''''''-.:..._--= ...''''.......-. ~·VanaIIO". Vcq -.. -- -" Toot~~¥~Olh i

"""l\..o,. Composite·,. :r .,'Vari.tion. Vq 1.3!i!1·IN --1: I--~"--':""'----I,

.' .'• • o • • •Total Composite Variation Trace

36 GEAR TECHNOLOGY

method for finding the size of gear teeth. Referto AGMA Standard 2002, Tooth ThicknessSpecification and Measurement, for a moredetailed treatment. of this subject.

Elemental vs. Composite Measuremellt.There are two general methods in use for themeasurement of gear quality. These are the ele-mental and composite methods. Further, thereare two different composite methods-double-flank and single-flank.

Elemental Methods. Elemental measure-ment involves the measurement of discreteaspects of gear quality-such as involute, toothalignment (lead), pitch variation, runout, accu-mulated pitch variation and tooth size-byusing a small probe to explore the individualcharacteristic (see Fig. 8). It is very useful formedium-size gears, but difficult to use for veryfine pitch or very large diameter gears. TheAGMA standard limits elemental tolerances topitches coarser than 20 DP ..However, it is pos-sible to make elemental measurements as rilleas about 100 DP with some equipment Theupper limit for diameter is generally about 40".This limit is imposed bya lack of availableinspection machines, although there are a fewthat can go larger.

These methods are generally useful fordiagnostic purposes as wen as for qualitydetermination.

Double-Flank Composite Methods.Double-flank measurements are made byrolling the test gear in tight mesh with a mastergear while detecting center distance variation(see Fig. 9). The quality determination for thesame gear may come out different if it is mea-sured by elemental methods .. For this reason,both methods should not be used for the samepart. The maker and user should agree on themethod to be used.

Advantages. Thismethod provides a fastcheckthat uses inexpensive equipment. It isgood for the determination of runout prior toany subsequent finishing of the gear teeth, andit is excellent for the determination of func-tionaltooth thickness.

Disadvantages, It measures a composite ofall characteristics and is not as useful. for diag-nostics. It can tell when teeth are conjugate(very low tooth-to-tooth composite), but it isnot very good at teUing how non-conjugate theteeth are. It measures both sides of the teeth at

~I

the same time and can produce some strangetooth-to-tooth results. It is also possible to havesome very bad involute shapes but 110t havethis method produce large tooth-to-tooth varia-tions.

It also measures the characteristics of gearqua.lity in a radial direction (center distancevariation). Gears don't operatethis way. Theyoperate in a tangential direction,

When gears are made by certain finishingoperations, such as shaving and abrasive hob-bing. it is possible to have .8 double-Hank mea-urement show very little runout (maybe a few

[en thousandths of an inch) when in reality it hasseveral thousandth ..of an inch accumulated pitchvariation. Remember that gears function tangen-tially. Runout is a radial measure, while accumu-lated pitch is a.tangential measure (see Fig. 10).

Single-Flank Composite Methods, Single-flank measurements are made by rolling two,te t gears or a test gear and a master geartogether at 'their proper mounting distance andwith backlash. Transducers measure the angularmosion and record any characterlstics ofnonuniform motion (see Fig, 1]). This isa truetangential measurement and is indicative of thefunctional characteristics of the gear. Thisnonuniform motion is called tran mission error,

Ad:I'antuges. Single-flank measurement is atruly functional, tangential measure .. WI is good.for diagnostic purposes. U is especially usefulfor the measure ofpro.file shape and conjugacyas weU as for accumulated pitch variation,

Disadvantages ..ft. is not good for measuringtooth alignment (lead) and size. It. is a slowerlest than the double-flank method. II. usesequipment that is more expensive and notasreadily available.

Wbi.ch Inspeetions &.0 Pedorm?Obviously • if a print call for certain i.nspec-

tions, these must be done. However, one alsoshould think of what are the most importantcharacteristics desired oftae gears. Quietness?Positlonal accuracy? Strength and durability?'Size? Somecombination of these? The greate t

mea urementeffortand best techniques shouldbe applied to the most. important parameters.For examplecif positional accuracy is most.important, a lot of time hoold not be spentmeasuring runout. It can be very misleading.See Fig. ]2 for a chart of recommended mea-suri_ng methods. Standards now in process with

Double-Flank Test

*.001'

lMicrodex Precision Index

Single-Flank Test

fig. 10 - !lunout vs, accumulated pitch.

Variation

,.- ---

TotalTr8!l5!!li.ssion

_"I- ITootlllo

Tooth ---- Tr.ans!!Ijssion ---

,"----------- Variation --------'"

fig. 11 - Single·flank cempnsite acuon measurement.

Important Quality CriteriaMeasurement Method

Onter 'of Preference 1, 2, 3 AccuracyStrength or

Surface Durability Tooth SizeNoise

El£MENTAt,ProfileLead'Pite h VariationAce. Pitch Var.lIlunout

2

3

2

112

11Z

SIZEfunct Tooth Thick.SpanOver Pins or WireVernier Tooth 'M lc,

1223

DOUBLE·fLANK COMPoTOGIMo·ToothTotal CompoFunct Tooth Thick.

3 33

SINGLE·FIANK COMPoTooth-te-ToothTotal Compo

M1CROF1NISHRoughness-Stylus

WAVINESSContact PatternSingls, Rank

- - -

Fig. !2 - !Qualitv criteria lIS. measuring method. I

SEP'TEMBEA/OCTOBE.A '99~· ,31

Finish

2I

Profile Tolera nc e

the ISO accwacy eomminee include one thatde(IDes "famdles" ,of inspeclionlOle:mnces dI31.apply lO various applications. One should putthe most effort on the proper group of toler-ances as it applies te the application. In otherwords, spend yOOJ'measurement money wise~y.

Q.uestioll .,he Specifications. It is wise ~orthe gear maker to spend some time with thegear user to arrive allthe most important speci~fications and measuring methods. The impor-tance of agreemem OD 'these points can beshown byexample;h is not unusual for some-one to specify an AGMA Q8 quality level butwant to holdlOOth thickness toa tolerance of..001". 'The pmb~em is that theamoDnt of.runout allowed. by level Q8. may not be com-patible w~th the specified. tooth thickness lOler-ance, It may be necessary to make a Q10 orhigher gear in 'order to hold the lOOm thicknessv.anation widlin the specified tolerance, Tbjscosts more money ..

Q.uesliolJ .'he SlIJlldard's. Many times theprint will only eall foran AGMA Q number.These quali~y levels have been established pri-marily for gear rating evaluation. Dejpeoding011 theapplicatioo, this specification will notnecessarily guarantee satisfactory jperfonnance.For example: ira posiitional accuracy is theprime concern, Ithis infonnation. alone will notbe enough, The AGMA Q number ,only speci-fies CilIUIoul and pitch variation. Accumulatedpitch and pitch variationare better measures.Also, p.rofUe and lead arecontralled by Kcharts. These K charts givea very broad con~1101 of profile and lead. They have 00 be blUMto allow (or the effects of ruaout onllle variousteeth around a gear. See Fig. J3, fOr a descrip-tion of a K chan.

Fig. 14 shows involute 'charts ef a mastergear with and without. ronoUL This same thingcan happen wim toolh, alignment .or lead charts.In other words, involute isn't being evaluatedseparately. The K chans are evaluating a com-bination of in.volute and. nmout, .•

Start of Tip Round

High Point of Tooth Chart Must BeTangent to Reference Line.

Tolerance· Zone

EdItor"s, Nom: The second part of this artick, CO\'-

er.ing diagnostics, .~QSlUing equipment and' .inspec-tion prtJelices among V,s. competitors. will appearintire next issue.

Acknowl dgement: clMGMA. Pre.seflled ,a/ 21 al.Annual Gear .M/lII~facllUjflg Symposium .•Oct .. 10'-12,. J994. Repril1led with permissiOll.

ContrOilliameter

10R'eference line

fi,g. 13 - AGMA K chart.

Involute Results - Wim IRurlom

LEFT FLANK4 3 2

RIGHT FLANK234

~~- [~i~- _t--==!_ ! - -1- I 'f~ 1-:---

~ ~~t !"'!t.oOozc I, I I \ ! -

1--=.EF---IT! I i I I --: 1-'-:-'-

j

E: re- i II \! ! - ! I -Ii ,E -

I ~ 1 I .. " i~- , I f !~ f 0 _:-j:.:i - f\ l.. i t:= _(I 1 1 __ - t.:..:..c-I-

~ 1= q ;~-_-:j:.c'- i n t i lB=f1t= ~ L~;:-cJ: - l=i .;..! j f-R=P.:j ;::f J~

~.:;: -==:::- !:c:::=--,=-f- -~- t ~ ~~- I ! -F---:::=G.r I -t g- ~la-=/=.1- 1 -~. -=

l-""lr~¥.}>4 "IT .'\~""".:<0- 81\1+;.I ....~I:., " SCALE I_f-= ..~ ~: ~~,:!':~'~~~I1:' , rowtr.:TI flJ+f' M"'" _. -- _.1

Ir.~ :0,,1.1.:.1. '".' __ '''s ••

IInvolu:te Results - Wimout R'unout

Fig. 14 -Involule results 01 master gear with end without runout,