RecentDevelopmentsGear Metrology

IH..W. SiekerA..C.M. Ilaboratory Pty. Ltd..

Moorabbin, Vi,ctoria. Australia

Summary: Metrology is a vital component ofgear manufacturing, Recent changes in this area,due in large part to tile advent of computers, arehighlighted in this article by comparison withmore traditional methods.

IntroductionVarious deviation from the true form of circu-

largears limit their ability to transmit uniformangular velocity at their designed speed andpower. These deviations or errors are introduc-ed during the production of the gear elements.The ability to measure these variations enabletheir magnitude to be determined and controlledduring manufacture.

The various possible errors occurring in cir-cular gearing are:

• Tooth Thickness (Backlash)

• Run-out Errors• Pi tch Errors.•Tooth Form Errors

- profile- alignment- surface finish ..

The types of circular gears in cornmon usewhich can exhibit some or all of the above errorsare involute spur and helical gears and bevelgears, both straight helical and spiral bevel.

This article will concentrate on involute gear-ing; however, some comments on bevel gearswill be made.

The ability (0 measure the errors present in thevarious cutting tool ,such as hobs, shaping cutters,and shaving cutters, as well as the gears them-selves, is also useful.

H.W.Siekeiris rite manager (1/ A.c.M.Laboratory PI),. u«Moorabbill. Australia.He is a member Df theEngineering Society andthe institution ofEngineers. Australia,

NOV E t,4 e E R JOE C E 'II.! B E R I 9 9 I 21

Traditional/Cia steal InstrumentsIn order to highlight the advantages of the

latest developments in gear metrology. a briefsummary of the traditional/classical instrumentsused to measure the various gear errors will bepresented first. The reader is referred to thevarious texts and papers listed in the bibliogra-phy for more detailed information,

Tooth Thickness. Three ma:in methods havebeen prevalent in the measurement of tooththickness of involute gears.

The first method involves the use of aninstrument called a gear tooth caliper (Fig. 1).Itconsists of a depth gauge, which is used to ser aknown distance down from tile outside diameterofthe gear, and a caliper to measure the tooth

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thickness at this depth, Calipers are available formodules 1 mm to 50 rnrn,

This tool has the following disadvantages:a) It relies on an easily worn, very sharp edge

at the end of the caliper jaws to accuratelymeasure thetooth thickness,

b) It relies on the outside diameter of the gearfor its datum,

c) It relies on operator skill.d) It is limited to about ,001 "- ,OOQ"accuracy.This method's advantage is that it is inex-

pensive.TJlJesecond method uses the flange microme-

ter and is called the base tangent method. Thisinsnument takes span measurements across anumber of teeth (Fig. 2), which are then relatedto the actual tooth thickness by the involutegeometry ofthe gear, Micrometers can measuremodules from 0.5 mm to ] I mm,

The main disadvantages of this method are:a) Pitch errors can influence the result,b) Profile errors can influence the result.c) Tip or root relief may make a valid mea-

surement impossible.d) It relies on operator kill.The main advantages are:a) his more accurate than the gear tooth

caliper.b) h is not influenced by variations in the

outside diameter of the gear.The third method involves "measurement over

rollers", where two rollers are placed on oppo-site sides of the gear., and the distance acrossthese rollers is measured (Fig. 3). This value canbe related to tooth thickness by the known geom-etry of involute gearing,

This method ha the following disadvantages:a) It is limited to gears smallenough to bespanned by available micrometers and the avail-

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abJe sizes of rollers.b) The measurements are affected by errors

in tooth spacing and profile.The method's advantage is that it .is not in-

fluenced by variation in the outside diameter ofthe gear,

All of the above methods are manual andrequire skill and dexterity. As such, they are notsuitable for the measurement of all the teeth ongears with large numbers of teeth or on gearsmade in large quantities. The methods are mostsuitable for spot checks in small batch produc-tion situations.

Other methods available are:I) Measurement of center distance at tight

mesh. (See section on Dual Hank Rolling.)2) Measurement of backlash at operating

center distance. This method requires the abilityto accurately a emble the gears at their nominalcenter distance with axes parallel.

Run-Out Errors. Radial run-out errors aredefined as "the total range of reading of a fixedindicator. with the contact point applied to asurface rotated without axial movement. about afixed axis, and measured perpendicular to theaxis of rotation." The eccentricity is then alsoavailable, as it is half this radial. run-out

This type of error traditionally ha been mea-sured by inserting a ball (or cylinder) into eachtooth space, and measuring the radial variationin distance from the center of rotation to the ball(See Fig. 4.,.

Radial run-out measurements made in thisway also reflect variations ill tooth thickness.When radial run-out readings are plotted, theinfluence of each factor can be seen. Run-outerrors are seen as a smooth, sinusoidal variation,while tooth thickness variations are seen as

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fluctuations about a smooth curve drawn throughall reading.

There are also automatic teo ters available whichmeasure thi error on a eominuou ly rotatinggear and plot the resulting error graph. The ete ten are available for module ranges of 1 mmto 40 mm and .0.1 mm to 20 mm respectively.

The double-flank rolUng te l cam ill 0 be u ed,ince in this test the run-out error is evident as ainu aida] shaped variation with a period equal

to on revolution of the gear. (See section onDual Flank Rcllmg Test.)

Pi,tch Errors. The threetypes of pitch errorson spurand helical gears are pitch variation(devialion) Ip; tooth-to-tooth pitch error Iu;and cumulative pitch error. Fp.

Toe cla sic method of mea uring the cumula-tive pitch error is the index method, in which thegear is mounted on all angular dividing head(Fig. 5). The gear is then rotated through thenominal angular pitch, and deviations of eachtooth relative to the first are noted and plotted.

The next more common pitch error measuredis the teeth-to-tooth pitch error ..Thi. error is thechange in pitch between uccessivepair ofteeth. A such. any instrument which can mea-ure the change in pitch from one pair ofteeth to

the nexI can measure this error. A hand-heldinstrument that can do 'this i the Maag pitchmeasuring instrument type TIC. These instru-ments were available for normal modules rangesof approximately 2 mm to 10 mm. However.being hand-held and operated, this becomes avery tedious test on gear with more than alimited number of teeth. Auromati.c ver ions ofthis tester have been available for at lea I 20'year, and these testers mea ure the tooth-to-tooth pitch error on continuou I.y rotating gears

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by inserting two probes to measure the rcotb-ro-tooth pitch error for that pair, and then retractingthe probes until the next pair comes into position.

Pitch variation errors require measurement ofthe absolute pitch between two teeth and com-parison with the nominal pitch. The Maag pitchmeasuring instrument mentioned above is ca-pable of doing this test as well as the teeth-to-tooth te t. It must. however, be set to the nominalpitch using gauge blocks 'Ora setting master.

AU of the above errnrs can be related math-ematically (Ref. 8). This fact, coupled withrecent advances in computer technology, hasallowed the automatic pitch tester describedhere to measure the tooth-to-tooth pitch error.calculate the other two pitcb errors, and plat allthree for a complete picture of the pitch errors ofthe gear under test (See Fig ..6).

The tester must understand Ihat pitch errorsand run-out errors are inseparable when present.If run-out errors are either introduced or re-moved during 'lh.etest, the pitch error measuredwill not give a true representation of the gear'sactual performance in its final location. As thehand-held pitch measuring instruments do notrefer their measurements to all axi of rotation,the resulting pitch errors are not affected bymeasurement-process-induced run-out errors.However. run-out errors present during manu-facture will be evident as pitcherrors On thegear. Pitch testers, in which the test piece ismounted and rotated about an axis, will beaffected by run-out errors, introduced or re-moved ill setting up the test

Profile Errors. Actual measurement, as dis-tinct from contact bearing patterns of profileerror, has until recently been limited to involutegears. Bevel gears, especially of spiral form,have not been measurable from firs t principles.

Becau e of the deflnition of the involute, pro-file checking machines have been available formany years. The early resters relied on the lise ofba e circle discs for each gear to be checked(Fig. 7). Later machines overcame thi limitationby the use of various mechanism to eitherbridgethe gap between a limited .nurnber of base circledi c or toeliminate them completely (Fig. 8).The e testers all generate the true involute on II!

probe which is in contact with the gear toothunder te 1. Deviations in involute profile are de-tected by the probe and recorded for later analysis.

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Advance in compurertechnology have en-abled the recording of the involute error indigital form. This in turnallows computerenaly-sis. which eliminates the weake t Hnk in themea uremenr process: the human interpreta-tion of the error curve. The use of mathemati-cally rigorou techniques for thi analysis cangive an unbiased and consistent interpretationof the re ults ..

The accuracy ofthese machines can be deter-mined by well-understood tests 011 their geom-etry and construction. Becan e the software doe.no.t control the accuracy of generation of theinvolute on me probe tip, it ionly neces -ary to.te t the software against known rna ter to ver.ifyits accuracy.

Alignment Errors ..Alignment errol'S are oftenreferred to as lead and/or helix errors. Theseerrors have also been measured for many yearson involute tester. modified with the nece saryrnechani m to generate the nominal lead rno-lion on the probe. The probe then detects aria-tion mIlle same way a for the involute error .Error analy is ha been enhanced by the use ofcomputer technology in exactly the same way afor involute errors.

Surface Finish. This feature has been mea-sured by the lise of surface finish te ters, In somecases, the e te ter have been fitted to invo.hJle/lead re ling machines to allow easier re ring ofgear tooth surface fini h.

Meshing Tests. Me hingtests are functio.naltests to determine the actual performance of a

gear or gear pair. These test fall into the ectionon dual and ingle flank rolling tests.

Dual Flank Rolling Te r. hllhis re t, the gearare brought into tight. mesh so that both flanksate in contact. (Fig. 9) One gear. usually a mastergear, L mounted ana fixed haft The other gearis mounted all a shaft. constrainedto move inaradial direction. As the gears are rotated. thevariations in center distance are mea tired andoften recorded.

This dual. flank rolling en-or or cornpe ite errorL then a combination of all the primary erroralready discussed above. A plot of thiserrornormally has two major component (Fig.l.O).The low frequency component is most com-manly a sociated with run-out errors. while thehi.gh frequency component is associated withpitch errors. Because a composite error is genet-ated, thi test i only useful. asa go/no go te t, IIis not good for idenlifying individual errors ..andsubsequently, rectifying a particular proce s.

·ingleHank Rollillg Tilln this test, the gearpair are positioned at their nominal center dis-tance. The relative angular mali on of the twogears are then measured. For a perfect gear pair.the motion of the output gear would be unifonnrelative to that of the input gear. Any errorswould be reflected as anon-uniformity in angu-lar motion onthe output gear.

Because the gears are mounted at their nomi-nal center distance, only one flank will be incontact. Also. one gear needs to. be driven whilethe other is braked. Thiste t, therefore, comes

NOV!E Me E RID E CElli B E R I 9 ~ I 31

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In the past, the difficulties involved in compar-ing the relative rotary motions of two rotatinggear. has meant that. this test, although theoreti-cally desirable, was physically impractical.

New Dev,elopmentsThe major changes in gear metrology have

been brought about by advances in electronic/computer technology. The availability of largeamounts of computing power in ever cheaperand smaller packages has spawned significantchanges in all fields of technology,

The basic aims and principles of gear metrol-ogy have not changed. However, the methods bywhich these can be achieved have changed dra-matically. These changes will be presented inthe remainder of this article.

CNC 3-D Measuring Machines. The last 5 to10 years have seen very rapid developments inthe versatility of the computer nurnericall y con-trolled, three-dimensional co-ordinate measur-ing machine (CNC 3-D CMM). Computers arebecoming faster, more accurate, and have largeramounts of affordable memory in the form ofvolatile, random access memory, (RAM) andpermanent (haed) discs. Therefore, the softwareon which all 3-D CMM's rely has become moreand more sophisticated,

In this light, there has emerged two groups ofCNC 3-D CMM's. The first is the genera] pur-pose machine (Fig .. 11), which is primarily de-signed for the meas urement of components thatare not necessarily circular in nature. Thesemachines are able to measure gears, but at a costin speed and efficiency of measurement. This isbecause these machines have heavy and cumber-some arrangement for moving the measuringprobes to allow for many variations in workpieceshape and orientation.

The second class of CMM's has been de-signed specifically for the measurement of sol-ids of revolution, This allows the de igner totailor the machine to measure this class ofworkpiece much more quickly and efficientlythan the universal type of CMM (Fig. 12). Ma-chines are available to caterto gear diametersfrom 5 mm up to 2.6 m, They can also be used tomeasure general type of workpieces, but due totheir specific design, this is slower and moredifficult than for the general purpose type of

CMM. Both of these testers can have 4 axes:three orthogonal and one rotational.

Therefore, a general rule can be stated: ifmostly 110n-gear type cornponen ts are to be mea-sured with only occasional inspection of gears, auniversal type of 3-D CMM i applicable, Thereverse holds true if the major amount of workfor the 3-D CMM is gear inspection. Also, due tothe small tolerances generally present in gearspecifications, only the more accurate versionsof general purpose .3-D CMM's should be con-sidered for use as gear measuring machines.

The new 3-D gear measuring machines(GMMs) are, by their very nature, computercontrolled. They also rely on CNC for control-ling the motion of the measuring probe. Thistype of control aUows each machine to measurea number of parameters on the workpiece. Thisis in contrast to the previous generation of ma-chines, which by their mechanical. nature, wereonly able to measure one or, at most, two param-eters ..Now it is possible to place a gear on one ofthese new 3-D GMM's and instruct the tester tomeasure all of the primary parameters for thatgear without further human intervention. Thisresults in major time savings for any given levelof thoroughness of gear rneas urernent, The auto-mation of the test sequences is even more usefulwhen coupled to automatic loading facilities inlarge batch evaluation.

All measurements are processed in digitalform, and this immediately allows the storage ofthese results for comparison with later batches.These statistical process. control (SPC) abilitiesare a major advance, especially for manufactur-ers of large quantities of gears.

AI 0, some of these new 3-D CMM's andGMMs can measure other forms of gearing, withthe addition of the appropriate software pack-ages. The most notable advance has been theability to measure spiral bevel gears in such away that information relation to the actual cor-rections to the production machine settings are

available. This can only lead to better bevel.gears with, one hopes, more interchangebilitythan was available in the past. The ability tomeasure the condition ofthe various gear cuttingtooL (shaping, shaving, and hobs), again via theaddition of software modules, also increases theusefulness of the GMM to the owner.

For similar expenditure, the purchaser of theN Q v E M B E RIO E C E M B E R 1 9 9 1 3·3

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The verification of the accuracy of these ma-chines requires the measurement of not only themechanical accuracy of the machines, but alsothe accuracy of the CNC software control whichactually generates the theoretical profile of thegear under test. This is in contrast to the genera-tion-type machines described in the sections onprofile and alignment errors, which generatethese profiles mechanically. On the new ma-chines, interactions between the CNCcontrolsoftware and the computer evaluation softwareneeds to be understood and thoroughly checked.

Transportable CNC LeadlInvolute Testers.Another development closely associated withthe development of the fixed CNC controlled 3-D GMM described in the previous section is thetransportable CNC lead/involute tester.

The largest fixed 3~D CNC GMM can acceptgears up to 2.6 rn in diameter. In the heavyengineering field many gears are larger than thismaximum, and the measurement of the lead and

involute profiles on these gears has previouslynot been possi ble,

The transportable gear measuring machineconsists of a 3-axis CNC gear measuring ma-chine which is designed to be fitted to the gearproduction machine tool (Fig. 13). This effec-tively allows the measurement of'any gear diam-eter capable of being produced with modules inthe range of 2 mm to 4.0 mm.

The transportable gear measuring machinecan also measure gears on alarge surface plateif necessary. The development ofthis tester hasfinally lifted the limit placed on gear metrologyby the largestavailable dedicated testers.

The comments on verification of fixed 3-DGMMs apply equally as well. 1£0 these testers.

Pitch/Run-Out Testers. As discussed in thesection on pitch errors, automatic pitch and run-out testers have been available for at least 20years. These testers were able to automaticallymeasure the pitch errors on both tooth flanks ,aswen as the run-out error present on a gear.However, this process invclved three physicalsetups and passes around the gear.

The latest developmentin this area involvesthe ability of an automatic pitch tester to mea-sure the pitch errors on both flanks, along withthe run-out error in one pass of the gear. Thisresults in a time saving on the order of 3. whichbecomes especially significant on gears withlarge numbers of teeth.

Rolling Testers ..Advances in rotational a:ndvibration transducers as wen as indigital signalprocessing have resulted in improvements inthis type of testing. The dual flank rolling testwave fonn can now be digitally analyzed toseparate out orne of the component errors,such as the detection and location of nicks, run-out, and tooth-thickness average.

The single flank rolling test, previously noteffective because of signal processing limita-tions, has now become viable. Testers are nowavailable which can detect nicks and the likeli-hood of gear whine, as well as measure theerrors in angular velocity of the transmittedmotion.

The angular velocity errors are further ana-lyzed in the frequency domain to' separate outthe component frequencies contributing to theoverall transmission errors. Further analysis toassociate angular velocity variations with thenumber of teeth presentallows each individualerror component. to be analyzed as a function ofrotational speed. This gives powerful knowl-edge to the gear engineer, who can then use thisinformation to eliminate the causes of gearnoise and vibration.

ConclusionsAlthough the aims of gear metrology have not

changed, the equipment and methods now avail-able to the gear metrologist have given him/hervery powerful tools with which to measure gears.

The new gear metrology machines can mea-sure many, if not all, the parameters of a gearmuch more quickly and with more confidencethan ever before. Measurements previously con-sidered too difficult for routine application cannew be performed easily.

Computershave played a major part in mak-ingthese advances possible. They have made thecontrol. of CNC 3-D GMMs and CMMs pos-sible, as well as the collection and storage oflarge amounts of data. Their unbiased assess- Reprinted/rom Vol. ME J'5, No.1. 1989. Transactions 0/ment of this data" together with the clear presen- Mechanical Engineering, "Special Issue: Gearing," The

ration of the results. has given much faster and Institution of Engineers, Australia. Used witn permission.

wider access to the results of gear metrology.This access has enabled much more effectiveaction to be taken to minimize the errors found.

However, these advances should betemperedwith caution, as the new machines are essen-tially only as good as the software driving themand the people operating them ..It is very easy tohave blind faith in impressively presented re-sults. buta wary eye must be kept out for hiddensources of error. 1.1References :

l. GAYLER, I.F.W. & SHOT80LT, C.R ..Metrologyfor

Engineers. Cassell & Company Ltd., London, January

1968, pp. 124·152.

2. HUME, K.J. Engineering Metrology. Macdonald & Co.

(Publishers) Ltd., London, 1967, pp. 306-316.

3. HUME. KJ. & SHARP,. G.H. Practical Metrology.

Macdonald & Co. (Publishers) Ltd. London, Vol. 3, 1959,

pp.81·87.

4. L1SSAMEN, A.J. Metrology for the Technician, The

English Universities Press Ltd., London, 1967, pp. 1.21-

135.

5. SCARR, A.LT. Metrology and Precision. Engineering,

McGraw Hill Publishing Co. Ltd., London, 1967, pp. 160·

178.

6. SCOLES. C.A. & KIRK, R. Gear Metrology. Macdonald

& Co. (Publishers) Ud., 1969.

7. AMERICA SOCIETY OF TOOL & MANUFACTUR·

ING ENGINEERS. Handbook of Industrial Mmology.

1967,pp.424-449.

8. SJEKER, H.W. ·'The Mea.su:rement of Small Gears,"

Shan Course on Gear Marw!aclur,e &: Measuremem,

Swinburn Institute of Technology, Vol. 2. 1982, pp.

222-261.

9. SIM, P.J. "Introduction to Gear Measurement." Short

Course 011 Gear Manufacture & Measurelllent. Swinburn

In titute of Technology, Vol. 2,1982, pp. 191-221.

10. SIM, P.J. "Measurement of Large Gears:' Short Course

orr Gear Manufacture & Measurelllerrt. Swinbum Institute

of Technology, Vol. 2, .1982, pp. 282-294.

1I. SlM, p.J. "Geometry of Spur &. Helical Gears - Methods

of Calculation, "CSlRO Divi ion of Applied Physics. Tech-

nieal Memorandum No.5, 1982.

12. TEMPERLEY. N.C. "New Portable Instrumentation

for Large Gear Metrology." Dimensional. Measurement ill

Precision & Heavy Engineering Symposium. CSIRO Divi-

sion ofApplied Physics, October, 1986, pp. 157·/79.

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