1、93FTM6IEffect of Radial Runout onElement Measurementsby: I. Laskin, Consultant; R. E. Smith, R. E. Smith and E. Lawson, American Sykes Co.IAmerican Gear Manufacturers AssociationTECHNICAL PAPEREffect of Radial Runout on Element MeasurementsI. Laskin, Consultant; R. E. Smith, R. E. Smith and E. Lawso
2、n, AmericanSykes Co.The statementsandopinionscontainedhereinarethoseof theauthorandshouldnotbeconstruedas anofficial actionoropinionof the AmericanGearManufacturersAssociation.ABSTRACT:Radial runoutinagearcancontributesubstantiallytomeasuredvaluesof Profile,Pitch,Index,andinhelicalgears,ToothAlignme
3、nt(Lead)Variations.Thispapertakeseachof these variationsin turnandforAGMA Standardmeasurementmethods,gives the equationthatrelateslhemeasuredvalues to the amountof radialrunoutin an otherwise ideal gear.To demonstratethese relationships,the resultsof actual measurementsarecomparedto values calculate
4、dfromtheseequations. The testgearusedwas aspeciallydesignedmastergear,itself withoutappreciablerunout,butwithapresetamountof runoutintroducedby mountingon an eccentricarbor.Forthese comparisons,both CNC and other types ofinspectionequipmentwere used. Measurementsarealso providedforthe mastergearwith
5、out the preset runout.There is also discussionof howtheguidanceprovidedby theequationscanbe usedtoaidinterpretationof gear inspectiondata, to explaindifferences betweenmeasurementmethods,andto encouragerevision of element tolerances.Copyright 1993AmericanGear ManufacturersAssociation1500 KingStreet,
6、Suite 201Alexandria,Virginia,22314October, 1993ISBN: 1-55589-599-9Effect of Radial Runout on Element MeasurementsIrving Laskin, Consultant, Sharon, MARobert E. Smith, R.E.Smith IF.l EEq161For wide face gears whose measured face width is three-quarters ofthe lead or greater, the Tooth Alignment Varia
7、tion will be independentof face width and the selection of the teeth, as indicated in thefollowing equation:= V_ _ COSl_._ for: IFMI I- 1 tEqTest Gear and MeasurementsA test procedure was used to examine the accuracy of the equations given above.- A special helical test gear was designed and manufac
8、tured. See Table 2(a) for thegear design data and Table 2(b for the additional calculated gear data required by theequations. The gear itself was made with very little Runout with respect to its datumbore. It was also very accurate in terms of the other element variations. Measurements onthis test g
9、ear, made relative to its bore, are listed in Table 3.- Eccentricity was introduced Snto this gear by two methods, each selected to suitthe gear locating feature on the inspection equipment used for the specific measurement.One method involved the use of a special arbor with center holes at each end
10、 and anoutside diameter ground eccentric to the centers, with the direction of the eccentricityidentified. When fitted snugly into the gear bore with the orientation of theeccentricity controlled, this arbor introduced the specified runout magnitude anddirection. In the second method, the test gear
11、was mounted on the rotating table of theinspection equipment with its bore displaced from the table axis so as to introduce asimilar runout. The data defining the eccentricity and other aspects of the inspectionset-ups are given in Table 2(c). Related data used in the equations and calculated from a
12、combination of gear and set-up data, are listed in Table 2(d).- The test gear with its superimposed runout was inspected using both traditionalequipment and computer controlled equipment. (The results were essentially the same andonly those from the latter are reported here. Measurement traces are s
13、hown in Figures14(a), (b, and (c). Selected measurement data are listed in Table 4.Calculated MeasurementsUsing the set-up data and the design data listed in Table 2, selected measurementdata was calculated for comparison to the actual measurement data. This comparison isshown in Table 4. The small
14、differences can be attributed to some approximations in theset-up positioning of the probe, to the small variatlons in the test gear, and to theinherent variability in the measurement processes.Comments and RecommendationsThe equations presented here can be used to evaluate the effect of Runout (due
15、 toeccentricity) on the other element Variations. If future versions of the AGMA InspectionHandbook will continue the practice of defining these other Variations as to include theeffect of Runout, then the equations for the tolerances should be revised to incorporatethe results from these equations.
16、 For example, Profile and Pitch tolerances shouldreflect the fact that the same Runout adds more to each of the corresponding Variation ingears with small numbers of teeth than it does in gears with large numbers of teeth.Also, Tooth Alignment tolerances for helical gears should reflect how the cont
17、ribution ofRunout to Tooth Alignment Variation is effected by the relationship of face width to leadand not merely by face width by itself.The AGMA Handbook should also consider defining additional (or substitute) Profile,Index and Fitch, and Tooth Alignment Variations from which the effect of Runou
18、t has beenremoved. Such variations will better predict how the gear with perform in operation whereeccentricity has, at best, a secondary influence. Separating the effect of Runout fromthe current types of measurement data is now practical with modern data processingtechniques. Numerical methods sui
19、table for such calculations should be developed andpublished in an AGMA document.Differences among the various makes of inspection equipment in tooth surfaceidentification and direction and location of measurements suggests that AGMA make greaterefforts to standardize these inspection reporting feat
20、ures. At the very least, thoseusing the results of Index and Pitch measurements should be helped to recognize thatdirection and location (diameter can influence the proper interpretation of inspectiondata. Where computer controlled equipment calulates inspection results indirectly fromother types of
21、 measurements, as for example Runout data from Index measurements, aCalibration Standard is needed to reveal any shortcomings of such procedures. In theabsence of such a Standard, qualifying tests should employ eccentric test gears of few.teeth and high helix angles to uncover possible software limi
22、tations.AcknowledgementsM Gleason Works, Rochester, NY; R.B.Smith rec;on oFEccen_/_._,._ Face _/id_h, FToo,K=i_ ot Measurement Plane_t Measurement Po;n-t I -IM= “ MeasuremenPlaneFigure 6:HetlcaL Gear with Measurement Point MLocated ReLative to Eccentricity eiEccenric ProFlte- IIConcenr;c ProFile III
23、 OekM-_Bt+ EM QekM-C_Bi+EMB,se Circ,e _.L I /LJ Tooh _ /_f _Eccenrlclty LineQekM - elM +(k- I)T M,L= e sinekM - O(Bt+ EM(o) Eccentrlc and Concentric ProFies (b) Me_suremen vs, FccentrlciyFigure 7:ProFile Measurement on Eccentric Gear, LeFt Flank12ProFileV_ri_ionM_ +I I N _ , N K=t+ IN:_l_,- _:“_.7-i
24、,.,_IIIIOez C . _C D “-(o) ProFileIroces on sinecur e+ J _ Slope- -7 Max, SLope -L Max, S_ope _ J(C) FOP C Ioc_ilons (best“i_Ox_utt SlOpe)(b) Profile tr_CeS For It locations (,worst S moxEnumstope)Figure Bl Proqile Measuremens, LeF Flanke SIFI C)ekM + (l)Mt - (_ PHI MxL- cos _p._e_._.-e_.*(k_ZI)_Mea
25、surementLine I _ _ Tooth ProfileEccentr,c,ty I ,_ Bolt P_obe / /_. I P_c_o,o_- C_II.eosur-_-_,enlCircle-_ / Eccentric ProFile ie sinE)ekM+(1)Mt- OpMITooth No. R Concentric ProFileC,(a) Eccentric ond Concenlrlc ProFiles ) Meosurement vs. EccenricllyFigure 9_ Index Meosuremen on Eccentric Gear, Le?t F
26、lankPeak oathe _ Vx(tot)=TotatMxL 4- _cos qbl_l; Index VarlatlonEccenirlclt_“ I “_ Ec.centrlclty(to_ - p)_W( I _ l Piic:hVariolionOelMT j4“_J_ _ _/|L_ _1_(_l,rlt_ pm._) 4 IT ! 2 3 N-PN-1 N 1 k (tooth(a) Index Neasuremens, left Flank number)MxR 4-Eccentricltv Peak Eccentrlciytooih(0n-t-_pr_i)“r 1 2 3
27、 N-2 N-I N I k(b) Index Neasurements, right FrankFigure I0: Index Heasurenents90“-(mt- _pint)I- “ “ + Peak, IMxR _ _ Eccentricityright Flank_ IFlankRight 2(mt_epnt) _ _ _ _-= _III 2 3 N-2N-IN 2 k(toothI I number)ILeft Reverse Peek IFlank I.eFt Flank IMxL -I- Peek, let Flank IFigure 11:Index Measurem
28、ents Ptotted Back-to-Back14MxL Mp_l-m- _ MP(3-4)2 3 4 N-2N-1 N I _, k (equlvalent“ (N-I.5) (N+,5)L-vp (- pitch variation) tooth number)(-)(b) Pich MeasuremensFigure 12; Index and Pich VariationsToOhNo,K I“ L (lead) -(a) Full cycte tooth alignment (b) Narrow (c) _/idemeesuremens ace traces 6ce racesF
29、igure 13: Tooth Alignment Meosurements15PI“IIGERR DEPT. INVOLUTE PMI GERR nEPT. LERD “:“ tf t I | I I | I I I I n l_;_l i_.-t-?L, , , I ! I ! i I ! I II_iLLi : i i“ ,_ i i i_.-P, , _l i l i t t I i Lill_“Z_-_I ; _ 7 i I _ t I i ! | i_-| I I t 1%J1i i i I /I I t_-_ _ - LJ_.LI t ! , t t , -ii-FI Ii-i_
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35、I,.u I , i _l.l I . _ I , i , , i i i -hltiLI.J i I - , , ,. I-F- I 1 I I i , , II I. I_, i _ifl.i “=_iT_r I I I I I I I 11 I I I I I I I I I I7 I I I I I t I I I I I t I I I_ IIII._?F _? i ! I tI i I I t 1 1 , ,w . . ._ .“ . oI . . .ore = :- m ;. :“ _ m = =o= m oI _ MlJ4 _Cr_rON _YbTKMS(a). Profile
36、 Measurements (c). Tooth Alignment (Lead)MeasurementsVERZDEX (t:m) Version 0.56index VariationLeft 0.00020 in/div RightTooth Pitch Index 0.0040 0.0020 0.0 0,0020 0.0040 Index Pitch ToothVal Vat I I I, , ,I Var Vat1 34.5 ; _ 2 5 12 2,9 37.4“ l 4 7 2.Z 23 -0.6 36.7 _ .,. g 8 5.I 34 -3.8 32.9 c i 17 o
37、7.2- 4S -5.8 27.1 i t _4 0 7.0 56 -G.7 20.4 _ ) 30 :, 6.3 6, 35.2 4 9 7; -T.4“ 3,08 -6.1 6.9 , : 37.4“ 2.| 89 -3.8 3.1 . : 36.4 -i.O 9i0 -i,l 2.0* i -_ 32.4 -4.0 _011 1.9 3.9 _ -i 26.-% -6.| II12 _e.7 8.5 : 19.1 -7.i 1213 g.6 IS.1 ; I 12.0 -?.2* 1314 7.3“ 2_.5 : I 6.0 -6.0 1_,15 6.8 29.2 V i 2.8 -3.2 1._1 5.4. 54.7 , , _ 2.0“ -0.8 1 Figure 14. Measurements onI._! :I.I Test Gear with RunoutMaximum Pitch Variation = -0.00074 in. Maximum Pitch Variat:ion = 0.00072 i_.Total Index Variation = 0.00354 in. Total Index Veriation = 0.0035+ in(b). Index and Pitch Measurements
