AGMA-92FTM9-1992.pdf

92 FTM9 RepresentativeFormAccuracyof Gear ToothFlankson the Predictionof Vibrationand Noise of PowerTransmission by: Aizoh Kubo and Tetsuya Nonaka, Kyoto University Naoya Kato, Sony Corporation Shogo Kato and Toshio Ohmori, Toyota Motor Co. Ltd. AmericanGearManufacturersAssociation TECHNICALPAPER Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 10:42:36 MDTNo reproduction or networking permitted without license from IHS -,-,- RepresentativeForm Accuracyof Gear Tooth Flanks on the Predictionof Vibrationand Noise of Power Transmission Aizoh Kuboand TetsuyaNonaka,Kyoto University Naoya Kato, Sony Corporation Shogo Kato and Toshio Ohmori, Toyota Motor Co., Ltd. Japan TheStatementsandopinionscontainedhereinarethoseoftheauthorandshouldnotbeconslruedasanofficial actionor opinion of the American Gear ManufacturersAssociation. ABSTRACT: Gear noise and vibration are troublesome problemsin power transmission systems. Recent research has shown that accuracy in three dimensionaltooth flank form, whichis usuallyrepresentedby toothform and tooth lead form, isan important factors in noise and vibration. In this paper theauthorsdiscuss investigationinto whatform accuracyof geartooth flank has agood correlationwith gear vibration and noise, when the scattering of accuracy in tooth flank form cannot be avoided. Copyright © 1992 American Gear ManufacturersAssociation 1500 King Street, Suite201 Alexandria,Virginia,22314 October, 1992 ISBN:1-55589-589-1 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 10:42:36 MDTNo reproduction or networking permitted without license from IHS -,-,- RepresentativeForm Accuracyof Gear Tooth Flanks on the Predictionof Vibrationand Noise of PowerTransmission byAizohKUBOKyoto University TetsuyaNONAKAKyoto University NaoyaKATOSONYCorporation Shogo KATOToyota Motor Co,Ltd, Toshio OHMORIToyota Motor Co.Ltd,JAPAN 1.IntroductionIn this paper, we investigate what form accuracy of gear tooth flank has a good correlation with gear vibration and noise, when the scattering of Gear noiseand vibrationwhile runningare one of the mostaccuracy in tooth flank form cannot be avoided.This gives also an troublesome problem in power transmission gears. It has become clear byinformationabout how much tolerancecan be allowedduringgear recent research that gear manufacturing accuracy, especially the accuracy inmanufacturing to realize silent gear drive unit. three dimensional tooth flank form which is usually represented by tooth formandtooth lead form, is important factor for this problem. But actually,2.NoiseMeasurementofAutomotivePower even thoughwe investigate how we could expect the reduction of gear noiseTransmission and vibration according to the improvement of form accuracy of the gear tooth flank comparing previous forms, and gear dimensions and accuracy areTo investigategear noise of drive unit for automotivepower specifiedby this results of investigation and the gear manufacturingistransmission, 6 helical gear pairs (a,.f) whose tooth flank forms were ordered, there are many times that the prediction does not come true.different to each other were prepared.These gears were manufactured by a In most of these investigation to find the optimum tooth flank formprocess of bobbing, shaving and case hardening. Changing only this gear pair and the optimum gear dimensions, the tooth flank form is assumed to he I .Elecgric,_otor same on each tooth flank of a gear. But when we measure the form accuracy_2.To r qu em e,_s ur i ng of gear tooth flanks of actu_l gears from the production line, we find that theL_m3.Load lugd evice 4,Microphon formaccuracyis considerably differentbetweeneachtoothofa gear. Wecanm anticipate therefore one thing as the reason for the discrepancy between_IDRIVE GEAR_ predictions and the actual state, that we do nat consider the scattering of tooth flank acearacy on each tooth. When the target form aceuracy of tooth flank_ IRIV_GEt_q'_I3_- and gear dimensions are predicted to obtain quiet gears without considering_DRIVE PINIONGEAR the deviation of actual tooth flank form from the target form and without0UTQ_qL_PUTL._ considering the scattering of tooth flank form on each tooth of a gear, that target tooth flank form is in actual not the optimum form.This proposesDRIVESHAFT|_RING GEAR i._._d also a big question what kind of accuracy in tooth flank form should be specified at gear designing and manufacturing to obtain a good result forFig.1Schema of the setup for noise measurement noisereduction,fromthe automotive gear box 1 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 10:42:36 MDTNo reproduction or networking permitted without license from IHS -,-,- in a gear drive unit, the gear noise was measured from 100 mm out side ofcomponents accordingto involute erroris shown at the mesh frequency fz and the gear box and the mesh frequency component of the test gear pair in theits twice 2fz. noise was investigated, (Fig.l). The measurement was worked out under theFigure 4 shows the relation between the mesh frequency component of torque constant condition and increasing the driving speed gradually andthe measured gear noise and that of the single flank rolling test.As the continuously. The transmitting torque values for gears(a).(e) were 0.5, 1.0,single flank rolling test was cardedout under no loadingand the noise 2.0 kgf m ( i.e. 4.9, 9.8, 19.6 Nm) on the coasting tooth flanks and for measurementwas carded out under several loading levels, the data for a gear gear(f) 2.0, 3.0, 6.0 kgf m ( i.e. 19.6, 29.4, 58.8 Nm) on the driving toothpair is indicated by a vertical line in the figure. Concerning to the results on flanks. The mesh frequency component of gear noise was taken by using acoasting tooth flanks (a).(e), we can find a rough positive correlation trackingfilter. In all the measured results, the peak value was observed at betweenthe results of single flank rolling lest and the noise level, but the 2500 Hz mesh frequency, in this gear drive unit, this peak value is considered changing of the sound level of a gear pair due to the changing of transmitting to be the most important on the noise problem. load is considerably large. The result on the driving tooth flank (f) shows no In order to check the quality of test gears on conjugate action,the correlation.If we could carry out the measurementof loaded transmission single flank rolling test of these gears was carried out. The set up of the test error i.e., single flank rotlifig test under loading, the correlationwould is illustrated in Fig.2:An electric motor 1 drives the test gears under no become better. But it is not common and practicalto carry out the loading.Two precise rotary encoders 4 and 5 mounted on the driving and measurement of loaded transmission error.In the actual gear production driven gear shafts respectivelymeasure the rotational angle of each gear shaft industriestoday, the quality control for tooth flank accuracy of gears is and a processing unit 7 calculates the difference of the rotationalangles. This mostly managed by the measuremenl oftransverse tooth form and tooth lead signal is given to the FFT analyzer to obtain the Fourier spectra of the single form.To reflectthe informationof measured transmissionerror to the flank rolling test. One example of the Fourier spectra measured is shown in productiontechnologyand to the quality control of gears, the relation Fig.3. The big amplitude in low frequency region is caused by the run out between the factors in gear production engineering and the transmission error and the cumulativepitch deviationof the test gears.The frequency of the gears manufactured must be clarified, but it is not yet.On the other _Ihand, whena definite indexcancorrelate theformaccuracy oftoothflank with the running noise of gear drive unit,it will work well in gear designing and quality control technique in today's gear production.The relation I1.Electricmotorbetweenrunningnoiseofgearddveand the transmissionerroror vibrational 2.Torquemeasuring _x_F_“_I3.lie sh i ng t ee t hexcitation force of the gears which are calculated as functions of the gear & and5.Rotaryencoder 6.Lo ad i ng d ev i c edimensions, accuracy of tooth flank form and driving condition is therefore 7.Cal c u 1aI:i onoft hsinvestigated in the coming part of this investigation. transmissionerror I8.£FTThe form accuracy ofprofile and leadof four teethwhich are located at I _._J-90 degree intervals around each test gear were measured. From this result, the error surface for the accuracy of three dimensional tooth flank form is generated: the error surface is defined on the plane of action by the difference Fig.2Schema of the set up for single flank rolling test SO !1d tO_e _80 gN*_e- O_b L_I_a ,_,o70 uJE ewo I.U N',.- :_-.J _6GIT_iI, 00.20.40.60.81.01,21A1.6 fzcomponent2fz componentfz COMPONENT OF MEASURED DEVIATION OF(ym) /% .SINGLEFLANKROLLINGTEST(fzcomponent) o5olco_5o26b2_o FREQUENCY(Hz) Fig.4 Relation between the single flank rolling test and the noise Fig.3An exampleofthe frequencyanalysisof theresultlevel of gearbox whichhas thatgearpair (inmeshing ofsingle flank rolling testfrequencycomponent) 2 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 10:42:36 MDTNo reproduction or networking permitted without license from IHS -,-,- betweenactual toothflankand the ideal involutehelicoid Ill.Thesee all the data together, there we cannot find any correlation between transmission error of each gear pair can be simulated using the error surfacestransmission error and noise level. for driving and driven gearsl2.Sl. In actual gears there exists pitch error and 3.Comparison between Measured and Simulated tooth flank form on each tooth of a gear is somewhat different.When we Single FlankRolling Test call the sum of the error surfaces of driving and driven gears as “composite error surfaces“, the number of meshing tooth pair, i.e. the number of different The meshing frequency componentof measured result of the single compositeerror surfaces is therefore the least commonmultiple of the tooth flank rolling test is compared with that of simulated transmissionerror under number of driving gear and that of driven gear. That means, the simulation very light torque (4.9 Nm): The measured signal of the single flank rolling for the power transmitting state of this gear pair should be carried out for this test was processed by low cut filter, as seen in the Fig.6(a), and the walking serial existing state of composite error surfaces.But it takes too much time average over three meshing periods of this processedsignal was calculated, and money and is impractical.Moreover it is not yet known, how we could the example of this is seen in Fig.6(b).This wave form was then averaged feed back the informationdata obtained by such a huge simulationto the into one meshing period.That figure is then here incorporatedas the actual gear productiontechnology.The feasible method in practice is only measured wave form of single flank rolling test which is periodic in one the simulation for a gear pair that has a single figure of composite error tooth meshing period and can be comparedwith the simulatedtransmission surface which represents the quality ofthe gear pair. error under light load. As a first trial for the representativeform accuracy of gear tooth Asthe first trial, we have selected the average composite error surface flanks, the average form of error surfaces of all 4 measured tooth flanks was of gear pair as the representativeform accuracy of test gear pair.Figure 7 incorporated.The transmission error of test gears were simulated using the compares the wave form of the simulated transmissionerror under light load sum of these representativeerror surfaces of driving and driven gear.Figure 5 with that of the measuredsingle flank rolling test:The abscissa takes the shows the correlationbetween the meshfrequencycomponentof the pro_ess of gear mesh for three pitches and the ordinate takes the varying part simulated transmission error and the measured peak value of the meshing of the transmissionerror which is expressedby the differencebetween frequency component of gear noise from the gear box. The ordinate is noise positions of driving and driven tooth flanks on the line of action. The zero level and the abscissa is the meshing frequency component of transmission transmissionerror in these figures correspondsto the average delay of error. We can understand the reasonable tendency that the noise levelfor each rotationalangle of driven gear to the driving gear.The dottedcurve gear pairbecomes higher astheir transmission errorbecomes larger,except in correspondsto the measured wave form and the black curve to the simulated the case of (f). But as noise level is very different to each gear pair, when we one. v 9o_“ .20t _PROGRESSOF MESHING(deg) 8P,(a)Wave form for two rotaions ofgear “gr_ZOOMDATA(Walkingaveraged) ,O,_/c_: f_0_“ _ -(pir:ch) /_PROGRESSOF MESHING Ti,x-,/kwith which the noise levels are low, the scattering of formdeviation among _0j_W_all the tooth flanks measared isbounded in a small range. On the other hand, “_for the gear pairswhose noise levelare high, the scattering of form deviation is verylarge.Thisisespecially clearonthepinion ofthegearpair(d), Fig.8.Figure 9 shows the error surface of each tooth flank DI,.,D4 of the '_3 -21 2Gears (c)pinion of (d): Each figure is very different.At electing the representative &toothformofthepinionintheforegoing investigation,wehaveadopted the /! _/_xx/_xxt_waverage value of these error surfaces, and as the result, convex and concave opartsofeacherrorsurface compensate eachothertobuildrelatively smooth _._/_averaged error surface, and that smooth figurehas represented the tooth flank _/_v“_/form accuracy of this pinion. The simulated transmission error using this -z_._smooth error surface has become therefore lower than the actual and it has made the correlationin Fig.5 poor. _2Gears(d) It is assumed now that the model for pinion (d) has one tooth flank _=t“t“xx,'/xform on every tooth flank and that tooth flank formis the same as the worst /ttt“_one (D3) among all of the teeth. The transmission error is simulated with - o _x_,._this model and compared with the experimental form , cf: Fxg.lO.It is -f IIx/i /recognized that the