1、92 FTM9Representative Form Accuracy of GearTooth Flanks on the Prediction ofVibration and Noise of Power Transmissionby: Aizoh Kubo and Tetsuya Nonaka, Kyoto UniversityNaoya Kato, Sony CorporationShogo Kato and Toshio Ohmori, Toyota Motor Co. Ltd.American Gear Manufacturers AssociationTECHNICAL PAPE
2、RRepresentative Form Accuracy of Gear Tooth Flanks onthe Prediction of Vibration and Noise of PowerTransmissionAizoh Kubo and Tetsuya Nonaka, Kyoto UniversityNaoya Kato, Sony CorporationShogo Kato and Toshio Ohmori, Toyota Motor Co., Ltd.JapanTheStatementsandopinionscontainedhereinare thoseof the au
3、thorand should notbe conslruedas an official action oropinion of the American Gear ManufacturersAssociation.ABSTRACT:Gear noise and vibration are troublesome problems in power transmission systems. Recent research has shown thataccuracy in three dimensionaltooth flank form, which is usually represen
4、tedby tooth form and tooth lead form, is animportant factors in noise and vibration.In this paper the authors discuss investigationinto what form accuracyof gear tooth flank has a good correlation withgear vibration and noise, when the scattering of accuracy in tooth flank form cannot be avoided.Cop
5、yright 1992American Gear ManufacturersAssociation1500 King Street, Suite 201Alexandria, Virginia, 22314October, 1992ISBN: 1-55589-589-1Representative Form Accuracy of Gear Tooth Flankson the Prediction ofVibration and Noise of Power Transmissionby Aizoh KUBO Kyoto UniversityTetsuya NONAKA Kyoto Univ
6、ersityNaoya KATO SONY CorporationShogo KATO Toyota Motor Co,Ltd,Toshio OHMORI Toyota Motor Co.Ltd, JAPAN1. Introduction In this paper, we investigate what form accuracy of gear tooth flankhas a good correlation with gear vibration and noise, when the scattering ofGear noise and vibration while runni
7、ng are one of the most accuracy in tooth flank form cannot be avoided. This gives also antroublesome problem in power transmission gears. It has become clear by information about how much tolerance can be allowed during gearrecent research that gear manufacturing accuracy, especially the accuracy in
8、 manufacturing to realize silent gear drive unit.three dimensional tooth flank form which is usually represented by toothform and tooth lead form, is important factor for this problem. But actually, 2. Noise Measurement of Automotive Powereven though we investigate how we could expect the reduction
9、of gear noise Transmissionand vibration according to the improvement of form accuracy of the geartooth flank comparing previous forms, and gear dimensions and accuracy are To investigate gear noise of drive unit for automotive powerspecified by this results of investigation and the gear manufacturin
10、g is transmission, 6 helical gear pairs (a,.f) whose tooth flank forms wereordered, there are many times that the prediction does not come true. different to each other were prepared. These gears were manufactured by aIn most of these investigation to find the optimum tooth flank form process of bob
11、bing, shaving and case hardening. Changing only this gear pairand the optimum gear dimensions, the tooth flank form is assumed to heI . Elecgric,_otorsame on each tooth flank of a gear. But when we measure the form accuracy _ 2. To r qu e me,_s u r i n gof gear tooth flanks of actu_l gears from the
12、production line, we find that the L_m 3. Load lug d e vice4, Microphonformaccuracyis considerablydifferentbetweeneachtoothof a gear. Wecan manticipate therefore one thing as the reason for the discrepancy between _IDRIVE GEAR_predictions and the actual state, that we do nat consider the scattering o
13、f toothflank acearacy on each tooth. When the target form aceuracy of tooth flank _ IRIV_GEt_q_I 3 _ -and gear dimensions are predicted to obtain quiet gears without considering _ DRIVE PINION GEARthe deviation of actual tooth flank form from the target form and without 0UTQ_qL_PUT L._considering th
14、e scattering of tooth flank form on each tooth of a gear, thattarget tooth flank form is in actual not the optimum form. This proposes DRIVESHAFT| _ RING GEARi._ ._dalso a big question what kind of accuracy in tooth flank form should bespecified at gear designing and manufacturing to obtain a good r
15、esult for Fig.1 Schema of the set up for noise measurementnoise reduction, from the automotive gear box1in a gear drive unit, the gear noise was measured from 100 mm out side of components according to involute error is shown at the mesh frequency fz andthe gear box and the mesh frequency component
16、of the test gear pair in the its twice 2fz.noise was investigated, (Fig.l). The measurement was worked out under the Figure 4 shows the relation between the mesh frequency component oftorque constant condition and increasing the driving speed gradually and the measured gear noise and that of the sin
17、gle flank rolling test. As thecontinuously. The transmitting torque values for gears(a).(e) were 0.5, 1.0, single flank rolling test was carded out under no loading and the noise2.0 kgf m ( i.e. 4.9, 9.8, 19.6 Nm) on the coasting tooth flanks and for measurement was carded out under several loading
18、levels, the data for a geargear(f) 2.0, 3.0, 6.0 kgf m ( i.e. 19.6, 29.4, 58.8 Nm) on the driving tooth pair is indicated by a vertical line in the figure. Concerning to the results onflanks. The mesh frequency component of gear noise was taken by using a coasting tooth flanks (a).(e), we can find a
19、 rough positive correlationtracking filter. In all the measured results, the peak value was observed at between the results of single flank rolling lest and the noise level, but the2500 Hz mesh frequency, in this gear drive unit, this peak value is consideredchanging of the sound level of a gear pai
20、r due to the changing of transmittingto be the most important on the noise problem.load is considerably large. The result on the driving tooth flank (f) shows noIn order to check the quality of test gears on conjugate action, thecorrelation. If we could carry out the measurement of loaded transmissi
21、onsingle 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 correlation wouldis illustrated in Fig.2: An electric motor 1 drives the test gears under nobecome better. But it is not common and practical to carry out thel
22、oading. Two precise rotary encoders 4 and 5 mounted on the driving and measurement of loaded transmission error. In the actual gear productiondriven gear shafts respectively measure the rotational angle of each gear shaft industries today, the quality control for tooth flank accuracy of gears isand
23、a processing unit 7 calculates the difference of the rotational angles. This mostly managed by the measuremenl of transverse tooth form and tooth leadsignal is given to the FFT analyzer to obtain the Fourier spectra of the single form. To reflect the information of measured transmission error to the
24、flank rolling test. One example of the Fourier spectra measured is shown in production technology and to the quality control of gears, the relationFig.3. The big amplitude in low frequency region is caused by the run out between the factors in gear production engineering and the transmission erroran
25、d the cumulative pitch deviation of the test gears. The frequency of the gears manufactured must be clarified, but it is not yet. On the other_I hand,whena definiteindexcancorrelatetheformaccuracyoftoothflankwith the running noise of gear drive unit, it will work well in gear designingand quality co
26、ntrol technique in todays gear production. The relationI 1. Electric motor betweenrunningnoiseofgearddve and the transmission erroror vibrational2. Torque measuring_x_ F_“_ I 3. lie s h i ng t e e t h excitation force of the gears which are calculated as functions of the gear& and 5. Rotary encoder6
27、. Lo ad i ng d ev i c e dimensions, accuracy of tooth flank form and driving condition is therefore7. Ca l c u 1a I:i on of t hs investigated in the coming part of this investigation.transmission errorI 8. FT The form accuracy of profile and lead of four teeth which are located atI_._ J- 90 degree i
28、ntervals around each test gear were measured. From this result,the error surface for the accuracy of three dimensional tooth flank form isgenerated: the error surface is defined on the plane of action by the differenceFig.2 Schema of the set up for single flank rolling testSO! 1 dtO _ e_ 80g N*_e-O_
29、 bL_I _ a,_,o 70uJEewoI.U N,.-:_-.J_ 6G I T _ i I , , ,0 0.2 0.4 0.6 0.8 1.0 1,2 1A 1.6fz component 2fz component fzCOMPONENTOFMEASUREDDEVIATIONOF (ym)/%. SINGLEFLANKROLLINGTEST (fzcomponent)o 5o lco _5o 26b 2_oFREQUENCY(Hz)Fig.4 Relation between the single flank rolling test and the noiseFig.3 An e
30、xampleofthe frequencyanalysis of the result level of gear box whichhas thatgear pair (inmeshingofsingleflankrollingtest frequencycomponent)2between actual tooth flank and the ideal involute helicoid Ill. The see all the data together, there we cannot find any correlation betweentransmission error of
31、 each gear pair can be simulated using the error surfaces transmission error and noise level.for driving and driven gearsl2.Sl. In actual gears there exists pitch error and 3. Comparison between Measured and Simulatedtooth flank form on each tooth of a gear is somewhat different. When we Single Flan
32、k Rolling Testcall the sum of the error surfaces of driving and driven gears as “compositeerror surfaces“, the number of meshing tooth pair, i.e. the number of differentThe meshing frequency component of measured result of the singlecomposite error surfaces is therefore the least common multiple of
33、the toothflank rolling test is compared with that of simulated transmission error undernumber of driving gear and that of driven gear. That means, the simulationvery light torque (4.9 Nm): The measured signal of the single flank rollingfor the power transmitting state of this gear pair should be car
34、ried out for thistest was processed by low cut filter, as seen in the Fig.6(a), and the walkingserial existing state of composite error surfaces. But it takes too much timeaverage over three meshing periods of this processed signal was calculated,and money and is impractical. Moreover it is not yet
35、known, how we couldthe example of this is seen in Fig.6(b). This wave form was then averagedfeed back the information data obtained by such a huge simulation to theinto one meshing period. That figure is then here incorporated as theactual gear production technology. The feasible method in practice
36、is only measured wave form of single flank rolling test which is periodic in onethe simulation for a gear pair that has a single figure of composite error tooth meshing period and can be compared with the simulated transmissionsurface which represents the quality of the gear pair.error under light l
37、oad.As a first trial for the representative form accuracy of gear toothAs the first trial, we have selected the average composite error surfaceflanks, the average form of error surfaces of all 4 measured tooth flanks wasof gear pair as the representative form accuracy of test gear pair. Figure 7inco
38、rporated. The transmission error of test gears were simulated using thecompares the wave form of the simulated transmission error under light loadsum of these representative error surfaces of driving and driven gear. Figure 5with that of the measured single flank rolling test: The abscissa takes the
39、shows the correlation between the mesh frequency component of thepro_ess of gear mesh for three pitches and the ordinate takes the varying partsimulated transmission error and the measured peak value of the meshingof the transmission error which is expressed by the difference betweenfrequency compon
40、ent of gear noise from the gear box. The ordinate is noise positions of driving and driven tooth flanks on the line of action. The zerolevel and the abscissa is the meshing frequency component of transmissiontransmission error in these figures corresponds to the average delay oferror. We can underst
41、and the reasonable tendency that the noise level for eachrotational angle of driven gear to the driving gear. The dotted curvegear pair becomes higher as their transmission error becomes larger, except incorresponds to the measured wave form and the black curve to the simulatedthe case of (f). But a
42、s noise level is very different to each gear pair, when weone.v9o _ _“.20t_ PROGRESS OF MESHING (deg)8P, (a) Wave form for two rotaions of gear“ g r _ ZOOM DATA (Walking averaged),O,_/ c _ : f _ 0 _ “_- (pir:ch)/ _ _ PROGRESS OF MESHINGT i , x-,/k with which the noise levels are low, the scattering
43、of form deviation among_0 j_ W _ all the tooth flanks measared is bounded in a small range. On the other hand,“_ for the gear pairs whose noise level are high, the scattering of form deviationis verylarge. Thisisespeciallyclearonthepinionof thegearpair(d),Fig.8. Figure 9 shows the error surface of e
44、ach tooth flank DI,.,D4 of the _ 3-2 12 Gears (c) pinion of (d): Each figure is very different. At electing the representative& toothformofthepinionin theforegoinginvestigation,wehaveadoptedthe/ / !_ /_xx /_xx t_w average value of these error surfaces, and as the result, convex and concaveo partsofe
45、acherrorsurfacecompensateeachotherto buildrelativelysmooth_ _._/ _ _ averaged error surface, and that smooth figure has 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 act
46、ual and it hasmade the correlation in Fig.5 poor._2 Gears (d)It is assumed now that the model for pinion (d) has one tooth flank_= t“ t“xx ,/x form on every tooth flank and that tooth flank form is the same as the worst/ t tt “_ one (D3) among all of the teeth. The transmission error is simulated wi
47、th- o _ x_,._ this model and compared with the experimental form , cf: Fxg.lO. It is - f I I x/i / recognized that the simulated wave form become very similar to the result oft “l I , measured single tooth flank rolling test. This result suggests that the mainI I I-2 1 2 3 causeof poorcorrelationin
48、Fig.5is in the averagingprocessto get the_2 Gea rs (e) representative composite error surface and the worst composite error surfacelooksto representfar betterthe qualityof gearpairconcerningto its/_ J_ i_/_ transmission error._ 4. Representative Form Accuracy of Gear ToothI I I-_ _ 2 3 Flanks and In
49、dex for Gear Noise2 Gears(f)The result of the former chapter indicates the procedure to make a goodprediction for transmission error: The simulation model assumes here that_o “ “_-_ “_“_-_“_- ,_ x_ -_,._ j -,_ _,e -.,_./- all the tooth pairs coming in mesh have a same composite error surface for_ form accuracy of tooth flanks of a gear pair. The individual simulations are_,_* carded out foreach of the possible composite error surfaces of a gear pair and_ the worst result of the meshing frequency component of
