1、93FTM11The Relative Noise Levels of Parallel Axis GearSets with Various Contact Ratios andGear Tooth Formsby: R. J. Drago, J. W. Lenski and R. H. Spencer,Boeing Defense and Space Group;M. Valco, Lewis Research Center, U.S. Army;E Oswald, Lewis research Center, NASAAmerican Gear Manufacturers Associa
2、tionI ITECHNICAL PAPERhe Relative Noise Levels of Parallel Axis Gears Sets withVarious Contact ratios and Gear Tooth FormsR. J. Drago, J. W. Lenski and R. H. Spencer, Boeing Defense and Space Group;M. Valeo, Lewis Research Center, U.S. Army; and F. Oswald, Lewis ResearchCenter, NASAThe statements an
3、d opinions contained herein are those of the author and should not be construed as an official action oropinion of the American Gear Manufacturers Association.ABSTRACT:The real noise reduction benefits which may be obtained through the use of one gear tooth form as compared to another isan important
4、 design parameter for any geared system, especially for helicopters in which both weight and reliability arevery important factors. This paper describes the design and testing of nine sets of gears which are as identical as possibleexcept for their basic tooth geometry. Noise measurements were made
5、at various combinations of load and speed for eachgear set so that direct comparisons could be made. The resultant data was analyzed so that valid conclusions could bedrawn and interpreted for design use.Copyright1993American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Vtrgi
6、nia, 22314October,1993ISBN: 1-55589-623-5The Relative Noise Levels of Parallel Axis Gear SetsWith Various Contact Ratios and Gear Tooth FormsByRaymond,I. Drago,PEAssociateTechnicalFellowBoeingHelicoptersRobertH. Spencer JosephW.Lenski,Jr.StaffEngineer AssociateTechnicalFellowBoeingHelicopters Boeing
7、HelicoptersMarkJ. Valco FredB. OswaldAerospaceEngineer ResearchEngineerLewisResearchCenter/U.S.Army LewisResearchCenterNASAIINTRODUCTION modified contact ratios and the gear tooth form,separately and in combination, for spur and helicalThe problem of gear noise in helicopter transmissions gears, on
8、the noise levels produced by otherwiseis ever present. The main exciting forces which identical spur and helical gears. In order toproduce this noise are the meshing forces of the gear accomplish this objective, a program was defined toteeth in the transmission. While this is certainly an design app
9、ropriate gears (Table I), fabricate aoversimplification, since many factors influence sufficient number of test specimens, and conduct thetransmission noise aside from the gear mesh forces, testing required.the simple fact rernain._ that if the basic excitingforces are reduced and no amplifying fact
10、ors are While a wide range of specimens is shown, they werepresent, the overall noise level of the system will be all configured as nearly alike as practical, within thereduced, limitations imposed by manufacturing considerationsand the test stand. Testing was conducted in a singleAmong the several
11、ways in which the gear tooth mesh gear box under controlled conditions whichmeshing forces may be reduced, two of the most were maintained as nearly identical as possible.directly applicable to helicopter transmissions are the Acoustic intensity measurements were taken with theform of the teeth and
12、the overall contact ratio. Both aid of a robot to insure repeatability of measurementapproaches are quite attractive for an aerospace between gear sets and to minimize human techniqueapplication since, unlike other “treatment“ methods, influence.which are applied with penalties to either systemweigh
13、t or performance, these approaches have thepotential for reducing noise without causing any TEST GEAR DESIGNincrease in overall system weight or reducingperformance. In fact, both approaches also offer the Eight (8) sets of gears, four (4) spur and four (4)possibility of .actually providing improved
14、 gear helical as listed in Table I, compatible with theperformance in terms of longer life, higher load NASA Lewis gear noise test rig, were designed. Ofcapacity, improved reliability, and reduced weight the four sets of spur gears, two sets have an involutewhile simultaneously reducing noise levels
15、, tooth form and two utilize a nouinvolute, constantradius of curvature tooth form. All gears wereThe objective of this program was to define, by designed in accordance with normal Boeingcontrolled testing and actual noise measurements, the Helicopters practice so that, except for size, they areeffe
16、ct of changes in the profile, face, and representative of typical helicopter gears.Table I Gear Noise Test MatrixContact RatiosConfiguration Tooth Form TvlaeProfile Face Modifie.d1. Conventional Involute Spur 1.25 0.00 1.25Spur Baseline2. HCR-INV Involute Spur 2.15 0.00 2.153. Conventional Involute
17、Helical 1.25 1.25 1.77Single Helical Baseline4. DoubleHelical Involute Helical 1.25 1.25 1.775. HCR-INV Involute Helical 1.25 1.75 2.156. HCR-INV Involute Helical 2.15 2.25 3.117. NIF Baseline NonInvolute Spur 1.25 0.0 1.258. NIF-HCR NonInvolute Spur 2.15 0.0 2.15Figure 1 - Test GearsTable II - Basi
18、c Test Gear ConfigurationIIPinion GearNumber of Teeth 25 31Diametral Pitch, Transverse 8.Center Distance 3.50Pressure Angle, Transverse 25 (Std Profile Contact Ratio)20 (High Profile Contact Ratio)Face Width (Spur recorded acoustic intensity spectra in the analyzer for each node of the grid; andtran
19、smitted the spectra to the computer for storage on_ disk.The aconstie intensity probe consists of a pair ofaEAr_NmSEat_ phase-matched 6 mm microphones mounted face-to-face with a 6 mm spacer. The probe has a frequencyrange (1 dB) of 300-10,000 I-Iz. Measurements wereFigure 2 - Nasa Gear Test Rig mad
20、e at a distance of 60 mm between the acousticcenter of the microphones and the gearbox top.A 20 node measurement grid was drawn on the top The 20 intensity spectra collected at each operatingcover of the gear box and used to insure repeatability condition were averaged, then multiplied by theof the
21、noise measurements and to aid in avoiding radiation area to compute an 800 line sound poweroperator induced errors. The grid covers an area 228 spectrum. The radiation area was assumed to be thex 304 mm (9 x 12 in) centered on the 286 x 362 mm area of the grid plus one additional row and column(11.2
22、5 x 14.25 in) top. A cutaway section of the test of elements or 0.0910 m2. The aetnal area of the topgear box is shown in Figure 3. All data was collected is 0.1034 mz. The measurement grid did not extendcompletely to the edges of the gearbox top becausethe edge of the top was bored to a stiff mount
23、ingflange which would not allow much movement andmeasurements taken close to the edge of the topwould be affected by noise radiated from the sides ofthe box. Noise measurements from the gearbox sideswere not attempted for the following reasons:(1) the top is not as stiff as the sides; thus, noiserad
24、iation from the top dominates(2) the number of measurement locations were keptreasonable; and(3) shafting and other projections made suchmeasurements difficult.Sound power measurements were made over a matrix 9_.)_;II ,_ _ “:.of nine test conditions: 3 speeds (3000, 4000, 5000rpm) and at 3 torque le
25、vels (60, 80 and 100 percent Figure 4 - Robot Noise Measurement Systemof the reference torque 256 N-m (2269 in-lb). Duringeach intensity scan, the speed was hetd to within 5rpm and torque to _-2N-m. At least five complete sets PROCESSING SOUND POWER DATAof scans were performed on each gear set.The s
26、ound power data as captured by the methodAcoustic intensity data were recorded over the outlined above consists ofmany data files of 800 linebandwidth 896-7296 Hz. On the 800 line analyzer, sound power spectra. A typical spectrum is shown inthis produced a line spacing of 8 Hz. We chose this Figure
27、5. This trace (taken at 5000 rpm and 100frequency range because it includes the first three percent torque) includes the first three harmonies ofharmonies of gear meshing frequency for the speed gear mesh frequency. Each harmonic is surrounded byrange (3000-5000 rpm). In addition to the intensity a
28、number of sidebands.data, signals from two microphones and twoaecelerometers were recorded on four-channel tape.Ba_I ,n_ S_e“ fieor_ No 4/8I_1_if_Frequeem: 9, kHzFigure 5 - Baseline Spur SpectrumTo characterize gear noise data, it was decided toreduce the 800 line sound power spectra to a singlenumb
29、er that would represent each gear meshharmonic. For the subject report, this is referred to asFigure 3 - Test Gear Box Cutaway Section the harmonic sound power level. Five alternativeswere considered for reporting of each harmonic level:(1) The amplitude at gear mesh frequency only (no Bo_,_ _p_rG N
30、o 4/8sidebands)(2) The value oftbe largest amplitude mesh frequency stharmonic or sideband, whichever is highest _ i _f q(3) The log sum of the sound intensity amplitudes ina fixed-width frequency band centered on the mesh _frequency.(4) A value similar to (3) except the size of the 8 _ ,_ , ,_ ,9 _
31、 _ 2_ _ 2, _5frequency band varied with speed. The total number F_,=_. kH_of values added is not constant.(5) Sum of gear mesh and fixed number of sidebands. Figure 6 - Enlargement of Figure 5(Around First Harmonic)Alternative (5) was chosen for computing theharmonic sound power level. We used three
32、 pairs ofsidebands plns the harmonies (i.e., seven peaks) in thecalculation. Sound power levels were converted to Cl=t (6/v/-n) ( 1 )Watts prior to calculating sums.where:In the analysis of the intensity data, each harmonic ofgear mesh frequency was defined by several digital C_ = confidence limit,
33、dBlines of the frequency analyzer. In order to capturethe total effective magnitude at each harmonic, while t = probability distribution (“Studentaccounting for speed drift, ete, the peak value and two t“ distribution)frequency lines on either side of the peak weresummed. These values were converted
34、 to dB (re 10_2 8 = standard deviation of data, dBW) to define a mesh harmonic level. Since sevenpeaks were used, 35 values (5x7) were summed to n = number of samples (typically 5)produce the mesh harmonic sound power level Figure6 illustrates the data (marked with the symbol “*“) The values for the
35、 “t“ distribution are found in anyused to produce the harmonic sound power level. This standard statistics text. A confidence level of 95is a portion of the spectrum of Figure 5 showing the percent corresponds to a 5% probability. The numberfirst harmonic (at 2083 Hz). The sideband spacing of degree
36、s of freedom in the “t“ distribution is the(for 5000 rpm) is 83 Hz, thus there are about 10 number of samples minus 1 (typically 4).analyzer lines per sideband. At lower speeds, thereare fewer analyzer lines per sideband. To estimate the effect due to sample-to-samplevariation, two sets of gears for
37、 each design werefabricated and tested. Each gear was inspected inDATA SAMPLING detail in accordance with typical production helicopterstandards. The overall accuracy of the gears wasIn order to be assured that data measured on each found to be consistent with what we expect ofgear set could be reli
38、ably compared with data from production helicopter gears of similar size andother gears, it was desired to have sufficient records eonfignration. Based on our evaluation of the gearto establish a 95% confidence level of 1 dB. This tooth inspection data, the variation between the twolevel is well bey
39、ond the practical difference (i.e., a sets of gears is reasonably typical of normalchange of about 3 dB) which most persons with production for gears in the same manufacturing lot.normal hearing can detect. Lot to lot variations may be and differences betweendifferent manufacturers of the same parts
40、 certainlyBased on these considerations, the confidence limit will be higher but the overall trend of the effectis given by Equation 1: should be about the same.6We have also noted that a large difference in noise Better load capacity, due to lower messes, is anotherlevel is sometimes observed on la
41、rge production gear factor but will be ignored for our purposes.boxes simply as a result of rebuilding them after theywere disassembled for a visual inspection, eventhough no parts were chon_ged.Considering this effect, z_.000in addition to the manufacturing variability checks, we BASEUNESPURalso ch
42、ecked for variability due to disassembly and 1so.000reassembly. _We accomplished this by testing three “builds“ of the _ 12o,ooofirst gear set. Each build used exactly the same partsand each was accomplished by the same technician _“ eo.ooousingthe sametools,andmiscellaneousparts. _0 HeR i:HELICAL40
43、,000TEST GEAR LOADING0 , I , , I , ,1.500 2000 2,500The loads applied to the test gears during this 1.000program presented a problem in the design of the TORQUE(INCH-LBS)experiment. Obviously, if the overall gear geometry iskept constant, the stress levels under identical torque Figure 8 - Contact S
44、tress v TorqueIn order to provide an overview of the stress levels to3o,ooor which these gears were subjected during testing,8ASEUNESPUR Figures 7, 8, Id1361 51/2269, _ 31d1816 4W1361 4kr2269 5k/18t6Speed(rpm)t Torque(in*lb) BaselineSpur HCRSpur NIFSpur NIFHCRSpurFigure 19 - Modified Contact Ratio E
45、ffectTooth Form - In general, the noninvohite tooth form, Figure 21 - Tooth Form Effectwhether standard (configuration 7) or high profilecontact ratio (configuration 8), resulted in slightly13While the difference between standard and highprofile contact ratio spur gears is not really a tooth 4000 RP
46、M Relative To Spur Baselineform variation in the strictest sense of the concept, it _ 10 Increaseis often referred to as such. Based on the testingconducted herein, the high profile contact ratio gear _ 5sets (configurations 2 & 8) resulted in lower noise _ 0levels th_n their standard contact ratio
47、counterparts if- !(configurations 1 & 7, respectively). This effect was _= (5)especially pronounced at the lower speed end of the-_ (10)test range and there were some exceptions, especially 8.at the 4,000 RPM condition. Still, since high profile oE 15)contact ratio does not cause any additional load
48、ing onthe system (as would a helical gear), it is a viable, _ (20)and possibly preferable option in many cases. 1361 1861 2269Torque (in*lb) HCR Spur 3 BaseHelca121.5de9 _ 0o_ Hek:alm Hellca128_dog Heka1353 dog NIFSlUr NIF HCRSpurSpread Hei_l3000 RPM Relative To Baseline Spurm 15 Figure 23 - 4,000 R
49、PM Noise SummarylO Increase-J_, 5#- 0_ 5000 RPM RelativeTo BaselineSpur09 v(10) “_ Increase“_(15)8_(20) a _0_,_ (5) _ L _ -(25) 1361 1861 2269 o=Torque(in*lb) u) (10)0.1 HCRSpur BaseHehca121.5dog Q DoubleHelicM E Hehca128.9deg _.rl:lHehca1353 rJegi“i NIF Spur NIF HCRSpur I_ SpreaclSingLeHelical (1Oo= ReductionFigure 22 - 3,000 RPM Noise Summary _ (20)ra 1361 1861 2269Torque(in*lb)I HCRSI_r t_ BaseHeka121.5 deg B Double Helical I Helical28.9 deg Helical 35.3 deg El NIF Spur NIF HCR Spur SpreadHercalCONCLUSIONSThe results of
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