Influence of Gear Design onGearbox Radiated Noise

Fred B. Oswald, Dennis P. Townsend, Mark J. ValcoRobert H. Spencer, Raymond J. Drago & Joseph W. Lenski, Jr.

IntroductionA major source of helicopter cabin noise

(which has been measured at over 100 decibelssound pressure level) is the gearbox. Reductionof this noise is a NASA and U.S. Army goal. Arequirement for the Army/NASA AdvancedRotorcraft Transmission project was a 10 dBnoise reduction compared to current designs.

The main exciting forces which produce gearnoise are the meshing forces of the gear teeth inthe transmission. While many factors influencetransmission noise, the simple fact remains that ifthe basic exciting forces are reduced and noamplifying factors are present, the overall noiselevel of the system will be reduced.

Among the several ways in which the gear toothmeshing forces may be reduced, two of the mostdirectly applicable to helicopter transmissions arethe form of the teeth and the overall contact ratio.Both approaches are attractive for an aerospaceapplication since, unlike sound absorbing treat-ments, these approaches have the potential forreducing noise without reducing performance orincreasing overall system weight. Both approachesalso offer the possibility of improving gear perfor-mance in terms of longer life, higher load capacity,greater reliability and reduced weight, while simul-taneously reducing noise levels.

Helical gears, as compared to spur gears, typ-ically produce lower noise levels. Winter (Ref. I)

provides a concise summary on the variation ofexcitation levels with face contact ratio. There islittle other definitive data which defines the noiseadvantage of helical gears for accurate, groundgears. Similarly, anecdotal information indicatesthat higher contact ratios, both face and profile,also tend to reduce noise levels but, again, harddata is not readily available.

While helical gears provide some noise reduc-tion, their use also generates a thrust load whichmust be dealt with in the design of the overall sys-tem, especially the support bearings, gear blankdesign and housing structure. Double helicalgears, which cancel the thrust loads from eachhelix within the gear blank, provide relief from netthrust problems. However, the noise properties ofdouble helical gears have not been reported.

Noninvolute tooth forms have been investigat-ed for possible use in helicopter transmissions inrecent years. Testing of high profile contact ratio,noninvolute tooth form gears (HCR-NIF) hasshown that the load capacity can be substantiallyhigher than that of conventional involute gears,and the bending load capacity (at high loads) wasat least equal to that of the involute gears (Ref. 2).These investigations, however, have centeredalmost universally on the load capacity and noton noise generation.

This program was conducted as part of theAdvanced Rotorcraft Transmission Project (Ref.

Table 1 - Test Gear Configurations

Transverse Contact RatioConfiguration Tooth Form Type Pressure Angle Profile Face Total

1. Spur Baseline Involute Spur 25 1.3 0.0 1.3

2. HCR Spur Involute Spur 20 2.1 0.0 2.1

3. Helical Baseline Involute 21.5° Helical 25 1.3 1.25 2.6

4. Double Helical Involute 38.2° Helical 25 1.3 2.50 3.8

5. Helical Involute 28.9° Helical 25 1.3 1.76 3.1

6. HCR Helical Involute 35.3° Helical 20 2.1 2.25 4.4

7. NIP Spur Baseline Noninvolute Spur 25 1.3 0.0 1.3

8. NIF-HCR Spur Noninvolute Spur 20 2.1 0.0 2.1I

10 GEAR TECHNOLOGY

3). Its objective was to define, by controlled test-ing, the effect on noise levels due to changes inthe profile and face contact ratios and the geartooth form. These factors were varied both sepa-rately and in combination.

The test gear configurations were selected tobe representative of those used in helicoptertransmissions. The test gear designs include fourdifferent types of spur gears (low and high con-tact-ratio in both involute and noninvolute pro-files), as well as five different helical (single anddouble) gear designs with various profile and facecontact ratios. The gears were designed to be asnearly identical as possible, except for deliberatedifferences in tooth geometry and contact ratio.

Testing was conducted under controlled condi-tions (torque, speed, oil flow, temperatures, etc.).Acoustic intensity measurements were taken withthe aid of a robot to insure repeatability of mea-surements between gear sets and to minimize theinfluence of operator technique. Results present-ed here include trends of the sound power at meshfrequency and narrow-band spectra of soundpower. Preliminary results from this programwere earlier presented by Drago (Ref. 4).

Test GearsEight sets of test gears were designed. Four of

these are spur gears. Two sets have an involutetooth form, and two utilize a noninvolute, con-stant radius of curvature profile. All gears weredesigned in accordance with standard aerospacepractice so that, except for size, they are repre-sentative of typical helicopter gears. The eightgear designs are summarized in Table I and areshown in Fig. I. Additional test parameters areshown in Table 2.

Fig. 1 also shows a gear set which is not listedin Table 1. This was not one of the planned testvariants. During the manufacture of the test gears,the double helical gear drawings went out with adrafting error such that both helices were manu-factured with the same hand. The resultant gearset (known officially as "spread single helicalgears" and unofficially as "OOPS" gears), areshown in the upper right corner of Fig. l.Although these gears probably would not be usedin a production environment, we decided to testone pair of them anyway.

Apparatus & ProcedureTest Facility. The NASA Lewis gear noise rig

(Fig. 2) was used for these tests. This rig featuresa single-mesh gearbox powered by alSO kW(200 hp) variable speed electric motor. An eddycurrent dynamometer loads the output shaft. Thegearbox can be operated at speeds up to 6000rpm. The rig was built to carry out fundamental

Transverse Module, mm(diametral ptich, in-])

studies of gear noise and the dynamic behavior ofgear systems. It is designed to allow testing ofvarious configurations of gears, bearings,dampers and supports. To reduce unwantedreflection of noise, acoustical baffles covered testcell walls, floor and other nonmoving surfaces.The material attenuates reflected sound by 20 dBor more for frequencies of 500 Hz and above.

Instrumentation and Test Procedure. Exper-imental modal test results from a previous testingprogram (Ref. 5) provided the first five naturalfrequencies and modes of vibration of the gear-box top. The natural frequencies were checked toassure that gear mesh frequencies did not coin-cide with important modes of the gearbox. Also,from previous analytical work, we know that tor-sional modes of the gear system are well abovethe 6000 rpm speed limit of the rig.

Fred B. OswaldDennis P.Townsendare with the NASA LewisResearch Center,Cleveland, OH.

is with the U.S. ArmyResearch Laboratory atNASA Lewis ResearchCenter.

Robert H. SpencerRaymond J. DragoJoseph W. Lenski, Jr.are with Boeing Helicopters,Philadelphia, PA.

JANUARY/FEBRUARY 1998 11

Acoustic intensity measurements were per-formed, under stable, steady-state operating con-ditions, with the aid of a computer-controlledrobot designated RAIMS (Robotic AcousticIntensity Measurement System). The RAIMSsoftware (1) commanded the robot to move anintensity probe over a prescribed measurementgrid; (2) recorded acoustic intensity spectra in theanalyzer for each node of the grid; and (3) trans-mitted the spectra to the computer for storage ondisk. The gearbox, robot and intensity probe areillustrated in Fig. 3. RAIMS is more completelydescribed in Refs. 6 and 7.

The acoustic intensity probe consists of a pairof phase-matched 6 mm microphones mountedface-to-face with a 6 mm spacer. The probe has afrequency range (±l dB) of 300-10,000 Hz.Measurements were made at a distance of 60 mmbetween the acoustic center of the microphonesand the gearbox top.

At each operating condition, the intensityspectra collected from the twenty nodes of thegrid were averaged, then multiplied by the area tocompute an 80l-line sound power spectrum. The

r'"Fig. 3 - Test gearbox and RAIMS robot.

9B

7B

5Bal"0

JBciW~a0..0Z::Ja(fJ

Fig. 4 - Spectra for spur gears (from bottom, Configurations 1,2,7,8) at 100% speed,100% torque.12 GEAR TECHNOLOGY

area was assumed to be the area of the grid, plusone-half additional row and column of elements,or 0.0910 m2. The actual area of the top is 0.1034m2. We did not extend the measurement gridcompletely to the edges of the gearbox topbecause the edge of the top was bolted to a stiffmounting flange which would not allow muchmovement, and measurements taken close to theedge of the top would be affected by noise radi-ated from the sides of the box.

Noise measurements from the gearbox sideswere not attempted for the following reasons: (1)the top is not as stiff as the sides; thus, noise radi-ation from the top dominates at most frequencies;(2) the number of measurement locations werereduced; and (3) shafting and other projectionsmade such measurements difficult.

Sound power measurements were made over amatrix of nine test conditions: 3 speeds (60, 80and 100% of 5000 rpm) and at 3 torque levels(60, 80 and 100% of the reference torque 256 N-m (2269 in-lb)). During each intensity scan, thespeed was held to within ±5 rpm and torque to ±2N-m. At least five complete sets of scans wereperformed on each gear set.

Acoustic intensity data were recorded over thebandwidth 896-7296 Hz. On the 80l-line analyz-er, this produced a line spacing of 8 Hz. We chosethis frequency range because it includes the firstthree harmonics of gear meshing frequency forthe speed range (3000-5000 rpm).

Processing Sound Power Data. The soundpower data captured by the method outlinedabove consists of many data files of sound powerspectra. Sample spectra for the four spur gearconfigurations are shown in Fig. 4, and spectrafor the five helical gear configurations in Fig. 5.Each spectrum includes the first three harmonicsof gear mesh frequency. The harmonic frequen-cies are marked with a "." on the top border. Eachharmonic is surrounded by several sidebands.The most prominent sidebands were related tothe pinion shaft frequency. Gear shaft sidebandswere not prominent.

To characterize the measurements, we decidedto reduce each 80l-line sound power spectrum toa few numbers that would represent the gearmesh noise. We call these numbers the harmonicsound power levels.

We considered five methods for determiningthe sound power level.

(1) Record only the value at the mesh fre-quency harmonic. This means to ignore side-bands even though they were often significant.

(2) Check the harmonic frequency and severalsidebands and record the highest value.

(3) Add together the values within a fixed-width frequency band centered on the mesh fre-quency. This means more sidebands would beincluded at lower speeds where the sidebandspacing is less.

(4) Similar to (3), except the size ofthe frequencyband would vary with speed. This means the numberof values added together would not be constant.

(5) Add the values at the mesh frequency andat a fixed number of sidebands on each side of themesh frequency.

Alternative 5 was chosen for calculating har-monic sound power levels. We used three pairs ofsidebands at pinion shaft spacing (i.e., 7 peaks).Sound power values were converted to watts priorto calculation of sums.

To reduce effects of speed drift and signalleakage, we took the value at the peak plus twofrequency lines on each side. In other words, weadded together five values at each peak. Sinceseven peaks were used, 35 values (5 x 7) wereadded together to produce each harmonic soundpower level. Fig. 6 shows the data (marked withsymbols "*,, and "+") used to compute one har-monic sound power level. This is from the toptrace in Fig. 4 near the first harmonic at 2083 Hz.(We deliberately chose an unusual example whereone sideband is higher than the mesh frequency.)The sideband spacing at 5000 rpm is 83 Hz; thus,there are about 20 analyzer lines per sideband. Atlower speeds, there are fewer analyzer lines persideband.

Data Sampling. To be assured that data fromeach gear set can be reliably compared with datafrom other gears, we needed to have sufficientrecords to establish a 95% confidence level of ± 1dB. This is well beyond the practical difference(i.e., a change of about 3 dB) which normal hear-ing can detect.

We performed at least five complete sets ofscans on each pair of gears tested. From these setsof measurements, we computed mean values andconfidence limits of the harmonic sound powerlevel. (For the calculation of mean and confi-dence limit, dB values were used. We did notconvert back to watts.) The confidence limit wascalculated from

whereC 1= confidence limit, dBt = probability distribution

("Student t" distribution)8 = standard deviation of data, dBn = number of samples (typically 5)

Values for the "t" distribution can be found inany standard statistics text. We chose a 95% con-

9B

7B

5B

al JB-0

0:"w5;00-0Z::::>0(j)

Fig. 5 - Spectra for spur gears (from bottom, Configurations 3, 5, 6, 4 and "OOPS") at100% speed, 100% torque.

al-0 BB0:-W5;00-0Z 6B::::>0(j)

fidence level, which corresponds to a probabilitylevel of 0.05. The number of degrees of freedomin the t distribution is the number of samplesminus 1.

The mean values of the three harmonic soundpower levels were used to compute a single"composite" noise level for each test condition byadding the sound power (in watts) and then con-verting to dB. It is these composite values that wecompare for the various gear configurations.

To estimate the effect due to sample-to-samplevariation, two sets of gears for each design werefabricated and tested. Each gear was inspected inaccordance with typical production helicopterstandards. The overall accuracy of the gears wasconsistent with production helicopter gears ofsimilar size and configuration. The variationbetween the sets of gears is reasonably typical ofnormal production for gears in the same manu-facturing lot. Lot-to-lot variations (not testedhere) may be higher, but the overall trend of theeffect should be about the same.

A large difference in noise level is sometimesobserved on production gearboxes simply as a

JANUARY/FEBRUARY 1998 13

result of rebuilding them after disassembly forinspection, even though no parts were changed.Considering this effect, in addition to the manu-facturing variability checks, we also checked forvariability due to disassembly and reassembly.

We checked for variability by testing three"builds" of the first gear set. Each build usedexactly the same parts, and each was accom-plished by the same technician using the sametools and parts.

ResultsA very large amount of data was collected dur-

ing this test program. An overview is presented inthe composite noise level bar charts of Figs. 7-8.

Spur Gears. We tested gears with both invo-lute and noninvolute tooth forms and with bothstandard and high profile contact ratios. Thoughthe noise levels (Fig. 7) generally increased withspeed, in general, the high contact ratio spurgears (Configs. 2, 8) were 2 dB quieter than thestandard contact ratio gears (Configs. 1,7) regard-less of the tooth form. Similarly, the involutetooth form gears (Configs. I, 2) were quieter (by3-4 dB) than their noninvolute counterparts(Configs. 7, 8).

EO '00

:s-' "w>w '"-'a:wS .500..0 .0

Z::J0(fJWI-Ui0D..

'":2i0U so

- J ,,,

,

J,

~~ ~

:,

,

Fig. 8 - Helical gear composite noise levels.14 GEAR TECHNOLOGY

Helical Gears. The single helical gearsinclude three different helix angles and both stan-dard and high profile contact ratios. As in thespur gears, an increase in the contact ratio corre-lates with a decrease in the noise level. Increasingthe face contact ratio from about 1.15 (Config. 3)to 1.6 (Config. 5) decreases the noise level sub-stantially in every case, though the results athigher speeds are more dramatic than at lowerspeeds. Also, at every operating condition, thecomposite noise level of a helical gear (Fig. 8) isless than the level for a spur gear with similarprofile contact ratio.

The combination of high profile and high facecontact ratio further decreases gear noise. Indeed,the high profile and high face contact ratio design(Config. 6) with profile and face contact ratios of2. I and 2.1 respectively was the lowest noise gen-erator at almost every operating condition.

Helical gears used in helicopters tend to haverelatively low face contact ratios (helix angles arekept low to minimize thrust loading and the extraweight associated with reacting to the thrust);thus, this result is especially interesting, since itsuggests that it may be possible to trade off helixangle against increasing profile contact ratio toimprove the noise level without the weight penal-ty associated with accomplishing the same reduc-tion with helix angle alone.

A surprising result, the double helical gear setwas noisier (by 4 dB on average) than its singlehelical (OOPS gear) counterpart. The OOPS gearset is essentially a single helical set with a gap inthe middle of the tooth face. Its effective facecontact ratio is similar to that of the high contactratio helical gears (Config. 6).

The double helical phenomenon appears to berelated to axial shuttling, which occurs as thedouble helical pinion moves to balance out thenet thrust loading. The shuttling is due to thepresence of small mismatches in the relative posi-tions of the teeth on each helix. No matter howaccurate the gear is, some mismatch will alwaysbe present; thus, this is an unavoidable phenome-non.

While the thrust balancing characteristic of adouble helical gear is a valuable design feature,since it greatly simplifies the bearing system, aprice is paid in terms of noise and vibration as thegear set shuttles back and forth.

Since the per helix face contact ratio, facewidth, profile contact ratio, etc. are identical forthe OOPS and the double helical gear sets, theonly operational difference is the lack of axialshuttling. The double helical set will be in a con-stant equilibrium-seeking state because of the

theoretically zero net thrust load, while the OOPSgear set will run in a fixed axial position becauseof the net thrust load.

This test provides some insight into the mag-nitude of the noise penalty which is paid whendouble rather than equivalent single helical gearsare used. Since these test gears are all very accu-rate (typical for helicopter gears), it should beobvious that a larger penalty would be paid ifgears of lesser quality were to be used, becausethe lower the gear quality is, the more shuttlingwould be likely to occur.

Sample, Build & Specimen Variations. Atleast five sets of noise scans at each operatingcondition were taken. Our goal was to obtain con-fidence limits within 1 dB for each value of har-monic sound power level. This goal was met onabout 60% of the test sets.

During other testing, the authors have notedsignificant variations in the measured (and per-ceived) noise level of the same gear system beforeand after disassembly. In some cases, this varia-tion was of considerable magnitude. To investi-gate this phenomenon, the first set of baselinespur gears (Config. I), was assembled, tested, dis-assembled, reassembled and then tested again.This process was repeated until the gears hadbeen tested three times.

The largest minimum-to-maximum build varia-tion was 7.8 dB (at the high speed, low torque con-dition), while the minimum build variation was 0.7dB (at the medium speed condition). The averagebuild variation was about 3 dB. While no real pat-tern is apparent, it appears that the variationdecreased slightly with increasing load.

Since we tested two samples of each of theeight gear designs, we can compare the "build"variation to the variation between "identical" parts.For the eight gear designs, the average part-to-partvariation in the composite noise levels was 2.8 dB.One would expect the variation between samplesof the same part to equal or exceed the variationfrom rebuilding the same parts. The "build" testwas performed at the beginning of the test pro-

gram. Increased experience may have reduced thevariation for later tests.

The factors considered above point out the dif-ficulty in defining a noise reduction effort in thatthe variations due to unintended effects are oftenof the same order of magnitude as the changeswhich may be attributed to gear configuration ortreatment. Such differences should exceed thevariations due to sample and build effects andthose observed among different specimens of thesame part before they can be considered signifi-cant in themselves.

ConclusionsNine different spur and helical gear designs

were tested in the NASA gear-noise rig to com-pare the noise radiated from the gearbox top forthe various gear designs. Sound power measure-ments were made under controlled conditions fora matrix of operating conditions. The followingconclusions were made:

1. The most significant factor for noise reduc-tion within a gear designer's control was the totalcontact ratio. Gear noise may be reduced byincreasing either the profile or face contact ratio.

2. The noninvolute tooth form spur gears havea 3--4 dB noise penalty compared to their conven-

tional involute counterparts.3. The high contact ratio spur gears (with a

58% increase in profile contact ratio) showed anaverage noise reduction of about 2 dB over stan-dard gears.

4. The noise level of double helical gears aver-aged about 4 dB higher than otherwise similarsingle helical gears.

5. In noise reduction tests, variation due tounintended effects, such as testing different partspecimens or even reassembly with the sameparts, may be of the same order of magnitude asthe effect of deliberate design changes. 0

References:1. Winter, H. et al. "Investigations on the

Excitation of Vibrations and Noise at Spur and HelicalGears," Proceedings, ASME 1989 International PowerTransmission Gearing Conference, Chicago, IL, Apr.25-28, 1989, pp. 765-772.

2. Townsend, Dennis P. et al. "Evaluation of HighContact Ratio Spur Gears With Profile Modifica-tions," NASA TP-1458, Sept., 1979.

3. Bill, R. C. "Summary Highlights of theAdvanced Rotorcraft Transmission (ART) Program,"AIAA Paper 92-3362, July, 1992.

4. Drago, R. J. et al. "The Relative Noise Levelsof Parallel Axis Gear Sets with Various ContactRatios and Gear Tooth Forms," AGMA Report 93-FTM-ll, Oct., 1993. (Also NASA TM-106431.)

5. Oswald, F. B. et al. "Effect of OperatingConditions on Gearbox Noise," ASME publicationDE-Vol. 43-2, pp. 669-674, Sept., 1992. (AlsoNASA TM-I05331.)

6. Flanagan, P. M. & W. J. Atherton. "Investiga-tion on Experimental Techniques to Detect, Locateand Quantify Gear Noise in Helicopter Transmis-sions," NASA CR-3847, 1985.

7. Atherton, William J. et al. "AutomatedAcoustic Intensity Measurements and the Effect ofGear Tooth Profile on Noise," Mechanical SignatureAnalysis-Machinery Vibration, Flow-InducedVibration and Acoustic Noise Analysis, S. Braun etaI., eds., ASME, pp. 109-113, 1987. (Also NASATM-100155.)

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