NASA

AVSCOMTechnical Memorandum 105330

Technical Report 91—C-030

Comparison of Analysis and Experimentfor Gearbox Noise

Fred B. OswaldLewis Research CenterCleveland, Ohio

A.F. Seybert and T.W. WuThe University of KentuckyLexington, Kentucky

and

William AthertonCleveland State UniversityCleveland, Ohio

Prepared for theSixth International Power Transmission and Gearing Conferencesponsored by the American Society of Mechanical Engineersand Journal of Mechanical DesignPhoenix, Arizona, September 13-16, 1992

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https://ntrs.nasa.gov/search.jsp?R=19920016153 2020-05-15T03:17:23+00:00Z

COMPARISON OF ANALYSIS AND EXPERIMENT FOR GEARBOX NOISE

Fred B. OswaldNational Aeronautics and Space Administration

Lewis Research CenterCleveland, Ohio 44135

A.F. Seybert and T.W. WuThe University of KentuckyLexington, Kentucky 40506

and

William AthertonCleveland State University

Cleveland, Ohio 44115

ABSTRACT

Low-contact-ratio spur gears were tested in the NASA gear-noise rig to study the noise radiated from the top of the gearbox.Experimental results were compared with a NASA acoustics code tovalidate the code for predicting transmission noise.

The analytical code is based on the boundary element method(BEM) which models the gearbox top as a plate in an infinite baffle.Narrow-band vibration spectra measured at 63 nodes on the gearboxtop were used to produce input data for the BEM model. The BEMcode predicted the total sound power based on this measuredvibration.

The measured sound power was obtained from an acousticintensity scan taken near the surface of the gearbox at the same63 nodes used for vibration measurements. Analytical and experi-mental results were compared at four different speeds for soundpower at each of the narrow-band frequencies over the range of400 to 3200 Hz. Results are also compared for the sound powerlevel at meshing frequency plus three sideband pairs and at selectedgearbox resonant frequencies. The difference between predicted andmeasured sound power is typically less than 3 dB with the predictedvalue generally less than the measured value.

INTRODUCTION

A major source of helicopter cabin noise (which has beenmeasured at over 100 dB sound pressure level) is the gearbox.Reduction of this noise is a NASA and U.S. Army goal. Gearmeshnoise is typically in the frequency range of 1000 to 3000 Hz, a rangeimportant for speech. A requirement for the Advanced RotorcraftTransmission project is a 10-dB noise reduction compared to currentdesigns. A combined analytical and experimental effort is underwayto study effects of design parameters on noise production. Animportant part of the project is performing experiments in theNASA Lewis gear-noise facility to verify analytical codes.

Various analytical codes are available to simulate gear dyna-mics, vibration, and noise. These include DANST (dynamic analy-sis of spur-gear transmissions) (Lin et al., 1987a, 1987b, and 1989);

GEARDYN (gear dynamics) (Boyd and Pike, 1987 and Pike, 1981);and GRD (geared rotor dynamics) (Kahraman et al., 1990). Finiteelement methods may also be used to predict the structural vibra-tion properties of a gearbox.

The acoustic modeling code used to predict the noise pro-duced by gear vibration is the boundary element method for acous-tic prediction (BEMAP). BEMAP uses the technique of boundaryelement anal ysis to predict gearbox noise (or other structural noise)from vibration data (Seybert et al., 1990).

Part of the effort of NASA gear-noise research is directedtoward validating computer codes so that the codes may be used asdesign tools. Earlier work in this project produced dynamic loadand stress data for validation of a popular NASA gear dynamicscode (Oswald et al., 1991) and dynamic friction measurements(Rebbechi et al., 1991). A related project provided validation datafor BEMAP code predictions for radiated sound power using asimple laboratory apparatus (Seybert et al., 1992).

The goal of this effort was to provide experimental data froman actual gearbox to verify BF,MAP predictions. Results presentedinclude narrow-band spectra comparing measured and computedsound power, and sound power comparisons at mesh frequency andat several modal frequencies.

TEST FACILITY AND TEST SPECIMENS

The facility used for these tests is the NASA Lewis gear-noiserig (Fig. 1). This rig consists of a single-mesh gearbox driven by a150-kW (200-hp) variable speed electric motor. An eddy-currentdynamometer loads the output shaft. The gearbox can be operatedat speeds up to 10 000 rpm input or 6000 rpm output. The rig wasbuilt to carry out fundamental studies of gear noise and the dyna-mic behavior of gear systems. It is designed to allow testing ofvarious configurations of gears, bearings, dampers, and supports.To reduce unwanted reflection of noise ; acoustic-absorbing foambaffles covered the test cell walls, floor, and other nonmovingsurfaces. The material used attenuates reflected sound by at least20 dB for frequencies of 500 IIz and above.

Dynamometer I

Optional

Optional output flywheel-

input flywheel Test

(a) Layout.

(b) Test gearbox showing measurement grid and RAIMS robot withsound intensity probe.

Figure 1.—NASA gear-noise rig.

A poly-V belt drive was used as a speed increaser between themotor and gearbox input shaft. A soft coupling was installed on theinput shaft to reduce input torque fluctuations, which were causedby nonuniforrnity at the belt splice.

The test gears were identical spur gears (operating at 1:1ratio) machined to AGMA Class 15 accuracy. The gears have lineartip relief chosen for optimum operation at a design load. Test gearparameters are shown in Table I.

TABLE L—TEST GEAR PARAMETERS

Spur gear type .......... Standard involute, full-depth toothNumber of teeth ................................ 28Module, mm (diametrical pitch in.' l) ............. 3.175 (8)Face width, mm (in.) ....................... 6.35 (0.25)Pressure angle, deg .............................. 20Nominal (100 percent) torque, N-m (in.-lb) ..... 71.77 (635.25)Theoretical contact ratio ......................... 1.64Modification amount, mm (in.) .............. 0.018 (0.0007)Modification start, deg .................. .......... 24. 5

A 63-node measurement grid was marked out on the top ofthe gearbox. The grid covers an area 228 by 304 mm (9 by 12 in.)centered on the 286- by 362-mm (11.25- by 14.25-in.) top. Thegearbox with its measurement grid and some instrumentation areshown in Fig. 1(b).

INSTRUMENTATION AND TEST PROCEDURE

An experimental modal test was performed to determine themodes of vibration and natural frequencies of the gearbox top. An800-line, 2-channel dynamic signal (FFT) analyzer collectedfrequency-domain data. Commercial modal software running on apersonal computer was used for the analysis. The modal tests wereperformed with the top installed on the gearbox and with the gear-box heated to operating temperature. The structure was excitedsequentially at each of the 63 nodes using a load-cell-equippedmodal hammer to measure excitation forces. The response wasmeasured with a small piezoelectric accelerometer mounted at areference location near the center of the gearbox top.

Gearbox vibration was measured by two piezoelectric acceler-ometers with a frequency range of 5 to 10 000 Hz. A fixed accelero-meter was located at the reference node and a movable accelerometerwas used for measurements at each of the 63 nodes on the top.

The analyzer captured the magnitude spectrum for the mov-able accelerometer and the phase spectrum between the accelero-meters. The data were transferred to a desktop computer andconverted to real and imaginary components of velocity. Thesevelocity components were used to produce an input data file forBEMA P.

Immediately after the accelerometer scan (under stable opera-ting conditions), an acoustic intensity scan was performed with theaid of a computer-controlled robot designated RAIMS (roboticacoustic intensity measurement system). The RALMS software(1) commanded the robot to move an intensity probe over a pre-scribed measurement grid; (2) recorded acoustic intensity spectra inthe analyzer for each node of the grid; and (3) transmitted thespectra to the computer for storage on disk. RAIMS is describedmore completely in Flanagan and Atherton (1985) and in Athertonet al. (1987).

The acoustic intensity probe consists of a pair of phase-matched 12-mm (0.5-in.) microphones mounted face-to-face with a12-mm (0.5-in.) spacer. The probe has a frequency range (tl dB)of 125 to 5000 Hz. Measurements were made at a distance of75 mm (3 in.) between the acoustic center of the microphones andthe gearbox top.

The intensity spectra from each of the 63 measurement loca-tions collected at each operating condition were averaged, thenmultiplied by the radiation area to compute an 800-line soundpower spectrum. The radiation area was assumed to be the areaof the grid plus one additional row and column of elements or0.0910 m 2 . The actual area of the top is 0.1034 m 2 . The measure-ment grid did not extend completely to the edges of the gearbox topbecause (1) the edge of the top was bolted to a stiff mounting flangewhich would not allow much movement and (2) measurementstaken close to the edge of the top would be affected by noiseradiated from the sides of the box. (To keep the experimental effortreasonable, neither noise nor vibration measurements wereattempted on the gearbox sides.)

Vibration and intensity measurements were made at four testconditions: 3000, 4000, 5000, and 6000 rpm and at a constant94 percent of the reference torque level of 71.8 N-m (635 in.-lb).

During measurements, speed was held to within t8 rpm and torqueto ±1 N-m. All frequency-domain data were recorded over thebandwidth 0 to 3200 Hz.

1 ZIX Y X '`--Y

(a) 1/1 mode, 511 Hz. (b) 211 mode, 975 Hz.

X l' Y X Y

(c) 1/2 mode, 1273 Hz. (d) 2/2 mode, 1631 Hz.

Figure 2.—Gearbox vibration modes.

ANALYTIC MODEL

The BEMAP program is based on the boundary elementmethod (BEM) (Seybert et al., 1985, 1986, 1987, 1990, 1991, and1992). BEMAP can compute several acoustic parameters on, inside,or outside the structure of interest including sound intensity, soundpressure level, sound radiation efficiency, and the total sound power.For this work, a public-domain PC version of BEMAP was used.This version is called BEMAP100 and will be available through theComputer Software Management and Information Center(COSMIC) at the University of Georgia. BEMAP100 (referred tohere as BEMAP) is limited to 100 nodes and 70 elements.

Using BEMAP, the gearbox top was modeled as a plate in aninfinite baffle. Inputs to BEMAP include the geometry of thestructure and, for each mode, the vibration frequencies and thenodal velocity components. Hence, for 63 nodes and 800 frequencies,50 400 pairs of velocity values were required. BEMAP computed an800-line sound power spectrum for the gearbox top based on theaccelerometer data. Several specialized computer programs weredeveloped for this project. These programs collect and transformmeasured data, produce input files ; extract the required output data(from a large BEMAP output file), and plot spectra comparingBEMAP predictions with measured sound power.

A B C D80 r-

70

60

50

40NO

30 —

M

a^

3Aa 80

c

u) 70

A, B, C, D Vibration modes

M Gear mesh frequencyM S Sideband frequency

YA S X Measured valueBEMAP prediction

S SX

A B C D

(b) 4000 rpm, 94-percent torque.

A B C D

800 1200 1600 2000 2400 2800 3200

60

50

40

(a) 3000 rpm, 94-percent torque.

B C D

30kJ I uljM I I III

400 800 1200 1600 2000 2400 2800 3200 400

Frequency, Hz

(c) 5000 rpm, 94-percent torque. (d) 6000 rpm, 94-percent torque.

Figure 3.—Comparison of BEMAP prediction and measurement for sound power.

3

The 63-node grid (7 nodes x 9 nodes) produced 48 quadri-lateral linear elements (6 elements x 8 elements). The BEMAPmodel requires that the spacing between nodes be not more than 1/4of the acoustical wavelength. The nodal spacing was 38 mm, hencethe highest frequency meeting this requirement is 2250 Hz.

RESULTS AND DISCUSSION

The first four vibration modes (from modal tests) are shownin Fig. 2. Seybert et al. (1991) reported modes at slightly differentfrequencies. This difference is due to different clamping conditionsfor the top. A soft cork gasket under the gearbox top has beenreplaced by a rubber O-ring in a machined groove. (The O-ringallows stiffer clamping.)

Measured and computed sound power spectra for the four testconditions are shown in Figs. 3(a) to (d). The gearmesh frequency,three pairs of sidebands around the mesh frequency, and the fre-quencies of the first four modes are indicated in the figure. Themeasured sound power is generally about 3 dB higher than predictedvalues. The spectra from lower speeds show better correlation thanthose from higher speeds.

The acoustic data used for the spectra in Fig. 3 were used tocompute the mesh sound power. The mesh sound power is definedhere as the sum of the sound power at gearmesh frequency plus atthree pairs of sidebands (i.e., the sum of seven values). Themeasured and computed mesh sound power are compared in Fig. 4.

O Noise at mesh and sideband frequencies90 F V Noise at modal frequencies

VMeasured value = predicted value —,

a 80030CL

070 V

V)

U V VV

a 60V V.V

5050 60 70 80 90

Measured sound power, dB

Figure 4.—BEMAP predictions for sound power comparedto experimental data.

Also compared in Fig. 4 are values of the sound power at modalresonance frequencies. (These values are computed over an 80-Hzbandwidth centered at each of the first four modal resonancefrequencies.) The absolute difference between measured valuesand BEMAP predictions averaged 2.4 dB. Measured values weretypically higher than predicted values.

At 3000 rpm, the 0 to 3200 Hz measurement bandwidth con-tains the second harmonic of gearmesh frequency (2800 IIz) as wellas the fundamental (1400 Hz). A noise peak at the second harmonicfrequency can be seen (but is not marked) in the traces shown in

Fig. 3(a). At speeds higher than 3000 rpm, all higher harmonics lieoutside the bandwidth. For consistency of analysis, no higherharmonics were included in the calculated mesh sound power.

The vibration data used by BEMAP were taken only fromthe gearbox top. This limitation was imposed by the 100-nodelimitation and also to keep the effort required for collecting andprocessing the measurement reasonable. (It required about 2 hr ofgearbox operating time to collect data for each operating condition.The 800-frequency BEMAP analysis took 11 hr of computing timeon a desktop computer.)

Using BEMAP with the measured vibration data provides aprediction for noise radiated solely from the top of the gearbox.The measured sound power also includes some low-frequency noiserefracted or reflected frorn the motor, shafting, or other noisesources. Low-frequency noise would be expected to contaminate themeasurements because the acoustic baffles decline in absorptionability at low frequencies and because low-frequency noise is morelikely to be refracted to the intensity probe. Because of this low-frequency noise, frequencies below 400 Hz are not shown in thespectra of Fig. 3. Even somewhat above 400 Hz, there were a fewfrequency bands in which the sound intensity flow direction wastoward the gearbox; hence, the intensity was negative. Thesefrequencies show up as gaps in the spectra.

The coarseness of the measurement grid is a source of errorfor frequency measurements above 2250 Hz. Other noise sources(such as the motor and the shafting) contribute to error primarily atlow frequencies (below approximately 400 Hz). Noise from the sidesof the gearbox will make the measured sound power higher than theBEMAP predicted value. These errors are caused by limitations ofthe measurement and not by the analysis code itself.

CONCLUSIONS

Measurements of gearbox noise were made in the NASA gear-noise rig for comparison with predictions from thethe acoustic com-puter code BEMAP. The computer predictions are based on mea-sured vibration data. The analytical and experimental results forsound power were compared for four different operating speeds tovalidate the code as a design tool for predicting radiated trans-mission noise. The following conclusions were obtained.

1. The spectral traces for computed sound power are similarto spectra of measured sound power. This indicates that theanalysis successfully predicts the sound radiation properties of thegearbox.

2. The predicted and measured sound power were comparedat gearmesh frequencies and at modal resonance frequencies. Thesevalues agree, within an average error of 2.4 dB, with the predictedsound power generally less than the measured value.

REFERENCES

Atherton, W.J., Pintz, A., and Lewicki, D.G., 1987, "AutomatedAcoustic Intensity Measurements and the Effect of Cear ToothProfile on Noise," Mechanical Signature Analysis-MachineryVibration, Flow-Induced Vibration, and Acoustic Noise Analysis,S. Braun, et al., eds. ASME, pp. 109-113 (also, NASA TM-100155).

Boyd ; L.S. and Pike, .J.A., 1987, "Expansion of Epicyclic GearDynamic Analysis Program," HSER-10853, Hamilton Standard,Windsor Locks, CT, NASA CR-179563.

Flanagan, P.M. and Atherton, W.J., 1985, "Investigation onExperimental Techniques to Detect, Locate and Quantify GearNoise in Helicopter Transmissions," NASA-CR-3847.

Kahraman, A. et al., 1990, "Dynamic Analysis of Geared Rotorsby Finite Elements," NASA TM-102349.

Lin, H.H., Huston, R.L., and Coy, J.J., 1987a, "On DynamicLoads in Parallel Shaft Transmissions. 1: Modelling andAnalysis," NASA TM-100180.

Lin, H.H., Huston, R.L., and Coy, J.J., 1987b, "On DynamicLoads in Parallel Shaft Transmissions. 2: Parameter Study,"NASA TM-100181.

Lin, H.H., Townsend, D.P., and Oswald, F.B., 1989, "ProfileModification to Minimize Spur Gear Dynamic Loading," 1989International Power Transmission and Gearing Conference, 5th;Proceedings, ASME, Vol. 1, pp. 455-465 (also, NASA TM-89901)

Oswald, F.B., et al., 1991, "Comparison of Analysis and Experi-ment for Dynamics of Low-Contact-Ratio Spur Gears," NASATM-103232, Proceedings of 13th Biennial Conference on MechanicalVibration and Noise, ASME, Miami, FL, 1991.

Pike, J.A., 1981, "Interactive Multiple Spur Gear Mesh DynamicLoad Program," '.NASA CR-165514.

Rebbechi, B., Oswald, F.B., and Townsend, D.P., 1991, "Dyna-mic Measurements of Gear Tooth Friction and Load," '_NASATM-103281.

Seybert, A.F., et al., 1985, "An Advanced Computational Methodfor Radiation and Scattering of Acoustic Waves in ThreeDimensions," Acoustical Society of America, ,Journal, Vol. 77, No. 21

pp. 362-368.

Seybert ; A.F., et al., 1986, "A Special Integral EquationFormulation for Acoustic Radiation and Scattering for AxisymmeticBodies and Boundary Conditions," Acoustical Society of America,Journal, Vol. 80, No. 4, pp. 1241-1247.

Seybert, A.F. and Rengarajan, T.K., 1987, "The Use of CHIEF toObtain Unique Solutions for Acoustic Radiation Using BoundaryIntegral Equations Combined Helmholtz Integral Equation Formu-lation," Acoustical Society of America, Journal, Vol. 81, No. 5,pp. 1299-1306.

Seybert, A.F., Wu, T.W., and Wan, G.C., 1990, BEMAP User'sManual, Version 2.43, Dept. of Mech. Eng., University of Kentucky,Lexington ; KY.

Seybert, A.F., et al., 1991, "Acoustical Analysis of Gear IIousingVibration," NASA TM-103691, Proceedings of American HelicopterSociety Technical Specialists Meeting, Philadelphia, PA, 1991.

Seybert, A.F., et al., 1992, "Validation of Finite Element andBoundary Element Methods for Predicting Structural Vibration andRadiated Noise," NASA TM-105359.

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

1992 Technical Memorandum4. TITLE AND SUBTITLE 5- FUNDING NUMBERS

Comparison of Analysis and Experiment for Gearbox Noise

WU 505-63-366. AUTHOR(S)

Fred B. Oswald, A.F. Seybert, T.W. Wu, and William Atherton

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONNASA Lewis Research Center REPORT NUMBER

Cleveland, Ohio 44135-3191

and E-6696Propulsion Directorate

U.S. Army Aviation Systems Command

Cleveland, Ohio 44135-319 1

9. SPONSORING/MONITORING AGENCY NAMES(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING

National Aeronautics and Space AdministrationAGENCY REPORT NUMBER

Washington, D.C. 205460001

and NASA TM- 105330

U.S. Army Aviation Systems Command AVSCOM TR--91—C-030St. Louis, Mo. 63120-1798

11. SUPPLEMENTARY NOTESPrepared for the Sixth International Power Transmission and Gearing Conference sponsored by the American Society of Mechanical Engineers and Journalof Mechanical Design, Phoenix, Arizona, September 13-16, 1992. Fred B. Oswald, NASA Lewis Research Center, A.F. Scybert and T.W. We, TheUniversity of Kentucky, Lexington, Kentucky, 40506, and William Atherton, Cleveland State University, Cleveland, Ohio, 441 15. Responsible person,Fred 13. Oswald, (216) 433-3957.

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Unclassified -UnlimitedSubject Category 37

13. ABSTRACT (Maximum 200 words)

Low-contact-ratio spur gears were tested in the NASA gear-noise rig to study the noise radiated from the top of thegearbox. Experimental results were compared with a NASA acoustics code to validate the code for predictingtransmission noise. The analytical code is based on the boundary element method (BEM) which models the gearbox topas a plate in an infinite baffle. Narrow-band vibration spectra measured at 63 nodes on the gearbox top were used toproduce input data for the BEM model. The BEM code predicted the total sound power based on this measured vibration.The measured sound power was obtained from an acoustic intensity scan taken near the surface of the gearbox at the same63 nodes used for vibration measurements. Analytical and experimental results were compared at four different speedsfor sound power at each of the narrow-band frequencies over the range of 400 to 3200 Hz. Results are also comparedfor the sound power level at meshing frequency plus three sideband pairs and at selected gearbox resonant frequencies.The difference between predicted and measured sound power is typically less than 3 dB with the predicted value generallyless than the measured value.

14. SUBJECT TERMS 15. NUMBER OF PAGES

Gear noise; Acoustic intensity; Vibration; Boundary element method; Sound power 616. PRICE CODE

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