Investigation of GearRatde Phenomena

.Allred Rust, Franz K. 'Brandl & Ge!rhard E. Thien,AVL List iGmbH, IGiraz,.Austrial

The acceptance by discerning customers ofpassenger cars is dependent upon both the actualnoise level and the subjective noise character.

The subjective noise character itself can con-tain, among other features. undesirable noisephenomena which become apparent at certainpoints in the vehicle operating range. One suchcritical phenomenon is gear rattle, which ismainly present under low speed, high load con-ditions. Due to changes in the angular velocityof the crankshaft, gear rattle under drivingcondition occurs at the unloaded gears andsplines. It is influenced by a combination offeatures, such as the inertia of the flywheel,clutch, and all gears, the transmission drag, andthe resonant. characteristics of the driveline.The effect on airborne noise is also influencedby the characteristics of the vibration transferpaths from the gear teeth meshes Vi.B shafts andbearings to the transmission housing. To ana-lyze the interactions of these parameters, it isnecessary to conduct both vehicle tests, eitheron the road or with a chassis dynamometer, andto investigate the bare engine-transmission unitin an anechoic test cell The first part of theinvestigations reported in this article deals withthe definition by conventional methods of thenoise phenomena in the passenger compart-ment and a parallel application of a ubjective

100«Q:I....

" 90,."..l...." 80"0'"

1000 2000 4000 6000Engine Speed f· r/rnin

Fig. 1 • Noise of D. petrol .:engine and transmission(fu.llload, fifth gear).

30 GEAR TECHNOLOGY

noise character evaluation system. This is fol-lowed by a correlation analysis of the noisephenomenon recorded in the passenger corn-

partment with the noise at the source.Finally, a comprehensive investigation of

the noise phenomenon on the bare power unitand the potential ofkey parameters for reductionar the source will be described.

IntroductionGenerally, the noise level of today' s passen-

ger cars is of an acceptable standard, in term ofboth the objective noise level and the subjectivenoi e character. Legislative regulations limit theobjective noise level, The subjective noise char-acter, which consists of more than simply theobjective noise level, I. has to be ofhigh quality tomeet the demands of discerning customers. Un-der these circumstances. individual noise phe-nomena can. become annoying. although theobjective noise levels are hardly affected. Sucha noise phenomenon can arise from the gearrattle of a manual transmission. which occurseither in neutral. or under drive condi tions.? Neu-tral rattle is generated at idle with the transmis-sion in neutral and the clutch engaged .. Driverattle occurs at the unloaded gear meshing pointsunder driving conditions, usually at higher loadsand lower speeds. The annoying character ofranle noise is additionally intensified by the factthat it occurs in the speed range where transmis-sion noise is clearly audible, as it is hardlymasked by the engine noise due to the differentspeed dependencies.

At very low speeds, transmission noi e canbe similar to or even higher than engine noise,particularly in the ca e of a petrol engine instal-lation. However, the rate of noise increase withspeed is higher for engine noise:3.6

[Iransm a n2 _.> 6 dB/octave (1)[engine a n3 ••..n5 ·->9 ...15dB/octave (2)

I"" sound intensityn "" speed

As shown in Fig. I, for a power unit with a 1ltr, petrol engine, tile transmission noise is com-pletely ma ked byengine noi e at speeds above2500 r/min, The results in Fig .. l were obtainedfrom noise analysis of the complete power unitand of the engine only (with the rransmi sionwrapped in lead.) The transmi sion noise wascalculated a the difference between the e re-ults, However, at speeds higher than 2500 rl

min.llle difference became [00 mall for ana curatedetermination of the tran mis ion nor elevel. For litis reason, the curve for rhe Iran mis-sion noise was extrapolated (as fine line) fromthe level at 2500 r/min using a slope of 6 dB!octave. This article will consider only driverattle phenomena. The analysis of a typical gearrattle problem will be de eribed. This occurredin a front wheel drive pa enger car equippedwith a 1.1 Itr. petrol engine and five . peedmaaeal iran mi sian. and appeared a a dis-turbing component in interior noise.

IdentifleatlenThe basic investigations were performed in

an acoustic test cell with the bare engine-trans-mission unit. To ensure that the actual noiseproblem was treated on die bare power unit, therattle noi e was identified in the vehicle duringpreliminary road tests ..To achieve thi: , a micro-phone wa located close to the gearbox. urfacein the engine compartment. An accelerometerwas fixed to thegearbox l10llsing and an artifi-cial head measuring system 7po itio:ned at theco-driver's seat. A digital audio tape recorderwas used as a high quality signal storage device.By comparative listening. the actual interiornoise. the airborne sound from the gearbox. andthe structural vibration ofthegearbox hou ingvia headphones -jhe gear rattle phenomena awell a their typical range of engine operatingcondition - could be identified. Fig. 2 howsshe frequency spectra of airborne noise mea-sured first near the gearbox. and at the co-driver' eat position during road re ts: then Inthe te t cell, again do e to the gearbox, and at1 m from the power unit. The 25% load condl-'lion indicate. the beginning of gear rattle. Ob-viou :Iy. the gear rattle i a major contributor tohigh-frequency noise. which can be . een in thegood correlation between each diagram; thus,the engine operating range in which gear rattle

On, Road In Semi nechnlc THI ,- tilII 0 r--'-r.::--r--=-~-.100 ~~-~~~~~9O~--I----'1-.::""""~~80 b,....;:J5:tko,~....,......p."..JI:70 ~~-t-~~~~60 L-~_L-~_~~70 r-~-r-~-T-~60 I - I I

50 "\1 ' 'I40 -I~~I Cu~1tPrf!r\ Coil I

30 I 1''::' ",,;1;20 I I ~J. 1 BC

0.2 0.5 .1 2 5 Io A· Level

110 ....---.-...--r--__....I Cl"", ,<> Geart!u.

1.001--II-+k-.~;;.:::..=i_I~90 I--II+~~,....::=I'.--iV _,__ 11"-

70 -I{. :~:.;.~~..:..-\_flO I.U' II . - ~50 0.2 O.S 1 2 5 10

1/3 Oeta ve Band Center frequency - k Ii1-

-- IOO'll-Load (AI 25'l1- Load (B) -- 0 load lei----- 75'l1: Load (01 50'1 l,Q~d IE) -- Motored (F)

Fig. 2 • Comparison between read test and te t cell results (1500 r/min,tbifld gear).occurred could be limited to the speed rangefrom low idle to 2000 r/min and to the loadrange from about 25% to full load.

Origin Of Drive RaUI.eAs described in Ref. 2, drive rattle originates

from teeth impacts at the meshes of unloadedgears after pas iag the backla h point. The im-pacts occur whenever the angular acceleration ishigh enough to make the inertia torque at thedriven wheel greater than its drag torque:

.I.;t;:> T (3)- 'I' -dmg

.I' = moment of inertia of driven wheel,~= angular acceleration of driven wheelTdrng ;;;;:drag torque acting on driven wheelUsing this relationship" the true hold of gear

rattle can be defined in terms of the criticalangular acceleration, f crit, at which drive rattlebegins to occur:

~'crit = TdralJ (4)Therefore. rattle noise .isgenerated when theangular acceleration reaches high values. Thisfact is demonstrated in Fig. 3a, representing thetime trace of vibration acceleration recordedirnultaneously with the speed fluctuation mea-

sured atthe primary shaft. econdary shaft. andflywheel. Since the angular accelerationi thefirst derivative of the speed fluctuation (= angu-lar velocity). and since the hape of the speedfluctuation is similar to a sine wave. the maxi-mum angula tr acceleration oceur during the zero-crossing of the speed fluctuatlon. Within thesetime periods, high peaks of structural vibration.which. are caused by the ranle impacts. can beobserved. The propagation time of typically 80ms, for the vibration (ran. fer fromthe gearboxhousing is negligible. At all engine speed of1500 r/min, a time of 80 ms, corresponds to a

.A!lflred IRustis o· project engineer foracoustic research andde-velopment at A. VI..USI. HI'"'orKs (1II.1I0;SI! anc/l';bra·I;(m of tllgilll! • Iran mis-sions, and vehicles.

Flranz K., IBrandlis tile Marillga of the De-partment of Acoustic Re-search ami Developmentat A vt.u«.

Gerhard E. Thienis rill' .Head of th« FluidDynamics and Noise Sec-lioll of rhl' ACI1!1S1ic Re·searcl: (/lId D« velopmentDt!pl. at i\VI..List,

5 e PTE U B E 'R I 0 C T 0,8 E A 1 11112 :3'1

1\) Me.sued.

200 ~ .~ t~ I'" I'" " I~~" I' lbratlon at Gearbox Housing_2

0oo~' PC ,.4~_=::::_=:::.==~.==: (hlgh·pass filtered at 3kHz)

_:~&'4++""'1 ;~:~~~~:~Itionat:

_~~ ~fV:' :1::::::' -=' :4"~':-:·:'1~~::9~·S~colldary Shan

_~~Fr=of f-- f-31 F1y"h ~I0' 180 360 S4Q 720

Crank Ang]e - del!

B) Cllcllllled.,:l:

eEc

!Calcu Jared for Gear Me h 3

o.rs0.]0'0.03

0.]50.]00.05o

Impact At:Loaded FlllnkIii ffi.E tJ, LI ~

----~=ti±ri .ff8a j,lll. II---720°Crank An le

u"'.e,8

UII'loodedl Fl- nk

o eE=1:1 C",,,;.... E- 0E~:> -og

Q.

.§

4

2

oIII Gear Mesh 4_Gear Mesh 3_Gear Mesh 2.' Gear Mesh I

Reduced Relluce .Inertia ofBacklash Free-R. Wheels1-35%L (-50%)

Fig. 3 - Measured nd calculated time' history or dri,ve rattle impaets (]500rlmln, fuU load, fifth gear).

crank angle interval of less than one degree.Some further interesting aspects can be seen

in Fig. 331.At first, the speed fluctuation isdominated by the second order frequency of theengine speed due to the rotary force characteri -tics of the four-cylinder internal combustionengine, For this reason, impacts occur eighttimes per engine operating cycle on the funyrattling transmission. Secondly, the speed flue-tuations ofthe primary and secondary shaft aregreater than tho e of the flywheel. and they areadditionally shifted in phase. As will be illus-trated later, this fact i caused by a torsionalresonance in the power train with the clutch asthe dominant torsional, pring. Thirdly. at onegear meshing point, more than one impact canoccur at a given maximum angular accelera-tion. This is evident from Fig. 3.£1.where theresults were obtained from the transmissionequipped - apart from the gear engaged - withonly one free-running wheel.Jn this case all theimpacts could only originate from the one un-loadedgear mesh. A computer simulation ofgear rattle in the fully equipped transmissionsystem. carried out inparallel to the experimen-tal investigation, confirmed this fact and indi-cated typically several impacts per rever aloftooth loading. and characterized the impacts aselastic collisions. Fig. 3b shows the result ofsome of these calculations (including the effect

32 GE,t,R TECHNOLOGY

of some parameter variations).Key Parameters

The "primary" parameters which have aninfluence directly on the generation of rattlenoise. can be found in Eq, 4. These are Ihemoments of inenia of the free-running w.heel,the angular acceleration, and drag torque actingon the free-running wheel, A fourth parameternot appearing in Eq. 4. but representing a funda-mental condition for the generation of rattlenoise, is the tooth backlash. since zero backlashprecludes any gear rattle. Further possibilitiesfor treating gear rattle are provided by "second-ary" parameter acting on the propagation ofrattle noise to the DIn ide of the tran mi ion ..Here the que lion arises whether Ihe direct air-borne noi econtribution or the structural vibra-don component (coming from the meshes viatransfer paths) is more significant in the radia-tion of airborne noise from the surface of thetransmissicn housing. To find an answer, the.i asertion 10 Sefthe gearbox housing wa .deter-mined experimentally using a loudspeaker exci-tation inside the gearbox. A very high insertionloss was measured so that the contribution of thedirect airborne sound can be neglected, For ex-ample, at 1500 r/min engine speed. full load. andin fourth gear, more than 99% of the total soundpower being radiated frurmhesransmission sur-race originated from the structural vibrati.on com-ponent. For thi . rea on, it is useful to con iderailly those econdary parameters which have aninfluence either on the vibration tran fer fromthe gear me hes to the miter surface .of thetransmission or on the airborne sound radiationfrom the transmission surface.

Backlash. In accordance with experience,:!the computational analysis indicated only a smalleffect from backlash on gear rattle (Fig. 3b).Within the limits of current tolerances, theeffect of backlash is insignificant. However,zero backla h prevent gear rattle. since thetooth flanks can never .100 e contact and impactother flanks. Uafornmately, zero backlash iunrealistic for other reason , except where ~[can be provided by an additional device such asan anti-rattle plate.2

Drag Torque. For lower rattle noi e, the dragtorque of the free-running wheel. bas to be in-crea ed as shown in Bq. 4. Two major compe-nents contribute lathe drag torque.the frictiondue to the lubricant (viscosity, oil depth) and the

drag torque in the bearing of the free-runningwheel. W:ilthimthe experimental work, only thebearing drag torque was investigated. For thispurpose, the radial clearance between fre -run-ning whee Iand shaft (via the intermediate needlebearing) was reduced by 40% on all gears. Noeffect on ratrle noise could be found. From thecomputational analysis it wa concluded that tobe effective, the drag torque must be increa edto a certain extent so that condition (3) is DO

longer atisfied. If the drag torque increaseremains belowthis limit, then the impact en-ergy at the one t:ooth flank decrea es, but in-creases at the opposite flank. Clearly the 40%reduction of the radial clearances did not in-crea e the drag torque beyond the limit.

Angular A celeration. Benefits can be ob-tained from reducing the angular accelerationacting on the free-running wheels. here aresomepossibiliries for lowering the angular ac-celeration. First the output speed fluctuation ofthe engine depend. on, among other thing . themoment of inertia of the engine flywheel. Theproperties ofthe clutch disk also lJ'ongly influ-encethe input of speed fluctuation into thetransmission due to torsional resonance .8 Fi-nally, the transmission arrangement; i.e., its ge-ometry and gearrat.io, determines the "local"angular acceleration of each free-running wheel,The tor ional resonance onhe driveliae ysternwa found to 'be the key feature. affecting driverattle. Fig. 4a shows the driveline re onance atfull lead conditions. The peed fluctuation at therattle thre hold is plotted to iHuslrate the range'of drive rattle (shaded area). Here the speedfluctuation is defined as a percentage ratio ef thedifference between the maximum and minimuminstantaneous speed to the mean peed. Fig. 4aclearly illustrates the procedure for the elimina-tion of drive rattle. Tile La k is eitherto rai e therattle threshold above the maximum peed fluc-tuation .or to lower the maximum peed fluctua-tion below the rattle thresholdor to move bothlimits simultaneously. hl Fig. 4a the rattle thresh-old i nearthe spe-ed fluctuation of the flywheel,and the rattle condition disappears at higherspeed due to the ..vibration isolation" effectbetween flywheel and primary shaft. This occurstheoretically - for a simple mass-spring system -al. frequencies greater than v2x re onant fre-quency. In Fig. 4b the effect of a lower speed

. trated by a 30% increase of the flywheel inertia.The re ult isa dear reduction of the . peedfluctuation over the whole peed range. but par-ticularly at the resonant. speed. The possibility ofmoving the resonant speed out o:f the loweroperating speed range was mvestigated by meansof a soft. clutch (with 27~ less stiffness) a wella bya progressively stiff and highly dampedclutch. Both clutch di ks were te ted in cornbi-nation with the heavy flywheel. giving theresultsin Fig. 4b.. [t transpiredthat it is impos ible,withilnpracticallimits, I.Oslttift the resoaarn speedbelow the lowe. I. operating range; i.e., to obta:inan overcritical condition which would have beenthe best solution. On the other hand, the stiffclutch drastically reduces the . peed fluctuationinput to the tran mission approaching the rattlethreshold. However, tile rattle condition nowcontinue up to higher peeds, and the overallnoi e character becomes rougher in tile higherspeed range due to the high damping of thecluteh, which weakens the vibration isolationbetween crank haft and primary shaft in themid-frequency range. Thccffectofthe echangeson the airborne noise radiated from the wholepower of 1500 r/min, Since the frequency rangeabove 1 kHz is most significant for gear rattlenoise, the range of drive rattle is haded onlyabove l.kH.z in this figure. It indicates the greatbenefit to noise reduction which is obtainedwhen the torsional resonance i .suppressed. Bychance. at 1500 r/rnin engine speed, the speedflucnration is the arne for both the oft and the

pectra nearly

A) Original CO!ldition

. t.'!

I g,,,."R

Iii:,"':l'U..,I>.,.., .'Engine Speed = r/rm;"..1000 1500 2000

Engine Speed - r/min

113 Octave Band Center Frequency = lUiiC) Effect on Noise

fluctuation output from the engine is demon- Fig. 4 - Characteristics of dri\'eUne '~orsiomll resunanee (rourth gear I..

S 'E P T ~ M B E RIO C r ·0 B E R 1 8 11.2 33

coincide in Fig. 4c. The gear arrangement in thetransrni sion was found to be disadvantageouswith respect to gear rattle. As shown in Fig. 5,the original design (with the free-running wheelsof third and fourth gear placed 011 the primaryshaft) results in a very non-uniform distribu-tion of the local angular acceleration. It favorsgear rattle particularly at the free-running wheelsNos. 3 and 4, because of the high angularacceleration occurring at these wheels .. Thesituation does not change even when the mo-ments of inertia. of the free-funning wheels aretaken into account (Fig. 5. right side). A re-design of the gear arrangement - placement of

Gear Arrangement:

J=32 Modified

SecondarShaft

(l = Momem or Inertia or Free-running Wheel in 10.5 kgm2).

Angular Aeeclerauon Inertln Torque0.5

0.4

EZ

0.3

"::l,;;r<;

0.2!-.:'!!t:".s ~--c¥~~~~~A-~>

'3w....~~ ..~ ..~ ..~w.~a

[500.

~ I,- 1000 I----.......j.-I-----Ig I

'g~ ~" ~~ 500 I ~----~-++-++-__l; fJJ

10 3~ "

.Fig 5 - Effect of gear arrangement on local rattle cOltdiUion(assuming aspeed nuctnation input of 0.5% at ~500 r/min).

B) Effect of Combined MeasuresSlrllclurc Attenuation on Interior Noise

I

Srructual Vibralional (al Gearbox Housing) (Left Ear or Artilicnl Hend al Co-Driver's Seat

1

"7110 ~~60,?:- 100I---+----,I---+---I--l;;! ';' SOl--'.. k:=1,---+-lHI---Is w-~-.; 90 a ~ '10I---+-~L.:::fo./....-----!~;\--l~ 80 ~~\ l"l 30'---I-+--·+""+..~-tt--!

, 0 v.,-::.oJ ...~ d:: I~"eo

I

I·g 70 I---+--I--I-----I-~ -g 20 - Annoying ~ ABC D~ 6OL- __ ..J....-.JL-....1.._---1_....l g ]QFrcquency Band...! ....... Level of

0.2 0.5 2 5 10 '" 0.2 0.5 11 2 5]0 AnnoyingBand

113 Octave Band Center Frequency • kl-I'z

A) 'Gearbox. Vibration Wilh Increased

Vehicle Interior Noise

1/3 Octave Band Center Prequency - kHz

OriginalWith RibsWith Constrained Layer

Fig. 6 - Effed or various improvements (road test, 1500 rlmin, fun load,fourth gear).

34 GEAR TECHNOlOGV

the free-running wheels Nos. 3 and 4 on thesecondary shaft - would give a far better start-ing position for low gear rattle. Are-designedtransmission was not available as hardware.and it could not be tested, but the benefits forlow gear rattle noise in terms of a high rattlethreshold are evident in Fig. 5 due to the moreeven distribution and much [ower maximumvalues of the local angular acceleration.

Inertia Of Free-Running Gear Wheel. Thereare three effect on gear rattle arising from themoment of inertia of the free-running wheels.The fir ,t and mo t important one is its influenceon the rattle threshold. The rattle threshold ishigh if the inertia torque and, consequently, theinertia of each free-running wheel is low accord-ing to Eq, 4. The second effect is its influence onthe characteristics of the tooth impact, and thethird one is its effect 011 the driveline torsionalresonance. To test these effects the free-runningwheel of the second gear was selected, althoughthe free-running wheels Nos. 3 and 4 were foundto be the most prone to gear rattle (d. Fig. 5).However, the wheels 3 and 4 could not be pre-pared as low inertia wheel because of theirsmall size. Therefore, the larger wheel No.2 wasused for this test. Its original inertia was aboutthree times greater than that of wheel Nos. 3 or4(cf. Fig ..5). Two samples ofa low-inertia wheelNo.2 were prepared for experimental purposes ..The first was extremely light with an inertiareduction of 38%. The second version, used forthe final vehicle tests, was reduced in inertia by15%. The effect of the extremely low-inertiawheel on the torsional driveline resonance canbe seen in Fig, 4b,. which shows a clear up-shiftof the resonant speed. This speed shift, however,is not only caused by extremely light free-run-ning wheel No, 2, but also to an equal extent bythe removal of the sliding : leeve, which couldnot be installed together with the extremelylight wheels for technical reasons. The com-bined.effect (i.e .. in combination with the heavyflywheel and damped stiff clutch) on noise isillustrated in Fig. 4cas the lowest spectrumdefining the threshold of rattle noise. The corn-

putational simulation of a 50% reduction of theinertia of the free-running wheels confirmedthe noise reducing effect as shown in Fig. 3b.Moreover it can be seen that the impacts de-crease in magnitude and increase in numberwith a gain in its overall effect.

Vibratioll Transfer. Signiflcant elements inthe vlbration transfer path from the me h to theouter gearbox urface are the. haft bearing andthe structure attenuation of the gearbox, hou ing,In Ref. 3 theeffect of the bearing de. ign isde cribed with a gain in low noise of up to 4 dB.Within the pre ent work. 'the influence of thestructure attenuation was investigated. From vi-bration measurements on the running transmis-sion using a laser vibrometer, itwa found that atfrequencies above 2kHz the shat't vibration wascared)' higher thai] the vibration at the gearbox.

housing indicating a very low intermediate true-lure attenuation.

10 determine the potentia] for noise reduc-lion in term of the structure attenuation of thegearbox hou sing two tests we re carried OlIJ t Fir t

the walls of the gearbox housing were dampedby means of a constrained layer. Secondly thewalls were uiffened by rib . Fig. 6a . hows that.tile ribbing of the gearbox housing proved to be\lery effectiee. The reductina in vibration ve-locity reached up to 5 dB. The application of theconstrained layer also improved the situation.but to a mailer extent. Finally the combinedeffect of everal measures (by succe sive addi-tion of single measures) was tested in thevehicle during road tests ..As call be een fromthe noie levels (in the frequency band ignifi-cant forthe rattle audibihly in the interiornose) in Fig.6b, the combination of improvedgearbox housing (by ribs), increased flywheelinertia, and reduced inertia of free-runningwheel NO'. 2 (second version) gave the bestresults, so that the gear rattle in the vehiclecabin wa no longer audible.

ConclusionsIn automotive tran mis ions drive rattle is

excited by the angular aceeleration ari ing fromlow frequency peed fluctuation caused by thefluctuating torque output of the combustion ell-gine due to its gas and inertia forces. Work toeliminate gearrattle thre hold - expres ed by thecritical. peed fluctuation - above the actual max i-mum speed fluctuation. The rattle tare: hold de-pend upon the drag torque and the inertia of thefree-running gear wheels, as well as all.the localangular acceleration. Therefore. the followingpotential for improvement exist. The gear ar-rangement provide the opportunity to raise therattle threshold, The proper lay-out of the geararrangement at. the design stage is a powerful

tool to minimize gear rattle or at leastto providea good condition for later improvement . In thica. e. the major item to be taken into account isthe wheel hafiarrangement. The great iafluenceof the c1riveline resonance requires a carefultreatment. of the clutch and the distribution oflnertias. Since the resonance can hardly beavoided. the solution will always be a compro-mise. Therefore much effort hould be concen-trated on accompanying measure .such a a lowpeed Ilnctuation output from the engine and a

high rattle thre hold of the transmission, Sincethe vibration tran fer from the gear meshes to. theouter surface hat a great effect on the rattle noiseemitted by a transmis ion. its structure attenua-tion has to be of a high level, There can be somepotential for improvement by stiffening ordamping the housing walls and thereby In-crea ing the "audible" rsttlethre hold. 1.1

References.I. Brandl, F. K.. Schiffbaenker, H. and Thien G.E. "AConcept for Definition of Subjective Noise Charac-ter - as a Ba is for More Efficient Vehicle NoiseReduction Strategies." Internoise Conference. New-port Beach, Dec. 1989.2. Seaman, R. L., Johnson, C. E. and Hamilton, R.F."Component Inertial Effects on Transrniss ion De-sign." SAE 841686, Dearborn. Dec. 1984.,3. Optiz ..H. "Noise ofGear ." Philosophical Trans-action. oftbe Royal Society. London. Vol. 263 A, PP'369-380, 1968-69.4. Grover. E. C. and Anderton, D. "Nol e and Vibra-tion inTransmissions," Paper No.7. 2nd Int. Power Trans-mission Conference, Engineer's Digest. Vol. 32. No.9. Sept. 19715. Austen. A. E, W. and Priede, T. "Noise of Automo-tive Diesel Engines; Its Causes and Reduction." SAE[000. A, Detroit, Jail. 1965.6. Wu,. T. and Case, J.[, "Effect of Operating Puram-eier on Bare Engine and Engine Contribution Noi eLevels:" Noise Control ill Internal Combustion EII-gines ..Ed. by Baxa, John Wi,.ley & Sons, New York,11982.pp. 48,7. Genuit, K. "Investigation and Simulation of Ve-hicle Noise sing the Binaural Measurement Tech-nique." SAE 870959. Traverse City. Apri.11987.8. Fudala, G. J. Engle. T.C . and Karvelis, A. VA."Systems Approach to Reducing Gear Rattle." SAE870396. Detroit, eb, ]987.

Acknow;ledgement: Tire authors wish to thank allthe! F colleagues at A Vi., particularly Dr. H. .P. Hueblfrom the FE-Clilcu/alion department, who colltrib-uted to this project and paper b)t their works.

Reproducedfrom the Proceedings of tile Confer-ence 0/1 Gearbox Noise' and Vibration. 1990. bypermission of the Council of the lnstitution ofMechallical Engineers. London, England. Thearticle also appeared in lire April. /991. issue ofEUFQPQWfF Tr(wsmissio/l,

II E PTE II II E RIO C TOil ;E Rig ~ 2 35