Gear Whine Prediction With CAE for AAM

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1. Introduction

Gear whine is an automotive quality problem thatcan be perceived by any driver regardless of his/her lev-el of driving experience, but it tends to manifest itself inthe final stages of vehicle development when, in mostcases, effective design measures that can be takenagainst it are extremely limited. Consequently, power-train designers have a great need for CAE technologiesthat enable them to predict gear whine using a virtualpower train before the power train is physically con-structed.

Inputs to the transmission and other power-trainelements in the vehicle include the engine torque andaccompanying fluctuations, which are regarded as com-bustion-originated dynamic-excitation factors. Theseinputs, however, initiate only vibration within the growl-ing-sound frequency range, not vibration at whine fre-quencies, which are much higher. If gear-tooth shapeswere optimum and tooth meshing were perfect, thegears would transmit the input torque in a manner pre-cluding the generation of frequency components otherthan those related to engine-torque fluctuations. Inactual gear-tooth meshing, however, forced displace-ments resulting from meshing error causes meshingvibromotive forces to be generated during torque trans-mission. These vibromotive forces then constitute asource of vibration. Further, the complete power-trainsystem includes shafts and cases whose stiffness hasan influence on gear-tooth meshing in such a way thatthe meshing vibromotive forces have peaks at certainfrequencies.

In addition, if the vibration transmission processthat begins with tooth-meshing vibration and results incabin noise has resonance in the frequency band inwhich the meshing vibromotive forces have their peaks,there is a significant likelihood that annoying whine willoccur in the cabin during actual vehicle operation.

There is a good chance of being able to prevent suchwhine from occurring in the cabin if the frequency bandin which the dynamic meshing vibromotive forces havetheir peaks is known, the frequency band can be com-pared with the resonance frequencies of the body vibra-tion transmission system, and the peak vibromotive fre-quency band can be shifted away from the resonancefrequencies.

2. Creation of power-train model

At Mitsubishi Motors Corporation, in-house-devel-oped software was originally used for predictive simu-lation of the transmission error of gears. However, thecost of modifying this software to accommodate graph-ical user interfaces (GUIs) and sizeable databases (bothnecessitated by changes in the analysis requirements)recently prompted the introduction and test-employ-ment of commercially available Romax Designer soft-ware for this purpose. This paper describes gear whineanalysis performed by means of models created withthis software.

When the transmission is regarded as a vibrationtransmission system with a multibody spring-massstructure, the gears and shafts are compared to themasses and the stiffness of the gears, shafts, and bear-ings is compared to the springs. The frequency of peakvibromotive force in gear-tooth meshing in this analogycorresponds to the eigen value of the transfer functionmatrix.

The gears and shafts were modeled using GUIs, andthe bearing models were, as much as possible,retrieved from the database. When bearing modelswere not available from the database, characteristic val-ues such as preloads and rigidities were input to createthem. All these inputs allowed the software to automat-ically create simulation models consisting of springsand masses (Fig. 1). Each created model has six

Gear Whine Analysis with Virtual Power Train

Tadashi TAKEUCHI* Kazuhide TOGAI*

AbstractMeshing transmission error (TE) is well known as a contributing factor of gear whine, but sys-

tem-level prediction of transmission error and quantitative analysis of dynamic meshing vibromo-

tive force have not been analyzed adequately until now. This paper describes the use of a comput-

er-aided-engineering (CAE) model for the analysis of the dynamic gear meshing behavior and for

the prediction of dynamic transmission error from the input torque of the system. This paper also

describes the analysis of a dynamic vibromotive force at a bearing location where vibration is trans-

mitted to the vehicle body. The gear whine critical frequency can be predicted with the proposed

method at an early stage of passenger-car development when no prototype is available.

Key words: Gear Whine, Meshing Transmission Error, Noise, Vibration, and Harshness CAE,Bearing Dynamic Load, Gear Stress Analysis

* Advanced Powertrain Development Department, Research & Development Office

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degrees of freedom at each analysis point. In a trans-mission model, the stiffness of the clutch can be mod-eled as the input shaft’s torsion-spring characteristic.The overall model’s accuracy can be raised by the addi-tion of finite-element models of the transmission caseand differential case.

3. Analysis of NVH using virtual power-trainmodel

Stress and fatigue-life are the most common sub-jects of gear analyses, and the basic functions of theRomax software used in the effort described in thispaper support predictive calculation of them. The soft-ware also allows the dynamic gear-meshing vibromo-tive force to be predicted through calculation of theload-based meshing transmission error and dynamicvibration mode. The following parts of this paperdescribe the method employed for simulation of a five-speed manual transmission used in front-engine, front-wheel-drive vehicles and of a rear-wheel-drive drive-train (Figs. 2 and 3).

3.1 Vibromotive force source and vibration transmis-

sion system

(1) Transmission error as a source of vibromotive forceFluctuations in the force transmitted by two mesh-

ing gears do not occur as long as the teeth are continu-

ously and smoothly meshing while transmitting torque.In other words, for fluctuation-free force transmissionthe gears must be geometrically in an involute relation-ship (such that there is no interruption in tooth contactbetween one tooth pair and the next) and both gearsmust be stiff enough to resist deformation such thattheir relative positions never change (Fig. 4). In reality,however, unvarying tooth contact cannot be assuredowing to factors such as non-ideal tooth-shape design,tooth-shape errors that occur during gear production,deflection and deformation that occur in gears andshafts during operation under load, and resonance inthe system. These factors yield transmission error (TE).Actual TE measurements (shown in Fig. 5) indicate thatthe TE constitutes forced displacement (a source ofvibromotive force) that causes gear whine. Sincedeflection and deformation occurring in shafts, cases,and bearings during system operation contribute to theTE, an appropriate model of the whole system is essen-tial for prediction of the vibromotive force.(2) Vibration transmission system

Gear whine as initially generated by gear-toothmeshing is shielded by the case (carrier). Thus, the

Fig. 1 Modeling outline

Fig. 2 Model of manual transmission

Fig. 3 Model of rear-wheel-drive drive-train

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whine heard in the cabin is usually the result of vibra-tion that has originated from gear-tooth meshing,reached bearings by way of the resonance systemformed in the transmission, and propagated from thereto the vehicle body through the transmission mount-ings. Key vehicle-design objectives for gear whine min-imization are thus as follows: minimizing the TE thatoccurs under actual operating conditions and optimallyreducing the transfer paths vibration sensitivity to thecabin. For the first of these objectives, estimation of thevibromotive forces acting on the bearings is essential(Fig. 6).

3.2 Gear whine analysis process

In the employed gear whine analysis process, atransmission model including the torque input and out-put ends is created then the deflections of shafts andtilts of bearings are calculated through a static analysis.Using the calculation results, the TE is predicted. Next,the system’s vibration modes are calculated through adynamic analysis to determine the dynamic load inputsapplied to the bearings. This process is illustrated inFig. 7.

3.3 Static analysis

In the static analysis, the deflection and tilt of eachshaft and the static misalignment and TE involved ingear-tooth meshing are calculated.

In a manual-transmission model, deformation anddisplacement usually occur in each shaft due to inputtorque from the engine. With the transmission modelon which analysis was conducted, deflection was evi-dent in the output shaft due to low stiffness and the dif-ferential case showed a significant tilt although itsdeflections were very small in amount (Fig. 8).

The predictive calculation conducted on the modelalso revealed that the amount of misalignment involvedin gear-tooth meshing in the front differential was fargreater than the amounts occurring between speedgears and that the load-supporting stiffness of the trans-mission case made a large contribution to the misalign-ment (Fig. 9).

The analysis results described above suggest thatthe model in question has the characteristic of generat-

Fig. 4 Tooth meshing (J. Derek Smith)

Fig. 5 TE measurement example

Fig. 6 Vibration transmission concept

Fig. 7 Analysis process

Fig. 8 Static analysis example

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ing relatively large vibromotive forces in gear-toothmeshing at the front differential, rendering the front dif-ferential prone to whine generation.

Next, a rear-wheel-drive drive-train model was sub-jected to a simulation in which fluctuations in theamount of tooth-meshing misalignment in the rear dif-ferential were analyzed with regard to the stiffness ofthe differential case (Fig. 10). The results show that the

stiffness of the differential case influences tooth-mesh-ing misalignment in the rear differential.

Using the data derived from the abovementionedanalyses, calculation for prediction of the TE in final-dri-ve gear-tooth meshing was performed and a predictiveTE reduction attempt was made by modification ofgear-tooth shapes. The results are shown in Figs. 11

and 12, respectively.The abovementioned studies began with analyses

of the TE and tooth-contact loads. Next, the amount oftooth-meshing misalignment during rotation of gearswas calculated. Based on the calculation results, thelead, crowning, and tooth tip of gears were modified onthe desktop to optimize the TE and tooth-contact load.The results indicated that modifying the tooth shapebased on the calculation results enabled tooth-meshingTE values to be made significantly smaller than the orig-inal ones in the front differential and between speedgears.

3.4 Dynamic analysis

This section of the paper describes analysis of vibra-tion modes during gear rotation under loading.

Both the manual-transmission model and the rear-wheel-drive drive-train model include non-linear mod-els to simulate bearing stiffness, which causes thevibration mode to vary according to load conditions.With the manual-transmission model, the shafts, bear-ings, and gears were treated as a fully coupled internalsystem of the transmission for calculation of the vibra-tion mode (Fig. 13). From Fig. 13, it can be ascertainedthat when the gear is set at 4th and a 50 Nm torque isapplied to the input end in this mode the bend of eachshaft and the tilt of the 4th speed gear make a signifi-

Fig. 9 Misalignment calculation results

Fig. 10 Effect of differential-case stiffness manifested in

calculated tooth-meshing misalignment

Fig. 11 Calculated tooth-meshing TE values

for front differential

Fig. 12 Calculated tooth-meshing TE values

for individual speed gears

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cant contribution to vibration at approximately 3 kHz.Analysis of the rear-wheel-drive drive-train model wasconducted on the assumption that the elements formeda fully coupled system (as with the manual-transmis-sion model) and by simulation of the case where excita-tion forces were generated during tooth meshing in therear differential (Fig. 14). Through this analysis, it wasseen that, under a torque of 250 Nm applied to the dri-ve side end of the propeller shaft, there was a mode inwhich the drive power train was sensitive to vibrationsat 468 Hz and 627 Hz frequencies that originated fromexcitation by the rear differential meshing.

Fig. 15 shows how the dynamic tooth-surface con-tact stress for a given TE value varies in the drive powertrain model in accordance with changes in the loadingtorque. From this graph, it can be seen that the sys-tem’s modal resonance frequency varies with the load-ing torque.

3.5 Prediction of dynamic loading on bearings

Using the aforementioned TE calculation results andmodal analysis results, it is possible to calculate thedynamic loading on each bearing.

Fig. 16 shows the calculated dynamic loading on abearing in the rear-wheel-drive power-train model. Inthis graph, meshing frequencies are plotted against thex-axis, rotation speeds against the y-axis, and bearing

dynamic loads against the z-axis. The waveform indi-cated on the line rising diagonally in the graph corre-sponds to the basic frequencies and their harmonics.Each peak vibromotive force corresponds to resonancein the drive power-train system, which in turn corre-sponds to the frequency of the gear’s potential vibro-motive force that is applied to the vehicle body.

4. Comparison of experimental and simulat-ed results

The dynamic loading on a bearing predicted usingthe rear-wheel-drive power-train model was comparedwith an experimental measurement on the actual bear-ing to evaluate the validity of the simulation (Fig. 17).

The data used in the predictive calculation were therelevant design values, not values taken from an actualpower train through measurement. As shown by thegraphs, the predicted and experimentally measured

Fig.13 Modal shape analysis of manual-transmission

model (3 kHz)

Fig. 14 Analysis of modal flexibility of vibration resulting

from excitation by rear differential gear meshing

Fig.15 Variation in model resonance frequency

with loading torque

Fig. 16 Calculated dynamic loading on bearing

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peak frequencies of the bearing under a dynamic loadcondition agreed well. In this prediction, no influenceof differential carrier resonance on differential carriervibration was assumed because of the differential carri-er’s great stiffness.

5. Conclusion

Dynamic gear-tooth meshing behavior was simulat-ed using virtual models. The simulation enabled clarifi-cation of the following items: increases in gear-mesh-ing TE caused by deflection of the elastic system underthe torque loaded condition; dynamic vibration modespresent in shafts and gears; and the process of genera-tion of dynamic loading at the bearing locations fromwhich vibration is transmitted to the vehicle body.Simulation using the virtual models presented here willlikely provide an effective means for dealing with gear

whine problems from the earliest stages of vehicledevelopment as it can be used as a tool for design opti-mization.

6. Future challenges

Once the dynamic loads on bearings are known, it ispossible to predict vibration response through thetransfer paths by means of finite-element models. Ifonly the peak frequencies of vibration to which thepaths will respond are to be identified, detailed analysisof the vibration-damping characteristics of the vibrationtransmission system is not very important. In situationswhere prediction of the amplitude of vibration is neces-sary, however, adequate data on the system’s dampingcharacteristics are indispensable. For accurate predic-tion, a technique that enables the amount of the sys-tem’s vibration damping to be determined accurately isrequired. Research aimed at realizing such a techniqueis under way.

Finding a method for accurately determining thesystem’s response to vibration is a further issue towhich research efforts are to be directed. With accuratevibration-response data available, it will likely be possi-ble to predict the noise radiation.

References

(1) Smith, J. Derek: Gear Noise and Vibration, Macel Dekker,Inc. (1999)

(2) B. James, M. Douglas, “Development of a Gear WhineModel for the Complete Transmission System”,Transmission & Driveline System Symposium 2002 SAE2002-01-0700

(3) B. James, M. Douglas, D. Palmer, “Predicting the ContactConditions for Hypoid Gear Sets by Analysis and aComparison with Test Data”, Transmission & DrivelineSystem Symposium 2002 SAE 2002-01-1045

Fig. 17 Simulated and experimentally measured

dynamic loading on bearing

Tadashi TAKEUCHI Kazuhide TOGAI

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Gear Whine Prediction With CAE for AAM