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PAPER SERIES

2005-01-3806

Contact Fatigue Tests and Life Simulations Using

Computational Fracture Mechanics

Hong Lin, Robert R. Binoniemi, Gregory A. Fett

Douglas C. Burke and Thomas WoodardDana Corporation

Powertrain & Fluid SystemsConference and Exhibition

San Antonio, Texas USAOctober 24-27, 2005

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Contact Fatigue Tests and Life Simulations UsingComputational Fracture Mechanics

Hong Lin, Robert R. Binoniemi, Gregory A. Fett, Douglas C. BurkeandThomas WoodardDana Corporation

Copyright

ABSTRACT

Computational fracture mechanics based FATIG3Dprogram was used to simulate contact fatigue life ofrough surface contacts in boundary to mixed lubricationregimes. Two-rollers contact fatigue tests wereconducted and test results were compared withcalculated contact fatigue lives. Calculated contactfatigue life agreed with test results well with the selectedset of input data. The effect of several importantparameters in the input data on contact fatigue life wasevaluated computationally using FATIG3D. Theseparameters include: oil pressure distribution, crack facefriction, direction of friction, friction coefficient, initialcrack length, Hertzian stress, and residual stressdistributions. The results obtained in this work improvedbasic understanding and the application of FATIG3D insimulating contact fatigue behavior.

INTRODUCTION

Current market drivers for commercial vehicle heavy dutydrive axles are characterized by higher power density,longer warranty mileage, lube for life, reduced weightand improved efficiency and fuel economy. One outcomeof these drivers is that drive axle components must havelonger fatigue life under more severe operatingconditions. Drive axle primary gearing is the most criticalcomponent in a drive axle. Axle pinion and gear tooth

could have several failure modes: bending fatigue,surface wear and surface contact fatigue. In this paper,we investigate and simulate tooth surface contact fatigueunder high Hertz contact stress, rolling and sliding,boundary and mixed lubrication regimes.

Surface contact fatigue is a fatigue crack nucleation andpropagation process in which cracks nucleate andpropagate under repeated contact stress until flaking orspalling occurs. For product design and developmentpurposes, a reliable quantitative virtual simulation tool willbe useful which can predict contact fatigue life under a

given condition defined by load, speed, temperaturelubricant, material, surface finish and contact geometry.

A large amount of work has been carried out on thedevelopment of contact fatigue life prediction models

One classical approach, based on the pioneer work ofLundberg and Palmgren, was developed to predict rollingelement bearing contact fatigue life many years ago [1-5]. After more than 50 years of development andcorrelation with bearing life test data, this approach hasbeen widely accepted and has been adopted in rollebearing design standards. More recently Olver [6], Wangand Keer [7] has used the bearing life models to predictgear contact fatigue life by including the effect of surfaceroughness and sliding. In terms of fatigue damagemodels, the bearing life modeling approach is essentiallya stress-life (S-N) approach which correlates certaincritical stress term with total fatigue life that includes

both crack nucleation and crack growth life. This contactfatigue modeling approach was evaluated and used bythe authors, and the results were published in a separateSAE paper, SAE 2005-01-0795.

On the other hand, fracture mechanics approach hasalso been used to develop contact fatigue life modelsbased on the premise that crack propagation life may bethe dominant phase of contact fatigue life [8-20]. Themajority of fracture mechanics related work in contacfatigue life modeling has been conducted by tworesearch groups: Murakami and Kaneta of KyushuUniversity in Japan [8-11] and Keer Northwestern University of USA [12-16]. Murakami andKaneta studied two contact fatigue crack problemsanalytically using fracture mechanics: one is an inclinedsemi-circular surface crack under Hertzian contacloading, another is an elliptical crack embedded paralleto the surface under Hertzian contact loading. The stressintensity factors and crack opening/closing behavior werenumerically analyzed. Key theoretical conclusions of theanalysis were: (1) oil seepage into a surface crack is acrucial factor which causes pitting, (2) the crack openingdisplacement of a surface crack is controlled mainly bysurface traction, contact pressure, and oil hydraulicpressure, (3) both the direction and the magnitude o

2005-01-3806



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surface traction govern the oil seepage into the surfacecrack, (4) a sub-surface crack opens even undercompressive surface loading (Hertzian contact loadingwith surface traction), (5) a sub-surface crack opens notonly near the trailing tip of the crack behind the contactload, but also near the leading tip in front of the contactload.

Over the last two decades, Keer a contact fatigue analysis software FATIG3D based on athree dimensional contact fatigue model. Contact fatiguephenomenon is simulated by a cyclic Hertzian loadmoving across the surface of an elastic half-spacecontaining several planar cracks. The three modes ofstress intensity factors are determined based on thebody force method [14]. Fatigue crack growth rates arecalculated with a modified Paris law based on materialcrack growth test data. Hertzian stress, oil hydraulicpressure, surface traction, residual stress, and initialcrack size and angle are all considered and modeled.Recent developments include multiple crack growth andcoalescence, contact crack growth through thin filmcoatings, and rough surface induced stress field [15,16].

In summary, extensive studies have been conductedusing the fracture mechanics approach for contactfatigue modeling. Many fundamental aspects of theproblem have been modeled, such as oil pressure,surface traction, residual stress, etc. However, mostanalysis results are still in academic theoretical researchstage. The analysis models and life simulations have notbeen compared with experimental results yet. Moreover,several important engineering design relatedconsiderations such as surface finish, sliding speed andoil film thickness are not directly incorporated in theanalysis software FATIG3D. Obviously more research is

required in this field, especially in generatingexperimental data, preparing input data, and validatingthe analysis program and simulation results. In this workwe perform two-rollers contact fatigue tests with sampleshaving different surface roughness levels. Then weconduct contact fatigue life simulations using thecomputational fracture mechanics based programFATIG3D. The objectives of this work are: (1) to validatethe simulation tool by comparing the calculated contactfatigue life with contact fatigue test data, (2) to evaluatethe effect of several important factors on contact fatiguelife computationally, such as initial flaw size, Hertz stress,friction, residual stress, and the direction of surfacefriction.

THEORETICAL BACKGROUND

FATIG3D is a computer program developed for three-dimensional simulation of propagation and coalescenceof multiple cracks driven by cyclic contact load. Theprogram performs simulation of contact fatigue failures interms of crack growth under sliding and rolling contactfatigue loading cycles, and coalescence of adjacentcoplanar surface cracks. Stress intensity factors and

energy release rate along the crack fronts are calculatedin the three-dimensional crack analysis. For eachloading cycle, the rate of mixed mode crack growth isestimated from the stress intensity factors, and the newcrack front is determined by crack growth calculation witha modified Paris law. The stress conditions modeledinclude: Hertzian contact stress, lubricant pressure, andresidual stress. Subsurface stresses obtained by otheprograms (such as roughness-induced stresses) canalso be included. The program allows the use of severa

material layers with different Paris law coefficients, whichis an important capability to model coatings and casehardened steels.

A three-dimensional contact fatigue model is consideredas shown in Figure 1, where an elastic half spacecontaining multiple cracks is subjected a Hertzian linecontact loading moving across its surface. The halfspace initially contains multiple surface planar crackswith arbitrary shapes and angles of inclination. Under thecyclic contact loading the cracks can propagate and mayinteract with adjacent cracks, then coalesce into a largecrack, which leads to the formation of a surface pitting

failure.

The body force method is used to formulate the threedimensional cracks in an elastic half space under contactload problem. The body force method models a crack asa distributed eigen-strains, and the stress disturbancecreated by the crack is equivalent to the body forcegenerated by the eigen-strains. By equilibrating thestress components with the tractions applied on thecrack surface, a system of integral equations for thecracks problem is derived which relate crack openingdisplacement, load, and stress intensity factors of althree modes. The details of the body force method are

given in [14, 21].

Applied Loads and Stresses

The simulation of loading includes:

(a) Hertzian contact loading. The surface of the halfspace is loaded by normal pressure p and tangentiatractionq from the Hertzian line contact. Expressions fopand qare given by:

p x e p x e c( , ) ( ) / 1 0 1

2 21

q(x1,e) = f p(x1,e)

p0= maximum Hertzian contact stress,

c= contact radius,

f= friction coefficient,

e= x1coordinate of contact center.

The contact stress field created by the Hertzian linecontact can be found in Smith and Liu [21].



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(b) Lubricant pressure. To simulate effect of fluidseepage into the crack, two bounding forms of hydraulicpressure can be used: uniform hydraulic pressure equalto the contact pressure at the mouth of the crack, and alinear pressure distribution equal to the contact pressureat the mouth and zero at the bottom of the crack.

(c) Residual stress. Residual stresses can be given as astress vs. depth profile in the input data. An interpolationroutine is used to calculate the corresponding residualstresses on the crack surface.

(d) External stress data. Additional three-dimensionalstresses (such as stresses caused by surfaceroughness) can be inputted into the program fromexternal data files.

Modified Paris Law

The Paris power law is used to model the crack growth.To account for the mixed mode growth the stressintensity factors in the Paris law are modified based onthe distribution of the energy release rate along the crack

front [14]. The effective stress intensity factor is definedas a stress intensity factor that causes an equivalentmagnitude of energy release around the crack:

2/1222

Im )1

1( IIIIIaxeff KKKK

whereKis the range of the stress intensity factor duringa loading cycle. is the Poisson Therefore, the Paris law for the mixed mode crackpropagation is modified as

theff

theff

n

theff

KK

KKKKC

dN

da

if0

if)(

where

da/dN= crack advance per rolling cycle,

C, n= Paris law constants (material constants),

Kth = threshold stress intensity factor (materialconstant).

Numerical Procedure

The numerical procedure to calculate the growth of thecrack fronts is as follows:

Determine the stress intensity factors andenergy release rate (Keff) along each crack frontfor the current loading cycle,

Use the modified Paris law to calculate thegrowth rate, da/dN, at a finite number of pointsalong the crack fronts,

Allow the crack front point with the maximumda/dN to travel a distance "da" along the normato the crack front at that point and determine thenumber of cycles "dN." The distances coveredby the other points of the crack contour during"dN" are also calculated,

Determine the new shape of the crack frontsupdate the number of loading cycles.

CONTACT FATIGUE TEST

A two-rollers contact fatigue test system designed byPhoenix Tribology, UK was used in this work to conductthe contact fatigue tests. A photo of the test machine isshown in Figure 2. The test machine is designed to

simulate gear teeth contact fatigue and wear undecombined rolling-sliding and high contact stresscondition. The machine has two motors, one to provideinput power, and another to absorb power. Two motorsalso provide continuous slide to roll ratio control from 0%to 100%. Contact load is applied by means of a servocontrolled pneumatic bellows actuator with loadtransducer feedback signal for close loop load controlThe upper load roller (5 inch=127 mm diameter) ismounted in a carrier with bearings supporting on bothsides. The lower test roller (1 inch=25.4 mm diameter) ismounted in a housing and it is also supported by tworolling bearings.

An in-line torque transducer is installed on the shafconnecting the lower test roller and drive motor tomeasure the friction torque induced by the contact of thetwo rollers. The torque transducer was manufactured byHBM, Inc. model no. T10F-200Q-SU2-S-0-V0-N. Thetorque transducer consists of two parts: the rotor and thestator. The rotor has a measuring body with strain gagesand an adaptor flange. The adaptor flange providesconnection to the rotating shaft. The strain gagesmounted on the measuring body measure the frictionforce. The rotor electronics transmits the measuredsignals. An antenna ring on the stator receives themeasured signal and provides voltage signa

conditioning.

An oil lubrication system is included with heating andcooling capability. Load, motor speed and oil tanktemperature are controlled. There are three temperaturemeasurements: oil tank temperature, oil inletemperature and oil out temperature. A nozzle is used tospray a jet of oil continuously into the contact zone of thetwo rollers. Contact fatigue failure is detected by usingan accelerometer. Failure point is defined by theappearance of a macro pit with approximate size of 3mm by 3 mm which corresponds to a certain vibrationlevel of the two rollers measured by the accelerometer.



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STEEL, HEAT TREATMENT AND TEST OIL

Both load rollers and test rollers were made of PS17steel. The chemical composition of the steel wasanalyzed by using an ARL 3460 Metals Analyzer (a multielement, optical emission, and direct readoutspectrometer) and following ASTM E415-99a standard.The chemical composition of the PS17 steel is asfollows (weight %): C: 0.234%, Mn: 1.01%, Ni: 0.11%,Cr: 0.55%, Mo: 0.16%, P: 0.093%, S: 0.020%, Si:0.243%, Cu: 0.177%, Al: 0.029%, Ti: 0.003%, V: 0.005%,Fe: balance. Load rollers and test rollers were gascarburized, quenched and then tempered. Roller surfacehardness is normally within 6062 HRc, core hardness iswithin 4045 HRc. Effective case depth (depth at whichhardness is 50 HRc) is within 1.021.27 mm (0.040 0.050). Surface carbon after carburizing is normallybetween 0.8% and 0.9%. Material case is high carbon martensite with 20% retainedaustensite.

Test oil is the Roadranger SAE 75W-90 synthetic oil.Three groups of tests were conducted under the same

load, speed and oil tank temperature conditions. The testroller (25.4 mm diameter) rotational speed is 1400 RPM,the load roller (127 mm diameter) rotational speed is 399RPM, oil tank temperature is at 70 degree C. Frictioncoefficient was measured at the steady state runningcondition. The only difference in the three groups tests isthe surface roughness of the rollers. Rollers in the Group#1 and Group #2 have turned surface and relatively highsurface roughness levels. Group #3 rollers havesuperfinished surface which is very smooth. Threerepetitive tests were conducted in each group. Contactfatigue test results are summarized in Table 1 below.Contact fatigue test results in Table 1 show that as the

surface roughness of the rollers decreases, frictioncoefficient decreases and contact fatigue life increases.

In Table 1 surface roughness of the rollers are given interms of Ra, Rz and composite Rq. Ra is defined as thearithmetic average deviation of the surface profile to themean line over the evaluation area, Rz is the average offive largest peak to valley heights, and Rq is the rootmean square of the deviation of the surface profile fromthe mean line. The composite Rq of the two contactbodies is defined as:

Composite Rq = ( Rq12

+ Rq22

)1/2

The Lambda Ratio is defined as the ratio of minimum oilfilm thickness to the composite Rq. The minimum oil filmthickness was calculated by using a numerical programdeveloped by Zhu and Cheng at Northwestern University,IL, USA [22].

A typical macro pit on a failed test roller is shown in theFigure 3 below, pit size is approximately 3 mm by 3 mm.Some micro pits can also been seen near the macro pit.The sign of the friction coefficients corresponds to thedirection of the surface friction force. Negative friction

corresponds to negative sliding, i.e. test roller has slowersurface speed than that of the load roller.

COMPARISON OF CALCULATED CONTACT

FATIGUE LIFE WITH TEST DATA

When using any computational simulation tool, selecting

and determining input data is very critical, for idetermines the output results, along with the softwarealgorithm, and sometimes it is difficult to get.

To simulate contact fatigue life, FATIG3D requiresfollowing input data:

---materials properties: shear modulus, Poisson Paris law constants C and n, crack growth threshold

valueKth,

---initial cracks: number of cracks, location of the crackscrack size and angle,

---stress conditions: maximum Hertzian stress, contacradius along minor axis of the contact ellipse, coefficientof friction (COEF), direction of surface friction, oihydraulic pressure, crack face friction, residual stressand rough surface induced stress.

The following input data is used to calculate contacfatigue life using the FATIG3D program: steel sheamodulus=79.3 GPa (11500 ksi), Poisson modified Paris Law constants: C= 2.98x10

-9mm/cycle

(1.173x10-10

inch/cycle), n=4.19, Kth=0.33 MPa m1/2

These crack growth law constants were obtained fromour own test data. Hertz contact stress=2.7 GPa (390ksi), radius along contact ellipse minor axis=0.49 mm(0.01937 inch), uniform oil pressure along crack lengthwith crack face friction, as heat treated residual stressinitial crack length=25 micron (0.001 inch), the inclinedangle of the crack = 30 degree, i.e. 30 degree counterclockwise from the surface.

Initial crack length in the FATIG3D input data is selectedbased on the surface intergranular oxidation (IGO) layerdepth which is normally between 13 micron (0.0005 inch)and 25 micron (0.001 inch). Figure 4 shows the typicasurface IGO of carburized gear teeth. The three frictioncoefficients used in the FATIG3D calculations are

obtained from the measurements in the two roller contacfatigue tests with three different surface roughnessgroups, as shown in Table 1. Contact fatigue lifecalculation results with the three different frictioncoefficient (-0.068, -0.087, and -0.116) are shown in theTable 2. From Table 2, one can see that with theselected input data FATIG3D calculated contact fatiguelives agree with test data quite well.



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FATIG3D CONTACT FATIGUE LIFESIMULATIONS

In this section, FATIG3D program is used to study theeffect of several input parameters on contact fatigue lifecomputationally: oil hydraulic pressure, crack surfacefriction, coefficient of friction, direction of surface friction,initial crack size, Hertzian stress and the associatedcontact radius along minor axis, and residual stress

distributions along sample depth direction. Crackinclined angle =-30 degree remains constant for all thesimulations conducted in this section.

The first input parameter studied is the oil hydraulicpressure in the crack, which has strong effect on crackgrowth and contact fatigue life [10, 14]. FATIG3D hasthree options with regards to the oil pressure: uniformpressure along crack length, linear pressure distributionand no oil pressure. Table 3 shows the contact fatiguelife calculation results with uniform oil pressure and linearpressure. Initial crack length is 25 micron, and Hertzianstress is 2.7 GPa.

From the results shown in Table 3, it is obvious thatuniform oil pressure must be used in FATIG3Dsimulations. Linear pressure could not generate crackgrowth, which does not agree with the test data shown.Obviously, the option of no oil pressure will not generaterealistic results either.

The second parameter studied is crack face frictionwhich is related to crack closure effect. Crack closureoccurs when crack face friction exists. Table 4 shows thesimulation results with a 25 micron length crack, under2.7 GPa Hertz stress and with uniform oil pressure.

The simulation results show that crack face friction hassome effect on contact fatigue life. Longer contactfatigue lives are obtained with crack face friction due tothe crack closure effect. And the effect of crack facefriction is more significant as fatigue life becomes longer,especially when contact fatigue life N is larger than 5million cycles.

The third study is to evaluate the effect of initial cracklength and friction coefficient on contact fatigue life,under 2.7 GPa Hertz stress, uniform oil pressure andwith crack face friction. The simulation results are shownin Table 5 and also plotted in Figure 5.

From Table 5 and Figure 5, it is clear that both initialcrack length and friction coefficient has strong effect oncontact fatigue life. Higher friction and longer initial cracklength reduce contact fatigue life, which is expected fromboth fracture mechanics and tribology theories. Also theirinfluence becomes stronger as contact fatigue lifebecomes longer.

The fourth study is on the effect of the direction ofsurface friction (traction), initial crack length, and Hertzstress on contact fatigue life with uniform oil pressure

and crack face friction. The simulation results are shownin Table 6 and 7 below.The simulation results show that generally no crackgrowth under positive friction except when initial cracklength is large, i.e. 100 micron (0.002 inch) and frictioncoefficient is relatively large, i.e. 0.12.The combinationof the inclined angle of a surface crack, the direction ofmovement of the Hertzian contact pressure, and thedirection of surface traction (friction) is schematicallyillustrated in Figure 6. Basically, the combination of crackangle and the direction of friction determines the stressstate and the opening of the crack. In FATIG3D, if thecrack angle and the friction coefficient has the samesign, i.e. both positive or both negative, crack face wilsubject to tensile stress and the crack will open, whichwill produce much shorter contact fatigue lives thanthose with positive friction and negative crack angle, asshown in Table 6 and 7. Moreover, negative crack angletogether with negative friction produced contact fatiguelives in good agreement with the test data as shown inTable 2.

Figure 7, Figure 8 and Figure 9 shows the effect oHertzian stress and friction coefficient on contact fatiguelife with as carburized residual stress. These three plotsmay be viewed similar to the traditional S-N fatigue lifecurves. Initial crack length is 25 micron (0.001 inch) and13 micron (0.0005 inch) respectively. These three plotscover a wide range of contact fatigue lives from 100,000cycles to 1 billion cycles and some typical rough surfaceEHL contact situations with Hertz stress range 1.7 3.3GPa, friction coefficient range -0.06 to -0.12, and initiacrack length range 13 to 25 microns. As explained in theDISCUSSION section, these parameter rangescorrespond to wide range of operating conditions in

terms of surface roughness, sliding speed, rolling speedcontact stress and temperature.Figure 10 and Figure 11 shows the effect of residuastress distribution on contact fatigue life, with initial cracklength = 25 micron, and friction coefficient equals to 0.09 and 0.12 respectively. Residual stress from shopeening improves contact fatigue life significantlyespecially at long life regime when friction and contacstress is relatively low. A contact fatigue endurance limiis also observed with shot peened residual stress, whichdid not exist for all other simulations with as carburizedresidual stress distribution. The shot peened residuastress and as carburized residual stress distributions are

given in the Appendix.

DISCUSSION

From the contact fatigue simulation results usingFATIG3D shown in the section above, one can see thatseveral factors in the input data have very stronginfluence on pitting life. These factors include: oipressure distribution along crack face, crack face frictiondirection of friction, friction coefficient, Hertzian stress



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initial crack length, and residual stress distribution.However, most of these factors, except Herzian stressand residual stress, are not clearly linked to a typicalcontact fatigue operating environment. In other words,some key contact fatigue controlling parameters are notdirectly represented in the FATIG3D input data, such assurface speed, surface roughness, hardness, test oilproperties such as viscosity and viscosity index, andtemperature. This is a very important issue in usingFATIG3D for contact fatigue life prediction and product

design.

Currently, these operating related parameters can onlybe represented indirectly in FATIG3D program throughfriction coefficient, initial crack length and crack growthproperties. Friction coefficient depends on samplesurface speeds, sample surface roughness, test oil,temperature, and sample material in a complex manner.Initial crack length depends on surface materialmicrostructure and surface roughness. Sample hardnessis characterized indirectly by the crack growth data of thematerial. In general, mode I fatigue crack growth ratesincrease as sample hardness increases. However, it is

still not clear yet how Mode II and Mode III crack growthbehavior is related to hardness of the material. The threemodes of crack growth have been defined in manytextbooks on fracture mechanics [23]. Mode I is theopening mode where the displacements of cracksurfaces are perpendicular to the crack plane. Mode IIrefers to the in-plane shear mode where thedisplacement of crack surfaces is in the plane of thecrack and perpendicular to the leading edge of the crack.Mode III refers to the out of plane shear mode where thedisplacement of crack surfaces is in the crack plane andparallel to the leading edge of the crack.

Another issue is that FATIG3D only models crack growthlife. However, crack nucleation life may be dominantunder certain circumstances. Therefore crack nucleationlife modeling may need to be investigated and developedfor contact fatigue. Finally, crack closure is considered in

this work, and a very smallKth= 0.33 MPa m1/2

is usedto account for the short crack effect.

CONCLUSION

Computational fracture mechanics based FATIG3D

program was used to simulate contact fatigue life ofrough surface contacts in boundary to mixed lubricationregimes. Two-rollers contact fatigue tests wereconducted and test results were compared withcalculated contact fatigue life. Calculated contact fatiguelife agreed with test results well with the selected set ofinput data. The effect of several important parameters inthe input data on contact fatigue life was evaluatedcomputationally using FATIG3D. Based on thesimulation results, the following conclusions are drawn:

1. Uniform oil pressure along crack length needs tobe used in FATIG3D simulations in order to gemeaningful results.

2. Crack face friction also affects contact fatiguelife, especially when life is longer than 5 millioncycles.

3. Direction of friction is extremely importanNegative friction with negative crack angletogether produces contact fatigue life resultsclose to test data.

4. Initial crack length and Hertzian stress bothstrongly affect contact fatigue life. HigheHertzian stress and longer initial crack lengthreduces contact fatigue life, which is consistenwith the traditional S-N approach and fracturemechanics approach used in modeling fatiguedamage.

5. Residual stress distribution has very strongeffect on contact fatigue life. Residual stress

produced by shot peening improved contacfatigue life significantly.

6. A contact fatigue endurance limit exists with thehighly compressive residual stress generatedfrom shot peening. No endurance limit exists inother simulations conducted, which might be due

to the smallKth value used.

ACKNOWLEDGMENTS

Dana Corporation is acknowledged for supporting thiswork. Northwestern University Center for SurfaceEngineering and Tribology is acknowledged for providingthe FATIG3D program.

REFERENCES

1. Lundberg G., Palmgren A., Dynamic Capacity oRoller Bearings, Acta Polytechnica 7, 1947

Stockholm2. Zaresky E.V., Life Factors for Rollin Bearings, STLE

SP-34, STLE, 1999

3. Zaresky E.V., Comparison of Life Theories foRolling-Element Bearings, Tribology Transactions1996, 2, 237-248

4. Charles Moyer, Fatigue and Life Prediction oBearings, ASM Handbook, Vol. 19, 1996, 355-362.

5. Ioannides E., Life Prediction in Rolling Elemen

Bearings, Proc. 1st

World Tribology Congress, 1997Mechanical Eng. Publications, London, 281-289.

6. Kim T.H., Olver A.V., Fatigue and Brittle FractureAnalysis of Surface Engineered Materials in Rollingcontact, Elastohydrodynamics 96, Proceedings o



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the 23rd

Leeds-Lyon Symposium on Tribology, 1997,37-48.

7. Epstein D., Yu T., Wang J.Q., L. Keer, Hong Lin,

Dong Zhu, Mixed Lubrication and fatigue lifePrediction of Engineered Surfaces in a rolling/slidingcontact, WCCM6, 6

thWorld Congress in

Computational Mechanics, Beijing, 2004.8. Murakami Y., Kaneta M., Yatsuzuka H., Analysis of

Surface Crack Prapagation in Lubricated Rolling

Contact, ASLE Transactions, Vol. 28, 1985, 60-68.9. Kaneta M., Murakami Y., Okazaki T., Growth

Mechanism of Subsurface Crack due to HertzianContact, Transactions of ASME, J. Tribology, Vol.108, January, 134-139.

10. Murakami Y., Kaneta M., Fracture MechanicsApproach to Tribology Problems, ASTM STP 1020,Fracture Mechanics: Perspective and Directions,

1989, 668-687.11. Murakami Y., Sakae C., Ichimaru K., Three

Dimensional Fracture Mechanics Analysis f Pit

Formation Mechanism under Lubricated Rolling-Sliding Contact Loadings, ASLE Trans., Vol. 37,

1994, 445-454.12. Keer L.M., Bryant M.D., A Pitting Model for Rolling

Contact Fatigue, ASME J. Lubrication Technology,

1983, Vol. 105, 198-205.13. Miller G.R., Keer L.M., Cheng H.S., On the

Mechanics of Fatigue Crack Growth Due to Contact

Loading, Proc. Roy. Soc., London, Ser. A, A397,1985, 197-209.

14. Hanson, M. T., and Keer, L. M., 1992, "An Analytical

Life Prediction Model for the Crack Propagation inContact Fatigue Failure," ASLE Trans., Vol.35, pp.451-461

15. Kuo, C. H., and Keer, L. M., Bujold M.P., "Effects of

Multiple Cracking on Crack Growth and Coalescencein Contact Fatigue," Journal of Tribology, Vol.119,1997, pp. 385-390.

16. Polonsky I.A., Keer L.M., Numerical Analysis of the

Effect of Coating Microstructure on Three-Dimensional Crack Propagation in the Coating underRolling Contact Fatigue Conditions, Trans. ASME, J.

Tribology, Vol. 124, 2002, 14-19.17. Kim T.H., Olver A.V., Pearson P.K., Fatigue and

Fracture Mechanisms in Large Rolling Element

Bearings, Tribology Trans., Vol. 44, 2001, 4, 583-590.

18. Tsushima N., Rolling Contact Fatigue and FractureToughness of Rolling Element Bearing Steels, JSMEInt. J., Ser C, Vol. 36, 1993, 1-8.

19. Otsuka A., Sugawara H., Shomura M., A TestMethod for Mode II Fatigue Crack Growth Relating toa Model for Rolling Contact Fatigue, Fatigue

Fracture Engng. Mater. Struct., Vol. 19, 1996, 1265-1275.

20. Glodez S., Flasker J., Ren Z., A New Model for the

Numerical Determination of Pitting Resistance of earTeeth Flanks, Fracture Engng. Mater. Struct., Vol.20, 1997, 71-83.

21. Smith, J. O., and Liu, C. K., 1953, "Stresses Due toTangential and Normal Loads on an Elastic Solidwith Applications to some Contact Problems," ASME

Journal of Applied Mechanics, Vol.32, pp. 157-166.22. Zhu D., and Cheng H.S., 1989, An Analysis and

Computational Procedure for EHL Film Thickness

Friction and Flash Temperature in Line and PoinContacts, Tribology Transactions, Vol. 32, 3, 364370.

23. Broek D., 1991, Elementary Engineering FractureMechanics, fifth printing, Kluwer Academic

Publishers, Dordrecht, page 8-9.24. Lin H., Binoniemi R.R., Fett G.A., 2005, Contac

fatigue tests and contact fatigue life analysis, SAE

paper 2005-01-0795.

FIGURES

Rolling Direction

Hertzian Load

p

f*p2c e

x3

x2

x1

1

n

Figure 1. The three-dimensional contact fatigue modelwhere rolling and sliding contact of gear teeth issimulated by a Hertzian contact loading moving acrossthe surface of an elastic half-space.



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Figure 2. A photo of the two-rollers contact fatigue testmachine.

Figure 3. Typical macro pitting on a failed test roller, pitsize is about 3 mm by 3 mm.

Figure 4. Backscatter electron image of typical IGO atthe carburized surface, nital etch.

103

104

105

106

107

108

109

0

20

40

60

80

100

InitialCrackLength(micron)

Contact Fatigue Life (cycles)

Herzt Stress=2.7 GPa

As carburized RS

COEF=-0.06

COEF=-0.12

Figure 5. Initial crack size vs. contact fatigue life, at Hertzstress 2.7 GPa (390 ksi), negative friction, and 30degree crack angle, as carburized residual stress.



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Figure 6. A schematic plot shows the direction of frictionand its effect on crack opening.

104

105

106

107

108

1.2

1.6

2.0

2.4

2.8

3.2

3.6

HertzianStress(GPa)


Friction Coefficient

- 0.06

- 0.09

- 0.12

Figure 7. Hertz stress vs. contact fatigue life, effect offriction coefficient, initial crack radius = 25 micron (0.001inch), as carburized residual stress, uniform oil pressure.

104

105

106

107

108

109

1010

1.5

2.0

2.5

3.0

3.5

HertzianStress(GPa)


Friction Coefficient

-0.06

-0.09

-0.12

Figure 8. Hertz stress vs. contact fatigue life, effect offriction coefficient, initial crack radius = 13 micron(0.0005 inch), as carburized residual stress, uniform oi

pressure.

105

106

107

108

1.2

1.6

2.0

2.4

2.8

3.2

3.6

HertzianStress(GPa)


COEF= -0.09

Initial Crack Length

13 micron

25 micron

Figure 9. Hertz stress vs. contact fatigue life, effect oinitial crack length, friction coefficient=-0.09, as

carburized residual stress, uniform oil pressure.

Compressive

Tensile

Faster

Slower

Traction

Forces



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104

105

106

107

108

109

1.2

1.6

2.0

2.4

2.8

3.2

3.6

HertzianStress(GPa)


COEF = -0.09

Initial Crack length 25 micronNo residual stress

As carburized RS

Shot peened RS

Figure 10. Effect of Residual stress on contact fatiguelife, initial crack radius 25 micron (0.001 inch), frictioncoefficient=-0.09, uniform oil pressure

104

105

106

107

108

109

1.2

1.6

2.0

2.4

2.8

3.2

3.6

Hertzia

nStress(GPa)


Initial crack length=25 micron

COEF = -0.12No residual stress

As carburized RS

Shot peened RS

Figure 11. Effect of Residual stress on contact fatiguelife, initial crack radius: 25 micron (0.001 inch), frictioncoefficient=-0.12, uniform oil pressure

TABLES

Table 1. Two-rollers contact fatigue test results

GROUP #1 #2 #3

Test roller

Ra (micron)

1.7 1.0 0.05

Test RollerRz (micron)

9.1 6.8 0.90

RollersCompositeRq (micron)

2.3 1.5 0.11

HertzianStress(GPa)

2.7 2.7 2.7

TheLambdaRatio

0.15 0.21 3.0

FrictionCoefficient

- 0.116 - 0.087 - 0.068

Test Life(millioncycles)

0.126,0.228,0.252

1.64, 2.38,2.40

8.96, 14.5230*

AverageTest Life

(millioncycles)

0.202 2.14 17.8

* test was stopped at 30 million cycles without pitting

Table 2. Comparison of contact fatigue life, FATIG3DCalculations vs. Test Data

FRICTIONCOEFFICIENT

FATIG3D LIFE(MILLIONCYCLES)

AVE TEST LIFE(MILLIONCYCLES)

-0.116 0.42 0.202

-0.087 1.57 2.14

-0.068 4.92 17.8



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Table 3. Contact Fatigue Life (million cycles) vs. frictioncoeffcient, 25 micron crack, 2.7 GPa Hertz Stress

COEF UNIFORM

PRESSURE

LINEAR

PRESSURE

TEST DATA

-0.125 0.29 no crack growth No data

-0.116 0.42 No growth 0.202

-0.087 1.57 No growth 2.14

-0.068 4.92 No growth 17.8

-0.050 29 No growth No data

Table 4. Crack face friction effect on contact fatigue life(million cycles), 25 micron crack, 2.7 GPa Hertz Stress,uniform oil pressure

COEF WITH CRACK FACEFRICTION

NO CRACK FACEFRICTION

-0.125 0.29 0.25

-0.116 0.42 0.36

-0.087 1.57 1.36

-0.068 4.92 3.68

-0.050 29 12

Table 5. Effect of Initial Crack Length on ContacFatigue Life with two friction coefficients, HertzStress=2.7 GPa

INITIAL CRACK

LENGTH (MICRON)

LIFE N @COEF=-0.06

LIFE N @COEF=-0.12

102 15800 7790

51 0.59 million 67200

38 2.45 million 0.138 million

25 10.8 million 0.34 million

13 67.5 million 1 million

6.4 400 million 27 million

Table 6. Contact Fatigue Life under 2.7 GPa, ascarburized RS, uniform oil pressure, crack angle=-30degree

INITIAL CRACKLENGTH (MICRON)

LIFE N@COEF=- 0.12

LIFE N@COEF=+ 0.12

102 7790 29000

51 67200 No crack growth

Table 7. Contact Fatigue Life with crack length=25micron, as carburized RS, uniform oil pressure, rackangle=-30 degree

HERTZ STRESS(GPA)

LIFE N @COEF=-0.09

LIFE N @COEF =+0.09

3.41 360,000 No crack growth

3.12 600,000 No growth

2.7 1.24 million No growth



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APPENDIX

TYPICAL RESIDUAL STRESS AFTERCARBURIZING, QUENCH AND TEMPERING

DEPTH (MM) RESIDUAL STRESS (MPA)

0.0 -138

0.0254 -172

0.0508 -138

0.102 -103

0.152 -69

0.254 -35

TYPICAL RESIDUAL STRESS AFTER SHOTPEENING

DEPTH (MM) RESIDUAL STRESS (MPA)

0.0 -414

0.0254 -552

0.0508 -621

0.076 -414

0.102 -241

0.127 -241

0.254 -241


contact fatigue tests and life simulations using

Documents