Constantine M. Tarawneh1

e-mail: tarawneh@utpa.edu

Arturo A. Fuentes

Javier A. Kypuros

Lariza A. Navarro

Andrei G. Vaipan

Department of Mechanical Engineering,

The University of Texas-Pan American,

Edinburg, TX 78539-2999

Brent M. WilsonAmsted Industries Incorporated,

1700 Walnut Street,

Granite City, IL 62040

Thermal Modeling of a RailroadTapered-Roller Bearing UsingFinite Element AnalysisIn the railroad industry, distressed bearings in service are primarily identified using way-side hot-box detectors (HBDs). Current technology has expanded the role of these detec-tors to monitor bearings that appear to “warm trend” relative to the averagetemperatures of the remainder of bearings on the train. Several bearings set-out fortrending and classified as nonverified, meaning no discernible damage, revealed that acommon feature was discoloration of rollers within a cone (inner race) assembly. Subse-quent laboratory experiments were performed to determine a minimum temperature andenvironment necessary to reproduce these discolorations and concluded that the discol-oration is most likely due to roller temperatures greater than 232 �C (450 �F) for periodsof at least 4 h. The latter finding sparked several discussions and speculations in the rail-road industry as to whether it is possible to have rollers reaching such elevated tempera-tures without heating the bearing cup (outer race) to a temperature significant enough totrigger the HBDs. With this motivation, and based on previous experimental and analyti-cal work, a thermal finite element analysis (FEA) of a railroad bearing pressed onto anaxle was conducted using ALGOR 20.3TM. The finite element (FE) model was used tosimulate different heating scenarios with the purpose of obtaining the temperatures of in-ternal components of the bearing assembly, as well as the heat generation rates and thebearing cup surface temperature. The results showed that, even though some rollers canreach unsafe operating temperatures, the bearing cup surface temperature does not ex-hibit levels that would trigger HBD alarms. [DOI: 10.1115/1.4006273]

Keywords: railroad bearing thermal modeling, tapered-roller bearing heating, internalbearing temperatures, discolored rollers, excessive roller heating, thermal finite elementanalysis

Introduction

Tapered-roller bearings (see Fig. 1) are the most widely usedbearings in railroad cars. When operated under satisfactory load,alignment, and contaminant free conditions, the service life isexceptionally long. As a general rule, bearings will outlast thewheel life, and survive several reconditioning cycles prior tobeing retired. At the end of their life, bearings will initiate fatigue,particularly subsurface fatigue, rather than wearing out due tosurface abrasion. Fatigue failures, or spalling, can lead to materialremoval at the raceway surface which in turn will cause greasecontamination and increased friction that manifests itself as heatwithin the bearing. Excessive heat will lower the viscosity of thelubricant, which reduces the thickness of the fluid film that sepa-rates the rolling surfaces. As a consequence, metal-to-metal con-tact occurs, which can hasten the onset of premature bearingfailure. To identify distressed bearings in service, bearing healthmonitoring equipment is employed by the railroads to warn ofimpending failures as a method to ward off potentially cata-strophic events, such as derailments. The most common methodof monitoring bearing health is by conventional wayside hot-boxdetectors which are strategically located to record bearing cuptemperatures as the train passes. These devices are designed toidentify those bearings which are operating at temperaturesgreater than 105.5 �C (190 �F) above ambient conditions. Anextension of this practice is the tracking of temperature data andcomparing individual bearings against the averages of the remain-der along a train (Karunakaran and Snyder [1]). Identifying thosebearings which are “trending” above normal allows the railroads

to track bearings which appear to be distressed without waitingfor a hot-box detector (HBD) to be alarmed.

As a diagnostic aid, bearings which are identified as hot areremoved from service for later disassembly and inspection. Inmost cases, the cause of bearing overheating can be attributed toone of several known modes of bearing failure such as: spalling,water contamination, loose bearings, broken components, dam-aged seals, etc. However, in some cases, these early set-out bear-ings do not exhibit any of the commonly documented causes ofbearing failure and are, therefore, classified as nonverified.

Upon closer disassembly and inspection, it has been observedthat many of these nonverified bearings contain discolored rollersin an otherwise normal bearing. The discoloration of the steel isvisual evidence that these rollers have been exposed to tempera-tures greater than what is expected during normal operating condi-tions. Hence, initial work performed by the authors of this paperfocused on determining conditions that would replicate the discol-oration observed in the rollers. A laboratory furnace was used toheat numerous rollers to elevated temperatures in various

Fig. 1 Detailed component view of a typical railroad tapered-roller bearing

1Corresponding author.Manuscript received May 3, 2011; final manuscript received January 21, 2012;

published online July 12, 2012. Assoc. Editor: Chenn Zhou.

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environments. Results indicated that the visual discolorationwhich best matched that observed in bearings removed from serv-ice were rollers heated in grease to temperatures over 232 �C(450 �F) for periods of at least 4 h (Tarawneh et al. [2]). The latterfinding stirred many discussions and speculations among peoplein the railroad industry as to whether rollers can be at such ele-vated temperatures for these extended durations without generat-ing sufficiently high temperatures at the cup surface to trigger hot-box detectors. To this end, a number of dynamic laboratory testswere carried out to explore several defects and/or hypotheticalscenarios that can lead to bearing overheating. Details regardingthese dynamic tests can be found elsewhere (Tarawneh et al. [2]).Simultaneously, several static experiments were conducted usingcylindrical heaters embedded in two rollers in order to betterunderstand the heat transfer paths within the bearing assembly(Tarawneh et al. [3]). The data acquired from the static experi-ments were used to determine overall heat transfer coefficients forheat dissipation from the bearing cup and heat loss to the axle,which allowed for the derivation of analytical expressions for thetemperatures of the bearing cup and the bearing/axle interface.

However, even though the aforementioned work offered greatinsight into the thermal behavior of tapered-roller bearings, it hadits limitations. Only external bearing cup temperatures could berecorded in the dynamic experiments since it is not feasible tomeasure the temperatures of the internal components of the bear-ing while it is rotating. In the static tests, monitoring the tempera-ture of the rollers was possible, but the case studies were limitedto a setup utilizing two cartridge heaters embedded in two rollersto provide the heating source. Additional embedded heaters couldhave been used, but it would have added greatly to the complexityof the experimental setup and instrumentation, not to mention thetime and effort involved in conducting these experiments.

Numerical simulations tend to be a more economical means ofobtaining prompt results and an efficient way to overcome the exper-imental challenges and limitations. Hence, ALGOR 20.3TM was uti-lized to develop a finite element (FE) model for a class K tapered-roller bearing mounted to an axle, as shown in Fig. 2. The findingsof the previous experimental and analytical work performed by Tar-awneh et al. [2] and [3] were used to devise the FE model and vali-date its accuracy. The FE model was then utilized to run severaldifferent bearing heating simulations that provided definitiveanswers as to whether it is possible for rollers to heat to high temper-atures without heating the cup surface to a sufficient temperaturenecessary to trigger any HBD alarms. The paper presented here pro-vides a thorough summary of the results attained from the aforemen-tioned steady-state thermal finite element analysis (FEA).

Literature Review

Many studies have utilized the FE method to develop models toanalyze specific phenomena of interest concerning different types

of bearing assemblies and their components. In most cases, exper-imentally acquired data are used to validate the accuracy of thederived FE models. Overstam [4] performed FE simulations usingthe MSC.MARC code to study the effect of bearing geometry on theresidual stress-state in cold drawn wires, and verified the simula-tion results with data acquired from full-scale industrial experi-ments. Wei et al. [5] used FE simulations to demonstrate that theirproposed design of a deep end-cavity roller would enable astraight-profile-roller bearing to perform similar to a logarithmic-profile-roller bearing by eliminating the sharp edge-stresses at thetwo apexes of the rollers. Furthermore, the FE analysis shows thatthe deep end-cavity roller design reduces the centrifugal force act-ing on the outer race of the bearing while saving material andreducing the weight of the bearing. Demirhan and Kanber [6]used ANSYS to investigate the stress and displacement distributionson cylindrical roller bearing rings. The study concluded that thestresses and displacements have different distribution characteris-tics on the inner and outer faces of the rings and are not uniformlydistributed along the height of the rings because of large stressesat the contact points. Vernersson [7] developed a FE model forheat transfer from the rolling wheel into the rail where a film withthermal contact resistance is placed at the wheel-rail contact inter-face. The proposed FE model, which is validated by experimentalresults, can be used to efficiently design tread braking systems forboth freight and passenger trains. Other works that utilized the FEmethod to study magnetic and journal bearings are reported inSchmidt and Weiland [8], Awasthi et al. [9], and Sukumaran Nairand Prabhakaran Nair [10].

Theoretical investigations of bearing overheating were carriedout by Dunnuck [11] and Wang [12] who explored two abnormaloperating conditions: (1) a jammed roller bearing and (2) a stuck-brake situation. A partially jammed roller bearing is one that isrotating with velocities greater than zero but less than the epicy-clic speed, whereas, a fully jammed roller bearing is one that hasno angular velocity with respect to the cage. The theoreticalstudies revealed that the maximum temperature within the bearingassembly can reach 268 �C for a jammed roller and 126 �C for astuck-brake, compared to the normal operating condition tempera-ture of 81 �C. However, the study also concluded that the stuck-brake heating scenario resulted in only a small increase in theexternal surface temperature of the bearing cup, which suggeststhat it would be difficult to detect a stuck-brake situation from thecup surface temperatures. In a related study, a dynamic model ofthe torque and heat generation rate in tapered-roller bearingsunder excessive sliding conditions was developed using the pro-gram SHABERTH (Wang et al. [13]). The investigation focusedon jammed roller bearings, and the model was run with anassumed ambient temperature of 25 �C (77 �F), a load per row of80,000 N (18,000 lb), and a rotational speed of 560 rpm whichcorresponds to a train speed of 97 km/h (60 mph). The study con-cluded that the heat generated in the bearing was proportional tothe number of jammed rollers.

In yet another theoretical work, thermally induced failures inrailroad class F (61=2� 12) tapered-roller bearings observed in lab-oratory experiments when the bearings were operating at highspeeds were modeled using finite element analysis with ABAQUS

and FORTRAN (Kletzli et al. [14]). The experiments were conductedby the Association of American Railroads (AAR), and showedthat new (defect-free) bearings failed after 200–300 h of operationat a speed of 161 km/h (100 mph), but none failed at 129 km/h(80 mph). The study concluded that the increase in the heat gener-ation is a direct consequence to the grease starvation mechanismcaused by the high operating speeds, which results in a larger fric-tion coefficient.

A few studies were conducted using simplified experimentalsetups designed to mimic the operation of roller bearings (Farn-field [15] and Hoeprich [16]). The main outcome of some of theseexperiments was that bearing temperatures predominantlydepended on speed and not on load, and that increasing theamount of lubrication slightly raises bearing temperatures.

Fig. 2 Mesh results for the solid model of the bearing-axle as-sembly that was used to perform the finite element analysis inthis study

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Theoretical modeling of the thermal effects in plain journal bear-ings was reported in Wang and Zhu [17], Fillon and Bouyer [18],Wang et al. [19], Li et al. [20], and Ma and Taylor [21] with lim-ited experimental validation. In addition, Briot et al. [22] lookedinto the thermal transport conductance between the rings of aroller bearing.

The thermal and dynamic behavior of railroad tapered-rollerbearings has been explored extensively through several experi-mental and theoretical studies conducted by the authors of this pa-per. First, in a series of five papers, Tarawneh et al. ([3], [23], and[24]) and Cole et al. ([25] and [26]) examined the heat transferpaths within tapered-roller bearings, and heat transfer to the bear-ing from an adjacent hot railroad wheel. Experimentally validatedanalytical expressions were developed to describe the surface tem-perature of the bearing cup, the temperature at the cone-axle inter-face, and the temperature along the wheel web. Additionally, theaforementioned studies resulted in the determination of heat trans-fer coefficients for heat dissipation from the bearing and wheelsurfaces which can be used to devise reliable FE models. Second,in a series of four papers, Tarawneh et al. ([2], [27]–[29]) investi-gated the warm bearing temperature trending problem and wereable to identify the root cause of this troubling phenomenon. Itwas concluded that vibration induced roller misalignment is thelikely cause for the bearing temperature trending phenomenonseen in service (Tarawneh et al. [27]), and an on-track field testconducted by the authors in collaboration with The Union PacificRailroad, Rail Sciences Incorporated, and Amsted Rail Industriesvalidated the results obtained from the laboratory testing (Taraw-neh et al. [28]). Furthermore, vibration signatures of temperature-trended bearings in field and laboratory testing are provided inTarawneh et al. [29].

From the literature review provided here, the need for reliablenumerical models that can predict internal bearing temperaturesbecomes apparent. With this motivation, the authors utilized theirearlier experimental results and analytical models to develop a FEmodel that can be used to simulate numerous normal and abnor-mal operating scenarios, that are otherwise very complex and timeconsuming to duplicate in a laboratory setting, and acquire inter-nal and external bearing temperatures. The developed model canprove to be a very useful tool in future thermal research of railroadtapered-roller bearings. Knowing the temperature distributionwithin the internal components of the bearing during normal andabnormal operating conditions can help bearing manufacturersexplore possible design modifications to their bearings to dissipatethe heat more efficiently or select appropriate lubricants that canwithstand the internal temperatures experienced by the bearings.

Finite Element Analysis

The main objective of the work presented here is to study howroller heating affects the temperature of the bearing assemblycomponents, especially the external surface of the cup, which isthe part of the bearing scanned by the infrared wayside hot-boxdetectors. To this end, a FE model was created and utilized to runseveral roller heating simulations in order to attain answers as towhether it is possible for certain rollers to heat to temperaturesabove 232 �C (450 �F) within the bearing and go undetected bythe HBDs. This study would be very challenging to performexperimentally due to the constraints imposed by placing conven-tional thermal sensors inside a rotating assembly. The followingtwo subsections, Bearing Modeling and Boundary Conditions,provide a detailed description of the developed FE model includ-ing the boundary conditions (BCs) used.

Bearing Modeling. A solid model of the bearing-axle assem-bly that was generated utilizing the three-dimensional graphingsoftware Pro/EngineerTM was used to develop the FE model forthis study. The axle is rendered as a simple cylinder with a0.1572 m diameter and a 2.2 m length, which is sufficient in sizeto act as a heat sink. The bearing is modeled after a class K rail-

road tapered-roller bearing with some minor modifications thatsimplified the geometry and resulted in a significant reduction tothe computational time. First, no cages, seals, wear rings, orgrease were included in the model; this was done because the ther-mal resistances of the polyamide cages and grease are large com-pared to the rest of the bearing assembly, so the majority of theheat will flow from the rollers to the bearing cup and inner cones.Recent advances in bearing seal technology have resulted in mini-mal contact low friction seals. Furthermore, these seals constitutea small fraction of the total weight of the bearing and are sepa-rated from the rest of the internal bearing components by a combi-nation of air and grease which both have high thermal resistances.The wear rings are in contact with the axle, which constitutes avery large body of metal and acts as a heat sink. Hence, the omis-sion of the aforementioned components from the FE model willnot have a significant effect on the results acquired from thisstudy. The latter statement is validated both experimentally andtheoretically as will be shown later in this paper.

The second assumption is concerned with the contact areabetween the rollers and the cup and cone raceways. Under normaloperating conditions, only the upper hemisphere of a railroadbearing is loaded; therefore, larger contact areas exist between therollers and the cup and cones in this region. However, since therollers of a bearing enter and exit the loaded zone continuously asthey execute multiple revolutions in a second, an average contactarea was applied to all 46 rollers in the bearing. Hence, in themodel, the contact area between each roller and the cup and coneraceways is 123.96 mm2, which represents 3.68% of the total sur-face area of the roller. The contact area was obtained by first esti-mating the initial contact area of the rollers with the cup andcones using the Hertzian line contact theory (Brandlein et al. [30]and Harris and Kotzalas. [31]), and then using FE analysis todetermine the load distribution on the upper hemisphere of afully-loaded bearing (full load corresponds to a force of 159,000N (35,750 lb) per bearing applied through the bearing adapter),which was then used to calculate the amount of roller compres-sion. A detailed description of this methodology is provided else-where (Alnaimat [32]). Note that the contact area used in themodel represents the average contact area of all the rollers withina cone assembly when fully-loaded. A sensitivity analysis thatwas carried out to investigate the effect of the contact arearevealed that the results changed by less than 4% when the contactarea was varied by 610%.

Once the model was completed, it was imported into ALGOR20.3TM and discretized into 68,086 elements with a mesh size of 4.0mm, which is the largest element size that can be used without jeop-ardizing the convergence of the FE model while keeping the compu-tational time relatively low (�20 min on a DELL OPTIPLEX 755Minitower, Core 2 Duo E8200/2.66 GHz processor). The conver-gence analysis run on the model revealed that the attained results var-ied by less than 0.7% when the mesh size was changed by 610%.The final meshed model is illustrated in Fig. 2.

The ALGOR “bricks and tetrahedral” solid mesh type optionwas used since it generates the most accurate mesh utilizing thefewest elements. Even though the use of brick and hexahedralelements can sometimes yield better results [33], the generatedmesh contains many more elements, which substantially increasesthe analysis time. In this study, the use of hexahedral elementsresulted in an insignificant improvement on the acquired results(<0.5%) while more than tripling the analysis time. Note that,while the mesh contained six-node wedge, five-node pyramid, andfour-node tetrahedral elements toward the center of the model, themajority of the solid mesh consisted of eight-node brick elements.The benefit of using a small number of nonbrick elements (i.e.,wedge, pyramid, tetrahedral) is to significantly reduce the numberof elements needed to accomplish the solid mesh, thus, decreasingcomputational time. Additionally, surface knitting (i.e., the pro-cess of recognizing where two parts have surfaces in contact andthen splitting the surfaces) was used in order to properly applyconvection loads.

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For the finite element thermal analysis, different solvers wereconsidered to work out the system of equations including the iter-ative algebraic multigrid (AMG) and the Sparse solver. Whilethere were no significant differences in the performance of the dif-ferent solvers, the iterative AMG solver with a convergence toler-ance of 0.000001was selected based on the analysis time for ourmodel (the iterative AMG solver takes 30% less time to run thanthe Sparse solver). Furthermore, the application of radiation to themodel required a nonlinear iterative approach in order to solve thesteady-state heat transfer analysis. To start the nonlinear iterativeprocess, the ambient temperature was used as the default nodaltemperatures. Then, in each successive iteration, the radiation heattransfer rate was estimated based on the prior estimate of thenodal temperatures. The resulting temperatures were then com-pared to the prior estimate of the nodal temperatures. The iterativeprocess was stopped when the relative norm (i.e., the relativechange in temperature between iterations) was less than a relativetolerance of 0.001. If the difference was not acceptable based onthe relative tolerance, the radiation heat rates were recalculatedand the process repeated. Note that, the convergence tolerancedetermines how accurate of a solution is found to the matrix ofequations (i.e., the smaller the tolerance, the more accurate the so-lution), whereas, the relative tolerance is used to prescribe thequality of convergence of the temperatures due to the radiationloads and to stop the iterative process.

At this point, a comment is in order regarding the FE modeldeveloped for this study. In service, a railroad bearing is mountedat the end of the axle next to the wheel and is coupled to the side-frame of the railcar via an adapter. Thus, the bearing is connectedto a semi-infinite body of metal and can conduct heat to the axlethrough the inner cones and to the side-frame through the cup sur-face in contact with the adapter. The model utilized in this investi-gation uses a bearing that is pressed onto the middle of a 2.2 maxle in order to provide comparable heat conduction paths to theones the bearing experiences in service, without the added com-plexity that the actual setup would impose on the FEA. Further-more, the bearing overall heat transfer coefficients used in thisstudy were acquired utilizing an experimental setup similar to theone depicted by the FE model (Fig. 2) with a full-load applied tothe bearing through the adapter using a hydraulic cylinder (Taraw-neh et al. [3]). Hence, based on the above discussion, the FEmodel devised for this investigation is assumed to approximatethe actual setup of a bearing in service.

Boundary Conditions. The validity of the FE model dependsgreatly on the correctness of the BCs applied when running thesimulations. With this in mind, the BCs used for this study werederived from previously conducted experimental efforts (Taraw-neh et al. [2], [3], and [24]), a well-established textbook in thefield of heat transfer (Incropera et al. [34]), and from materialspecifications provided by the bearing manufacturer. Four majorBCs, which are described in this section, were utilized; namely:conduction, convection, radiation, and heat flux.

The heat conduction coefficients for the bearing assemblyand axle were provided by the bearing manufacturer. For thebearing steel, AISI 8620 with a thermal conductivity of46.6 W �m�1 �K�1 was used, and for the axle steel, AISI 1060with a thermal conductivity of 51.9 W �m�1 �K�1 was chosen. Asensitivity analysis was performed to ensure that variations in thethermal conductivity values due to temperature have a marginaleffect on the reported results; the results differed by less than 1%when both thermal conductivity values were changed by 610%.Note that the thermal conductivity values for both AISI 8620 andAISI 1060 do not change by more than 7% over the range of tem-peratures reported in this study.

Convection and radiation BCs for the bearing were acquiredfrom the results of previous experimental testing conducted by theauthors. Tarawneh et al. [3] provides an overall heat transfer coef-ficient Ho¼ 8.32 W �K�1 for the bearing cup, which takes into

account forced convection generated by a 5 m � s�1 airstream andradiation to an ambient at a temperature of 25 �C. However, sincethe software used for the FE simulations requires convectioncoefficients to be entered in units of W �m�2 �K�1, the externalsurface area of the bearing cup Acup¼ 0.1262 m2 was used toobtain the heat transfer coefficient in the appropriate units(ho¼ 65.9 W �m�2 �K�1). The latter overall heat transfer coeffi-cient was applied to the external (exposed) surface of the bearingonly, as illustrated in Fig. 3.

For the axle, the cylinder-in-cross-flow correlation, Eq. (1), andthe flow over a flat surface correlation, Eq. (2), given in Incroperaet al. [34] (Chap. 7, p. 427 and 410, respectively), were utilizedto calculate the convection heat transfer coefficient from the cir-cumferential surface and the two ends of the axle, respectively.Both correlations yielded a convection coefficient value ofhaxle¼ 25 W �m�2 �K�1 corresponding to a 6 m � s�1 airstreamand a 25 �C ambient temperature.

Nu ¼ 0:3þ 0:62Re1=2Pr1=3

1þ 0:4=Prð Þ2=3h i 1=4

1þ Re

282; 000

� �5=8" #4=5

¼ hLc

k; Pe � 0:2 (1)

Nu ¼ 20:3387 Re 1=2Pr 1=3

1þ 0:0468=Prð Þ2=3h i1=4

8><>:

9>=>; ¼

hLc

k; Pe � 100 (2)

where

Re ¼ VLc

v; Pe ¼ Re Pr (3)

In Eqs. (1)–(3), the characteristic length, Lc, is equal to the diame-ter, D, of the axle. Table 1 provides the numerical values for theproperties and parameters appearing in Eqs. (1)–(3). Note that,even though the correlations given in Eqs. (1) and (2) are for astationary cylinder, the acquired convection coefficient is stillvalid for a rotating cylinder since the air-flow across the cylinderis moving relatively fast (Re¼ 55811� 100). The literaturereview conducted by the authors revealed three references (Joneset al. [35], Badr and Dennis [36], and Kendoush [37]) which con-clude that the effect of convection produced by a rotating cylinderneed only be considered when the air-flow across the cylinder is

Fig. 3 Solid model of the bearing-axle assembly showing howthe boundary conditions (BCs) were applied for the FE analysesconducted for this study. Note: (1) heat flux was applied to thecircumferential surface of the rollers only, (2) bearing overallheat transfer coefficient was applied to the bearing externalsurfaces (i.e., bearing cup external surface and side walls, andbearing cone side walls), and (3) axle heat transfer coefficientand radiation were applied to all exposed surfaces of the axle.

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relatively slow (i.e., flows with a Re 100). Furthermore, a sensi-tivity analysis was carried out to assess the effect of the axle con-vection coefficient on the reported results; the results differed byless than 5% when the axle convection coefficient was increasedby 20%.

The only parameter needed to calculate radiation from the axleto the ambient was emissivity, and it was measured to be about0.96 from previous experimentation (Tarawneh et al. [24]). Again,a sensitivity analysis was performed on the emissivity value usedin this study, which revealed that the results differed by less than1% when the emissivity value was lowered by 20%.

Finally, to simulate heat generation within the bearing assem-bly, heat flux was applied to the circumferential surface of therollers, as depicted in Fig. 3. The appropriate heat flux value wasdetermined through a trial-and-error process starting with an over-all heat input of 11.5 W per roller (normal operation conditions)and increasing this input until the desired external cup tempera-ture was achieved. The acquired heat input per roller was then di-vided by the surface area of the roller to obtain the heat fluxvalue. Here, it is assumed that the rollers are the source of heatwithin the bearing which is justified considering the mass of theroller (0.145 kg) relative to the mass of the bearing cup (11.53 kg)and cone (3.9 kg). To illustrate this, consider an abnormal opera-tion condition in which debris gets wedged between a roller andan adjacent cage bar causing the roller to become fully or partial

jammed and resulting in excessive sliding friction between theroller and the cup and cone raceways. Since the mass of the rolleris very small compared to the mass of the cup and cone, it is safeto assume that it will heat at a much faster rate than the other twocomponents, thus, becoming the heat source.

Discussion of Results

Thirteen different bearing heating scenarios, summarized inTable 2, were simulated for this study. The first five cases arebased on previous experimental work conducted by Tarawnehet al. [2], whereas, the remaining eight cases simulate hypotheticalheating scenarios that can result from abnormal roller operationleading to excess frictional heating. The results of both, the FEanalysis and the previously validated lumped-capacitance theoret-ical model (Tarawneh et al. [3] and [23]), are presented and com-pared hereafter. An in-depth discussion is reserved for six of thethirteen simulated cases, with the purpose of highlighting pivotalinformation that can help answer the question posed earlier in thispaper; i.e., is it possible to have rollers reaching 232 �C (450 �F)within a cone assembly without heating the bearing cup to a tem-perature that will trigger the HBDs?

FE Model Validation. As stated earlier, the first five heatingscenarios listed in Table 2 were intended to replicate five of the

Table 1 Numerical values for the properties and parameters appearing in Eqs. (1)–(3)

Property Film temperature Thermal conductivitya Kinematic viscositya Velocity Characteristic length Prandtl numbera

Symbol Tf k � V Lc PrUnits K W �m�1 �K�1 m2 � s�1 m � s�1 m NoneValue 310 27.0� 10�3 16.9� 10�6 6.0 0.1572 0.706

aAll thermal properties were obtained at Tf from Ref. [34], Appendix A, p. 941.

Table 2 Summary of the performed finite element (FE) simulations. The average cup temperatures provided in the table wereobtained by averaging six nodes simulating the thermocouples placed around the circumference of the middle of the cup 60 degapart.

CaseNo. Description of heating scenario

Qtotal

(W)Qroller

(W)Maximum average

roller temperature (�C)Average cup

temperature (8C)

1 Normal operation. All 46 rollers are heated equally to produceTcup¼ 50 �C (see Fig. 5)

529.0 11.5 55.0 50.2

2 One welded roller. 45 rollers heated to normal operationconditions; one roller abnormally heated

672.5 155.0 120.8 57.5

3 Six welded rollers. 40 rollers heated to normal operationconditions; six rollers on one cone assembly abnormally heated(see Fig. 6)

712.0 42.0 75.9 59.0

4 Twisted cage bar. 44 rollers heated to normal operation conditions;two adjacent rollers abnormally heated (see Fig. 7)

1086.0 290.0 218.2 79.2

5 Added debris. One cone assembly (23 rollers) heated to normaloperation conditions; the other cone assembly abnormally heated

908.5 28.0 83.3 68.6

6 Two hot rollers. 44 rollers heated to normal operation conditions;two rollers, one on each cone assembly, abnormally heated

754.0 124.0 110.7 59.7

7 Two hot rollers. 44 rollers heated to normal operation conditions;two rollers, one on each cone assembly, abnormally heated (seeFig. 8)

1484.5 489.3 291.8 90.2

8 Three hot rollers. 43 rollers heated to normal operation conditions;three consecutive rollers abnormally heated (see Fig. 9)

1287.4 264.3 232.0 88.5

9 Four hot rollers. 42 rollers heated to normal operation conditions;four consecutive rollers abnormally heated

1438.2 238.8 233.4 96.8

10 Misaligned roller. 45 rollers heated to normal operation conditions;one roller abnormally heated

1249.0 731.5 388.6 80.0

11 Abnormal operation. All 46 rollers are heated equally to produceTcup¼ 72 �C

979.8 21.3 80.4 71.9

12 Abnormal operation. All 46 rollers are heated equally to produceTcup¼ 80 �C

1163.8 25.3 90.8 80.7

13 Abnormal operation. All 46 rollers are heated equally to produceTcup¼ 130.5 �C (see Fig. 10)

2208.0 48.0 149.5 130.5

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dynamic experiments performed for a previous study (Tarawnehet al. [2]) aimed at identifying possible causes of warm bearingtemperature trending. These dynamic tests were performed in alaboratory with an ambient temperature of 25 �C utilizing adynamic bearing tester that maintained a speed setting of 536 rpmcorresponding to a train traveling with a velocity of approximately91.7 km h�1 (57 mph) at full load (which corresponds to a forceof 159,000 N (35,750 lb) per bearing). The source of heating inthose five dynamic tests is known, which makes them uniquelyinvaluable for validating the FE model by providing a basis forcomparison with the lumped-capacitance analytical model. Abrief description of the first five heating scenarios follows.

Scenario number one, normal operation, simulates a bearingrunning under normal operating conditions. This model representsa healthy bearing with an average cup temperature of approxi-mately 50.0 �C (this temperature is the average of six thermocou-ple readings positioned 60 deg around the circumference of thecup at the middle of the bearing). The aforementioned temperaturewas acquired from the dynamic testing described earlier in thissection.

Scenario number two, one welded roller, represents the case inwhich one roller in the cone assembly was welded to the steelcage causing it to slide on the cup raceway instead of roll, thus,generating excess heat through friction. The remaining 45 rollerswere assumed to be operating normally. In field service, this sce-nario simulates a case in which a wear particle or debris becomeswedged between the roller and the cage or one of the racewayscausing it to slide on the raceway rather than roll. The experimen-tal results for the welded roller case indicate that the average cuptemperature is about 57.4 �C.

Scenario number three, six welded rollers, is similar to the pre-vious scenario but replicates the test in which six rollers in onecone assembly were welded to the steel cage, thus, producing slid-ing friction. The remaining 40 rollers were assumed to be operat-ing normally. Again, in service, this case might occur if multiplewear particles from a spalled raceway, for instance, get lodgedbetween the rollers and the cage. The average cup temperature forthis case is 58.9 �C, which is only slightly higher than that of theone welded roller case.

Scenario number four, twisted cage bar, simulates the case inwhich a cage bar, in one cone assembly, was bent toward the conerace causing the two adjacent rollers to rub the cage generatingexcess heat. The latter case can occur in the field from a suddenlarge impact caused by a bad joint in the track. The average cuptemperature obtained from the laboratory test data is 79.2 �C indi-cating that this case produced significant frictional heating.

Scenario number five, added debris, as the name suggests, rep-licates the test in which debris (a mixture of sandblaster sand andmetal filings) was added to the raceway of one cone assemblythrough a hole in the adjacent seal. The added debris causes the23 rollers in that cone assembly to operate abnormally whichresults in increased frictional heating produced by the sliding ofrollers. In field service, the latter case can occur in a number ofways, namely; debris generated from spalled raceways, contami-nants introduced to the bearing assembly by accident when theseals are removed to conduct a visual inspection, or in extremeweather conditions when the train goes through sandstorms. Theaverage cup temperature attained experimentally for this case is68.6 �C.

The other eight heating scenarios, described in Table 2, werederived from the first five cases and were intended to provide agood understanding of the effects of abnormal roller operation,and demonstrate that it is possible to have one or more rollersheating to temperatures above 232 �C without triggering waysideHBDs.

At this point, a comment is in order on the cup temperature. Arotating bearing with one or two hot rollers would have the hotrollers sweeping round and round the cup, uniformly heating thecup, even at modest train speeds. Our FE model is nonrotating, sothe cup temperature is high near the hot rollers and lower around

the circumference of the cup. To simulate the averaging of cuptemperature that a rotating bearing would produce, a spatial-average of the acquired cup temperatures was used to obtain a sin-gle value that represents the average cup temperature reported inthis study. The spatial averaging simulates the “time averaging”that a rotating bearing would yield. A numerical example will pro-vide a framework for understanding this averaging effect. In atrain moving at a leisurely 11.2 m � s�1 (25 mph), a 91.4 cm (36in) diameter wheel sees 234 revolutions per minute (rpm). Taraw-neh et al. [3] show that the thermal response time of the bearingcup is measured in tens of minutes, indicating that thousands ofroller orbits would spread the heating over the entire bearing cupon a moving train.

To validate and quantify the accuracy of the results acquiredfrom the FE model, both an experimental and a theoretical tech-nique were employed. The experimental method required the useof a dynamic bearing tester (pictured in Fig. 4) powered by a 22kW (30 hp) motor that is managed by a smart controller. The con-troller has outputs that can be monitored via a data acquisitionsystem to record the axle speed and the power required to run thebearings. In an experiment aimed at replicating the normal opera-tion of bearings, four fully assembled healthy class K bearingswere run utilizing the aforementioned dynamic bearing tester at aspeed of 91.7 km h�1 (57 mph) with a full load. The steady-statepower exerted by the motor to rotate all four bearings at the setspeed and load was found to be approximately 2100 W, whichcorresponds to 525 W per bearing. The average cup temperatureof each of the four bearings was about 50.0 �C in a room with anambient temperature of 25.0 �C. The latter power input acquiredexperimentally is within 1% of the value obtained by the FEmodel for the case of normal operation given in Table 2. Here, itis important to note that the power input per bearing obtainedexperimentally by the authors is much lower than the 1307 W the-oretical value reported in Dunnuck’s [11] thesis for similar operat-ing conditions. In fact, the only way to attain a power valuesimilar to that of Dunnuck’s was to run the dynamic bearing testerat 136.8 km h�1 (85 mph) and 135% load setting, which are farfrom normal operating conditions.

The theoretical technique for validating the devised FE modelinvolved the systematic comparison of the average axle surfacetemperature (this is the average temperature of the surface of theaxle covered by one cone assembly) attained from each of thesimulations to that obtained from the analytical method developedpreviously by Tarawneh et al. [3]. The theoretical expressionsderived for the axle surface temperature are the following:

T2ðtÞ ¼Qin

HoTþ2 tþð Þ þ Ta (4)

where

Fig. 4 A picture of the dynamic bearing tester used to conductthe laboratory experiments

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T2þðtþÞ ¼ J

1þR�RJþ 2Jr

�ð1þRþrÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1þRþrÞ2� 4rð1þR�RJÞ

qþð1þRþrÞ2� 4rð1þR�RJÞ

264

375� e

�ð1þRþrÞþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1þRþrÞ2�4rð1þR�RJÞp

2

� �tþ

þ 2Jr

ð1þRþrÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1þRþrÞ2� 4rð1þR�RJÞ

qþð1þRþrÞ2� 4rð1þR�RJÞ

264

375 � e

�ð1þRþrÞ�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1þRþrÞ2�4rð1þR�RJÞp

2

� �tþ

(5)

In Eqs. (4) and (5), T2 is the axle surface temperature, Tþ2 is thenormalized axle surface temperature, Ta is the ambient tempera-ture, Qin is the total heat input generated by the bearing, tþ is thenormalized time, J is the Bessel function, r is the normalized ther-mal diffusivity, Ho is the cup side overall heat transfer coefficient,H1 is the axle side overall heat transfer coefficient, and R is theaxle to cup side overall heat transfer coefficient ratio, H1/Ho.Here, it is important to highlight that the parameters Ho and H1

were determined by comparing bearing temperature data acquiredexperimentally to the analytical expression obtained from theoryutilizing nonlinear regression routines available in the MATLAB

TM

optimization toolbox. Detailed relations for the terms in Eq. (5)can be found elsewhere (Tarawneh et al. [3]).

The FE model is validated by inputting the value of the appliedtotal heat rate, Qtotal, from each simulation into Eq. (4) and calcu-lating the corresponding axle surface temperature, T2, which isthen compared to the average axle surface temperature predictedby the FE model. The results of the comparison are presented inTable 3. Note that the percent difference in the axle surface tem-perature between the analytical method and the FE model is lessthan 2%, which indicates a very good agreement between the twomethods.

Hence, based on the experimental and theoretical validationsprovided here, the developed FE model can be used to run bearingheating simulations and acquire reliable predictions of the temper-ature of the internal components of the bearing assembly withoutthe complexity and limitations imposed by laboratory testing andinstrumentation.

Selected Cases of Interest. For the sake of brevity, six of thethirteen heating scenarios were chosen for an in-depth discussionas these cases provide the reader with a comprehensive under-standing of the conducted study. Note that in Table 2, the columnlabeled “Qtotal” indicates the total heat input to the bearing,whereas, the column labeled “Qroller” specifies the heat input tothe abnormal roller(s), with all other normally operating rollerswithin the bearing assembly producing only 11.5 W.

The first scenario to be discussed is that of “normal operation”(simulation 1 in Table 2), which is a fundamental heating scenariothat represents a healthy bearing in service. Dynamic testing ofnumerous healthy bearings in a laboratory maintained at an ambi-ent temperature of 25 �C revealed that their average cup tempera-ture is approximately 50 �C (122 �F), and the power input perbearing is about 525 W. The FE model simulation replicating thelatter normal heating scenario indicates that the total heat input,Qtotal, needed to attain the 50 �C cup temperature is about 529 W(within 1% of the experimentally obtained value), which trans-lates into a roller heat input, Qroller, of 11.5 W (for each of the46 rollers), and a maximum average roller temperature of 55 �C.Thus, under normal operating conditions, the temperature of therollers is only about 5 �C (9 �F) hotter than the average cup tem-perature. Figure 5 shows the results of the simulation along withthe temperature distribution. Note that the axle was suppressedfrom the visual results to provide a better temperature visualiza-tion of the bearing surface.

In the heating scenario “six welded rollers” (simulation 3 inTable 2), the FE model simulation presented in Fig. 6 replicatesthe laboratory dynamic test in which six rollers in one cone as-sembly were welded to the steel cage bars causing them to slideon the cup raceway rather than rotate. The results indicate that theoperating temperature of the welded rollers was about 76 �C,which is 21 �C (�38 �F) hotter than the temperature of a roller innormal operation, yet, the average cup temperature of the bearingwith six welded rollers was only 9 �C above that of a normallyoperating bearing. The latter provides initial proof that a numberof rollers within a bearing may experience considerable heatingevents without affecting the average cup temperature significantlysince the bearing cup averages all the roller temperatures. Furtherevidence of the aforementioned can be seen in the following FEmodel simulation.

The “twisted cage” heating scenario (simulation 4 in Table 2),shown in Fig. 7, simulates the test in which one of the cage bars ina steel cone assembly was bent toward the cone race forcing twoadjacent rollers to misalign and rub against the cage bar producing

Table 3 Comparison of temperature values between the analytical model and the FE analysis

Finite element (FE) model Analytical method

Simulations Total heat input Qtotal (W) Axle temperature (�C) Axle temperature (�C) % difference T2

1 Normal operation 529.0 52.0 51.4 1.22 One welded roller 672.5 59.4 58.6 1.43 Six welded rollers 712.0 61.4 60.6 1.44 Twisted cage bar (two hot rollers) 1086.0 80.7 79.2 1.95 Added debris (one raceway) 908.5 71.6 70.4 1.86 Two hot rollers 754.0 63.4 62.7 1.37 Two hot rollers 1484.5 100.3 99.1 1.28 Three hot rollers 1278.4 90.8 89.3 1.89 Four hot rollers 1438.2 98.6 96.8 1.810 Misaligned roller 1249.0 88.5 87.4 1.311 Abnormal operation (Tcup¼ 72 �C) 979.8 75.1 73.9 1.612 Abnormal operation (Tcup¼ 80 �C) 1163.8 84.5 83.1 1.713 Abnormal operation (Tcup¼ 130.5 �C) 2208.0 137.4 135.3 1.6

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excessive frictional heating. The simulation results illustrate howthe two misaligned rollers reach an operating temperature of218.2 �C (425 �F), whereas, the average cup temperature does notexceed 80 �C, which is only 30 �C above that of a bearing in nor-mal operation. Therefore, even though the latter bearing containstwo hot rollers operating at unsafe temperatures, conventionaltrack-side HBDs will not trigger an alarm since these devices willonly alert when a bearing cup temperature is 105.5 �C (190 �F)above ambient temperature. Rollers operating at very high tem-peratures will degrade the lubricant and can cause grease starva-tion, which may lead to bearing seizure and eventual catastrophicfailure.

The abovementioned FE model simulations are based ondynamic bearing testing that was previously conducted in the lab-

oratory. The FE model results provide internal temperature datathat could not be obtained experimentally due to instrumentationlimitations associated with placing temperature sensors inside arotating bearing. To further investigate the effect of hot rollers onthe temperature of the bearing cup, which is the surface scannedby the infrared wayside HBDs, several hypothetical heating sce-narios were explored; three of which are discussed hereafter.

The question posed earlier in this paper as to whether it is possi-ble for certain rollers to heat to temperatures above 232 �C(450 �F) within the bearing and go undetected by the HBDs canbe answered by looking at the results of simulations 7–10. Simula-tion 7 in Table 2, shown in Fig. 8, models the case in which tworollers, one on each cone assembly, are operating abnormally. The

Fig. 8 Thermal FE analysis results for two hot rollers (one oneach cone assembly) (heating scenario 7 in Table 2)

Fig. 9 Thermal FE analysis results for three consecutive hotrollers (heating scenario 8 in Table 2)

Fig. 10 Thermal FE analysis results for all rollers heatedequally to produce a 130.5 �C average cup temperature (heatingscenario 13 in Table 2)

Fig. 6 Thermal FE analysis results for six welded rollers in onecone assembly (heating scenario 3 in Table 2)

Fig. 7 Thermal FE analysis results for twisted cage bar (heat-ing scenario 4 in Table 2)

Fig. 5 Thermal FE analysis results for normal operation condi-tions. Axle was suppressed from the visual results to provide abetter temperature visualization of the bearing surface (heatingscenario 1 in Table 2).

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motivation behind this simulation is to determine the roller tem-perature and heat rate associated with a bearing cup temperatureof 90 �C, which is still about 40 �C below the hot-box alarmthreshold assuming an ambient temperature of 25 �C. The resultsindicate that, in order to produce a 90 �C bearing cup temperature,the two hot rollers must generate a heat rate of 489 W if theremaining 44 rollers are assumed to be operating normally (pro-ducing 11.5 W each). The roller temperature associated with thisheat rate is about 292 �C, which is hot enough to produce distinctroller discoloration without triggering the HBDs.

In the heating scenario “three hot rollers” (simulation 8 inTable 2), shown in Fig. 9, it is assumed that three adjacent roll-ers are caught misaligned while entering the loaded zone of thebearing, thus, heating abnormally to an elevated temperature of232 �C. The main goal of this simulation is to determine thebearing cup temperature associated with this hypothetical heat-ing scenario. The results of this simulation demonstrate that theaverage bearing cup temperature is 88.5 �C even though thereare three hot rollers operating abnormally at an elevated temper-ature that can cause distinct discoloration in these rollers.Again, the 88.5 �C bearing cup temperature is well below theHBD threshold for an ambient temperature of 25 �C and, there-fore, this bearing will most likely continue to operate abnor-mally while undetected by conventional wayside bearing healthmonitoring equipment. Simulations 9 and 10 in Table 2 are twoother hypothetical heating scenarios that demonstrate how cer-tain rollers can reach unsafe operating temperatures withoutheating the bearing cup anywhere close to the hot-box alarmthreshold.

Finally, simulation 13 in Table 2, shown in Fig. 10, provides aninsight into the operating conditions that would lead to a bearingcup temperature of 130.5 �C, which would trigger the HBD alarm.The results reveal that all 46 rollers within the bearing have toreach an operating temperature of 149.5 �C, generating a totalheat input of 2208 W, in order for the bearing cup to reach130.5 �C. This heating scenario demonstrates the extreme operat-ing conditions that must occur before conventional wayside detec-tors tag that bearing for removal from service.

Conclusions

The purpose of the work presented in this paper is to demon-strate that it is possible to have certain rollers within the coneassemblies operating at unsafe elevated temperatures withoutheating the bearing cup to levels that would trigger the HBDalarm. A theoretical approach was sought because of instrumenta-tion limitations associated with monitoring internal temperaturesof a rotating bearing. To this end, a FE model of a railroadtapered-roller bearing pressed onto an axle was developed. The

boundary conditions used for the FE model were derived frompreviously conducted experimental and theoretical work. Themodel was validated experimentally and theoretically by compar-ing the axle temperature obtained from the FE results to that cal-culated from an analytical expression derived from theorydeveloped in a previous study. The systematic comparison of theaxle temperature values revealed that the results agreed to within2%.

Thirteen different heating scenarios were investigated in thisstudy; five of which were intended to duplicate previously per-formed dynamic bearing tests. The studied cases varied from nor-mal operation to bearings having certain rollers misbehaving tobearings heating to levels that would trigger HBDs. In each case,the temperatures and heat generation rates within the bearing weredetermined for a specified external surface cup temperature. Theambient temperature used in all the simulations listed in Table 2 is25 �C (77 �F).

The FE model results revealed that rollers in a bearing operat-ing normally are only 5 �C hotter than the bearing cup tempera-ture; however, abnormally operating rollers such as stuck ormisaligned rollers can reach temperatures that are significantlyhigher than the bearing cup temperature without heating the cupto levels that will trigger an alert. The latter is of concern becauserollers operating at elevated temperatures will have adverseeffects on the material properties of the bearing raceways, thecages, and also the grease condition. Considering the fact thatmost lubricants used in railroad bearings start to degrade whenoperated at temperatures above 125 �C for prolonged periods, hav-ing a few rollers operate at temperatures at or above 232 �C willmost likely contribute to the accelerated deterioration of thegrease, and in extreme conditions, can result in grease starvationand premature bearing failure. Since conventional wayside bear-ing monitoring equipment will only alert the railroad if the bear-ing cup temperature reaches 105.5 �C (190 �F) above ambient, it islikely that certain rollers will continue to operate at unsafe tem-peratures and go undetected until they cause enough damage tothe internal components of the bearing that will raise the bearingcup temperature to alarm levels. At that time, however, it mightbe already too late to avoid catastrophic bearing failure. Theaforementioned raises the question about the need for continuousbearing condition monitoring systems as opposed to conventionalwayside detection equipment.

In summary, a validated FE model was developed for a railroadtapered-roller bearing that can provide insight into the operatingtemperatures of the internal components of the bearing for a speci-fied external bearing cup temperature, which has proven to be avery arduous task to accomplish experimentally. The usefulnessof the devised FE model is demonstrated in Table 4, which pro-vides relevant temperature results acquired from the simulations

Table 4 Relevant temperatures obtained through the FE simulations

Finite element—temperature results

Simulations Cup 1st raceway (�C) Cup 2nd raceway (�C) Cup average (�C) Roller average (�C) Roller max (�C)

1 Normal operation 50.3 50.3 50.2 55.0 55.02 One welded roller 58.7 56.2 57.5 61.7 120.83 Six welded rollers 60.6 57.5 59.0 63.7 75.94 Twisted cage bar (two hot rollers) 86.2 73.5 79.2 80.5 218.25 Added debris (one raceway) 71.9 65.5 68.6 71.1 83.36 Two hot rollers 59.8 59.8 59.7 65.7 110.77 Two hot rollers 90.4 90.4 90.2 100.6 291.88 Three hot rollers 96.6 81.2 88.5 88.9 232.09 Four hot rollers 107.9 87.6 96.8 94.9 233.410 Misaligned roller 81.8 76.9 80.0 89.1 388.611 Abnormal operation (Tcup¼ 72 �C) 72.0 72.0 71.9 80.4 80.412 Abnormal operation (Tcup¼ 80 �C) 80.9 80.9 80.7 90.8 90.813 Abnormal operation (Tcup¼ 130 �C) 130.8 130.8 130.5 149.5 149.5

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that can aid the railroad industry and researchers in future thermalanalyses of railroad bearings.

Acknowledgment

The authors wish to thank Amsted Rail’s bearing division,BRENCO, Inc., for support of this work and permission topublish.

NomenclatureA ¼ surface area, m2

D ¼ diameter, mHo ¼ cup side overall heat transfer coefficient, W �K�1

H1 ¼ axle side overall heat transfer coefficient, W �K�1

h ¼ convection heat transfer coefficient per unit area,W �m�2 �K�1

ho ¼ cup side overall heat transfer coefficient per unit area,W �m�2 �K�1

J ¼ Bessel functionk ¼ thermal conductivity, W �m�1 �K�1

Lc ¼ characteristic length, mNu ¼ Nusselt numberPe ¼ Peclect numberPr ¼ Prandtl numberQ ¼ heat input, WR ¼ axle to cup side overall heat transfer coefficient ratio,

H1/Ho

Re ¼ Reynolds numberT1 ¼ average surface temperature of the cup, �CT2 ¼ average temperature of the axle surface covered by one

cone assembly, �CTa ¼ ambient temperature, �C

Tþ ¼ normalized temperaturet ¼ time, s

tþ ¼ normalized timeV ¼ velocity, m � s�1

Greek Symbolsa ¼ thermal diffusivity, m2 � s�1

m ¼ dynamic viscosity, Pa � st ¼ kinematic viscosity, m2 � s�1

r ¼ normalized thermal diffusivity

Subscriptsaxle ¼ surface area of axle not covered by the bearingcup ¼ bearing cup

in ¼ inputroller ¼ heat input to the roller(s) that are operating abnormallytotal ¼ total heat input

AcronymsAMG ¼ algebraic multigrid

BC ¼ boundary conditionFE ¼ finite element

FEA ¼ finite element analysisHBD ¼ hot-box detector

References[1] Karunakaran, S., and Snyder, T. W., 2007, “Bearing Temperature Performance

in Freight Cars,” Proceedings of the Bearing Research Symposium Sponsoredby the AAR Research Program in Conjunction With the ASME RTD 2007 FallTechnical Conference, Chicago, Illinois, Sept. 11–12.

[2] Tarawneh, C. M., Wilson, B. M., Cole, K. D., and Reed, M., 2008, “A Metallur-gical and Experimental Investigation Into Sources of Warm Bearing Trending,”Proceedings of the 2008 IEEE/ASME Joint Rail Conference, Wilmington, DE,Apr. 22–23, paper No. JRC2008–63028.

[3] Tarawneh, C. M., Cole, K. D., Wilson, B. M., and Alnaimat, F., 2008,“Experiments and Models for the Thermal Response of Railroad Tapered-Roller Bearings,” Int. J. Heat Mass Transfer, 51, pp. 5794–5803.

[4] Overstam, H., 2006, “The Influence of Bearing Geometry on the ResidualStress State in Cold Drawn Wire Analyzed by the FEM,” J. Mater. Process.Technol., 171(3), pp. 446–450.

[5] Wei, Y., Qin, Y., Balendra, R., and Jiang, Q., 2004, “FE Analysis of a NovelRoller Form: A Deep End-Cavity Roller for Roller-Type Bearings,” J. Mater.Process. Technol., 145(2), pp. 233–241.

[6] Demirhan, N., and Kanber, B., 2008, “Stress and Displacement Distributions onCylindrical Roller Bearing Rings Using FEM,” Mech. Based Des. Struct.Mach., 36(1), pp. 86–102.

[7] Vernersson, T., 2007, “Temperatures at Railway Tread Braking. part 1:Modeling,” Proc. Inst. Mech. Eng., F J. Rail Rapid Transit., 221(2), pp.167–182.

[8] Schmidt, E., and Weiland, T., 2006, “Application of a Computationally Effi-cient Air-Gap Element Within the Finite Element Analysis of MagneticBearings,” IEEE Trans. Magn., 42(4), pp. 1263–1266.

[9] Awasthi, R. K., Jain, S. C., and Sharma, S. C., 2006, “Finite Element Analysisof Orifice-Compensated Multiple Hole-Entry Worn Hybrid Journal Bearing,”Finite Elem. Anal. Des., 42(14/15), pp.1291–1303.

[10] Sukumaran Nair, V. P., and Prabhakaran Nair, K., 2004, “Finite Element Anal-ysis of Elastohydrodynamic Circular Journal Bearing With MicropolarLubricants,” Finite Elem. Anal. Des., 41(1), pp.75–89.

[11] Dunnuck, D. L., 1992, “Steady-State Temperature and Stack-Up Force Distri-butions in a Railroad Roller Bearing Assembly,” M.S. thesis, University of Illi-nois at Urbana-Champaign, Urbana, IL.

[12] Wang, H., 1996, “Axle Burn-Off and Stack-Up Force Analyses of a RailroadRoller Bearing Using the Finite Element Method,” Ph.D. thesis, University ofIllinois at Urbana-Champaign, Urbana, IL.

[13] Wang, S., Cusano, C., and Conry, T. F., 1993, “A Dynamic Modelof the Torque and Heat Generation Rate in Tapered RollerBearings Under Excessive Sliding Conditions,” Tribol. Trans., 36(4), pp.513–524.

[14] Kletzli, D. B., Cusano, C., and Conry, T. F., 1999, “Thermally InducedFailures in Railroad Tapered Roller Bearings,” Tribol. Trans., 42(4), pp.824–832.

[15] Farnfield, N. E., 1972, “Thermal Investigations of Roller Bearings,” Tribology,5(3), p. 104.

[16] Hoeprich, M. R., 1996, “Rolling-Element Bearing Internal Temperatures,” Tri-bol. Trans., 39(4), pp. 855–858.

[17] Wang, X. L., and Zhu, K. Q., 2006, “Numerical Analysis of Journal BearingsLubricated With Micropolar Fluids Including Thermal and Cavitating Effects,”Tribol. Int., 39(3), pp. 227–237.

[18] Fillon, M., and Bouyer, J., 2004, “Thermohydrodynamic Analysis of a WornPlain Journal Bearing,” Tribol. Int., 37, pp. 129–136.

[19] Wang, X. L., Zhu, K. Q., and Wen, S. Z., 2001, “Thermohydrodynamic Analy-sis of Journal Bearings Lubricated With Couple Stress Fluids,” Tribol. Int., 34,pp. 335–343.

[20] Li, X. K., Davies, A. R., and Phillips, T. N., 2000, “A Transient ThermalAnalysis for Dynamically Loaded Bearings,” Comput. Fluids, 29, pp.749–790.

[21] Ma, M. T., and Taylor, C. M., 1996, “An Experimental Investigation of Ther-mal Effects in Circular and Elliptical Plain Journal Bearings,” Tribol. Int.,29(1), pp. 19–26.

[22] Briot, J. M., Bourouga, B., and Bardon, J. P., 1997, “Thermal Transport Con-ductance Between the Rings of a Roller Bearing,” Rev. Gen. Therm., 36(8), pp.610–623.

[23] Tarawneh, C. M., Cole, K. D., Wilson, B. M., and Freisen, K., 2007, “ALumped Capacitance Model for the Transient Heating of Railroad TaperedRoller Bearings,” Proceeding of the 2007 ASEE-GSW Annual conference,March 28–30, Paper No. T2C5.

[24] Tarawneh, C. M., Fuentes, A. A., Wilson, B. M., Cole, K. D., and Navarro, L.,2009, “Thermal Analysis of Railroad Bearings: Effect of Wheel Heating,” Pro-ceedings of the 2009 ASME Joint Rail Conference, Pueblo, CO, March 3–5,Paper No. JRC2009–63055.

[25] Cole, K. D., Tarawneh, C. M., and Wilson, B. M., 2009, “Analysis of Flux-Base Fins for Estimation of Heat Transfer Coefficient,” Int. J. Heat Mass Trans-fer, 52, pp. 92–99.

[26] Cole, K. D., Tarawneh, C. M., Fuentes, A. A., Wilson, B. M., and Navarro, L.,2010, “Thermal Models of Railroad Wheels and Bearings,” Int. J. Heat MassTransfer, 53, pp. 1636–1645.

[27] Tarawneh, C. M., Wilson, B. M., Cole, K. D., Fuentes, A. A., and Cardenas, J.M., 2008, “Dynamic Bearing Testing Aimed at Identifying the Root Cause ofWarm Bearing Temperature Trending,” Proceedings of the 2008 ASME RTDFall Technical Conference, Chicago, IL, Sept. 24–26, Paper No.RTDF2008–74036.

[28] Tarawneh, C. M., Kypuros, J. A., Wilson, B. M., Snyder, T. W., Gonzalez, B.A., and Fuentes, A. A., 2009, “A Collaborative On-Track Field Test Conductedto Verify the Laboratory Findings on Bearing Temperature Trending,” Proceed-ings of the 2009 ASME Joint Rail Conference, Pueblo, CO, March 3–5, PaperNo. JRC2009–63056.

[29] Tarawneh, C. M., Kypuros, J. A., Fuentes, A. A., Wilson, B. M., Gonzalez, B.A., Rodriguez, G., and Maldonado, R. K., 2009, “Vibration Signatures of Tem-perature Trended Bearings in Field and Laboratory Testing,” Proceedings of the2009 ASME RTD Fall Technical Conference, Ft. Worth, TX, Oct. 20–21, PaperNo. RTDF2009-18038.

[30] Brandlein, J., Eschmann, P., Hasbargen, L., and Weigand, K., 1999,Ball and Roller Bearings: Theory, Design and Application, 3rd ed., Wiley,New York.

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[31] Harris, T. A. and Kotzalas, M. N., 2006, Advanced Concepts of Bearing Tech-nology: Rolling Bearing Analysis, 5th ed., Taylor & Francis, London.

[32] Alnaimat, F., 2007, “Thermal Analysis of Railroad Tapered Roller Bearings,”M.S. thesis, University of Texas-Pan American, Edinburg, TX.

[33] Melosh, R. J., 1963, “Structural Analysis of Solids,” ASCE J. Struct. Div.,89(4), pp. 205–223.

[34] Incropera, F. P., DeWitt, D. P., Bergman, T. L., and Lavine, A. S., 2007, Fun-damentals of Heat and Mass Transfer, 6th ed, Wiley, New York.

[35] Jones, J., Poulikakos, D., and Orozco, J., 1988, “Mixed Convection From aRotating Horizontal Heated Cylinder Placed in a Low-Speed Wind Tunnel,”Int. J. Heat Fluid Flow, 9(2), pp. 165–173.

[36] Badr, H. M., and Dennis, S. C. R., 1985, “Laminar Forced Convection From aRotating Cylinder,” Int. J. Heat Mass Transfer, 28(1), pp. 253–264.

[37] Kendoush, A. A., 1996, “An Approximate Solution of the Convective HeatTransfer From an Isothermal Rotating Cylinder,” Int. J. Heat Fluid Flow, 17(4),pp. 439–441.

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