Proceedings of ACOUSTICS 2016 9‐11 November 2016, Brisbane, Australia ACOUSTICS 2016 Page 1 of 10
Wear simulation for boundary lubricated, radially loaded,
spherical roller bearings
Cameron D. Milne1 and Paul A. Meehan1
1
School of Mechanical & Mining Engineering, The University of Queensland, Brisbane, Australia
ABSTRACT
The wear of railway axle bearings is an important phenomenon. Rail companies must keep their rolling stock in a serviceable condition as excessively worn bearings can contribute to safety issues such as vibrations, excessive clearances and possibly even derailments. At present, maintenance scheduling is typically performed at predetermined time intervals. Predicting the wear and degradation of the bearings, would enable operators and bearing manufacturers to 1) optimise the design and maintenance of the bearings, and 2) quantitatively determine the best time to replace the bearings. This paper presents a model developed for predicting the wear in radially loaded spherical roller railway axle bearings. It uses a slice method to calculate the roller load, traction and creep distribution along the roller for the contact mechanics, and predicts wear using a frictional power model. The model is first validated with the wear in a thrust bearing in the literature and then used to predict wear in the radial bearing. The wear contribution from each roller in the loading zone due to the radial loading is calculated and combined for an overall wear profile.
1. INTRODUCTION
The wear and degradation of railway axle bearings poses a great cost to the rail industry. The sheer number of rolling stock and the physical demands needed to overhaul a single bearing means that replacing the axle bearings is a big task, and costs the operators in the order of millions of dollars to service a single fleet of trains. In the literature, there have been several contributions which relate to the issue at present: Modelling of a spherical roller thrust bearing in the mild wear stage was successfully performed by Olofsson et al (Olofsson, Andersson, and Bjorklund 2000). This forms the central part of this paper. In other work, Nilsson et al (Nilsson, Svahn, and Olofsson 2006) counted the number of scratches from diamond particles on the contacting surfaces of a bearing and then attempted to predict the wear after a much longer running time. For a view on the position of wear in the overall picture of bearing damage, El‐Thalji and Jantunen (El‐Thalji and Jantunen 2014) provide a good introduction. There are many wear formulae in the literature. The most common is the Archard (Archard 1953) , and the frictional power wear methods, used in the study of wheel‐rail contact by Meehan and Daniel (Meehan and Daniel 2008). A feedback model for wear was used by Meehan et al (Meehan et al. 2009), to simulate the wear in wheel‐rail contact. This is described more in Section 2. Contact fatigue is a common failure mode for rolling element bearings, however this failure mode has not been observed in the present application with the bearings of interest in this study. The present research provides a description of the modelling processes used to determine the wear profile of a railway axle bearing (radially loaded spherical roller bearing), which may help to indicate the expected life of the bearing. 2. MODELLING In the model, an iterative method was implemented, following the feedback loop shown in Figure 1. This feedback loop is based on that by Meehan et al (Meehan et al. 2009) . It is iterative as it calculates the wear in the bearing over time, depending on the feedback of previous worn profiles. This makes it adaptive, which is appropriate as the wear for each cycle depends on the effects of the previous wear cycles. As each iteration of the loop runs, there are several major stages of calculation. 1. The simulation starts with a new, unworn profile, then takes into account the previous wear. 2. The loading on each roller (which may depend on a dynamic condition) is calculated 3. The normal force determines the amount of frictional power generated in the sliding and slip regions of the rolling contact. The frictional power is determined by the contact mechanics. The contact mechanics for each roller is calculated based on the slice method used by Olofsson et al (Olofsson, Andersson, and Bjorklund 2000). The pressure on each slice depends on the profile of the roller and raceway, which change
as wear occurs. The changing conditions of the lubricant and the amount of third body particles present are assumed to affect the value of the friction coefficient used at this step. The amount of wear debris present is dependent on the worn volume removed from the bearing raceways.
4. The change in wear height for one iteration for each slice in the roller/raceway contact depends on the frictional power from the previous step. The value of the wear coefficient used at this step is assumed to be affected by 3rd body effects and lubricant film effects.
5. The wear height is accelerated for each slice using a single acceleration factor, which linearly scales the wear for one revolution to extend to multiple revolutions for each iteration.
6. The iteration increments, with the new iteration using the previous worn profile as a basis for the calculation of the next profile. Figure 1. Feedback model for adaptive wear prediction 2.1 Thrust bearing To develop a reliable model for the wear in a railway axle bearing (radially loaded spherical roller bearing) (the radial bearing model), the method used by Olofsson et al (Olofsson, Andersson, and Bjorklund 2000), for a spherical roller thrust bearing (the thrust bearing model), was chosen to provide a benchmark validation from the literature. Olofsson et al’s (Olofsson, Andersson, and Bjorklund 2000) analysis of the thrust bearing determines the normal load in the contact between the raceway and the roller. The contact is broken up into slices perpendicular to the axis of the roller. The Palmgren (Palmgren 1959) relation for determining the normal load on a cylinder‐to‐cylinder contact is used, by dividing by l (the effective contact length), to work out the normal load per unit length at each slice. The relation for the normal load per unit length is given in Equation 1, where is the normal approach (how much the original circular profiles overlap), is the effective contact length and is the normal load per unit width. Figure 2 shows the contact broken into slices, the normal approach and the normal load applied.
P A a t a in in c w E a o a o t o it a t t a Proceedings of ACOUSTICS 20 Figure Each slice allowing the w he load on ea are added up nsufficient fo ncreased unt ontact width where is t Equations 1 a across the rol of the geome as the differen of sliding) awa This creep he roller. Bec on the creep) teratively inc The rollin are the zero‐s he two inters hrust bearing and the zero‐s f ACOUSTICS 2 016 2. Cross‐sect
e of the rolle wear to be c ach slice by “ and multipli or the nomina til the nomina h (the half‐wid the semi‐con and 2 are use ler. There is try of the rol nce in velocit ay from the l p culminates cause there c ) must cance reased until t ng cone is an sliding points section point g with the ro sliding lines. 2016 tion of bearin
er has its ow alculated in a “pushing dow ied by the sli al contact loa al contact loa dth of the co ntact width, ed in the cal nominally no ller‐raceway ty of the rolle ines of no slip s in a differen can be no net l. To calculat the net tracti imaginary co s/lines). In be ts, the creep lling cone illu ng roller‐racew wn individual a 2‐D manne wn” the roller ice width to ad, is incre ad has been a ntact patch) is Poisson culation of t o net traction contacting su er and contac p. nt traction fo t traction in t te when the t ional force on one‐shaped s etween the tw is in the opp ustrated, alon way contact. Equation 1. , and er across the r profile (givi give a total n eased, meani achieved. In t is given by Eq 41 n’s ratio, and he traction o n transmitted urface, there ct patch, divid orce being ap the contact, t traction forc n the roller th surface which wo intersecti posite directio ng with the d From (Olofss (the m contact patc ng a and t normal load ng that the t the plane goi quation 2, d G is the sh of the slices, d within a rol e are regions ded by the ve pplied to the the positive a es cancel, a hrough the co h intersects t on points, th on. Figure 3 B direction of th 9‐11 Novemb son, Andersso meaning the ch. The thrus therefore a (an integral). total normal ing along eac hear modulu in order to w ler‐raceway c of positive a elocity of the roller depen and negative “rolling cone ontact is zero the curved co e creep is in B) shows a d he creep on t ber 2016, Bris on, and Bjork roller radius st bearing mo for each sli . If the total load increase ch of these sl
s of the bea work out the contact. How nd negative c contact patc nding on the traction forc e angle” (see o. ontact at two one directio iagram of a s the roller‐rac sbane, Austral Page 3 of 1 ( klund 2000);
at that slice odel calculate ce). All the normal load es as well. ices, the sem ( aring materia e creep profi wever, becaus creep (define ch – a measu position alon ces (dependin Figure 3 B)) o places (thes n, and outsid spherical rolle ceway contac lia 10 1) e), es s is is mi‐ 2) al. le se ed re ng ng is se de er ct,
s t in t c w t “ C w c w h w t o a Figure showing the the pag The posit he roller in th ncreasing the raction (then lose to zero, The formu where is the he semi‐cont for each slic Coulomb frict The creep
where is orresponding wear can now height can be where is th he number o of the simulat amount of slid The geom e 3. A) Cross‐ rolling cone, ge, dot in circ ion of the tw he simulation e rolling cone n summing th
the angle is i ula for the tra
e traction, tact width,
e”. This form ion relation, p ratio , is ba the radius g slice. Once w be calculat described by e wear for ea of revolutions tion, the wea ding present metry used fo ‐section of th positive and cle is the dire wo intersectio n is also depe e angle (start he total tract increased slig action is from is the coeffic is the shear mula holds w as in Equatio ased on the a
of the rollin the creep pro ted to determ y the Archard ach pass, is s (an accelera r is accumula in the contac r the thrust b he railway axl negative cre ction out of t on points is d endent on the ting with an ion) for each ghtly and the m Johnson (Jo 1 1 cient of frictio r modulus of where there i on 3 ii), is use actual roller r ng cone for ofile has bee mine the fina d wear model ∆ s a “dimensio ation factor) ated and outp ct. bearing mode e bearing. B) ep and the ze the page. Fro determined b e rolling cone initial guess h value of the traction is ca ohnson 1960) 4 1 on, is the n the bearing is partial slid d.
radius and the
each slice, a n established al worn prof l as in Equatio onal” wear co and is the put as a grap el used for va Cross‐sectio ero sliding po om (Olofsson, by the rolling e angle. The r ), working ou e rolling cone alculated aga ) and is given , normal load p material, i ding in the co
e rolling cone
and is t d, the wear ca
ile of the rac on 5, | | oefficient tha number of r h on the scre lidation was n of a spheric oints. Cross in , Andersson, cone angle. rolling cone a ut the creep e angle. If the in. in Equation 3 per unit lengt s Poisson’s r ontact. Whe e radius, as sh he actual ra an then be ca ceway. The w at includes th rollers in the een. The cree that for the S cal roller thru n circle is the and Bjorklun The creep o angle is found and then w e sum of the 3 i), th, is the cr ratio and sub
re there is f hown in Equa
adius of the alculated for worn change he effect of h bearing. Ove ep gives an in SKF 29416 E t ust bearing direction int d 2000) n each slice o d by iterative orking out th traction is no ( reep ratio, script mean ull sliding, th ation 4, ( roller for th each slice. Th e in the profi
( hardness. er the duratio dication of th type bearing. o of ely he ot 3) is ns he 4) he he le 5) is on he .
P A 2 r t w p w a R t b c t r r Z Proceedings of ACOUSTICS 20 2.2 Radial B Similar co ailway axle b hese change with respect positions. This wear in the be The geom assumed that Radial Loadin The radia he top of the bearing). The learance in t he loaded ro Figure 4. In Figure oller bearing ollers at angl The meth Zhaoying (Cha 1. Deter total (for a f ACOUSTICS 2 016 Bearing ontact mecha bearing (the r s include pro
to the race s means that earing taking metry used fo the rollers d ng l loading on t e bearing, as few rollers he bearing (u llers at the to . Diagram of t 2016)). This f 4, Fr is the to s), Q0 is the
e to Q0 in t
hod used to d angsen and Z rmine an app radial load a a double‐row 2016 anics analysis radial bearing ovision that t ways, there t the wear ne into account r the axle be o not suffer s the railway a opposed to which carry ur) and the to op. Figure 4 s the roller loa figure shows otal applied r load on the t the loaded zo determine th haoying 1991 proximate sta pplied to one roller bearin to that desc g model), wit the loading i e will be diff eeds to be ca t all contribut aring is that significant we axle bearings the even loa the load all otal radial loa hows a diagr d distribution that the top adial load to top roller, in one. e load on ea 1). The follow arting value fo e side of the g). cribed for the th some chan s radial mea ferent load c alculated at s tions of varyi for an NTN‐S ear, and the w means that t ad distributio have differe ad applied to ram of the loa n in a roller b roller is the the bearing line with and ach roller in t wing steps are or the load o bearing and 4.08 e thrust beari nges to incorp ning that, de contributions everal differe ngly loaded r SNR radially lo wear is captu the all of the on in the thru ent normal l o the bearing ad distributio bearing (modi most highly l (or one side d opposite to the bearing is e taken in ord n the top roll Z is the num 8 S 9‐11 Novemb ng model wa porate the ne epending on s from the r ent positions rollers. oaded spheri ured mostly b load is conce ust bearing m oads applied . The wear is on in a radial ified from (W oaded in the of the bearin o Fr. Q is the s based on th der: ler (Q0) using ber of rollers Side View of B ber 2016, Bris as used in the ew geometry the position rollers at diff s, giving a sim ical roller typ by the racewa entrated to a model (axially d, depending s contributed roller bearing Wuxi Handa Be loaded zone ng for double e load on eac hat found in g Equation 6 w s in one side Bearing sbane, Austral Page 5 of 1 e model of th y. In particula n of the rolle ferent angul mulation of th pe bearing. It ays. a few rollers y loaded thru g on the radi to, by each g. earing Co. Ltd . e‐row spheric ch of the othe Changsen an where is th of the bearin ( lia 10 he ar, rs ar he is at st ial of d cal er nd he ng 6)
2. Determine the maximum normal approach of the roller‐raceway contact (this is the same as in Figure 2). This is calculated using the same iterative method for the normal load distribution in the thrust bearing model (where is incremented until the correct total normal load Q0 is achieved).
3. Determine the load distribution factor from Equation 7 1 2 1 2 (7) where is the radial clearance in the bearing. 4. Determine from the lookup table in Changsen and Zhaoying (Changsen and Zhaoying 1991). 5. Determine Q0 from Equation 8: (8) The new Q0 is different to the Q0 determined in Step 1, and therefore will have changed. Therefore,
Steps 2 to 5 are iterated, until Q0 converges. 6. Once the final value of Q0 has been found, the loads on each of the other rollers in the bearing can be obtained using Equation 9 1 1 2 1 (9) where is the load on the roller at angle from .t is a constant, with the value of 2/3 for a point contact (correct for a ball or spherical roller bearing). The effect of the total radial load, Fr on the load on each roller in one half of one side of the bearing (the roller loads are symmetrical) (the number of rollers per side of the bearing, Z, is 22) is shown in Figure 5 A). Figure 5. A) Dependence of roller load on total radial load in a spherical roller bearing. For this case, the radial clearance is 0.145 mm, B) Dependence of roller load on radial clearance in a spherical roller bearing. For this case, the bearing load is 20000 N per side of the bearing. This figure shows that as the total radial load is increased, the load on the rollers increase, with more rollers being engaged in the loading as the load increases (e.g. Roller 3 at 1.0x104 N). Due to the upward radial load, the rollers in the bottom half of the bearing will always be unloaded (for rollers 6 to 11, 0).
P A r R t b w w t is w is d e E w fo a p r la t r Proceedings of ACOUSTICS 20 The effect adial clearan Rollers 1 and he load as t bearing. This p When dev wear height p where ∆ is t he contact fo s used becaus For the ra where ∆ is th s the frictiona density, is t effectively the Equation 13: where ∆ is t or each slice absolute valu , therefore t power wear m espond more For each ast roller enc he accelerati ace in the loa Figure 6. in one revo 2016)) This f f ACOUSTICS 2 016 t of radial cle ce, all of the 2 increase, w the radial cle
plot is for the veloping the per slice. the change in or each slice a se wear does adial bearing he change in al power, the rolling ve e tractional lo the change in (from Equati es are used b the change i model can giv e appropriate iteration of t countered by ion factor is a aded zone ov Diagram repr olution. Wear figure shows 2016 earance on th upper rollers while the loa earance incre e spherical ro thrust bearin n wear depth and | | is the s not depend model, the fr wear depth, is the friction elocity, is t oad per unit n wear depth ons 3 i) and i because wea in wear dept ve a more acc ely to changes he feedback the raceway applied to th ver one revolu resenting the r accumulatio that the wea he roller load s are loaded. d on rollers eases, indica oller bearing w ng model, th ∆ h for each slic e absolute va on direction rictional pow nal power we he traction in length, Equa ∆ h for each slic ii)) and | | is r does not d th per slice i curate predic s in the greas loop (see Fig y (as the shaft is profile. Fig ution of the s e accumulatio on is signified ar on the inne passe ds is shown in . As the radia 3, 4, 5 and 6 ating a more with Fr = 2000 e Archard we ∆ | ce, is the w alue of the cr ). wer wear mod ∆ 2 ear coefficien n the contact tion 5 can be | || ce, | | is the s the absolute epend on dir is sensitive t ction of wear se condition. gure 1), the w t and cage ro gure 6 shows shaft. on of wear on d by the grey er race accum es the loaded n Figure 5 B) al clearance s 6 all decrease e concentrate 00 N. ear model (E | wear coefficie reep in the co del is used, as nt, 2 is the c t and is the e modified fo | absolute val e value of the rection. | | i
o the friction r in the roller wear profiles otate) are sum s an example n the inner ra bars. (modifi mulates despi zone. 9‐11 Novemb . In this plot, tarts to incre e. Fewer rolle ed load distr quation 10) w ent, is the ontact for eac s shown in Eq contact lengt e sliding velo or the radial b ue of the trac e creep in the s dependent n coefficient. r/raceway co from the firs mmed for on of the wear ce from the c ed from (Wu te the varyin Sid ber 2016, Bris it can be see ease from zer ers are engag ribution at t was used to pressure per ch slice (the quation 11: h, is the be ocity. Since bearing mode ctional load p e contact for on the fricti . This means ntact, and it st roller enco e revolution accumulatin contributions xi Handa Bea ng loads it enc de View of Be sbane, Austral Page 7 of 1 en that at zer ro, the load o ged in carryin he top of th determine th (1 r unit length absolute valu (1 (1 earing materi and el, as shown (1 per unit lengt each slice. Th on coefficien s the friction will be able t untered to th first, and the g on the inne s of each rolle aring Co. Ltd counters as it earing lia 10 ro on ng he he 0) in ue 1) 2) ial is in 3) th he nt, nal to he en er er t
This is performed by defining the code that determines the individual roller loads (based on the total radial load on the bearing) as a function that can be called during simulation. This means that it provides different individual roller loads depending on the total radial load on the bearing. The total radial load is able to varied as often as once per iteration (and this is affected by the acceleration factor). The bearing loads are generated and stored in a vector when the simulation is initialising, so that complicated loading patterns can be simulated (e.g. statistical variation). The outer race is assumed to be held loosely in the housing, allowing the wear to be uniformly distributed around the inner and outer raceways. 3. RESULTS The thrust bearing model was run as a simulation with the parameters as in Table 1 and the results and descriptions can be seen in Sections 3.1 and 3.2. Table 1. Parameters used in the thrust bearing simulation.
Parameter Symbol Value (thrust, radial) Units
Coefficient of friction μ 0.05 Shear Modulus G 79000 N/mm2 Poisson’s Ratio ν 0.3 Density of Steel ρ 7800 kg/m3 Length to centre of roller (thrust) 86.3 mm Angle of roller to bearing axis (radial) 11.5 degrees Inner Race radius (radial) 107.5 mm Outer race radius (thrust, radial) 114, 104 mm Roller radius (transverse) 109.5, 100 mm Roller diameter (thrust, radial) 25.48, 19.7 mm Roller width (thrust, radial) 30, 27.6 mm Number of rollers (thrust, radial) m 15, 22 Number of slices along the roller 1000 Axial load (Contact load tuned to) , Radial load (per side of bearing) 113000 (4153), 20000 N (Dimensional) Wear coefficient k, k1 15 10‐10 mm2/N Frictional Power wear coefficient k2 0.78 10‐16 kg/(N*mm) Number of revolutions of the shaft per cycle pass (thrust, radial) 6000, 10 million Number of cycle passes (thrust, radial) 80, 50
3.1 Final Wear Profile for the Thrust Bearing Model
The thrust bearing model was run, to compare with the results of Olofsson et al (Olofsson, Andersson, and Bjorklund 2000). A close approximation was able to be achieved to the experimental wear profile as shown in Figure 7.
P A c r (s m in “ d e 3 a w Proceedings of ACOUSTICS 20 Figure 7 simulatio The simul ulminates in esults show t side peaks) a must cancel. T n pure rolling zero‐sliding” deviations mo experimentall 3.2 Initial C It is evide are loaded in A) Figure 8 shows that wear in the si f ACOUSTICS 2 016 . Experiment on replicating lated wear is a different t three peaks nd inner neg The lines of n g, there is litt points well. ost likely caus ly determined onditions a ent from Figu the axle bear 8. A) Traction t the top rolle imulation of t 2016 ally measure g Olofson et a s asymmetric traction force in wear. This gative (middle no slip indica tle to no wea The magnitu sed by the no d wear due to and Final W re 8 A) that o ring for 2000 curves for ea er has the mo the radial bea of the d wear profil al’s (Olofsson al but reason e being appli s is because t e peak) tracti te the positio ar in these re de of the we ominal geome o the idealise Wear Profile only the top f 0 N (per side ach roller for ost traction, t aring. The ho e roller, starti le from (Olofs , Andersson, nably close to ed to the ro there can be on forces tha ons of zero t egions. The si ear is similar t etry used in t ed conditions
for the Rad
five rollers (t of the bearin B) r an applied lo this is due to orizontal axis ng from the o sson, Anders and Bjorklun o the experim ller dependin no net tract at depend on ractional forc mulation res to the magnit the model. Th s of the mode dial Bearing op roller; 2nd ng). oad of 20000 the higher lo in each figure outer end at 9‐11 Novemb son, and Bjor nd) wear resu mental result ng on the po ion transmitt the creep (s ce, or pure ro ult approxim tude of the m he simulated el. g Model top and 3rd t N per side o ad it support e represents 0 mm. ber 2016, Bris rklund) and t ult, used for v ts. The creep osition along ted, and the ee for examp olling. As the mates the pos measured wea wear is smo top rollers do of the bearing ts). B) The pro the distance sbane, Austral Page 9 of 1 hrust bearing validation. in the conta the roller. Th outer positiv ple Figure 8 A re is no slidin sitions of thes ar profile, wit other than th own each sid g. (This figure ogression of along the ax lia 10 g ct he ve A)) ng se th he e) xis
From Figure 8 B) it can be seen that there are three main peaks of wear, with little to no wear at the points of no‐slip. Each colour represents the wear profile at that point in the life of the bearing. 500M revs translates to roughly 10 years of wear. The wear progresses evenly over life of the bearing. The traction and wear curves are asymmetrical, due to the fact that the rolling cone intersects the contact asymmetrically giving asymmetrical wear. It can be seen that the points of no slip in Figure 8 B) correlate well with the central intersections of the zero‐ traction line in Figure 8 A). This is due to the fact that where there is no traction, there is no sliding and thus, no wear.
4. CONCLUSIONS
A initial thrust bearing model of a spherical roller bearing has been compared to Olofsson et al’s (Olofsson, Andersson, and Bjorklund 2000) article, and the simulation of the wear profile is reasonably close to the experimental profile. Using this model with some changes for the new geometry and radial loading, a prediction of the wear in a railway axle bearing (the radial bearing model) was able to be made with calculations of the load on each roller in the loaded zone of the bearing. This was performed along with predictions of the traction in the contact, all of which may be important for determining the lifetime of the bearing. This paper contributes to the literature by extending the models used by Olofsson et al (Olofsson, Andersson, and Bjorklund 2000) and Meehan et al (Meehan et al. 2009) to be used for radially loaded spherical roller bearings, as can be found in passenger train fleets. With this research, it is possible to determine the wear in the bearings, according to the frictional power wear formula, giving an indication of the life of the bearing. ACKNOWLEDGEMENTS This research is supported and made possible by the Rail Manufacturing CRC, Bombardier Transportation, NTN and the UQRS scholarship scheme. REFERENCES Archard, J. F. 1953. 'Contact and rubbing of flat surfaces', Journal of Applied Physics, 24: 981‐88. Changsen, W., and Z. Zhaoying. 1991. Analysis of Rolling Element Bearings (Mechanical Engineering Publications Limited: London). El‐Thalji, I., and E. Jantunen. 2014. 'A descriptive model of wear evolution in rolling bearings', Engineering Failure Analysis, 45: 204‐24. Johnson, K. L. 1960. "Tangential Tractions and Micro‐slip in Rolling Contact." In Rolling Contact Phenomena, edited by J. B. Bidwell. Michigan: Elsevier.
Meehan, P. A., P. A. Bellette, R. D. Batten, W. J. T. Daniel, and R. J. Horwood. 2009. 'A case study of wear‐type rail corrugation prediction and control using speed variation', Journal of Sound and Vibration, 325: 85‐105.
Meehan, P. A., and W. J. T. Daniel. 2008. 'Effects of wheel passing frequency on wear‐type corrugations', Wear, 265: 1202‐11.
Nilsson, R., F. Svahn, and U. Olofsson. 2006. 'Relating contact conditions to abrasive wear', Wear, 261: 74‐78.
Olofsson, U., S. Andersson, and S. Bjorklund. 2000. 'Simulation of mild wear in boundary lubricated spherical roller thrust bearings', Wear, 241: 180‐85.
Palmgren, A. 1959. Ball and Roller Bearing Engineering (Philadelphia).
Wuxi Handa Bearing Co. Ltd. 2016. 'Spherical Roller Bearings', Accessed April 7. http://www.skf16.com/sale‐104415‐ spherical‐roller‐bearings.html.