Sed Orders for Reprits to reprits@bethamsciece.ae 106 The Ope Mechaical Egieerig Joural, 2015, 9, 106-110 Ope Access Load Calculatio ad Desig of Roller Crowig of Truck Hub Bearig Xitao Xia,1, Shujig Dog 1, Limig Su 2 ad Tiaju Che 3 1 Hea Uiversity of Sciece ad Techology, Luoyag, 471003, P.R. Chia 2 Luoyag Bearig Research Istitute, Luoyag, 471003, P.R. Chia 3 Pittsburg State Uiversity, Pittsburg, KS 66762, USA Abstract: Double-row tapered roller bearig 353112 is used i trucks, ad the exteral load ad pressure distributio of the bearig are calculated combiig with the specific operatig coditios. Tapered roller bearigs typically employ roller profile modificatio to equalize the load distributio, miimizig the stress cocetratio at the roller eds. Doig FEA (fiite elemet aalysis o the cotact stress with the chagig roller crowig betwee roller ad races, the appropriate roller profile ad the crow drop of roller ca be achieved. Fially the best cotrol equatio of roller crowig is obtaied. It has importat guidig sigificace for the improvemet of roller crowig desig of truck hub bearigs. Keywords: Hub bearigs, load distributio, roller crowig, stress aalysis. 1. INTRODUCTION The hub bearig is a importat compoet for trasmittig movemet ad force i the truck. Typically truck wheel bearigs require tapered roller bearigs to operate uder heavy combied radial ad thrust loadig at varyig operatig coditios. The topic discussed i this paper is the force situatio ad roller crowig of doublerow tapered roller bearig 353112 i the axles of trucks. Life of bearigs has bee a subject of cosiderable iterest to both bearig maufactures ad desigers. The improvemet of bearig life has always bee a cocered issue, which ot oly ivolves bearig materials ad maufacturig level, but also ivolves the loadig situatio [1-4] ad desig scheme of bearigs, especially geeratrix profile selectio [5] ad the crow drop of rollers. The stress cocetratio should be avoided i elastic cotact problems because failure would occur at the eds [6, 7]. The cotributio of roller crowig to the bearig life has bee studied cosiderably by the researchers [8, 9]. I this paper exteral load ad load distributio of the truck hub bearig are calculated i terms of the specific workig coditios. Accordig to the techical parameters of the bearig, the crow drop of roller ca be obtaied by combiig the operatig coditios, FEM aalysis ad optimal roller profile. 2. CALCULATION OF THE TRUCK HUB BEARING 2.1. Calculatio of Exteral Load of the Bearig Exteral load of hub bearig is trasmitted from the wheels to the hub bearig. Takig the ed of the larger force of truck hub bearig as research object, the radial force ad axial force are give as [10]: Address correspodece to this author at the Hea Uiversity of Sciece ad Techology, 48 Xiyua Road, Luoyag, Postcard: 471003, P.R. Chia; Tel: +86-1394929 7723; E-mail: xiaxt1957@163.com 1874-155X/15 = f w ( 1 2 Wg + h L h Wa (1 F a =! a g where is the radial force, F a is the axial force, W is the mass of rear axle o the truck, g is gravitatioal acceleratio, h is the height of the ceter of the mass, L h is the distace of rear wheels, a is the lateral acceleratio, which ca be described by the multiple of g, ad geerally takig a maximum of 0.55 g, f w is the impact coefficiet for the force due to differet workig coditios, ad ( idicates the axial force which keeps opposite directio with that of the lateral acceleratio. Structure parameters of the truck are show i Table 1. Table 1. 2015 Betham Ope Structure parameters of the truck. Structure Parameters W L h f w h value 4.5 t 1590 mm 1 898 mm Through equatios (1 ad (2, we get: =35749 N, F a = 19662 N 2.2. Calculatio of Theory Load Distributio of the Roller Bearig for the truck is the double-row tapered roller bearig 353112, ad its techical parameters are show i Table 2. Two rows of rollig elemets are uder ouiform load after the bearig is subjected to radial ad axial loads. For roller bearigs, if F a 1.909 taα, the the loadig process is oly o oe roller colum of the bearig. Load distributio ca be calculated as a sigle-row tapered roller bearig [11, 12]. (2
Load Calculatio ad Desig of Roller Crowig of Truck Hub Bearig The Ope Mechaical Egieerig Joural, 2015, Volume 9 107 Table 2. Techical Parameter of the bearig. Techical Parameter Value Outer coe agle, α Ier coe agle, β Flage agle, γ 14.8 11.7 77.95 Small ed diameter of roller, d 1 9.061 Large ed diameter of roller, d 2 10.258 Number of rollers i the bearig, z 22 2 Effective legth of roller, l w 20.65 Legth of roller, l 21.65 Ier diameter, d 60 Outer diameter, D 102 Bearig width, B 90 where,! = 1 2 1+ " ' a ta# & " r ( The agle of load distributio is therefore:! 1 = cos "1 (1" 2# (7 By equatio (3, roller load of the arbitrary positio ca be writte as: Q! 1" 1 ( 1" cos! ' & 2# ( By Itroducig radial itegral J r (ε ad axial itegral J a (ε of the load distributio, the equilibrium equatio of the bearig is expressed as: ZJ r (! cos" (9 (8 The bearig meets the coditio of F a 1.909 taα, so load distributio could be calculated as a sigle-row tapered roller bearig. It is ecessary to establish the loaddisplacemet relatioship of the rollig elemets with their races to solve the load distributio. The followig assumptios are also made: (1 Geerally the speed of the truck bearig is ot particularly high, so the cetrifugal force ad gyroscopic momet produced by the bearig are very small. That will ot have a sigificat impact o load distributio of the roller. Cetrifugal force ad gyroscopic momet are cosidered abset at all cotacts. (2 There is a permaet cotact causig stress alog the etire legth of the tapered roller; frictio force of the roller is igored. (3 Frictio momets of the roller are eglected. For roller bearigs, the relatioship of load- displacemet ca be writte as: Q = K! (3 where =1.11 ad K=7.86 10 4 l 8/9 Havig bee subjected to radial ad axial forces, the relative displacemet of ier ad outer of tapered roller bearigs i the radial ad axial are respectively δ r ad δ a. Stipulatig the positio of the maximum load for the roller is θ=0, where θ is positio agle of rollers. The total deflectio i the arbitrary agle locatio is give by:! " =! a si# +! r cos" cos# (4 Whe θ=0, the maximum deflectio is give as:! max =! a si" +! r cos" (5 From equatios (4 ad (5, δ θ ca be obtaied as follows:! " =! max 1# 1 ( 1# cos" ( & ' 2 (6 F a ZJ a (! si" (10 where J r (! = 1 2! J a (! = 1 2! +# 1 "# 1 +# 1 "# 1 1" 1 ( 1" cos# ' & 2! ( cos#d# 1" 1 ( 1" cos# ' & 2! ( d# From equatios (10 ad (11, the maximum load for roller is give as: Q max = zj r (! cos" = F a zj a (! si" (11 Thus the maximum load for roller ca be calculated. The loadig area ad roller load are show i Fig. (1. Load of rollig elemet 7000 6000 5000 4000 3000 0 0 1 2 3 4 5 6 7 Positio agle of roller Fig. (1. Load of roller of the arbitrary positio. 3. FINITE ELEMENT MODEL OF THE TRUCK HUB BEARING 353112 I the hub bearig, the feature of cotacts of rollers ad their races is completely cosistet. Therefore usig a local
108 The Ope Mechaical Egieerig Joural, 2015, Volume 9 Xia et al. cotact model of a roller ad race, the overall roller crowig simulatio ca be aalyzed [13, 14]. For roller modelig, the geeratrix was geerated i the CAD software i the form of parametric equatio ad the imported i ANSYS to build the model. The, by settig the material properties, performig meshig, settig up the cotact pairs ad costrait coditios ad applyig the load, the maximum load of the roller has bee calculated i the previous sectio that is applied o the model. After all the pre-aalysis coditios are met, the operatio ca be performed. Miimum grid uit is 0.025 mm. Fiite elemet model is show i Fig. (2. Cotact stress betwee roller ad ier raceway (MPa 3200 3000 2800 2600 2400 2200 1800 1600 1400 1200 Covex metric of roller (mm Fig. (3. The extreme values variatio of cotact stress betwee differet roller crowig ad ier 2800 Fig. (2. Fiite elemet model. 3.1. The Aalysis of Results The idetical modelig method is employed. The mechaical behavior of straight geeratrix shape roller ad logarithmic geeratrix roller are aalyzed, respectively. By the theoretic calculatio, a set of the crow drop of roller is accepted as: 0.005 mm, 0.01 mm, 0.015 mm, ad 0.02 mm, ad the bearig material is GCr15. The extreme value of cotact stress betwee roller ad their races is show i Figs. (3, 4. Fig. (5 gives the extreme values variatio of cotact stress of differet roller crowig ad large rib of the ier, ad the maximum value is oly 400.7 MPa. Fig. (3 describes the variatio of extreme values of cotact stress betwee differet roller crowig ad ier race of the bearig. Fig. (4 is the variatio of extreme values of cotact stress betwee differet roller crowig ad outer From Figs. (3, 4, it is observed that whe the crow drop of roller is zero, the maximum value of cotact stress ca be obtaied ad the stress of roller ad ier race is greater tha that of betwee the roller ad outer Before the crow drop is less tha 0.005 mm, the extreme stress decreases quickly with the icrease of crow drop. This is because the pheomeo of stress cocetratio weakes gradually as the crow drop icreases, ad cotact stress is distributed uiformly. Whe the crow drop of roller is more tha 0.015 mm, the extreme value of stress begis to rise, but the rate of icrease is much smaller tha the rate of descet whilst the roller-race cotact surface decreases with the icrease of crow drop of roller ad the itermediate cotact stress begis to icrease. Cotact stress of differet roller crowig ad large rib of the ier i the Fig. (5 are quite smaller tha that i the Figs. (3, 4. Thus we take o accout of it i this paper. Cotact stress betwee roller ad outer raceway (MPa 2600 2400 2200 1800 1600 1400 1200 covex metric of roller (mm Fig. (4. The extreme values variatio of cotact stress betwee differet roller crowig ad outer cotact stress of roller ad large rib of the ier (MPa 410 400 380 360 340 320 300 280 260 240 covex matric of roller (mm Fig. (5. The extreme values variatio of cotact stress betwee differet roller crowig ad large rib of the ier.
Load Calculatio ad Desig of Roller Crowig of Truck Hub Bearig The Ope Mechaical Egieerig Joural, 2015, Volume 9 109 ad races, ad the uit is MPa. Fig. (6 shows that straight geeratrix roller has the larger cotact stress at the eds of roller. Fig. (7 shows that whe roller crowig is 0.005 mm, the eds of roller have obvious stress mutatio. Figs. (8, 9 show, respectively, that whe roller crowig is of 0.01 mm ad 0.015 mm, the cotact stress is maitaied uiformly alog the directio of roller geeratrix but begis to decrease gradually at the eds of roller. Fig. (10 shows that whe roller crowig is 0.02 mm, the variatio curve of cotact stress steepes ad the roller-race cotact surfaces decrease by degrees. So uder this workig coditio, the optimal crow drop of roller is 0.01 mm to 0.015 mm ad the best is close to 0.015 mm. Fig. (6. Cotact stress of roller of the straight geeratrix ad ier Fig. (9. Cotact stress of roller crowig of 0.015 mm ad ier Fig. (7. Cotact stress of roller crowig of 0.005 mm ad ier Fig. (8. Cotact stress of roller crowig of 0.01 mm ad ier The cotact stress of differet roller crowig ad ier race alog the roller geeratrix directio is show from Figs. (6-10. I the figures, abscissa is the effective legth of roller, ad the uit is mm. Ordiate is cotact stress of roller Fig. (10. Cotact stress of roller crowig of 0.02 mm ad ier Through data fittig, the equatio of roller crowig ca be give as: y= 9.906 10-4 l(1 0.00938x 2 (whe covex metric is 0.01 mm or y= 14.8594 10-4 l(1 0.00938x 2 (whe covex metric is 0.015 mm
110 The Ope Mechaical Egieerig Joural, 2015, Volume 9 Xia et al. where, y is the crow value (mm, the directio of x-axis is i agreemet with taget directio of the poit of maximum crowig value of roller geeratrix. The rage of x is x <10.325 mm. Fiite elemet aalysis methods have ot cosidered the ifluece of crow value of ier ad outer. CONCLUSION Accordig to the specific workig coditio, the force situatio of the truck hub bearig 35311-2R is achieved, ad the theoretical aalysis of force distributio of bearig is studied. Simultaeously, the fiite elemet aalysis software is applied to model ad stress of the bearig is aalyzed. Furthermore the optimal value of the crow drop of roller ad correspodig equatios are cocluded. The above equatio of roller crowig is derived oly for this truck hub bearig 353112, which does ot have uiversal applicability for other types of bearigs. CONFLICT OF INTEREST The authors cofirm that this article cotet has o coflict of iterest. ACKNOWLEDGEMENTS This project is supported by Natioal Natural Sciece Foudatio of Chia (Grat Nos. 51475144 ad 51075123. REFERENCES [1] W. Wag, F. Li, ad Y. W. Zhag, Car wheel hub bearig mechaics performace aalysis, Machiery Desig ad Maufacture, vol. 3, pp. 192-195, March 2014 (i Chiese. [2] Y. Xu, Y. P. Li, ad D. Hog, Aalysis of the calculatio ad the modes of breakdow of automobile hub bearig, Moder Maufacturig Techology ad Equipmet, vol. 6, pp. 49-50, 2009 (i Chiese. [3] M. Y. Li, ad K. Q. Wu, Load test ad load spectrum of auto hub bearig, Bearig, vol.6, pp.25-28, 1998 (i Chiese. [4] L. Wag, Q. C. Wag, ad Q. X. Pag, The stress aalysis of hub bearig based o multi- bech test load, Agricultural equipmet ad vehicle egieerig, vol. 6, pp. 11-14, 2009 (i Chiese. [5] L. Z. Yogjig, The umerical solutio of cotact stress aalysis of crow roller bearig, Foreig Bearig, vol. 5, pp. 16-18, 1988. [6] Z. W. Wag, L. Q. Meg, ad W. S. Hao, Fiite elemet method aalysis ad optimal desig of roller covexity of tapered roller bearig, Advaced Materials Research, vol. 139-141, pp. 1079-1083, 2010. [7] H. Rahejat, ad R. Gohar, Desig of profiled taper roller bearigs, Tribology, vol. 12, o. 6, pp. 269-275, 1979. [8] K. Nikpur, ad R. Gohar, Profiled taper rollers, Tribology, vol.12, o.6, pp. 203-208, 1975. [9] F. B. Oswald, E. V. Zaretsky, ad J. V. Poplawski, Effect of roller geometry o roller bearig load life relatio, Tribology Trasactios, vol.57, pp.928-938, 2014. [10] D. J. Huag, Z. Y. Weg, H. W. You, D. Yi, G. Gao, ad J. Mei, Method research of establishig load spectrum o durability test of the car hub bearig, Iteratioal Coferece o Mechaic Automatio ad Cotrol Egieerig, 2010, pp. 3132-3136. [11] S. E. Deg, Q. Y. Jia, ad Y. S. Wag, Rollig Bearig Desig Priciple, Bejig: Chiese Stadards Press, 2008 (i Chiese. [12] L. Hu, W. Z. Wag, ad Z. Q. Zhao, Lubricated cotact aalysis of roller large ed-flage i double-row tapered roller bearig, J. Tribology, vol. 1, pp.22-28, 2013 (i Chiese. [13] X. Y. Che, ad J. J. Ma, Some problems i the desig of covex metric of logarithmic roller, Bearig, vol. 11, pp. 2-4, 1994 (i Chiese. [14] W. W. Li, X. Y. Che, ad X. J. She, Numerical calculatio ad roller pressure aalysis of theoretical logarithm profile equatio, Chia Mechaical Egieerig, vol.15, pp.1788-1792, 2011 (i Chiese. Received: Jauary 8, 2015 Revised: Jauary 15, 2015 Accepted: Jauary 16, 2015 Xia et al.; Licesee Betham Ope. This is a ope access article licesed uder the terms of the Creative Commos Attributio No-Commercial Licese (http://creativecommos.org/liceses/by-c/4.0/ which permits urestricted, o-commercial use, distributio ad reproductio i ay medium, provided the work is properly cited.