3. CALCULATING THE PERFORMANCE OF YOUR BEARINGS SUMMARY OF SYMBOLS USED IN DETERMINATION OF APPLIED LOADS... 47 A. DETERMINATION OF APPLIED LOADS... 48 52. Gearig... 48.. Spur gearig.2. Sigle helical gearig.3. Straight bevel & zerol gearig.4. Spiral bevel & hypoid gearig.5. Straight worm gearig.6. Double evelopig worm gearig 2. Belt ad chai drive factors... 5 3. Cetrifugal force... 5 4. Shock loads... 5 5. Geeral formulas... 52 5.. Tractive effort ad wheel speed 5.2. Torque to power relatioship 6. Bearig reactios... 52 6.. Effective spread 6.2. Shaft o two supports 6.3. Shaft o three or more supports 6.4. Calculatio example B. BEARING LIFE... 53 64. Dyamic coditios... 53.. Nomial or catalog life... Bearig life..2. Ratig life..3. Bearig life equatios..4. Bearig equivalet radial load ad required ratigs..5. Dyamic equiavlet radial load..6. Sigle row equatios..7. Double row equatios.2. Adjusted life.2.. Geeral equatio.2.2. Factor for reliability a.2.3. Factor for material a 2.2.4. Factor for useful life a 4.2.5. Factor for evirometal coditios a 3.2.6. Select-A-Nalysis.3. System life ad weighted average load ad life.3.. System life.3.2. Weighted average load ad life equatios.3.3. Ratios of bearigs life to loads, power ad speeds.3.4. Life calculatio examples 2. Static coditios... 63 2.. Static ratig 2.2. Static equivalet radial load (sigle row bearigs) 2.3. Static equivalet radial load (2-row bearigs) 3. Performace 900 TM (P900) bearigs... 64 C. TORQUE... 65 68 Ruig torque M. Sigle row... 65 2. Double row... 66 45
46
SYMBOL DESCRIPTION UNITS b Tooth legth mm, i d c Distace betwee gear ceters mm, i D m Mea diameter or effective workig diameter of a sprocket, pulley, wheel, or tire mm, i D m Mea diameter or effective workig diameter of mm, i gear (D mg ), piio (D mp ), or worm (D mw ) D p Pitch diameter of gear (D pg ) piio (D pp ), or worm (D pw ) mm, i f B Summary of symbols used to determie applied loads Belt or chai pull factor F a Axial (thrust) force o gear (F ag ), piio (F ap ), or worm (F aw ) N, lbf F b Belt or chai pull N, lbf F o Cetrifugal force N, lbf F s Separatig force o gear (F sg ), piio (F sp ), or worm (F sw ) N, lbf F t Tagetial force o gear (F tg ), piio (F tp ), or worm (F tw ) N, lbf F te Tractive effort o vehicle wheels N, lbf F w Force of ubalace N, lbf G Gear, used as a subscript H Power kw, hp L Lead. Axial advace of a helix for oe complete revolutio mm, i M Momet N-m, lbf.i m Gearig ratio N Number of teeth i gear (N G ), piio (N P ), or sprocket (N S ) Rotatioal speed of gear ( G ), piio ( P ) or worm ( W ) rev/mi p Pitch. Distace betwee similar equally mm, i spaced tooth surfaces alog the pitch circle P Piio, used as a subscript r Radius to ceter of mass mm, i T Torque N-m, lbf.i V Liear velocity or speed km/h, mph V r Rubbig or surface velocity m/s, ft/mi W Worm gear, used as a subscript γ (gamma) () Bevel gearig - pitch agle of gear (γ G ) or piio (γ P ) degree (2) Hypoid gearig - face agle of piio (γ P ) ad root agle of gear (γ G ) degree η (eta) Efficiecy decimal fractio λ (lambda) Worm gearig - lead agle degree µ (mu) Coefficiet of frictio π (pi) The ratio of the circumferece of a circle to its diameter (π = 3.46) φ (phi) Normal tooth pressure agle for gear (φ G ) or piio (φ P ) degree φ x (phi x ) Axial tooth pressure agle degree ψ (psi) () Helical gearig - helix agle for gear (ψ G ) or piio (ψ P ) degree (2) Spiral bevel ad hypoid gearig - spiral agle for gear (ψ G ) degree or piio (ψ P ) 47
A. Determiatio of applied loads. Gearig.. Spur gearig (Fig. 3-) Tagetial force F tg = Separatig force F sg = F tg ta φ G (.9 x 0 7 ) H D pg G (ewtos) (.26 x 0 5 ) H = (pouds-force) D pg G F tp.3. Straight bevel ad zerol gearig with zero degrees spiral (Fig. 3-4) I straight bevel ad zerol gearig, the gear forces ted to push the piio ad gear out of mesh such that the directio of the thrust ad separatig forces are always the same regardless of directio of rotatio. (Fig. 3-3) I calculatig the tagetial force, F tp or F tg, for bevel gearig, the piio or gear mea diameter, D mp or D mg, is used istead of the pitch diameter, D pp or D pg. The mea diameter is calculated as follows: D mg = D pg b si γ G or D mp = D pp b si γ P I straight bevel ad zerol gearig F tp = F tg F sg F sp F tg Clockwise + Positive Thrust away piio apex CALCULATING THE PERFORMANCE OF YOUR BEARINGS 48 Fig. 3- Spur gearig..2. Sigle helical gearig (Fig. 3-2) Tagetial force F tg = Separatig force F F sg = tg ta φ G cos ψ G Thrust force F ag = F tg ta ψ G Note: for double helical (herrigboe) gearig F ag = 0 F sp Fig. 3-2 Helical gearig. (.9 x 0 7 ) H D pg G F ap F tp (ewtos) (.26 x 0 5 ) H = (pouds-force) D pg G F sg F tg F ag Fig. 3-3 Straight bevel ad zerol gears - thrust ad separatig forces are always i same directio regardless of directio of rotatio. Piio Tagetial force F tp = Thrust force F ap = F tp ta φ P si γ P Separatig force F sp = F tp ta φ P cos γ P Gear Tagetial force F tg = (.9 x 0 7 ) H D mp P (.9 x 0 7 ) H D mg G Couterclockwise (ewtos) (.26 x 0 5 ) H = D (pouds-force) mp P (ewtos) (.26 x 0 5 ) H = (pouds-force) D mg G
Thrust force F ag = F tg ta φ G si γ G Separatig force F sg = F tg ta φ G cos γ G F tp F ap F sp F ag F sg F tg Fig. 3-4 Straight bevel gearig..4. Spiral bevel ad hypoid gearig (Fig. 3-6) I spiral bevel ad hypoid gearig, the directio of the thrust ad separatig forces depeds upo spiral agle, had of spiral, directio of rotatio, ad whether the gear is drivig or drive (see Table 3-A). The had of the spiral is determied by otig whether the tooth curvature o the ear face of the gear (fig. 3-5) iclies to the left or right from the shaft axis. Directio of rotatio is determied by viewig toward the gear or piio apex. I spiral bevel gearig F tp = F tg I hypoid gearig F tp = F tg cos ψ P cos ψ G Hypoid piio effective workig diameter D mp = D mg N ( P cos ψ N G ) ( G ) cos ψ P Tagetial force F tg = (.9x 07 ) H (ewtos) D mg G = (.26 x 05 ) H (pouds-force) D mg G Hypoid gear effective workig diameter D mg = D pg b si γ G F tp F ap F sp Clockwise Couterclockwise Positive Thrust away from piio apex Negative Thrust toward _ + F ag F sg piio apex F tg Fig. 3-5 Spiral bevel ad hypoid gears - the directio of thrust ad separatig forces depeds upo spiral agle, had of spiral, directio of rotatio, ad whether the gear is drivig or drive. Fig. 3-6 Spiral bevel ad hypoid gearig. 49
Drivig member rotatio Right had spiral clockwise or Left had spiral couterclockwise F ap = F ag = Thrust force Drivig member F tp (ta φ P si γ P si ψ P cos γ P ) cos ψ P Drive member F tg (ta φ G si γ G + si ψ G cos γ G ) cos ψ G F sp = F sg = Separatig force Drivig member F tp (ta φ P cos γ P + si ψ P si γ P ) cos ψ P Drive member F tg (ta φ G cos γ G si ψ G si γ G ) cos ψ G Right had spiral couterclockwise or F ap = Drivig member F tp (ta φ P si γ P + si ψ P cos γ P ) cos ψ P Drive member F sp = Drivig member F tp (ta φ P cos γ P si ψ P si γ P ) cos ψ P Drive member Left had spiral clockwise F ag = F tg (ta φ G si γ G si ψ G cos γ G ) cos ψ G F sg = F tg (ta φ G cos γ G + si ψ G si γ G ) cos ψ G Table 3A Spiral bevel ad hypoid gearig equatios. CALCULATING THE PERFORMANCE OF YOUR BEARINGS 50.5. Straight worm gearig (Fig. 3-7) Worm F tw = (.9 x 07 ) H Tagetial force D pw W = (.26 x 05 ) H D pw W (ewtos) (pouds-force) F aw = (.9 x 07 ) H η Thrust force (ewtos) D pg G Separatig force F sw = Worm gear = (.26 x 05 ) H η (pouds-force) D pg G F aw = F tw η ta λ F tw si φ cos φ si λ + µ cos λ force F tg = (.9 x 07 ) H η Tagetial force (ewtos) D pg G = (.26 x 05 ) H η (pouds-force) D pg G F tg = F tw η ta λ F ag = (.9 x 07 ) H Thrust force D pw W = (.26 x 05 ) H D pw W F F sg = tw si φ Separatig force cos φ si λ + µ cos λ where: ( D pg ) λ = ta ta L = ( m D pw π D pw ) η = or or cos φ µ ta λ cos φ + µ cot λ (ewtos) (pouds-force) Metric system µ* = (5.34 x 0 7 ) V r 3 + 0.46 0.03 V r = Ich system D pw W (.9 x 0 4 ) cos λ V r 0.09 (meters per secod) µ* = (7 x 0 4 ) V r 3 + 0.235 0.03 V r = D pw W 3.82 cos λ V r 0.09 (feet per miute) *Approximate coefficiet of frictio for the 0.05 to 5 m/s (3 to 3000 ft/mi) rubbig velocity rage. FtG Fig. 3-7 Straight worm gearig. F ag F sg F sw F tw FaW
.6. Double evelopig worm gearig Worm F tw = (.9 x 07 ) H Tagetial force D mw W Thrust force = (.26 x 05 ) H D mw W F aw = 0.98 F tg (ewtos) (pouds-force) Use this value for F tg for bearig loadig calculatios o worm gear shaft. For torque calculatios use followig F tg equatios. F sw = 0.98 F tg Separatig force ta φ cos λ Worm gear Tagetial force F tg = (.9 x 07 ) H m η (ewtos) D pg W Table 3-B Belt or chai pull factor based o 80 degrees agle of wrap. D m Type Chais, sigle....00 Chais, double....25 V belts....50 F 2 = Tesio, slack side F b f B = (.26 x 0 5 ) H m η (pouds-force) D pg W F = Tesio, tight side or FtG = (.9 x 07 ) H η D pg G (ewtos) = (.26 x 05 ) H η (pouds-force) D pg G Use this value for calculatig torque i subsequet gears ad shafts. For bearig loadig calculatios use the equatio for F aw. F ag = (.9 x 07 ) H Thrust force (ewtos) D mw W = (.26 x 05 ) H D mw W F sg = 0.98 F tg Separatig force ta φ cos λ where: η = efficiecy (refer to maufacturer s catalog) D mw = 2d c 0.98 D pg Lead agle at ceter of worm λ = ta ) D pg ) = L ta ( m D pw ( π D pw 2. Belt ad chai drive factors (Fig. 3-8) (pouds-force) Due to the variatios of belt tightess as set by various operators, a exact equatio relatig total belt pull to tesio F o the tight side ad tesio F 2 o the slack side (fig. 3-8), is difficult to establish. The followig equatio ad table 3-B may be used to estimate the total pull from various types of belt ad pulley, ad chai ad sprocket desigs: F b = (.9 x 07 ) H f B D m (ewtos) = (.26 x 05 ) H f B (pouds-force) D m Stadard roller chai sprocket mea diameter P D m = si 80 ( N S ) Fig. 3-8 Belt or chai drive. 3. Cetrifugal force Cetrifugal force resultig from imbalace i a rotatig member: F c = = F w r 2 8.94 x 0 5 F w r 2 3.52 x 0 4 4. Shock loads (ewtos) (pouds-force) It is difficult to determie the exact effect shock loadig has o bearig life. The magitude of the shock load depeds o the masses of the collidig bodies, their velocities ad deformatios at impact. The effect o the bearig depeds o how much of the shock is absorbed betwee the poit of impact ad the bearigs, as well as whether the shock load is great eough to cause bearig damage. It is also depedet o frequecy ad duratio of shock loads. At a miimum, a suddely applied load is equivalet to twice its static value. It may be cosiderably more tha this, depedig o the velocity of impact. Shock ivolves a umber of variables that geerally are ot kow or easily determied. Therefore, it is good practice to rely o experiece. The Timke Compay has may years of experiece with may types of equipmet uder the most severe loadig coditios. A Timke Compay sales egieer or represetative should be cosulted o ay applicatio ivolvig uusual loadig or service requiremets. 5
5. Geeral formulas 5.. Tractive effort ad wheel speed The relatioships of tractive effort, power, wheel speed ad vehicle speed are: Metric system Effective bearig spread H = F te V 3600 (kw) = Ich system 5300 V D m (rev/mi) Idirect moutig H = = F te V 375 336 V D m (hp) (rev/mi) 5.2. Torque to power relatioship Metric system Effective bearig spread CALCULATING THE PERFORMANCE OF YOUR BEARINGS 52 T = H = Ich system 60 000 H 2π 2π T 60 000 (N-m) (kw) T = 395 877 H (lbf.i) 2π H = 2π T 395 877 6. Bearig reactios (hp) 6.. Effective spread Whe a load is applied to a tapered roller bearig, the iteral forces at each roller body to cup cotact act ormal to the raceway (see Fig. -5, page 4). These forces have radial ad axial compoets. With the exceptio of the special case of pure thrust loads, the coe ad the shaft will experiece momets imposed by the asymmetrical axial compoets of the forces o the rollers. It ca be demostrated mathematically that if the shaft is modeled as beig supported at its effective bearig ceter, rather tha at its geometric bearig ceter, the bearig momet may be igored whe calculatig radial loads o the bearig. The oly exterally applied loads eed to be cosidered, ad momets are take about the effective ceters of the bearigs to determie bearig loads or reactios. Fig. 3-9 shows sigle-row bearigs i a direct ad idirect moutig cofiguratio. The choice of whether to use direct or idirect moutig depeds upo the applicatio ad duty. Direct moutig Fig. 3-9 Choice of moutig cofiguratio for sigle-row bearigs, showig positio of effective load carryig ceters. 6.2. Shaft o two supports Simple beam equatios are used to traslate the exterally applied forces o a shaft ito bearig reactios actig at the bearig effective ceters. With two-row bearigs, the geometric ceter of the bearig is cosidered to be the support poit except where the thrust force is large eough to uload oe row. The the effective ceter of the loaded row is used as the poit about which bearig load reactios are calculated. These approaches approximate the load distributio withi a two-row bearig, assumig rigid shaft ad housig. However, these are statically idetermiate problems i which shaft ad support rigidity ca sigificatly ifluece bearig loadig ad require the use of computer programs for solutio. 6.3. Shaft o three or more supports The equatios of static equilibrium are isufficiet to solve bearig reactios o a shaft havig more tha two supports. Such cases ca be solved usig computer programs if adequate iformatio is available. I such problems, the deflectios of the shaft, bearigs ad housigs affect the distributio of loads. Ay variace i these parameters ca sigificatly affect bearig reactios.
6.4. Calculatio example Symbols used i calculatio examples a e Effective bearig spread mm, i A, B,... Bearig positio, used as subscripts c, c 2,... Liear distace (positive or egative) mm, i F Applied force N, lbf F r Radial bearig load N, lbf h Horizotal (used as subscript) H Power kw,hp K K-factor from bearig tables M Momet N-mm, lbf.i v Vertical (used as subscript) θ, θ 2, θ 3 Gear mesh agle relative to plae of referece defied i figure 3-0 degree Bearig radial reactios - Shaft o two supports Bearig radial loads are determied by:. Resolvig forces applied to the shaft ito horizotal ad vertical compoets relative to a coveiet referece plae. 2. Takig momets about the opposite support. 3. Combiig the horizotal ad vertical reactios at each support ito oe resultat load. Show are equatios for the case of a shaft o two supports with gear forces F t (tagetial), F s (separatig), ad F a (thrust), a exteral radial load F, ad a exteral momet M. The loads are applied at arbitrary agles (θ, θ 2, ad θ 3 ) relative to the referece plae idicated i figure 3-0. Usig the priciple of superpositio, the equatios for vertical ad horizotal reactios (F rv ad F rh ) ca be expaded to iclude ay umber of gears, exteral forces or momets. Use sigs as determied from gear force equatio. F tg q q 3 Plae of F ag q 2 F sg F Plae of Fig. 3-0 Bearig radial reactios. F ag Bearig A h v c F sg Vertical reactio compoet at bearig positio B c 2 F tg a e F M Vertical reactio compoet at bearig positio A v = F sg cos θ + F tg si θ + F cos θ 2 v Horizotal reactio compoet at bearig positio A h = F sg si θ F tg cos θ + F si θ 2 h Resultat radial reactio = (v 2 + h 2 ) /2 =(v 2 + h 2 ) /2 See page 62 for examples of bearig life calculatio. B. Bearig life. Dyamic coditios.. Nomial or catalog life... Bearig life May differet performace criteria dictate bearig selectio. These iclude bearig fatigue life, rotatioal precisio, power requiremets, temperature limits, speed capabilities, soud, etc. This guide deals with bearig life related to material associated fatigue spallig. Bearig B v = [ c (F sg cos θ + F tg si θ ) + (D pg b si γ G ) F ag cos θ +c 2 F cos θ 2 + M cos θ 3 ] a e 2 Horizotal reactio compoet at bearig positio B h = [ c (F sg si θ F tg cos θ ) + (D pg b si γ G ) F ag si θ +c 2 F si θ 2 + M si θ 3] a e 2 h v Bearig failure mode may ot be fatigue There are other factors that limit bearig life if ot specially cosidered i the iitial desig aalysis, such as iadequate lubricatio, improper moutig, poor sealig, extreme temperatures, high speeds, ad uusual vibratios (traslatioal ad torsioal). Also, proper hadlig ad maiteace must be provided. These factors will ot be addressed i this guide, but if preset i ay applicatio, a Timke Compay sales egieer or represetative should be cosulted. Bearig life is defied here as the legth of time, or the umber of revolutios, util a fatigue spall of a specific size develops. Sice metal fatigue is a statistical pheomeo, the life of a idividual bearig is impossible to predetermie precisely. Bearigs that may appear to be idetical ca exhibit cosiderable 53
life scatter whe tested uder idetical coditios. Thus it is ecessary to base life predictios o a statistical evaluatio of a large umber of bearigs operatig uder similar coditios. The Weibull distributio fuctio is commoly used to predict the life of a bearig at ay give reliability level...2. Ratig life (L 0 ) Ratig life, L 0, is the life that 90 percet of a group of idetical bearigs will complete or exceed before the area of fatigue spallig reaches a defied criterio. The L 0 life is also associated with 90 percet reliability for a sigle bearig uder a certai load. The life of a properly applied ad lubricated tapered roller bearig is ormally reached after repeated stressig produces a fatigue spall of a specific size o oe of the cotactig surfaces. The limitig criterio for fatigue used i Timke laboratories is a spalled area of 6 mm 2 (0.0 i 2 ). This is a arbitrary desigatio ad, depedig upo the applicatio, bearig useful life may exted cosiderably beyod this poit. If a sample of apparetly idetical bearigs is ru uder..3. Bearig life equatios The followig factors also help to visualize the effects of load ad speed o bearig life: Doublig the load reduces life to approximately oe-teth. Reducig the load by oe-half icreases life approximately te times. Doublig the speed reduces hours of life by oe-half. Reducig the speed by oe-half doubles hours of life. With icreased emphasis o the relatioship betwee the referece coditios ad the actual eviromet i which the bearig operates i the machie, the traditioal life equatios have bee expaded to iclude certai additioal variables that affect bearig performace. Techology permits the quatitative evaluatio of evirometal differeces, such as lubricatio, load zoe ad aligmet, i the form of various life adjustmet factors. These factors, plus a factor for useful life, are cosidered i the bearig aalysis ad selectio approach by The Timke Compay. CALCULATING THE PERFORMANCE OF YOUR BEARINGS Percetage of bearigs ot survivig 20 5 0 5 Ratig Life L 0 Average Life 2 3 4 5 6 7 8 9 0 2 3 4 specified laboratory coditios util a material associated fatigue spall of 6 mm 2 (0.0 i 2 ) develops o each bearig, 90 percet of these bearigs are expected to exhibit lives greater tha the ratig life. The, oly 0 percet would have lives less tha the ratig life. The example (fig. 3-), shows bearig life scatter followig a Weibull distributio fuctio with a dispersio parameter (slope) equal to.5. From hudreds of such tested groups, L 0 life estimates are determied. Likewise, ratig life ad load ratig are established ad verified. To assure cosistet quality, worldwide, The Timke Compay coducts extesive bearig fatigue life tests i laboratories i the Uited States ad i Eglad. This testig results i cofidece i Timke ratigs. Life i multiples of ratig life, L 0 Bearig life adjustmet equatios are: L a = a a 2 a 3 a 4 ( or For Timke bearigs, the average, or mea life, is approximately 4 times the L 0 life. Fig. 3- Theoretical life frequecy distributio of oe hudred apparetly idetical bearigs operatig uder similar coditios. L a = a a 2 a 3 a 4 ( C 90)0/3 P C 90)0/3 P (90 x 0 6 ) (revolutios) (.5 x 06) (hours) where: a = life adjustmet factor for reliability a 2 = life adjustmet factor for bearig material a 3 = life adjustmet factor for evirometal coditios a 4 = life adjustmet factor for useful life (spall size) 54
For the case of a pure exteral thrust load, F a, the previous equatio becomes: L a = a a 2 a 3 a 4 ( ( C a90)0/3.5 x 06) (hours) F a Traditioal L 0 life calculatios are based o bearig capacity, dyamic equivalet radial load (see page 60) ad speed. The Timke Compay method of calculatig L 0 life is based o a C 90 load ratig, which is the load uder which populatio of bearigs will achieve a L 0 life of 90 millio revolutios. The ISO method is based o a C load ratig, which produces a populatio L 0 life of millio revolutios. While these two methods correctly accout for the differeces i basis, other differeces ca affect the calculatio of bearig life. For istace, the two methods of calculatig dyamic equivalet radial load (pages 57) ca yield slight differeces that are accetuated i the life equatios by the expoet 0/3. I additio, it is importat to distiguish betwee the ISO L 0 life calculatio method ad the ISO bearig ratig. Comparisos betwee bearig lives should oly be made for values calculated o the same basis (C or C 90 ) ad the same ratig formula (Timke or ISO). The two methods are listed below. zoe is 80 degrees. I this case, iduced bearig thrust is: F a (80) = 0.47 F r K The equatios for determiig bearig thrust reactios ad equivalet radial loads i a system of two sigle-row bearigs are based o the assumptio of a 80-degree load zoe i oe of the bearigs ad 80 degrees or more i the opposite bearig...5. Dyamic equivalet radial load The basic dyamic radial load ratig, C 90, is assumed to be the radial load carryig capacity with a 80-degree load zoe i the bearig. Whe the thrust load o a bearig exceeds the iduced thrust, F a(80), a dyamic equivalet radial load must be used to calculate bearig life. The dyamic equivalet radial load is that radial load which, if applied to a bearig, will give the same life as the bearig will attai uder the actual loadig (combied axial ad thrust). The equatios preseted give close approximatios of the dyamic equivalet radial load assumig a 80-degree load ) The Timke Compay method L 0 = ( C 90)0/3 P L 0 = ( C 90)0/3 P 90 x 0 6 (revolutios) () ( 6).5 x 0 (hours) (2) where: L 0 = ratig life or catalog life (life expectacy associated with 90% reliability) C 90 = basic dyamic radial load ratig of a sigle row bearig for a L 0 life of 90 millio revolutios (3,000 hours at 500 rev/mi) P = dyamic equivalet radial load (see page 60) = speed of rotatio, rev/mi Note: for pure thrust loadig ad for thrust bearigs, equatios ad 2 become: L 0 = ( C a90)0/3 L 0 = ( C a90)0/3 90 x 0 6 (revolutios) (a) ( 6).5 x 0 (hours) (2a) where: C a90 = basic dyamic thrust ratig for a L 0 life of 90 millio revolutios = exteral thrust load 2) The ISO method (ISO 28) L 0 = ( C 3 )0/ P L 0 = ( C 3 )0/ P where: x 0 6 (revolutios) (3) ( 6) x 0 (hours) (4) 60 C = basic dyamic radial load ratig for a L 0 life of millio revolutios Note: The C ratigs used i equatios 3 ad 4 ad listed i the Bearig Data Tables are Timke C 90 ratigs modified for a L 0 of millio revolutios ad ot ISO 28 ratigs...4. Bearig equivalet loads ad required ratigs Tapered roller bearigs are ideally suited to carry all types of loadigs - radial, thrust ad ay combiatio of both. Due to the tapered desig of the bearig, a radial load will iduce a thrust reactio withi the bearig that must be opposed by a equal or greater thrust reactio to keep the coes ad cups from separatig. The umber of rollers i cotact as a result of this ratio determies the load zoe i the bearig. If all the rollers are i cotact, the load zoe is referred to as beig 360 degrees. Whe oly a radial load is applied to a tapered roller bearig, it is assumed that half the rollers support the load ad the load zoe i oe bearig ad 80 degrees or more i the opposite bearig. More exact calculatios usig computer programs ca be used to accout for parameters such as bearig sprig rate, settig ad supportig housig stiffess. The approximate equatio is: P = XF r + YF a The followig tables give the equatios to determie bearig thrust load ad the dyamic equivalet radial loads for various desigs. The Timke method alog with ISO method are show. The factors ecessary to perform the calculatios are show i the bearig tables. 55
..6. Sigle row equatios Combied radial ad thrust load Desig (exteral thrust,, oto bearig A) Bearig A Bearig B Bearig A Bearig B ISO method Timke method Thrust coditio Thrust coditio 2 Thrust coditio Thrust coditio 2 0.5 0.5 FrB + F Y ae A Y B 0.5 > 0.5 FrB + Y A Y B 0.47 0.47 + KA 0.47 > 0.47 + KA Net bearig thrust load Net bearig thrust load Net bearig thrust load Net bearig thrust load F aa = 0.5 + Y B F aa = 0.5 Y A F aa = 0.47 + F aa = 0.47 F ab = 0.5 Y B F ab = 0.5 Y A F ab = 0.47 F ab = 0.47 CALCULATING THE PERFORMANCE OF YOUR BEARINGS 56 Dyamic equivalet radial load if F aa P A = F aa e A if > e A P A = 0.4 + Y A F aa P B = L 0 life L 0A = 06 60 ( C A P A ) Thrust load oly 0/3 L 0B = 06( C B )0/3 60 P B Thrust coditio F aa = F ab = 0 Dyamic equivalet load P A = Y A F aa P B = 0 L 0 life L 0A = ( 06 C A)0/3 60 P A L 0B = ( B) 06 C 0/3 60 P B (hours) (hours) (hours) (hours) Dyamic equivalet radial load P A = if if F ab F ab e B, P B = > e B P B = 0.4 + Y B F ab Desig (exteral thrust,, oto bearig A) Bearig A Thrust load F aa = F ab = 0 Bearig B Dyamic equivalet radial load P A = 0.4 + F aa if P A <, P A = P B = L 0 life L 0A = ( C 90A)0/3 x 3000 x 500 (hours) L 0 life P A L 0B = ( C 90B )0/3 P B Thrust coditio F aa = F ab = 0 L 0A = ( C a90a)0/3 x 3000 x 500 F aa L 0B = ( C a90b)0/3 x 3000 x 500 F ab Bearig A x 3000 x Dyamic equivalet radial load P A = P B = 0.4 + F ab if P B <, P B = 500 (hours) Bearig B Thrust load F aa = F ab = 0 (hours) (hours)
..7. Double-row equatios Similar bearig series, = Desig (exteral thrust,, oto bearig A) B F rc B F rc Bearig A Bearig B Bearig C Bearig A Bearig B Bearig C Fixed Floatig Fixed Floatig Thrust coditio ISO method Thrust coditio Timke method F r e > e F r > 0.6 B 0.6 B Dyamic equivalet radial load Dyamic equivalet radial load P AB = B + Y AB P C = F rc P AB = 0.67 B + Y 2AB P C = F rc P A = 0.4 B + P B = 0 P C = F rc P A = 0.5 B + 0.83 P B = 0.5 B 0.83 P C = F rc L 0 life L 0AB = 06 60 L 0C = 06 60 ( C 0/3 (2)) P AB ( C 0/3 (2)) P C (hours) (hours) L 0 life L 0A = ( C 90A 500 )0/3 x 3000 x (hours) P A L 0B = ( C 90B 500 )0/3 x 3000 x P B (hours) L 0C = ( C 90(2)C)0/3 x 3000 x 500 (hours) P C C 90 (2) = dyamic radial load ratig for 2 rows Dissimilar bearig series KA =/ KB Desig (exteral thrust,, oto bearig A) B F rc B F rc Bearig A Bearig B Bearig C Bearig A Bearig B Bearig C Fixed Floatig Fixed Floatig Thrust coditio Timke method L 0 life > 0.6 B 0.6 B L 0A = ( C 90A)0/3 x 3000 x 500 (hours) P A Dyamic equivalet radial load P A = 0.4 B + P A = P B = 0 P B = + (FrAB +.67 ) + (FrAB.67 ) L 0B = ( C 90B)0/3 x 3000 x 500 (hours) P B L 0C = ( C 90(2)c)0/3 x 3000 x 500 (hours) P C P C = F rc P C = F rc 57
.2. Adjusted life.2.. Geeral equatio With the icreased emphasis o the relatioship betwee ratig referece coditios ad the actual eviromet i which the bearig operates, the traditioal life equatios have bee expaded to iclude certai additioal variables that affect bearig performace. The expaded bearig life equatio becomes: L a = a a 2 a 3 a 4 L 0 L a = adjusted ratig life for a reliability of (00 ) percet a = life adjustmet factor for reliability a 2 = life adjustmet factor for material a 3 = life adjustmet factor for evirometal coditios a 4 = life adjustmet factor for useful life L 0 = ratig life from equatios to 4 page 56.2.4. Factor for evirometal coditios - a 3 Calculated life ca be modified to take accout of differet evirometal coditios, o a comparative basis, by usig the factor a 3 which is comprised of three separate factors: a 3 = a 3k a 3l a 3m a 3k a 3l a 3m = life adjustmet factor for load zoe = life adjustmet factor for lubricatio = life adjustmet factor for aligmet a 3k - load zoe factor Load zoe is the loaded portio of the raceway measured i degrees (fig. 3-2). It is a direct idicatio of how may rollers share the applied load. Load zoe is a fuctio of the amout of edplay (iteral clearace) or preload withi the bearig system. This, i tur, is a fuctio of the iitial settig, iteral geometry of the bearig, the load applied ad deformatio of compoets (shaft, bearig, housig). a 3k = The omial or catalog L 0 life assumes a miimum of 80 load zoe i the bearig. CALCULATING THE PERFORMANCE OF YOUR BEARINGS 58.2.2. Factor for reliability - a Reliability, i the cotext of bearig life for a group of apparetly idetical bearigs operatig uder the same coditios, is the percetage of the group that is expected to attai or exceed a specified life. The reliability of a idividual bearig is the probability that the bearig will attai or exceed a specified life. Ratig life, L 0, for a idividual bearig, or a group of idetical bearigs operatig uder the same coditios, is the life associated with 90 percet reliability. Some bearig applicatios require a reliability other tha 90 percet. A life adjustmet factor for determiig a reliability other tha 90 percet is: a = 4.48 ( l 00 ) R 2/3 l = atural logrithium (Base e) Multiply the calculated L 0 ratig life by a to obtai the L life, which is the life for reliability of R percet. By defiitio, a = for a reliability of 90 percet so, for reliabilities greater tha 90 percet, a < ad for reliabilities less tha 90 percet, a >..2.3. Factor for material - a 2 For Timke bearigs maufactured from electric-arc furace, ladle refied, bearig quality alloy steel, a 2 is geerally =. Bearigs ca also be maufactured from premium steels that cotai fewer ad smaller iclusio impurities tha stadard bearig steels ad provide the beefit of extedig bearig fatigue life where it is limited by o-metallic iclusios. A higher value ca the be applied for the factor a 2. a 3k =/ Depedig o edplay or preload, to quatify a 3k requires computer aalysis by The Timke Compay. Iteral clearace Small preload Fig. 3-2 Load zoe effect - radial load applied. a 3m - aligmet factor 80 o load zoe Zero clearace 360 o load zoe Heavy preload For optimum performace ad life, the races of a tapered roller bearig should be perfectly aliged. However, this is geerally impractical due to misaligmet betwee shaft ad housig seats ad also deflectio uder load (fig. 3-3). a 3m = For catalog life calculatios, it is assumed that aligmet is equivalet to the ratig referece coditio of 0.0005 radias. a 3m <
Cup Coe Fig. 3-3 Misaligmet. Misaligmet Where: C g = geometry factor C l = load factor C j = load zoe factor C s = speed factor C v = viscosity factor C gr = grease lubricatio factor Note: The a3 l maximum is 2.88 for all bearigs. The a3l miimum is 0.20 for case carburized bearigs ad 0.06 for through hardeed bearigs. A lubricat cotamiatio factor is ot icluded i the lubricatio factor because our edurace tests are ru with a 40 µm filter to provide a realistic level of lubricat cleaess. Geometry factor - C g C g Is give for each coe part umber i the TS bearig tables (pages 64 to 256). Note that this factor is ot applicable to our P900 bearig cocept (see page 64). If misaligmet is greater tha 0.0005 radias, the bearig performace will be affected. However, the predicted life is depedet o such factors as bearig iteral geometry, load zoe ad applied load. P900 bearigs ca be tailored to suit particular applicatio coditios, like misaligmet with compoet profilig. Quatifyig a 3m, for actual operatig coditios or to determie the beefits of P900, requires a computer aalysis by Timke. Load factor - C l The C l factor is obtaied from figure 3-4. Note that the factor is differet for case carburized ad through hardeed bearigs. F a is the thrust load o each bearig which is determied from the calculatio method o page 64. Separate curves are give for loads give i Newtos or pouds. It is ecessary to resolve all loads o the shaft ito bearig radial loads (, ) ad oe exteral thrust load ( ) before calculatig the thrust load for each bearig. a 3l - lubricatio factor Ogoig research coducted by The Timke Compay has demostrated that bearig life calculated from oly speed ad load, may be very differet from actual life whe the operatig eviromet differs perceptibly from laboratory coditios. Historically, The Timke Compay has calculated the catalogue life adjustmet factor for lubricatio (a3 l ) as a fuctio of three parameters: Bearig speed Bearig operatig temperature Oil viscosity These parameters are eeded to determie the elastohydrodyamic (EHL) lubricat i the rollig cotact regio of rollig elemet bearigs. Durig the last decade, extesive testig has bee doe to quatify the effects of other lubricatio related parameters o bearig life. Roller ad raceway surface fiish relative to lubricat film thickess have the most otable effect. Other factors iclude bearig geometry, material, loads ad load zoe. The followig equatio provides a simple method to calculate the lubricatio factor for a accurate predictio of the ifluece of lubricatio o bearig life (L0a). a 3l = C g x C l x C j x C s x C v x C gr C l 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. 0 Fig. 3-4 Load factor (C l ). Load zoe factor - C j Case Carburized (Newtos) Through Hardeed (Newtos) Case Carburized (pouds) Through Hardeed (pouds) 0 0 00 000 F a 0000 00000 a) Calculate X, where X = F a K b) If X > 2.3, the bearig load zoe is less tha 80, the: For case carburized bearigs, C j = 0.747 For through hardeed bearigs, C j = 0.69 If X < 2.3, the bearig load zoe is larger tha 80 ad C j. ca be determied from figure 3-5. F r 59
Cj 0.9 0.8 0.7.747.69 Grease lubricatio factor - C gr For grease lubricatio, the EHL lubricatio film becomes depleted of oil over time ad is reduced i thickess. Cosequetly, a reductio factor (C gr ) should be used to adjust for this effect. For case carburized bearigs, C gr = 0.79 For through hardeed bearigs, C gr = 0.74 CALCULATING THE PERFORMANCE OF YOUR BEARINGS 60 Speed factor - C s C s is determied from figure 3-6 where rev/mi (RPM) is the rotatioal speed of the ier race relative to the outer race. Cs 000 00 0 Fig. 3-6 Speed factor (C s ). Viscosity factor - C v The kiematic viscosity lubricat [Cetistokes (cst)] is take at the operatig temperature of the bearigs. The operatig viscosity ca be estimated by usig figure 5-7, page 20 i Sectio 5 Lubricatig your bearigs. Viscosity factor (C v ) ca the be determied from figure 3-7. Cv 0.6 0.5 0000 000 00 0 TM = Trademark of The Timke Compay Case Carburized Through Hardeed 0 00 RPM Case Carburized Through Hardeed 000 0000 0 00 000 0000 Kiamatic Viscosity (cst) Fig. 3-7 Viscosity factor (C v ). Case Carburized Through Hardeed 0 0.5.5 2 2.5 X Fig. 3-5 Load zoe factor (C j )..2.5 Factor for useful life - a 4 The limitig criterio for fatigue is a spalled area of 6 mm 2 (0.0 i 2 ). This is the referece coditio i The Timke Compay ratig, a 4 =. If a larger limit for area of fatigue spall ca be reasoably established for a particular applicatio, the a higher value of a 4 ca be applied..2.6. Select-A-Nalysis TM Bearig Systems Aalysis aalyzes the effect may real life variables have o bearig performace, i additio to the load ad speed cosideratios used i the traditioal catalog life calculatio approach. The Timke Compay s uique computer program, Select-A- Nalysis, adds sophisticated bearig selectio logic to that aalytical tool. Bearig Systems Aalysis allows the desiger to quatify differeces i bearig performace due to chages i the operatig eviromet. The selectio procedure ca be either performace or price orieted..3. System life ad weighted average load ad life.3.. System life System reliability is the probability that all of several bearigs i a system will attai or exceed some required life. System reliability is the product of the idividual bearig reliabilities i the system: R (system) = R A R B R C... R I a applicatio, the L 0 system life for a umber of bearigs each havig a differet L 0 life is: L 0 (system)= 3/2 + 3/2 +...+ [( L 0A ) ( L 0B ) ( L 0 ) ].3.2. Weighted average load ad life equatios 3/2 2/3 I may applicatios bearigs are subjected to variable coditios of loadig, ad bearig selectio is ofte made o the basis of maximum load ad speed. However, uder these coditios a more meaigful aalysis may be made examiig the loadig cycle to determie the weighted average load. Bearig selectio based o weighted average loadig will take ito accout variatios i speed, load ad proportio of
time durig which the variable loads ad speed occur. However, it is still ecessary to cosider extreme loadig coditios to evaluate bearig cotact stresses ad aligmet. Weighted average load Variable speed, load ad proportio time: F wt = ( T F 0/3 +...+ T F 0/3) 0.3 a where, durig each coditio i a load cycle: T = proportio of total time F = load applied = speed of rotatio, rev/mi a = assumed (arbitrary) speed of rotatio for use i bearig life equatios. For coveiece, 500 rev/mi is ormally used. Uiformly icreasig load, costat speed: F wt = [ 3 ( F max 3/3 F mi 3/3 3 F max F mi where, durig a load cycle: F max = maximum applied load F mi = miimum applied load )]0.3 Note: The above formulas do ot allow the use of the life modifyig factor for lubricatio a 3l, except i the case of costat speed. Therefore, whe these equatios are used i the bearig selectio process, the desig L 0 bearig life should be based o a similar successful machie that operates i the same eviromet. Life calculatios for both machies must be performed o the same basis. To allow for varyig lubricatio coditios i a load cycle, it is ecessary to perform the weighted average life calculatio: Weighted average life L 0wt = T + T 2 +...+ T (L 0 ) (L 0 ) 2 (L 0 ) where, durig a load cycle: T = proportio of total time L 0 = calculated L 0 bearig life (page 55) for each coditio.3.3. Ratios of bearig life to loads, power ad speeds I applicatios subjected to variable coditios of loadig, bearig life is calculated for oe coditio. Life for ay other coditio ca easily be calculated by takig the ratio of certai variables. To use these ratios, the bearig load must vary proportioally with power, speed or both. Nevertheless, this applies oly to catalog lives or adjusted lives by ay life adjustmet factors. 6
The followig relatioships i table 3-C hold uder stated specific coditios: Coditio Equatio P ) Variable load (L 0 ) 2 = (L 0 ) 0/3 Variable speed ( P 2 2 H ) ( ) Variable power (L 0 ) 2 = (L 0 ) 0/3 Variable speed ( H 2 ) Costat load (L 0 ) 2 = (L 0 ) Variable speed ( 2 ( 2) 7/3 Coditio Equatio Costat power (L 0 ) 2 = (L 0 ) Variable speed ( Variable load (L 0 ) 2 = (L 0 ) Costat speed ( P 2 2) 7/3 P ) 0/3 H ) 0/3 Variable power (L 0 ) 2 = (L 0 ) Costat speed ( H 2 Table 3-C Life ratio equatios. P = Load, torque or tagetial gear force.3.4. Life calculatio examples Combied radial ad thrust load Desig (exteral thrust,, oto bearig A) A Bearig A Bearig B Bearig A Bearig B B CALCULATING THE PERFORMANCE OF YOUR BEARINGS 3202X C A = 89600 N Y A =.39 e A = 0.43 C 90A = 23200 N =.36 Thrust coditio 0.5 x 9000 < 0.5 x 7000 + 4000.39.48 ISO method Net bearig thrust load F aa = 0.5 x 7000 + 4000.48 F aa = 6365 N F ab = Speed = 600 rev/mi Operatig temperature = 60 C Oil viscosity = VG46 0.5 x 7000.48 F ab = 2365 N Thrust codito = 4000 N = 9000 N = 7000 N 0.47 x 9000 < 0.47 x 7000 + 4000.36.44 Timke method 320X C B = 88000 N Y B =.48 e B = 0.4 C 90B = 22800 N =.44 Net bearig thrust load F aa = 0.47 x 7000 + 4000.44 F aa = 6285 N F ab = 0.47 x 7000.44 F ab = 2285 N 62
ISO method Dyamic equivalet radial load Timke method Dyamic equivalet radial load 6365 = 0.707 ea = 0.43 9000 0.707 > 0.43 P A = 0.4 x 9000 +.39 x 6365 P A = 2447 N P A = 0.4 x 9000 +.36 x 6285 P A = 247 N P B = = 7000 N P B = = 7000 N L 0 life L 0A = 0 ( 6 89600 = 20006 hours 60 x 600 2447)0/3 L 0 life L 0A = ( 23200 )0/3 x 3000 x 500 = 260 hours 247 600 L 0B = 0 ( 6 88000 = 28325 hours 60 x 600 7000)0/3 Life adjustmet for lubricatio a 3l A = 0.0438 x (6365) 0.33 x 0.830 x (600) 0.636 x (20) 0.736 = 0.95 a 3l B = 0.03874 x (2365) 0.33 x 0.690 x (600) 0.636 x (20) 0.736 =.009 L 0aA = 20006 x 0.95 = 9026 hours L 0aB = 28325 x.009 = 29480 hours L 0B = ( 22800 )0/3 x 3000 x 500 = 28054 hours 7000 600 Life adjustmet for lubricatio a 3l A = 0.0438 x (6285) 0.33 x 0.830 x (600) 0.636 x (20) 0.736 = 0.954 a 3l B = 0.03874 x (2285) 0.33 x 0.690 x (600) 0.636 x (20) 0.736 =.020 L 0aA = 260 x 0.954 = 2066 hours L 0aB = 28054 x.020 = 3065 hours 2. Static coditios 2.. Static ratig The static radial load ratig C 0 is based o a maximum cotact stress withi a o-rotatig bearig of 4,000 MPa (580,000 psi) at the ceter of cotact ad a 80 load zoe (loaded portio of the raceway). The 4,000 MPa (580,000 psi) stress level may cause visible light briell marks o the bearig raceways. This degree of markig will ot have a measurable effect o fatigue life whe the bearig is subsequetly rotatig uder a lower applicatio load. If oise, vibratio or torque are critical, a lower load limit may be required. The followig formulas may be used to calculate the static equivalet radial load o a bearig uder a particular loadig coditio. This is the compared with the static radial ratig as a criterio for selectio of bearig size. However it is advisable to cosult The Timke Compay for qualificatio of bearig selectio i applicatios where static loads prevail. 2.2. Static equivalet radial load (sigle-row bearigs) The static equivalet radial load is the static radial load (o rotatio or oscillatio) that produces the same maximum stress, at the ceter of cotact of a roller, as the actual combied radial ad thrust load applied. The equatios preseted give a approximatio to the static equivalet radial load assumig a 80 load zoe (loaded portio of the raceway) i oe bearig ad 80 or more i the opposig bearig. 63
Desig (exteral thrust,, oto bearig A) Bearig A Bearig B Bearig A Bearig B Thrust coditio Net bearig thrust load Static equivalet radial load (P 0 ) 0.47 0.47 FrB + F K ae A F aa = 0.47 F ab = 0.47 + P 0B = for F aa < 0.6 / P 0A =.6.269 F aa for F aa > 0.6 / P 0A = 0.5 + 0.564 F aa CALCULATING THE PERFORMANCE OF YOUR BEARINGS 64 0.47 > 0.47 FrB + F K ae A 2.3. Static equivalet radial load (two-row bearigs) The bearig data tables do ot iclude static ratig for tworow bearigs. The two-row static radial ratig ca be estimated as: C 0(2) = 2C 0 where: C 0(2) = two-row static radial ratig C 0 = static radial load ratig of a sigle row bearig, type TS, from the same series (refer to part umber idex o page 2) Where radial ad thrust loads are applied cosult a Timke Compay sales egieer or represetative. 3. Performace 900 (P900) bearigs P900 bearigs permit critical applicatios to be dowsized with smaller, lighter bearigs, which allow upgraded power capacity, prologed life ad icreased reliability. P900 bearigs ca improve performace of stadard bearigs by a factor of 3 or more, withi the same space. P900 products offer: Exteded life from super-clea airmelt steel Icreased load-carryig capacity from ehaced bearig geometry Improved performace i thi lubricat film eviromets due to advaced surface fiishes Techologically advaced aalytical capabilities to apply these ehacemets. For more iformatio o these ew bearig capabilities, cotact a Timke Compay sales egieer or represetative. TM = Trademark of The Timke Compay F aa = 0.47 F ab = 0.47 where: F r = applied radial load F a = et bearig thrust load. F aa ad F ab calculated from equatios. Relative life 5 4 3 2 0 Effect of P900 geometry o bearig fatigue life Stadard geometry P900 Ehaced geometry.5 Load 50% C 90 Misaligmet 0.00 Radia 3.65 4.70 00% C 90 0.002 Radia 50% C 90 0.003 Radia 4.55 200% C 90 0.004 Radia Fig. 3-5 The ehaced geometry of P900 bearigs virtually elimiates edge stress cocetratios caused by high loads or misaligmet. Relative life Effect of P900 fiish processig o bearig fatigue life 5 4 3 2 0 Stadard fiish P900 Ehaced fiish λ = Lubricat film thickess Composite surface.20 Test coditio λ =. λ = 2. for F ab > 0.6 / P 0B = 0.5 + 0.564 F ab for F ab < 0.6 / P 0B =.6.269 F ab P 0A = Note: use the values of P 0 calculated for compariso with the static ratig, C 0, eve if P 0 is less tha the radial applied, F r. 2.5 Test coditio 2 λ = 0.4 4,60 Test coditio 3 λ = 0.6 λ = 2. Fig. 3-6 The fiishig process dramatically improves rollig cotact surface fiish ad fatigue life whe limited by surface distress. It also produces superior all-aroud surface topography ad rouder rollig surfaces.
C. Torque Ruig torque - M The rotatioal resistace of a tapered roller bearig is depedet o load, speed, lubricatio coditios ad bearig iteral characteristics. The followig formulas yield approximatios to values of bearig ruig torque. The formulas apply to bearigs lubricated by oil. For bearigs lubricated by grease or oil mist, torque is usually lower although for grease lubricatio this depeds o amout ad cosistecy of the grease. The formulas also assume the bearig ruig torque has stabilized after a iitial period referred to as ruig-i.. Sigle row Desig (exteral thrust,, oto bearig A) Bearig A Bearig B Bearig A Bearig B Thrust coditio 0.47 0.47 FrB + F K ae A Net bearig thrust load F aa = 0.47 + KB a) F aa > 2 f = F aa f 2 = f + 0.8 M A = k G A (µ) 0.62 ( f )0.3 F ab = 0.47 b) 0.47 < F aa 2 f, f 2 : use graph page 67 c) F aa = 0.47 f = 0.06 f 2 =.78 M A = k G A (µ) 0.62 ( 0.06F aa)0.3 2 f = 0.06 f 2 =.78 M B = k G B (µ) 0.62 ( 0.06F ab)0.3 0.47 > 0.47 FrB + F K ae A F aa = 0.47 a) F ab > 2 M B = k G B (µ) 0.62 ( f )0.3 F ab = 0.47 f = F ab f 2 = f + 0.8 2 b) 0.47 < F ab 2 f, f 2 : use graph page 67 c) F ab = 0.47 f = 0.06 f 2 =.78 f = 0.06 f 2 =.78 M B = k G B (µ) ( 0.62 0.06F ab)0.3 M A = k G A (µ) ( 0.62 0.06F aa)0.3 M A or M B will uderestimate ruig torque if operatig speed < k 2 ( G2µ K f 2 F r) 2/3 65
2. Double row Desig (exteral thrust,, oto bearig A) B B F rc Bearig A Bearig B Bearig A Bearig B Bearig C a) Fixed positio Load coditio Radial load o each row F r > 0.47 B Bearig B is uloaded K > 2 B M A = k G A (µ) 0.62 x ( ) 0.3 = B F aa = f = K B f 2 = f + 0.8 0.47 K 2 B 2( M A = k G A (µ) 0.6 f B)0.3 K f, f 2 : use graph page 67 CALCULATING THE PERFORMANCE OF YOUR BEARINGS 66 0.47 B b) Floatig positio = FrAB +.06 K F 2 ae = FrAB.06 K F 2 ae M C = 2 k G C (µ) ( 0.62 0.030 F rc)0.3 K C M A will uderestimate ruig torque if operatig speed < k 2 ( f 2 )2/3 G 2 µ K M AB will uderestimate ruig torque if operatig speed < k 2 (.78 )2/3 G 2 µ K M C will uderestimate ruig torque if operatig speed < k 2 ( 0.890 F rc)2/3 G 2 µ K C M = k G (µ) 0.62 ( 0.060 (FrA )0.3 0.3 + F 0.3 rb ) K M = ruig torque, N.m (lbf.i) F r = radial load, N (lbf) G = geometry factor from bearig data tables G 2 = geometry factor from bearig data tables K = K-factor = speed of rotatio, rev/mi k = 2.56 x 0 6 (metric) or 3.54 x 0 5 (ich) k 2 = 625 (metric) or 700 (ich) µ = lubricat dyamic viscosity at operatig temperature cetipoise. For grease use the base oil viscosity (fig 3-8). f = combied load factor (fig. 3-7) f 2 = combied load factor (fig. 3-7)
2.8 2.6 2.4 2.2 Combied load factors, f ad f2 2.0.8.6.4.2 f 2 f.0 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8.0.2.4.6.8 2.0 KFa/Fr Load coditio f ad f 2 KF a /F r > 2.0 f = KF a /F r f 2 = f + 0.8 0.47 KF a / F r 2.0 Use graph above KF a /F r = 0.47 f = 0.06 f 2 =.78 Fig. 3-7 Determiatio of combied load factors f ad f 2. 67
0000 7500 5000 4000 3000 2000 000 750 500 400 300 CALCULATING THE PERFORMANCE OF YOUR BEARINGS Dyamic viscosity, mpa.s (cetipoise, cp) 200 50 00 80 60 50 40 30 25 20 8 6 4 2 0 9 8 7 6 5 4.5 4 3.5 3 30 40 50 60 70 80 90 00 0 20 C 80 00 20 40 60 80 200 220 240 F Temperature 500 000 680 Fig. 3-8 Viscosities i mpa.s (cetipoise, cp) for ISO/ASTM idustrial fluid lubricat grade desigatios. Assumes: Viscosity Idex 90; Specific Gravity 0.875 at 40 C. 22 32 460 320 220 50 00 68 46 ISO/ASTM viscosity grade 68