Machine Design Databook Episode 3 part 2 ppsx

DESIGN OF BEARINGS AND TRIBOLOGY 23.55 DESIGN OF BEARINGS AND TRIBOLOGY Particular Formula 19 13 11 Average 800 15 Well ventilated 900 17 1000 (a) Thin shell not attached to radiating mass 10 20 30 40 50 60 70 k(tb ta), ft-ibf/min/in2/ F 21 90 - Average industrial bearing, unventilated - Well ventilated bearing 700 600 500 400 300 80 - Thin shell not attached to large radiating mass 200 100 (b) 0 20 40 60 80 100 120 140 160 Temperature rise (tb ta) FIGURE 23-45 The rate of heat dissipated from a journal bearing Hd ẳ T ỵ 18ị2 ðLdÞ 427k Customary Metric ð23-80cÞ where Hd in kcal/s, ðLdÞ in m , ÁT in 8C values of k are as given inside parentheses under Eq (23-80a) for US customary system units and values of k for customary metric units also given under Eqs (23-80a) and (23-80b) The difference in temperature (ÁT) of the bearing and of the cooling medium can be found from the equation The difference between the bearing-wall temperature tb and the ambient temperature ta , for three main types of lubrication by oil bath, by an oil ring, and by waste pack or drop feed BEARING CAP The bearing cap thickness T ỵ 18ị2 ẳ K Pv SI ðMetricÞ ð23-81Þ where P in N/m (kgf/mm ), v in m/s, and ÁT in K (8C) 2 K ¼ 0.475 (4:75  106 ) for bearings of light construction located in still air ¼ 0.273 (2:7  106 ) for bearings of heavy construction and well ventilated ¼ 0.165 (1:65  106 ) for General Electric Company’s well-ventilated bearing   t0 À tb Refer to Fig 23-46 for tb À ta ’ hc ¼ rffiffiffiffiffiffiffiffiffiffi 3Wa 2L Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð23-82Þ DESIGN OF BEARINGS AND TRIBOLOGY 23.56 CHAPTER TWENTY-THREE Particular Formula Drop feed ga vin ir Mo air Sti ir ll a ir Oil bath St 40 Mo ving Stil l r 50 Oil ring ill a 60 Moving air Oil film temperature rise above ambient, to ta, C 70 30 20 10 0 10 20 30 Temperature rise of wall above ambient tb ta, C 40 The deflection of the cap The thickness of cap from Eq (23-71) FIGURE 23-46 Relation between oil film temperature and bearing wall temperature y¼ Wa3 4ELh3 c 23-83ị s W hc ẳ 0:63a ELy ð23-84Þ where the deflection should be limited to 0.025 mm (0.001 in) EXTERNAL PRESSURIZED BEARING OR HYDROSTATIC BEARING: JOURNAL BEARING (Fig 23-47) The pressure in the lower pool of quadrant (Fig 23-47) P1 ẳ K1 Po 23-85aị where K1 ẳ 1ỵ   Po P0    ỵ 2:121" ỵ 1:93" 0:589" ð23-85bÞ Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY Particular 23.57 Formula L l1 l1 Oil pocket hmax b w d e hmin t h e Hydraulic resistance Constant pressure oil manifold (a) Oil inlet hole (b) Ps Oil inlet l1 (c) FIGURE 23-47 (a) and (b) schematic diagram of a full cylindrical hydrostatic bearing; (c) oil pressure distribution along the bearing [Shaw and Macks10 ] The pressure in the upper pool of quadrant (Fig 23-47) P ẳ K3 P o 23-86aị where K3 ẳ 1ỵ   Po P0    ỵ 2:121" ỵ 1:93"2 ỵ 0:589"3 23-86bị The pressure in the left pool of quadrant (Fig 23-47) P ¼ K2 P o where   P0 K2 ẳ 6:283 ỵ 3:425"2 ị Po The pressure in the right pool of quadrant (Fig 23-47) The flow of lubricant through the lower quadrant of the bearing from the manifold P ¼ K4 P o where   P0 K4 ẳ 6:283 ỵ 3:425"2 ị Po 23-87aị 23-87bị 23-88aị 23-88bị Q1 ẳ d P1 CPF1 96l1 23-89aị where CPF1 ẳ  2:121" ỵ 1:93"2 0:589"3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð23-89bÞ DESIGN OF BEARINGS AND TRIBOLOGY 23.58 CHAPTER TWENTY-THREE Particular The flow of lubricant through the left quadrant of the bearing from the manifold Formula Q2 ¼ d P2 C 768l1 PF2 23-90aị where CPF2 ẳ 6:283 ỵ 3:425"2 The flow of lubricant through the upper quadrant of the bearing from the manifold 23-90bị Q3 ẳ d P3 CPF3 48l1 23-91aị where CPF3 ẳ The ow of lubricant through the right quadrant of the bearing from the manifold  ỵ 2:121" ỵ 1:93"2 ỵ 0:589"3 23-91bị Q4 ẳ d P4 C 768l1 PF4 23-92aị where CPF4 ẳ CPF2 ẳ 6:283 ỵ 3:425"2 The total flow of lubricant through quadrant of the bearing from the manifold assuming P2 ¼ P4 ¼ P0 (good approximation) 23-92bị Q ẳ Q1 ỵ Q2 ỵ Q3 ỵ Q4 23-93aị Qẳ d Po G 48l1 23-93bị where G ¼ flow factor given by Eq (23-94) The flow factor in Eq (23-81b) G ẳ CPF1 K1 ỵ CPF2 K2 ỵ CPF4 K4 ị ỵ CPF3 K3 ẳ CPF1 K1 ỵ CPF2 K2 ỵ CPF3 K3 23-94ị since K2 ẳ K4 and CPF2 ẳ CPF4 The external load on the hydrostatic journal bearing     A0 A0 W ẳ P1 P3 ị A ỵ ẳ Po A ỵ FPFW 2 23-95ị where FPFW ¼ load factor given by Eq (23-95) The load factor FPFW ẳ K1 K3 23-96ị The pressure ratio connecting the dimensions of the bearing and its external resistances    Po d c lc ẳ1ỵ6 P0 dc dc l1 ð23-97Þ Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY Particular 23.59 Formula IDEALIZED SLIDER BEARING (Fig 23-48) Plane-slider bearing The pressure at any point x w U zy x x F x h L B FIGURE 23-48 Plane slider bearing with an angle of inclination The load carrying capacity U C B s1 where Pẳ Cs1 ẳ ẳ Wẳ 23-98aị 6x1 ð1 À x1 Þ ð À 2aÞða À  ỵ x1 ị2 h2 h1 ; B aẳ h2 ; B x1 ẳ 23-98bị x B 23-98cị 6UL Cs2 2 23-99aị where Cs2 ẳ ln The resultant shear stress at any point along the slider (Fig 23-48) ¼ aÀ 2 ỵ a 2a  U C B s3 23-100aị where   Ba  ỵ x1 ị 2y Cs3 ẳ B  3a  ỵ x1 À 2ax1 Þ Â ð À 2aÞða À  þ x2 Þ3  þ a À  þ x1 The shear stress at any point on the surface of the moving member of the bearing (i.e., slider at y ¼ 0) (Fig 23-48) U C B s4 where m ẳ Cs4 ẳ 23-99bị 23-100bị 23-101aị 6aa ị a  ỵ x1 2a ịa  ỵ x1 ị2 23-101bị The shear stress at any point on the surface of the stationary member of the bearing (i.e., shoe at y ¼ h) (Fig 23-48) U C B s5 where s ¼ Cs5 ¼ ¼ 23-102aị 6aa ị a  ỵ x1 2a ịa  ỵ x1 ị2 h2 h1 B and h ẳ Ba  ỵ x1 Þ Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð23-102bÞ DESIGN OF BEARINGS AND TRIBOLOGY 23.60 CHAPTER TWENTY-THREE Particular The frictional force on the moving member of the bearing (i.e., slider) Formula Fm ¼ ULCs6 where Cs6 ¼ À ln  The frictional force on the stationary member of the bearing (i.e., shoe) The distance of the pressure center from the origin of the coordinates, i.e., from the lower end of the shoe (Fig 23-48) aÀ a  À 2a À  Fs ¼ ULCs7 where Cs7 ¼ ln  The coefficient of friction  ð23-103aÞ  aÀ ð23-103bÞ ð23-104aÞ  ð23-104bÞ 2a À    aÀ À2ð2a À Þ ln 32 Fm a   ẳ 23-105ị ẳ a W 32a ị ln ỵ 6 a   a 2:52 ỵ 3a7 a Þð3a À Þ 6 a   7B " x¼6 aÀ À 2 ð À 2aị ln a ỵ 23-106ị Pivoted-shoe slider bearing (Fig 23-48 and Fig 23-52) The load-carrying capacity W¼ 6ULB2 CPW h2 23-107aị where CPW ẳ ln1 ỵ qị qq ỵ 2ị q2 23-107bị Refer to Table 23-17 for CPW The frictional force on the moving member of the bearing (i.e., slider) FmP ¼ ULB CPFm h2 23-108aị where CPFm ẳ ln1 ỵ qị q 2ỵq 23-108bị Take CPFm from Table 23-17 for various values of q The frictional force on the stationary member of the bearing (i.e., shoe) FsP ¼ ULB CPFs h2 23-109aị where ỵ qịa CPFs ẳ ln ỵ q 2ỵq Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð23-109bÞ DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY Particular The coefficient of friction 23.61 Formula ¼ FmP h2 ¼ W B  CPFm CPW  ¼ h2 C B P 23-110ị where CP ẳ coefficient of friction factor The distance of the pivoted point from the lower end of the shoe (Fig 23-39), i.e., the distance of the pressure center from the origin of the coordinates Take CP from Table 23-17 for various values of q   ð1 þ qÞð3 þ qÞ lnð1 þ qÞ À qð2:5q þ 3ị " xẳ B qq ỵ 2ị ln1 ỵ qị À 2q2 ð23-111Þ " The ratios x=B are taken from Table 23-17 DESIGN OF VERTICAL, PIVOT, AND COLLAR BEARING Pivot bearing (Figs 23-49, 23-50, and 23-53) FLAT PIVOT The total axial load on the flat pivot with extreme diameters of the actual contact d1 and d2 W ¼ p 2 d1 À d2 The friction torque based on uniform intensity of pressure with extreme diameters of the actual contact d1 and d2 Mt ¼ W The friction torque based on uniform wear with extreme diameters of the actual contact d1 and d2 Mt ¼ W The power absorbed by friction with d as the diameter of at pivot bearing 23-112ị P ẳ w w d1 ỵ d2 ð23-114Þ W dn 189;090 USCS ð23-115bÞ where P in hp, W in lbf, d in in, and n in rpm Oil Oil groove Radial oil groove ð23-113Þ W dn0 SI ð23-115aÞ 478 where P in kW, W in N, d in m, and n0 in rps P ¼ d (a) 3 d1 À d2 2 d1 À d2 d (b) FIGURE 23-49 Pivot thrust bearing CONICAL PIVOT The friction torque based on uniform intensity of pressure with extreme diameters of the actual contact d1 and d2 The friction moment which resists the rotation of the shaft in a conical pivot bearing for uniform wear The loss of power in vertical bearing 3 W d1 À d2 À d2 sin d1 where ẳ cone angle of pivot, deg W d1 ỵ d2 Mt ¼ sin Mt ¼ P ¼ 6:2  108 d Ln02 SI ð23-116Þ ð23-117Þ ð23-118aÞ where P in kW,  in Pa s, d and L in m, and n0 in rps Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY 23.62 CHAPTER TWENTY-THREE Particular Formula P ¼ 2:35  10À4 1 d Ln2 Customary Metric ð23-118bÞ where P in hpm, 1 in cP, d and L in cm, and n in rpm  d Ln2 P ẳ 2:35 107 Customary Metric 23-118cị where P in hpm, 1 in cP, d and L in mm, and n in rpm 0 d Ln2 P ¼ 2:35  106 Customary Metric ð23-118dÞ where P in hpm, 0 in kgf s/m2 , d and L in m, and n in rpm 0 d Ln2 P ¼ 2:35  10À3 If the journal and the bearing are eccentric and the distance between their axes is ", the power loss is calculated from formula Customary Metric ð23-118eÞ where P in hpm, 0 in kgf s/m2 , L and d in mm, and n in rpm 3:8 1 d Ln2 P ẳ USCS 23-118f ị where P in hp, 1 in cP, d and L in in, and n in rpm 6:2  108 d Ln02 q P ẳ SI 23-119aị 2"ị2 where P in kW,  in Pa s, d and L in m, and n0 in rps 1 d Ln2 P ẳ 2:35 107 q 2"ị2 Customary Metric ð23-119bÞ where P in hpm, 1 in cP, d and L in mm, and n in rpm 0 d Ln2 P ¼ 2:3  106 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi À ð2"Þ2 Customary Metric ð23-119cÞ where P in hpm, 0 in (kgf s/m2 ), d and L in m, and n in rpm 3:8  d Ln2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ¼ q1 USCS ð23-119dÞ 10 À ð2"Þ2 where P in hp, 1 in cP, L and d in in, and n in rpm Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY Particular 23.63 Formula Collar bearing (Fig 23-51) The average intensity of pressure with i collars The friction moment for each collar for uniform intensity of pressure The total friction moment for i collars for uniform intensity of pressure The friction moment for each collar for uniform rate of wear The total friction moment for i collars for uniform rate of wear The friction power in collar bearing Oil in W 2 0:784ðd1 À d2 Þi  3 W d1 À d2 Mte ¼ 2 i d1 À d2  3 d1 À d2 Mt ¼ W 2 d1 d2   W d1 ỵ d2 Mte ẳ i   d1 ỵ d2 Mt ẳ W Pẳ P ẳ 23-120ị 23-121ị 23-122ị 23-123ị 23-124ị Wd1 ỵ d2 ịn0 2;292;296 SI 23-125aị where P in kW, W in N, d in m, and n0 in rps w d P ¼ FIGURE 23-50a Collar thrust bearing Oil in The coefficient of friction for collar bearing w The coefficient of friction for collar bearing Wðd1 þ d2 Þn 252;120 USCSU ð23-125bÞ where P in hp, W in lbf, d in in, and n0 in rpm  ẳ 83:8 v0:5 p0:67 SI 23-126aị where v in m/s and P in N/m2  ¼ 0:016 v0:5 p0:67 USCS ð23-126bÞ where v in ft/min and P in psi d2 d1 FIGURE 23-50b Plain thrust bearing Allowable pressure P may be taken so that Pv value for v ranging from 0.20 to m/s (50 to 200 ft/min)  ¼ 1:73  10À3 v0:5 p0:67 Customary Metric ð23-126cÞ where v in m/s and P in kgf/mm2 Pv 707;505 SI ð23-127aÞ where P in Pa and v in m/s Pv Customary Metric ð23-127bÞ 0:0715 where P in kgf/mm and v in m/s Pv 20;000 USCS where P in psi and v in ft/min Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð23-127cÞ DESIGN OF BEARINGS AND TRIBOLOGY 23.64 CHAPTER TWENTY-THREE Particular Formula PLAIN THRUST BEARING (Fig 23-50b) 2 W ẳ K1 d1 d2 ị Recommended maximum load SI USCSị 23-128ị where K1 ẳ 0:3 ð48Þ, W in N (lbf), d1 and d2 in mm (in)   d ỵ d2 SI USCSUị 23-129ị nW P  ¼ K2 Approximate power loss in bearing where K2 ¼ 70  10À6 ¼ ð11  10À6 Þ P in W (hp), n0 in rps, and W in N (lbf) Q ¼ K3 P Lubrication flow rate to limit lubricant temperature rise to 208C SI USCSUị 23-130ị where K3 ẳ 0:03 10 (0.3), Q in m3 /s (q.p.m), and P in W s (hp) Thrust bearing Parallel-surface thrust bearing (Figs 23-51 to 23-52) Refer to Table 23-8 for P and Table 23-6 for Pv values The pressure at any point along the bearing P¼ 6UB KLP1 h2 where KLP1 ¼ 0 ¼ x1 lnẵ0 1ịx1 ỵ 1ị ln 0 2 x ;x ¼ 1 B ω w y x w y z ωr r z ω x (a) U x h d ð23-131aÞ B (b) FIGURE 23-51 Parallel-surface thrust bearing Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð23-131bÞ DESIGN OF BEARINGS AND TRIBOLOGY 23.80 CHAPTER TWENTY-THREE Particular Formula TABLE 23-32 Coefficient of friction  for rolling contact bearings TABLE 23-33 Safe working values of k for average bearing life Type of bearing  Material k  106 Self-aligning bearings Cylindrical roller bearings Thrust ball bearings Angular contact ball bearings Deep groove ball bearings Tapered roller bearings Spherical roller bearings Needle bearings 0.0016–0.0066 0.0012–0.0060 0.0013 0.0018–0.0019 0.0022–0.0042 0.0025–0.0083 0.0029–0.0071 0.0045 For un-hardened steel 3.80 For hardened alloy steel on flat races 6.89 For hardened carbon steel 4.80 For hardened carbon steel on grooved 10.34 races For hardened alloy steel grooved races 13.79 (having radius ¼ 0.67 ) USCSU* 550 1000 700 1500 2000 * US customary system units The equation for friction torque Mt ¼ Fr d ð23-149gÞ For values of , refer to Table 23-32 ROLLING ELEMENTS BEARINGS Definition, Dimensions and Nomenclature For nomenclature, other details and definition of a ball bearing Refer to Fig 23-49 For nomenclature, other details and definition of a taper roller bearing Refer to Fig 23-50 A rule of thumb used for ordinary ball and straight roller bearings    d ỵD n 8:33 where d, D in m and n0 in rps  d ỵD n 500;000 23-150aị 23-150bị where d, D in mm and n in rpm SPEED Effective speed The effective speed which determines the life of the bearing is found from the relation n ẳ n1 ặ n2 23-151ị where the plus sign is used when the races rotate in opposite directions and the minus sign is used when the races rotate in the same direction Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY Width 23.81 Snap ring groove Corner radius Seal or shield groove Shoulders Seal or shield notch Corner radius Inner ring raceway Outside diameter Bore Inner ring Inner ring land Separator Inner ring face Outer ring raceway Outer ring land Outer ring face Outer ring FIGURE 23-49 Ball bearing nomenclature (Courtesy: New Departure-Hyatt Bearing Division, General Motors Corporation.) Cup back face radius, r Bearing width Cup length Cup back face Cone back face rib Cage Cone back face Cone front face rib Cone length Cone bore Cup outside diameter Cup front face radius Cup front face Cone front face radius Cone Cone front face Roller Cone back face radius Cup Standout FIGURE 23-50 Nomenclature of tapered roller bearing Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY 23.82 CHAPTER TWENTY-THREE Particular Formula Limiting bearing speed The limiting bearing speed when the bearing outside diameter is less than 30 mm nl ¼ The limiting bearing speed when the bearing outside diameter is 30 mm and over nl ¼ Kn D À 10 For values of Kn refer to Table 23-34 23-153ị Feffg ẳ fk fd F 23-154ị 3Kn D ỵ 30 23-152ị GEAR-TOOTH LOAD The effective tooth load which is used in design of bearings The shaft load due to belt drive which is used in design of bearings For values of fk and fd refer to Table 23-35 Fbs ẳ fF 23-155ị For values of f refer to Table 23-35 TABLE 23-34 Values of Kn to be used in Eqs (23-l52) and (23-153) Constant, Kn Type of bearing Radial bearings Deep groove bearings Single row Single row with leeds Double row Magneto bearings Angular contact ball bearing Single row Single row paired Double row Self-aligning ball bearings Self-aligning bail bearings with extended inner ring Cylindrical roller bearing Single row Double row Tapered roller bearings Barrel roller bearings Spherical roller bearings Series 213 Thrust bearings Thrust ball bearings Angular contact thrust ball bearings Cylindrical roller thrust bearings Spherical roller thrust bearings Grease lubrication Oil lubrication 500,000 360,000 320,000 500,000 630,000 — 400,000 630,000 500,000 400,000 360,000 500,000 250,000 630,000 500,000 450,000 630,000 320,000 500,000 500,000 320,000 220,000 220,000 630,000 630,000 400,000 280,000 280,000 140,000 220,000 90,000 140,000 200,000 320,000 120,000 200,000 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY Particular 23.83 Formula TABLE 23-35 Value of factors fk , fd and f to be used in Eqs (23-154) and (23-155) Tooth load Particular fk Gear drive Precision gears (errors in pitch and form less than 0.025 mm) Commercial gears (errors in pitch and form 0.025 mm to 0.125 mm) fd Shaft load f 1.05–1.1 1.1–1.3 Prime movers and driven machines Shock-free rotary machines e.g electrical machines and turbo-compressors Reciprocating engines, according to the degree of balance Machinery subjected to heavy shock loading, such as rolling mills 1.0–1.2 1.2–1.5 1.5–3.0 Belt drive Vee-belts Single leather belts with jockey pulleys Single leather belts, balata belts, rubber belts 2.0–2.5 2.5–3.0 4.0–5.0 Full ball bearing sizes of different bearing series Refer to Fig 23-51 For summary of types and characteristics of rolling contact bearing9 Refer to Fig 23-52 Extra light series Light series Medium series Extra light series Light Medium series series (100) (200) (300) (100) (200) Relative proportions of bearings with same outside diameter (300) Relative proportions of bearings with same bore diameter FIGURE 23-51 Ball bearing size of bearing series (Courtesy: New Departure-Hyatt Bearing Division, General Motors Corporation.) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY 23.84 CHAPTER TWENTY-THREE Particular Formula STATIC LOADING Stribeck equation for permissible static load Fc ẳ kdb 23-156ị where k ¼ 686:5  106 (100)* for carbon steel balls ¼ 862  106 (125)* for hardened alloy steel balls Use a factor of safety of 10 Fc in N (lbf) and db in m (in) Stribeck equation for permissible static load for ball bearing Fc ¼ The radial load capacity of ball bearing 4:37Fr Z Fr ¼ kZdb 4:37 where db in m and Fr , Fc in kN Refer to Table 23-33 for values of k kZdb Refer to Table 23-33 for values of k Fr ¼ Radial load capacity of roller bearing BASIC STATIC LOAD RATING AS PER INDIAN STANDARDS ð23-157Þ ð23-158Þ ð23-159Þ kZldr 23-160ị where k ẳ 48:3 106 (7.0)* for hardened carbon steel ¼ 69  106 (10.0)* for hardened alloy steel ¼ 690  106 (100)* for carbon steel balls l, dr in m (in) and Fr in N (lbf) Fr ¼ Radial ball bearing The basic static radial load rating for radial ball bearing Cor ¼ fo iZD2 cos w ð23-161Þ where Cor in N and Dw in mm Refer to Table 23-36 for fo This formula is applicable to bearings with a crosssectional raceway groove radius not larger than 0:52Dw in radial and angular contact groove ball bearing inner rings and 0:53Dw in radial and angular contact groove ball bearing outer rings and selfaligning ball bearing inner rings The static equivalent load for radial ball bearings is greater of the two values given by the formulae Por ẳ Xo Fr ỵ Yo Fa 23-162ị Por ẳ Fr ð23-163Þ For values of Xo and Yo refer to Table 23-37 * Values outside the parentheses are in SI units in Pd and inside the parentheses are in US customary system units in kpsi Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Yes Load Carring Capacity For Use on Free-end Yes One direction only Excellent Good Contact angle 15 , 30 , 40 , Two bearings are usually mounted in opposition Clearance adjustment is necessary Yes Yes∗ Yes Duplex Angular Contact Ball Bearings Yes∗ Fair Two directions Poor Yes∗ Yes∗ Yes Yes Self Aligning Ball Bearings Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website × × Impossible Yes∗ Yes∗ Yes∗ Yes × Yes × × Yes Yes Yes Cylindrical Cylindrical Double Row Cylindrical Roller Cylindrical Roller Roller Bearings Roller Bearings Bearings with Bearings Angle Ring FIGURE 23-52 Types and characteristics of rolling bearings (Courtesy: NSK Corp.) * Can be used as free-end bearings if tap fit allows axial motion Legend Remarks Tapered Bore of Inner Ring Yes∗ For Use on Fixed-end Ring Separability Self-Aligning Capability Angular Misalignment Rigidity Low Noise and Torque High Accuracy High Speeds Combined Load Axial Load Radial Load Two bearings are usually mounted in opposition Double Row Angular Contact Ball Bearings Any arrangement of the pair is possible Features Angular Contact Ball Bearings Yes Yes × × Needle Roller Bearings Yes Tapered Roller Bearings Two bearings are usually mounted in opposition Clearance adjustment is necessary Magneto Bearings Yes Spherical Roller Bearings Yes Yes Double Row Tapered Roller Bearings Yes∗ Yes Yes∗ Yes Angular Contact Thrust Ball Bearings × × Yes Yes Yes × × Yes × × × × × × Thrust Ball Bearings with Aligning Seats Thrust Ball Bearings Yes × × × Cylindrical Roller Thrust Bearings Needle roller thrust bearings are available Deep Groove Ball Bearings Yes × × × Tapered Roller Thrust Bearings Yes Yes Spherical Roller Thrust Bearings This type should have oil lubrication Bearing Type DESIGN OF BEARINGS AND TRIBOLOGY 23.85 DESIGN OF BEARINGS AND TRIBOLOGY 23.86 CHAPTER TWENTY-THREE Particular Formula Radial roller bearing The basic static radial load rating for radial roller bearings The static equivalent radial load for roller bearings with 6¼ 08 is the greater of the two values given by the formulae The static equivalent radial load for radial roller bearings with ¼ 08 and subjected to radial load only, is given by the formula   D Cor ¼ 44 À we cos iZLwe Dwe cos Dpw 23-164ị Por ẳ Xo Fr ỵ Yo Fo 23-165ị For factors Xo and Yo refer to Table 23-38 Por ¼ Fr 23-166ị Coa ẳ fo ZD2 sin w 23-167ị THRUST BEARINGS Ball bearings The basic static axial load rating for single- or doubledirection thrust ball bearings where fo values are taken from Table 23-36 Z ¼ number of balls carrying load in one direction The static equivalent axial load Poa for thrust ball bearing with contact angle 6¼ 908 The static equivalent axial load for thrust ball bearings with ¼ 908 is given by the equation Poa ẳ Fa ỵ 2:3Fr tan ð23-168Þ This formula is valid for all ratios of radial load to axial load in the case of double-direction bearings For single direction bearings it is valid where ðFr =Fa Þ 0:44 cot and gives satisfactory but less conservative values of Poa for ðFr =Fa Þ up to 0:67 cot Poa ẳ Fa for ẳ 908 23-169ị Roller bearings The basic static axial load rating for single- and double-direction thrust roller bearings   D cos ZLwe Dwe sin Coa ẳ 220 we DPW 23-170ị where Z ¼ number of rollers carrying load in one direction The static equivalent axial load for thrust roller bearings with contact angle 6ẳ 908 Poa ẳ Fa ỵ 2:3Fr tan ð23-171aÞ This formula is valid for all ratios of radial load to axial load in the case of double-direction bearings For single-direction bearings, it is valid where ðFr =Fa Þ 0:44 cos and gives satisfactory but less conservative values of Poa for ðFr =Fa Þ up to 0:67 cot Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY 23.87 TABLE 23-36 Values of factor fo for radial ball bearingsa Factor fo Radial ball bearings Dw cos Dpw Radial and angular contact groove ball bearings Self-aligning ball bearings Thrust ball bearings 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 14.7 14.9 15.1 15.3 15.3 15.7 15.9 16.1 16.3 16 1.9 2 2.1 2.1 2.1 2.2 2.2 2.3 2.3 61.6 60.8 59.9 59.1 58.3 57.5 56.7 55.9 55.1 54.3 0.10 0.11 0.12 0.13 0.14 16.4 16.1 15.9 15.6 15 2.4 2.4 2.4 2.5 2.5 53.5 52.7 51.9 51.2 50.4 0.15 0.16 0.17 0.18 0.19 15.2 14.9 14.7 14.4 14.2 2.6 2.6 2.7 2.7 2.8 49.6 48.8 48.0 47.3 46.5 0.20 0.21 0.22 0.23 0.24 14.0 13.7 13.5 13.2 13.0 2.8 2.8 2.9 2.9 3.0 45.7 45.0 44.2 43.5 42.7 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 12.8 12.5 12.3 12.1 11.8 11.6 11.6 11.2 10.9 10.7 10.5 3.0 3.1 3.1 3.2 3.2 3.3 3.3 3.4 3.4 3.5 3.5 41.9 41.2 40.5 39.7 39.0 38.2 37.5 36.8 36.0 35.3 34.6 0.36 0.37 0.38 0.39 0.40 10.3 10.0 9.8 9.5 9.4 3.6 3.6 3.7 3.8 3.8 a The Table 23-36 is based on the Hertz’s point contact formula with a modulus of elasticity Eị ẳ 2:07 105 mPa and a Poisson’s ratio () of 0.3 It is assumed that the load distribution for radial ball bearings results in a maximum ball load of (5Fo =Z cos ), and for thrust ball bearings (Fo =Z sin ) Values of fo for intermediate values of (Dw cos =Dpw ) are obtained by linear interpolation (IS: 3823-1988, ISO: 76-1987) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY 23.88 CHAPTER TWENTY-THREE Particular Formula TABLE 23-37 Values of factors Xo and Yo for radial ball bearingsa for use in Eqs (23-162) Single row bearings Double row bearings Xo Yo Xo Yo Angular-contact groove ball bearings ¼ 158 ¼ 208 ¼ 258 ¼ 308 ¼ 358 ¼ 408 ¼ 458 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.46 0.42 0.38 0.33 0.29 0.26 0.22 0.6 1 1 1 0.5 0.92 0.84 0.76 0.66 0.58 0.52 0.44 Self-aligning ball bearings 6¼ 908 0.5 0.22 cot 0.44 cot Bearing type Radial contact groove ball bearings a Permissible value of Fa =Cor depends on bearing design (internal clearance and raceway groove depth) TABLE 23-38 Values of factors Xo and Yo for radial roller bearings with 6¼ 08 for use in Eq (23-165) Bearing type Xo Yo Single-row Double-row 0.5 1.0 0:22 cot 0:44 cot The static equivalent axial load for thrust roller bearings with ¼ 908 is given by the equation Poa ¼ Fa ð23-171bÞ C o ¼ fs P o ð23-172Þ CATALOGUE INFORMATION FROM FAG FOR THE SELECTION OF BEARING The basic static load rating where fs ¼ index of static dressing ¼ 1:5 to 2.5 for high degree ¼ 1:0 to 1.5 for normal degree ¼ 0:7 to 1.0 for moderate degree The equivalent static load Po ¼ Fr for ðFa =Fr Þ 0:8 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð23-173aÞ DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY Particular 23.89 Formula Po ẳ 0:6Fr ỵ 0:5Fa for Fa =Fr ị > 0:8 P o ẳ Xo Fr ỵ Yo Fa 23-173bị 23-173cị where Co and Po in kN For various values of factors Xo and Yo refer to Table 23-39 and Tables from FAG catalogue TABLE 23-39 Calculation of equivalent static and dynamic load Series Bearing type IS FAG SKF Static, Po Dynamic, P For dimensions, C, Ca , nmax , X, e Y, Yo refer to Table Deep groove ball bearings 02 03 04 62 63 64 62 63 64 Fr when Fa =Fr 0:8 0:6Fr ỵ 0:5Fa when Fa =Fr > 0:8 Fr when Fa =Fr e 0:56Fr ỵ YFa when Fa =Fr > e 23-60 23-61 23-62 Self aligning ball bearings 02 03 12 13 22 23 12 13 22 23 Fr ỵ Yo Fa XFr ỵ YFa 02 03 72B 73B 72B 73B 33 33A Fr when Fa =Fr 1:9 0:50Fr ỵ 0:26Fa when Fa =Fr >1.9 Fr þ 0:58Fa Fr when Fa =Fr 1:4 0:35Fr þ 0:57Fa when Fa =Fr > 1:14 Fr ỵ 0:66Fa when Fa =Fr 0:956 0:6Fr ỵ 1:07Fa when Fa =Fr > 0:95 23-69 N2 N3 N4 NU22 NU23 N2 N3 N4 NU22 NU23 Fr Fr 23-70 23-71 23-72 23-73 23-74 322A 22 23 322 02 03 Fr when Fa =Fr Yo 0:5Fr ỵ Yo Fa when Fa =Fr > Yo Fr when Fa =Fr e 0:4Fr ỵ YFa when Fa =Fr > e 11 12 13 14 511 512 513 514 511 512 513 514 Fa Fa 522 522 Single row angular contact ball bearings Double row angular contact ball bearings Cylindrical roller bearings 02 03 04 Tapered roller bearings Single thrust ball bearings Double thrust ball bearings Equivalent load 23-63 23-64 23-65 23-66 23-67 23-68 23-75 23-76 23-76B 23-77 23-78 23-79 23-80 23-81 23-82 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY 23.90 CHAPTER TWENTY-THREE Particular Formula DYNAMIC LOAD RATING OF BEARINGS The relation between two groups of identical bearings tested under different loads F1 and F2 , and length of lives L1 and L2 respectively as per experiments conducted by Palmgern L1 ¼ L2  F2 F1  m 23-174ị where m ẳ generally accepted ẳ 3.333 used by Timken ¼ used by New Departures L ¼ life in millions of revolutions ¼ life in hours at constant speed in rpm For various typical values of bearing life for various applications Refer to Tables 23-40 and 23-41 LIFE   m The Antifriction Bearing Manufacturers Association (AFBMA) statistically related formula for the rating life of bearing in millions of revolutions of a bearing subjected to any other load F, which is derived from Eq (23-174) For values of C for various types of bearings, refer to Table 23-42 Equation (23-175) can be written as C ¼ FL1=m (The International Organisation for Standardisation (ISO) defines the rating life of a group of apparently identical rolling elements bearings as that completed or exceeded by 90% of that group before rst evidence of fatigue) Lẳ C F 23-175ị ð23-176Þ where L in millions of revolutions BASIC DYNAMIC LOAD RATING AS PER FAG CATALOGUEa The load and life of bearings are related statistically as per ISO equation for basic rating life  L10 ¼ L ¼ C F  m or C 1=m ẳ L10 F 23-177aị where L10 ¼ rating life in millions of revolutions (i.e number of revolutions resulting in 10% failure) C ¼ basic dynamic load rating, N (obtained from manufacturer’s catalogue) F ¼ equivalent dynamic load (also with suffix e, i.e Fe ), N (also symbol P is used in place of F) a Note: The designer is advised to read carefully the manufacturer’s Catalogue, which explains how load rating and life are established Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website DESIGN OF BEARINGS AND TRIBOLOGY DESIGN OF BEARINGS AND TRIBOLOGY 23.91 TABLE 23-40 Typical values of bearing life for various applications TABLE 23-41 Life of bearings, Lh Application Class of machinery Life, kh Instruments and apparatus which are used occasionally 0.5 Aircraft engines 0.5–2 Design life, h Agricultural equipment Aircraft engines 3000–6000 500–1500 Automobile applications Race car Light motor cycle Heavy motor cycle Light car Heavy car Light truck Heavy truck Bus Boat gearing units Beater mills Briquette presses Domestic appliances Electrical motors (up to 0.5 kW) Electrical motors (up to kW) Electrical motors, medium Electrical motors, large Elevator cables sheaves Small fans Mine ventilation fans 500–800 600–1200 1000–2000 1000–2000 1500–2500 1500–2500 2000–2500 2000–5000 3000–5000 20000–30000 20000–30000 1000–2000 1000–2000 8000–10000 10000–15000 20000–30000 40000–60000 2000–4000 40000–50000 Gearing units Automotive Multi-purpose Machine tool Ship Rail vehicles Heavy rolling mill Grinding spindles Locomotive axle boxes, outer bearings Locomotive axle boxes, inner bearings Machine tools Mining machinery Paper machines 600–5000 8000–15000 20000 20000–30000 15000–25000 50000 and more 1000–2000 20000–25000 30000–40000 10000–30000 4000–15000 50000–80000 Rail vehicle axle boxes Mining cars Motor rail cars Open pit mining cars Street cars Passenger cars Freight cars 5000 16000–20000 20000–25000 20000–25000 26000 35000 Rolling Mills Small cold mills Large multipurpose mills Gear drives Ship gear drives Propeller thrust bearings Propeller shaft bearings 5000–6000 8000–10000 50000 and more 20000–30000 15000–25000 80000 and more Machines used for period where stoppage of service is of minor importance 4–8 Machine working intermittently whose service is essential 8–14 Machine working for h per day whose service is not fully utilized 14–20 Machine working for h per day whose service is fully utilized 20–30 Machines working continuously for 24 h Machines working continuously for 24 h with high reliability Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website 50–60 100–200 Light 200 N 27557 31115 33006 37788 41336 43561 52459 57339 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 23.92 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website 32 34 21 22 24 26 28 30 13800 15010 18894 21119 22367 00 01 02 03 04 05 90679 72451 3842 4067 5557 6323 8134 9957 SAE No 137798 148921 80017 88909 101528 113346 122245 46227 58341 56448 68012 72451 18002 21334 27296 34006 38455 6664 7242 9428 9957 14445 113346 122245 137798 56448 68012 72451 88906 101352 27117 31340 35880 44629 48341 Medium 300 Heavy 400 N N Double-row self-aligning TABLE 23-42 Values of C for various types of bearings 96011 106683 54223 60907 64896 78233 87122 32674 39122 42895 46227 48902 14445 19110 21830 24451 26009 3332 5067 5557 7115 9604 10309 Light 200 N 144472 166698 92463 99568 108907 117796 135583 53341 60901 68012 75568 82683 21335 25343 30890 40004 46227 6488 8007 8712 10596 14181 16229 76910 84456 92463 115671 124470 33040 42288 48902 58682 64896 28008 Medium 300 Heavy 400 N N Single-row deep groove 87122 90679 103135 126694 142247 52459 63563 69345 75568 80071 23559 31566 35564 40004 42895 5419 8271 9075 11554 15778 16895 Light 200 N 147921 147921 157809 85789 97794 111132 122245 135583 34672 40004 49794 62495 75568 82104 20002 26676 122245 135583 59564 62230 78233 97794 122245 Medium 300 Heavy 400 N N Double-row deep groove 184471 191139 106683 122245 137798 157809 173362 56448 63563 73784 78233 87122 32673 39122 44423 48902 50676 14220 18894 22367 25343 26676 10133 Light 200 N 260043 212596 153369 173362 92463 101528 108707 117796 144472 53341 60907 68012 75568 84456 21335 25343 30890 40004 46227 12005 16895 73784 81350 88906 113346 120221 22673 40004 47118 57340 63563 27558 Medium 300 Heavy 400 N N Single-row angular contact DESIGN OF BEARINGS AND TRIBOLOGY 1.15 1.24 1.34 1.45 1.56 1.68 1.82 1.96 2.12 2.29 2.47 2.67 2.88 3.11 3.36 3.63 3.91 4.23 4.56 4.93 5.32 6.70 100 500 1,000 1,250 1,600 2,000 2,500 3,200 4,000 5,200 6,300 8,000 10,000 12,500 16,000 20,000 25,000 32,000 40,000 50,000 63,000 80,000 100,000 200,000 1.06 1.15 1.24 1.34 1.45 1.56 1.68 1.82 1.96 2.12 2.29 2.47 2.67 2.88 3.11 3.36 3.63 3.91 4.93 25 Life, Lh hours 10 100 1.06 1.45 1.34 1.82 1.45 1.96 1.56 2.12 1.68 2.29 1.82 2.47 1.96 2.67 2.12 2.88 2.29 3.11 2.47 3.36 2.67 3.63 2.88 3.91 3.11 4.23 3.36 4.56 3.63 4.93 3.91 5.32 4.23 5.75 4.56 6.20 4.93 6.70 5.32 7.23 5.75 7.81 6.20 8.43 7.81 10.6 40 1.56 1.96 2.12 2.29 2.47 2.67 2.88 3.11 3.36 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 11.5 125 1.68 1.12 2.29 2.47 2.67 2.88 3.11 3.36 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 12.4 160 1.06 2.82 2.29 2.47 2.67 2.88 3.11 3.36 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 13.4 200 1.15 1.96 2.47 2.67 2.88 3.11 3.36 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 14.5 250 TABLE 23-42a Loading ratio C=P for different for ball bearings 1.24 2.12 2.67 2.88 3.11 3.36 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 15.6 320 1.34 2.29 2.88 3.11 3.36 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 16.8 400 1.45 2.47 3.11 3.36 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 18.2 500 1.56 2.67 3.36 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 19.6 630 1.68 2.88 3.63 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 21.2 800 1.82 3.11 3.91 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 22.90 1.96 3.36 4.23 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 19.6 24.7 2.12 3.63 4.56 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16-9 18.2 19.6 21.2 26.7 2.29 3.91 4.93 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.9 18.2 19.6 21.2 22.9 28.8 2.47 4.23 5.32 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 19.6 21.2 22.9 24.7 31.1 2.67 4.56 5.75 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 19.6 21.2 22.9 24.7 26.7 2.88 4.93 6.20 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 19-6 21.2 22.9 24.7 26.7 28.8 3.11 5.32 6.70 7.23 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 19.6 21-2 22.9 24.7 26.7 28.8 31.1 3.36 5.75 7.32 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 19.6 21.2 22.9 24.7 26.7 28 31.1 3.63 6.20 7.81 8.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 19.6 21.2 22.9 24.7 26.7 28.8 31.1 3.91 6.70 9.43 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.2 19.6 21-2 22.9 24.7 26.7 28.8 31.1 4.23 7.23 9.11 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.1 19.6 21.2 22.9 24.7 26.7 28.8 31.1 4.56 7.81 9.83 10.6 11.5 12.4 13.4 14.5 15.6 16.8 18.1 19.6 21.2 22.9 24.7 26.7 28.8 31.1 1000 1250 1600 2000 2500 3200 4000 5000 6200 8000 10000 12500 16000 Speed, rpm DESIGN OF BEARINGS AND TRIBOLOGY Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website 23.93 1.13 1.21 1.30 1.39 1.49 1.60 1.71 1.83 1.97 2.11 2.26 2.42 2.59 2.78 2.97 3.19 3.42 3.66 3.92 4.20 4.50 5.54 100 500 1,000 1,250 1,600 2,000 2,500 3,200 4,000 5,000 6,300 8,000 10,000 12,500 16,000 20,000 25,000 32,000 40,000 50,000 63,000 80,000 100,000 200,000 1.05 1.13 1.21 1.30 1.39 1.46 1.60 1.71 1.83 1.97 2.11 2.26 2.42 2.59 78 2.97 3.19 3.42 4.20 25 Life, Lh hours 10 1.05 1.30 1.39 1.49 1.60 1.71 1.83 1.97 2.11 2.26 2.42 2.59 2.78 2.97 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 6.36 40 1.39 1.71 1.83 1.97 2.11 2.26 2.42 2.59 2.78 2.97 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 8.38 100 1.49 1.83 1.97 2.11 2.26 2.42 2.59 2.78 2.97 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 8.98 125 200 1.05 1.60 1.71 1.97 2.11 2.11 2.26 2.26 2.42 2.42 2.59 2.59 2.78 2.78 2.97 2.97 3.19 3.19 3.42 3.42 3.66 3.66 3.92 3.92 4.20 4.20 4.50 4.50 4.82 4.82 5.17 5.17 5.54 5.54 5.94 5.94 6.36 6.36 6.81 6.81 7.30 7.30 7.82 7.82 8.38 9.62 10.3 160 1.13 1.83 2.26 2.42 2.59 2.78 2.97 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 11.0 250 1.21 1.97 2.42 2.59 2.78 2.97 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 11.8 320 TABLE 23-42b Loading ratio C=P for different lives for roller bearings 1.30 2.11 2.59 2.78 2.97 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 12.7 400 1.39 2.26 2.78 2.97 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 13.6 500 1.49 2.42 2.97 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 14.6 630 1.60 2.59 3.19 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 15.6 800 1.71 2.78 3.42 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 16.7 1.83 2.97 3.66 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 17.9 1.97 3.19 3.92 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 19.2 2.11 3.42 4.20 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 20.6 2.26 3.66 4.50 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 2.42 3.92 4.82 5.17 5.54 5.94 6.36 6.81 7.30 7.87 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 19.2 2.59 4.20 5.17 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.0 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 19.2 20.6 2.78 4.50 5.54 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 19.2 20.6 2.97 4.82 5.94 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 19.2 20.6 3.19 5.17 6.36 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 19.2 20.6 3.42 5.54 6.81 7.30 7.82 8.38 8.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 19.2 20.6 3.66 5.94 7.30 7.82 8.38 8.99 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 19.2 20.6 3.92 6.36 7.82 8.38 9.98 9.62 10.3 11.0 11.8 12.7 13.6 14.6 15.6 16.7 17.9 19.2 20.6 1000 1250 1600 2000 2500 3200 4000 5000 6200 8000 10000 12500 16000 Speed, rpm DESIGN OF BEARINGS AND TRIBOLOGY 23.94 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ... 191 139 1066 83 122 245 137 798 157809 1 733 62 56448 635 63 737 84 78 23 3 87 122 32 6 73 39 122 444 23 489 02 50676 1 422 0 18894 2 236 7 2 534 3 26 676 10 133 Light 20 0 N 26 00 43 21 2596 1 533 69 1 733 62 924 63 101 528 108707... 2. 8 2. 8 2. 9 2. 9 3. 0 45.7 45.0 44 .2 43. 5 42. 7 0 .25 0 .26 0 .27 0 .28 0 .29 0 .30 0 .31 0 . 32 0 .33 0 .34 0 .35 12. 8 12. 5 12 .3 12. 1 11.8 11.6 11.6 11 .2 10.9 10.7 10.5 3. 0 3. 1 3. 1 3. 2 3. 2 3. 3 3. 3 3. 4 3. 4 3. 5... 2. 64 2. 75 2. 87 3. 10 3. 33 3.57 3. 82 4.07 4 . 32 4.57 4. 82 5.08 30 .8 31 .3 31.8 32 .3 32. 8 33 .3 33. 8 34 .3 34.8 35 .3 35.8 37 .0 38 .3 39.6 40.9 42 .3 43. 6 44.9 46 .3 47.7 49.0 50.5 51.9 54.9 58.0 61 .2 64.5