上海交通大学：《Design and Manufacturing》课程教学资源（参考文献）Shigley's Mechanical Engineering Design ch11 rolling contact bearing

560 Budynas-Nisbett:Shigley's Ill.Design of Mechanical 11.Rolling-Contact T©The McGraw-Hill Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition Rolling-Contact Bearings 559 11-6 Combined Radial and Thrust Loading A ball bearing is capable of resisting radial loading and a thrust loading.Furthermore, these can be combined.Consider F and F,to be the axial thrust and radial loads. respectively,and Fe to be the equivalent radial load that does the same damage as the combined radial and thrust loads together.A rotation factor V is defined such that V=1 when the inner ring rotates and V=1.2 when the outer ring rotates.Two dimensionless groups can now be formed:Fe/VF,and Fa/VF.When these two dimensionless groups are plotted as in Fig.11-6,the data fall in a gentle curve that is well approximated by two straight-line segments.The abscissa e is defined by the intersection of the two lines.The equations for the two lines shown in Fig.11-6 are Fe VF=1 Fa whenV≤e (11-8a 层=+原， Fe Fa when VEr >e (11-86) where,as shown,X is the ordinate intercept and Y is the slope of the line for Fa/VF,>e.It is common to express Eqs.(11-8a)and (11-8b)as a single equation, Fe=XiVFr+YiFa (11-9列 where i=1 when Fa/VF,se and i=2 when Fa/VFr e.Table 11-1 lists val- ues of X1,Y1,X2,and Y2 as a function of e,which in turn is a function of Fa/Co, where Co is the bearing static load catalog rating. In these equations,the rotation factor V is intended to correct for the rotating- ring conditions.The factor of 1.2 for outer-ring rotation is simply an acknowledgment that the fatigue life is reduced under these conditions.Self-aligning bearings are an exception:they have V=1 for rotation of either ring. The X and Y factors in Eqs.(11-8a)and(11-8b)depend upon the geometry of the bearing,including the number of balls and the ball diameter.The ABMA Figure 11-6 The relationship of dimensionless group F/VF] % and Fa/[VF)and the straigh 00000 line segments represenfing the data. 是

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 11. Rolling−Contact Bearings 560 © The McGraw−Hill Companies, 2008 Rolling-Contact Bearings 559 11–6 Combined Radial and Thrust Loading A ball bearing is capable of resisting radial loading and a thrust loading. Furthermore, these can be combined. Consider Fa and Fr to be the axial thrust and radial loads, respectively, and Fe to be the equivalent radial load that does the same damage as the combined radial and thrust loads together. A rotation factor V is defined such that V = 1 when the inner ring rotates and V = 1.2 when the outer ring rotates. Two dimensionless groups can now be formed: Fe/V Fr and Fa/V Fr . When these two dimensionless groups are plotted as in Fig. 11–6, the data fall in a gentle curve that is well approximated by two straight-line segments. The abscissa e is defined by the intersection of the two lines. The equations for the two lines shown in Fig. 11–6 are Fe V Fr = 1 when Fa V Fr ≤ e (11–8a) Fe V Fr = X + Y Fa V Fr when Fa V Fr > e (11–8b) where, as shown, X is the ordinate intercept and Y is the slope of the line for Fa/V Fr > e. It is common to express Eqs. (11–8a) and (11–8b) as a single equation, Fe = XiV Fr + Yi Fa (11–9) where i = 1 when Fa/V Fr ≤ e and i = 2 when Fa/V Fr > e. Table 11–1 lists val￾ues of X1, Y1, X2, and Y2 as a function of e, which in turn is a function of Fa/C0, where C0 is the bearing static load catalog rating. In these equations, the rotation factor V is intended to correct for the rotating￾ring conditions. The factor of 1.2 for outer-ring rotation is simply an acknowledgment that the fatigue life is reduced under these conditions. Self-aligning bearings are an exception: they have V = 1 for rotation of either ring. The X and Y factors in Eqs. (11–8a) and (11–8b) depend upon the geometry of the bearing, including the number of balls and the ball diameter. The ABMA Fe VFr 0 e Fa VFr 1 Slope Y X Figure 11–6 The relationship of dimensionless group Fe/(VFr) and Fa/(VFr) and the straight￾line segments representing the data

Budynas-Nisbett:Shigley's Ill.Design of Mechanical 11.Rolling-Contact ©The McGraw-Hil Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition 560 Mechanical Engineering Design Table 11-1 Fa/IVF)≤e Fa/(VF)>e Equivalent Radial Load Fa/Co e X1 X2 Y2 Factors for Ball Bearings 0.014* 0.19 1.00 0 0.56 2.30 0.021 0.21 1.00 0 0.56 2.15 0.028 0.22 1.00 0 0.56 1.99 0.042 0.24 1.00 0 0.56 1.85 0.056 0.26 1.00 0 0.56 1.71 0.070 0.27 1.00 0 0.56 1.63 0.084 0.28 1.00 0 0.56 1.55 0.110 0.30 1.00 0 0.56 1.45 0.17 0.34 1.00 0 0.56 1.31 0.28 0.38 1.00 0 0.56 1.15 0.42 0.42 1.00 0 0.56 1.04 0.56 0.44 1.00 0 0.56 1.00 5e0.014ifF./0<0.014 Figure 11-7 Width series The basic ABMA plan for Diameter 3 boundary dimensions.These apply to ball bearings,straight roller bearings,and spherical roller bearings,but not to inch Dimension series ball bearings or tapered roller bearings.The contour of the comer is not specified. It may be rounded or chamfered,but it must be small enough to clear the fillet rodius specified in the standards. recommendations are based on the ratio of the thrust component Fa to the basic static load rating Co and a variable reference value e.The static load rating Co is tabulated, along with the basic dynamic load rating Cjo,in many of the bearing manufacturers' publications;see Table 11-2,for example. Since straight or cylindrical roller bearings will take no axial load,or very little, the Y factor is always zero. The ABMA has established standard boundary dimensions for bearings,which define the bearing bore,the outside diameter(OD),the width,and the fillet sizes on the shaft and housing shoulders.The basic plan covers all ball and straight roller bear- ings in the metric sizes.The plan is quite flexible in that,for a given bore,there is an assortment of widths and outside diameters.Furthermore,the outside diameters selected are such that,for a particular outside diameter,one can usually find a vari- ety of bearings having different bores and widths. This basic ABMA plan is illustrated in Fig.11-7.The bearings are identified by a two-digit number called the dimension-series code.The first number in the code is from the width series,0,1,2,3,4,5,and 6.The second number is from the diameter series

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 11. Rolling−Contact Bearings © The McGraw−Hill 561 Companies, 2008 560 Mechanical Engineering Design Fa/(VFr) e Fa/(VFr) e Fa/C0 e X1 Y1 X2 Y2 0.014* 0.19 1.00 0 0.56 2.30 0.021 0.21 1.00 0 0.56 2.15 0.028 0.22 1.00 0 0.56 1.99 0.042 0.24 1.00 0 0.56 1.85 0.056 0.26 1.00 0 0.56 1.71 0.070 0.27 1.00 0 0.56 1.63 0.084 0.28 1.00 0 0.56 1.55 0.110 0.30 1.00 0 0.56 1.45 0.17 0.34 1.00 0 0.56 1.31 0.28 0.38 1.00 0 0.56 1.15 0.42 0.42 1.00 0 0.56 1.04 0.56 0.44 1.00 0 0.56 1.00 ∗Use 0.014 if Fa C0 0.014. Table 11–1 Equivalent Radial Load Factors for Ball Bearings recommendations are based on the ratio of the thrust component Fa to the basic static load rating C0 and a variable reference value e. The static load rating C0 is tabulated, along with the basic dynamic load rating C10, in many of the bearing manufacturers’ publications; see Table 11–2, for example. Since straight or cylindrical roller bearings will take no axial load, or very little, the Y factor is always zero. The ABMA has established standard boundary dimensions for bearings, which define the bearing bore, the outside diameter (OD), the width, and the fillet sizes on the shaft and housing shoulders. The basic plan covers all ball and straight roller bear￾ings in the metric sizes. The plan is quite flexible in that, for a given bore, there is an assortment of widths and outside diameters. Furthermore, the outside diameters selected are such that, for a particular outside diameter, one can usually find a vari￾ety of bearings having different bores and widths. This basic ABMA plan is illustrated in Fig. 11–7. The bearings are identified by a two-digit number called the dimension-series code. The first number in the code is from the width series, 0, 1, 2, 3, 4, 5, and 6. The second number is from the diameter series 0 1 2 3 4 Diameter series Dimension series Width series Bore OD 01 2 3 00 02 03 04 10 12 13 20 22 23 30 31 32 33 r r Figure 11–7 The basic ABMA plan for boundary dimensions. These apply to ball bearings, straight roller bearings, and spherical roller bearings, but not to inch￾series ball bearings or tapered roller bearings. The contour of the corner is not specified. It may be rounded or chamfered, but it must be small enough to clear the fillet radius specified in the standards.

562 Budynas-Nisbett:Shigley's lll.Design of Mechanical 11.Rolling-Contact T©The McGraw-Hil Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition Rolling-Contact Bearings 561 Table 11-2 Dimensions and Load Ratings for Single-Row 02-Series Deep-Groove and Angular-Contact Ball Bearings Fillet Shoulder Load Ratings,kN Bore, OD, Width, Radius, Diameter,mm Deep Groove Angular Contact mm mm mm mm ds dH C1o C1o Co 10 30 9 0.6 12.5 27 5.07 2.24 4.94 2.12 12 32 10 0.6 14.5 28 6.89 3.10 7.02 3.05 35 11 0.6 17.5 31 7.80 3.55 8.06 3.65 公 40 12 0.6 19.5 34 9.56 4.50 9.95 4.75 20 14 1.0 25 41 12.7 6.20 13.3 6.55 3 5 15 1.0 30 14.0 6.95 14.8 7.65 30 1.0 35 55 19.5 10.0 20.3 11.0 35 72 1.0 41 65 25.5 13.7 27.0 15.0 40 80 18 1.0 46 72 30.7 16.6 31.9 18.6 45 85 1.0 33.2 18.6 35.8 21.2 50 90 20 1.0 56 82 35.1 19.6 37.7 22.8 55 100 21 1.5 63 90 43.6 25.0 46.2 28.5 60 110 2 1.5 70 99 47.5 28.0 55.9 35.5 65 120 2 1.5 74 109 55.9 34.0 63.7 41.5 70 125 24 1.5 114 61.8 37.5 68.9 45.5 75 130 25 1.5 86 119 66.3 40.5 71.5 49.0 80 140 26 2.0 93 127 70.2 45.0 80.6 55.0 85 150 28 2.0 99 136 83.2 53.0 90.4 63.0 90 160 30 2.0 104 146 95.6 62.0 106 73.5 95 170 32 2.0 110 156 108 69.5 121 85.0 (outside),8,9,0,1,2,3,and 4.Figure 11-7 shows the variety of bearings that may be obtained with a particular bore.Since the dimension-series code does not reveal the dimensions directly,it is necessary to resort to tabulations.The 02 series is used here as an example of what is available.See Table 11-2. The housing and shaft shoulder diameters listed in the tables should be used whenever possible to secure adequate support for the bearing and to resist the maxi- mum thrust loads (Fig.11-8).Table 11-3 lists the dimensions and load ratings of some straight roller bearings. To assist the designer in the selection of bearings,most of the manufacturers' handbooks contain data on bearing life for many classes of machinery,as well as information on load-application factors.Such information has been accumulated the hard way,that is,by experience,and the beginner designer should utilize this information until he or she gains enough experience to know when deviations are pos- sible.Table 11-4 contains recommendations on bearing life for some classes of machinery.The load-application factors in Table 11-5 serve the same purpose as fac- tors of safety;use them to increase the equivalent load before selecting a bearing

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 11. Rolling−Contact Bearings 562 © The McGraw−Hill Companies, 2008 Rolling-Contact Bearings 561 Fillet Shoulder Load Ratings, kN Bore, OD, Width, Radius, Diameter, mm Deep Groove Angular Contact mm mm mm mm dS dH C10 C0 C10 C0 10 30 9 0.6 12.5 27 5.07 2.24 4.94 2.12 12 32 10 0.6 14.5 28 6.89 3.10 7.02 3.05 15 35 11 0.6 17.5 31 7.80 3.55 8.06 3.65 17 40 12 0.6 19.5 34 9.56 4.50 9.95 4.75 20 47 14 1.0 25 41 12.7 6.20 13.3 6.55 25 52 15 1.0 30 47 14.0 6.95 14.8 7.65 30 62 16 1.0 35 55 19.5 10.0 20.3 11.0 35 72 17 1.0 41 65 25.5 13.7 27.0 15.0 40 80 18 1.0 46 72 30.7 16.6 31.9 18.6 45 85 19 1.0 52 77 33.2 18.6 35.8 21.2 50 90 20 1.0 56 82 35.1 19.6 37.7 22.8 55 100 21 1.5 63 90 43.6 25.0 46.2 28.5 60 110 22 1.5 70 99 47.5 28.0 55.9 35.5 65 120 23 1.5 74 109 55.9 34.0 63.7 41.5 70 125 24 1.5 79 114 61.8 37.5 68.9 45.5 75 130 25 1.5 86 119 66.3 40.5 71.5 49.0 80 140 26 2.0 93 127 70.2 45.0 80.6 55.0 85 150 28 2.0 99 136 83.2 53.0 90.4 63.0 90 160 30 2.0 104 146 95.6 62.0 106 73.5 95 170 32 2.0 110 156 108 69.5 121 85.0 Table 11–2 Dimensions and Load Ratings for Single-Row 02-Series Deep-Groove and Angular-Contact Ball Bearings (outside), 8, 9, 0, 1, 2, 3, and 4. Figure 11–7 shows the variety of bearings that may be obtained with a particular bore. Since the dimension-series code does not reveal the dimensions directly, it is necessary to resort to tabulations. The 02 series is used here as an example of what is available. See Table 11–2. The housing and shaft shoulder diameters listed in the tables should be used whenever possible to secure adequate support for the bearing and to resist the maxi￾mum thrust loads (Fig. 11–8). Table 11–3 lists the dimensions and load ratings of some straight roller bearings. To assist the designer in the selection of bearings, most of the manufacturers’ handbooks contain data on bearing life for many classes of machinery, as well as information on load-application factors. Such information has been accumulated the hard way, that is, by experience, and the beginner designer should utilize this information until he or she gains enough experience to know when deviations are pos￾sible. Table 11–4 contains recommendations on bearing life for some classes of machinery. The load-application factors in Table 11–5 serve the same purpose as fac￾tors of safety; use them to increase the equivalent load before selecting a bearing

Budynas-Nisbett:Shigley's lll.Design of Mechanical 11.Rolling-Contact T©The McGraw-Hill 563 Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition 562 Mechanical Engineering Design Figure 11-8 Shaft and housing shoulder diameters ds and dH should be adequate to ensure good bearing support. Table 11-3 Dimensions and Basic Load Ratings for Cylindrical Roller Bearings 02-Series 03-Series Bore, OD Width Load Rating,kN OD, Width, Load Rating,kN mm mm mm C1o Co mm mm C10 Co 25 52 15 16.8 8.8 62 17 28.6 15.0 30 62 16 22.4 12.0 72 19 36.9 20.0 35 72 17 31.9 17.6 80 21 44.6 27.1 40 80 18 41.8 24.0 90 23 56.1 32.5 45 85 19 44.0 25.5 100 25 72.1 45.4 50 90 20 45.7 27.5 110 27 88.0 52.0 55 100 1 56.1 34.0 120 29 102 67.2 60 110 2 64.4 43.1 130 31 123 76.5 65 120 23 76.5 51.2 140 33 138 85.0 125 79.2 51.2 150 35 151 102 75 130 2 93.1 63.2 160 1 183 125 8 140 26 106 69.4 170 190 125 85 150 28 119 78.3 180 41 212 149 90 160 30 142 100 190 43 242 160 95 170 3 165 112 200 264 189 100 180 34 183 125 215 4) 303 220 110 200 38 229 167 240 391 304 120 215 40 260 183 260 55 457 340 130 230 40 270 193 280 58 539 408 140 250 42 319 240 300 62 682 454 150 270 45 446 260 320 65 781 502

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 11. Rolling−Contact Bearings © The McGraw−Hill 563 Companies, 2008 562 Mechanical Engineering Design 02-Series 03-Series Bore, OD, Width, Load Rating, kN OD, Width, Load Rating, kN mm mm mm C10 C0 mm mm C10 C0 25 52 15 16.8 8.8 62 17 28.6 15.0 30 62 16 22.4 12.0 72 19 36.9 20.0 35 72 17 31.9 17.6 80 21 44.6 27.1 40 80 18 41.8 24.0 90 23 56.1 32.5 45 85 19 44.0 25.5 100 25 72.1 45.4 50 90 20 45.7 27.5 110 27 88.0 52.0 55 100 21 56.1 34.0 120 29 102 67.2 60 110 22 64.4 43.1 130 31 123 76.5 65 120 23 76.5 51.2 140 33 138 85.0 70 125 24 79.2 51.2 150 35 151 102 75 130 25 93.1 63.2 160 37 183 125 80 140 26 106 69.4 170 39 190 125 85 150 28 119 78.3 180 41 212 149 90 160 30 142 100 190 43 242 160 95 170 32 165 112 200 45 264 189 100 180 34 183 125 215 47 303 220 110 200 38 229 167 240 50 391 304 120 215 40 260 183 260 55 457 340 130 230 40 270 193 280 58 539 408 140 250 42 319 240 300 62 682 454 150 270 45 446 260 320 65 781 502 Table 11–3 Dimensions and Basic Load Ratings for Cylindrical Roller Bearings dS dH Figure 11–8 Shaft and housing shoulder diameters dS and dH should be adequate to ensure good bearing support

Budynas-Nisbett:Shigley's Ill.Design of Mechanical 11.Rolling-Contact ©The McGraw-Hil Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition Rolling-Contact Bearings 563 Table 11-4 Type of Application Life,kh Bearing-Life Instruments and apparatus for infrequent use Up to 0.5 Recommendations Aircraft engines 0.5-2 for Various Classes Machines for short or intermittent operation where service of Machinery interruption is of minor importance 4-8 Machines for intermittent service where reliable operation is of great importance 8-14 Machines for 8-h service that are not always fully utilized 14-20 Machines for 8-h service that are fully utilized 20-30 Machines for continuous 24-h service 50-60 Machines for continuous 24-h service where reliability is of extreme importance 100-200 Table 11-5 Type of Application Load Factor Load-Application Factors Precision gearing 1.0-1.1 Commercial gearing 1.1-1.3 Applications with poor bearing seals 1.2 Machinery with no impact 1.0-1.2 Machinery with light impact 1.2-1.5 Machinery with moderate impact 1.5-3.0 The static load rating is given in bearing catalog tables.It comes from the equations Co Mnbdp (ball bearings) and Co=Mnrled (roller bearings) where Co=bearing static load rating,Ibf(kN) n=number of balls n=number of rollers d=diameter of balls,in (mm) d=diameter of rollers,in (mm) l=length of contact line,in (mm) and M takes on the values of which the following table is representative: M in and lbf mm and kN Radial ball 1.78103 5.111013 Ball thrust 7.10103 20.4103 Radial roller 3.131013 8.991013 Roller thrust 14.2103 40.7八1013

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 11. Rolling−Contact Bearings 564 © The McGraw−Hill Companies, 2008 Rolling-Contact Bearings 563 Type of Application Life, kh Instruments and apparatus for infrequent use Up to 0.5 Aircraft engines 0.5–2 Machines for short or intermittent operation where service interruption is of minor importance 4–8 Machines for intermittent service where reliable operation is of great importance 8–14 Machines for 8-h service that are not always fully utilized 14–20 Machines for 8-h service that are fully utilized 20–30 Machines for continuous 24-h service 50–60 Machines for continuous 24-h service where reliability is of extreme importance 100–200 Table 11–4 Bearing-Life Recommendations for Various Classes of Machinery The static load rating is given in bearing catalog tables. It comes from the equations C0 = Mnbd2 b (ball bearings) and C0 = Mnrlcd (roller bearings) where C0 = bearing static load rating, lbf (kN) nb = number of balls nr = number of rollers db = diameter of balls, in (mm) d = diameter of rollers, in (mm) lc = length of contact line, in (mm) and M takes on the values of which the following table is representative: M in and lbf mm and kN Radial ball 1.78(10)3 5.11(10)3 Ball thrust 7.10(10)3 20.4(10)3 Radial roller 3.13(10)3 8.99(10)3 Roller thrust 14.2(10)3 40.7(10)3 Type of Application Load Factor Precision gearing 1.0–1.1 Commercial gearing 1.1–1.3 Applications with poor bearing seals 1.2 Machinery with no impact 1.0–1.2 Machinery with light impact 1.2–1.5 Machinery with moderate impact 1.5–3.0 Table 11–5 Load-Application Factors