The equivalent dynamic load used in Eq. (23-177a) is given by The Eq. (23-177a) in terms of L h hours of life The relation between fatigue life (L h ) in hours and the life in millions of revolutions (L) The Eq. (23-178b) can be written as The simplified form of Eq. (23-179b) The basic dynamic load rating from Eq. (23-180a) m ¼ life exponent ¼ 3.0 for ball bearing ¼ 10/3 for roller bearing Load ratio ðC =Pð¼ C=FÞÞand also taken from Tables 23-42a and 23-42b can be determined from Fig. 23-53. C can be obtained from manufacturer’s catalogue. F e ¼ XF r þ YF a ð23-177bÞ where F e ¼ P ¼ equivalent radial load for radial bearings or axial load for axial bearings F r ¼ radial load, N F a ¼ axial load, N X ¼ radial factor Y ¼ axial/thrust factor The values of X and Y can be found in tables of the manufacturer’s catalogue (e.g. FAG catalogue). L h ¼ 10 6 60n C F m ð23-178aÞ where L h ¼ L 10h ¼ nominal rating life, h L 10h ¼ L h ¼ 10 6 L 60n ð23-178bÞ Refer to Tables 23-43 and 23-44 for index of dynamic strengthening f L and L h . L 10h ¼ L h ¼ 500ð33 1 3 Þ60L 60n ð23-179aÞ L 10h ¼ L h ¼ 500 33 1 3 n C F m ð23-179bÞ Values of L 10h in hours as function of speed n and load ratio ðC=F ¼ C=PÞ are given in Fig. 23-53. f L ¼ C F f n ð23-180aÞ C ¼ f L f n F ¼ f L f n P ð23-180bÞ where F ¼ P f L ¼ index of dynamic stressing f n ¼ speed factor Refer to Fig. 23-56. Particular Formula DESIGN OF BEARINGS AND TRIBOLOGY 23.95 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 FIGURE 23-53 Nomogram chart f or determining c/p for ball and roller bearings (ISO-R281) (Note: Information on the calculation of load rating C and equivalent load P can be obtained from ISO Recommendation R281. Values of C for various types of bearing can be obtained from the bearing manufacturers.) ROLLER BEARINGS BALL BEARINGS Speed rev/min Load ratio C/P Rating life hours L h Million revolutions L=L 10 Speed rev/min Load ratio C/P Rating life hours L h Million revolutions L=L 10 30000 20000 15000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1800 1500 1200 1000 900 800 700 600 500 400 300 200 150 100 90 80 70 60 50 40 30 20 1.0 1.5 2 3 4 5 6 7 8 9 10 15 20 30 40 60000 50000 40000 30000 20000 10000 8000 6000 5000 4000 3000 2000 1000 800 600 500 400 300 200 100 80 60 50 40 30 20 10 8 6 5 4 3 2 1.0 200 300 400 500 600 700 800 900 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 15000 20000 30000 40000 50000 60000 70000 80000 90000 100000 150000 200000 300000 30000 20000 15000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1800 1500 1200 1000 900 800 700 600 500 400 300 200 150 100 90 80 70 60 50 40 30 20 1.0 1.0 2 3 4 6 8 2 1.5 10 20 30 40 50 60 80 100 200 300 400 500 600 7 6 5 3 4 800 1000 2000 3000 4000 5000 6000 8000 10000 20000 8 9 10 15 20 30 40 30000 40000 50000 60000 80000 100000 200000 300000 200000 150000 100000 90000 80000 70000 60000 50000 40000 30000 20000 15000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1500 1000 900 800 700 600 500 400 300 200 23.96 CHAPTER TWENTY-THREE 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 The value of index of dynamic stressing, f L , can be obtained from Eq. (23-179b) f L ¼ m ffiffiffiffiffiffiffiffi L h 500 r ð23-181aÞ For a life of 500 h, f L ¼ 1 Refer to Table 23-43 for f L of ball bearings Refer to Table 23-44 for f L of roller bearings and to Table 23-58 Particular Formula TABLE 23-43 Index of dynamic stressing f L for ball bearings for use in Eq. (23-180) f L ¼ 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L h =500 p L h L h L h L h L h L h L h hours f L hours f L hours f L hours f L hours f L hours f L hours f L 100 0.585 300 0.843 700 1.120 1750 1.520 4500 2.08 10000 2.71 30000 3.91 105 0.595 310 0.852 720 1.130 1800 1.535 4600 2.10 10500 2.76 31000 3.96 110 0.604 320 0.861 740 1.140 1850 1.545 4700 2.11 11000 2.80 32000 4.00 115 0.613 330 0.870 760 1.150 1900 1.560 4800 2.13 11500 2.85 33000 4.04 120 0.622 340 0.879 780 1.160 1950 1.575 4900 2.14 12000 2.85 34000 4.08 125 0.631 350 0.888 800 1.170 2000 1.590 5000 2.15 12500 2.93 35000 4.12 130 0.639 360 0.896 820 1.180 2100 1.615 5200 2.18 13000 2.96 36000 4.16 135 0.647 370 0.905 840 1.190 2200 1.640 5400 2.21 13500 3.00 37000 4.20 140 0.654 380 0.913 860 1.200 2300 1.665 5600 2.24 14000 3.04 38000 4.24 145 0.662 390 0.921 880 1.205 2400 1.690 5800 2.27 14500 3.07 3900 4.27 150 0.670 400 0.928 900 1.215 2500 1.710 6000 2.29 15000 3.11 40000 4.31 155 0.677 410 0.936 920 1.225 2600 1.730 6200 2.32 15500 3.14 41000 4.35 160 0.684 420 0.944 940 1.235 2700 1.755 6400 2.34 16000 3.18 42000 4.38 165 0.691 430 0.951 960 1.245 2800 1.775 6600 2.37 16500 3.21 43000 4.42 170 0.698 440 0.959 980 1.260 2900 1.795 6800 2.39 17000 3.24 44000 4.45 175 0.705 450 0.966 1000 1.260 3000 1.815 7000 2.41 17500 3.27 45000 4.48 180 0.712 460 0.973 1050 1.280 3100 1.835 7200 2.43 18000 3.30 46000 4.51 185 0.718 470 0.980 1100 1.300 3200 1.855 7400 2.46 18500 3.33 47000 4.55 190 0.724 480 0.987 1150 1.320 3300 1.875 7600 2.48 19000 3.36 48000 4.58 195 0.731 490 0.994 1200 1.340 3400 1.895 7800 2.50 19500 3.39 49000 4.61 200 0.737 500 1.000 1250 1.360 3500 1.910 8000 2.52 20000 3.42 50000 4.64 210 0.749 520 1.015 1300 1.375 3600 1.930 8200 2.54 21000 3.48 55000 4.80 220 0.761 540 1.025 1350 1.395 3700 1.950 8400 2.56 22000 3.53 60000 4.94 230 0.772 560 1.040 1400 1.410 3800 1.965 8600 2.58 23000 3.58 65000 5.07 240 0.783 580 1.050 1450 1.425 3900 1.985 8800 2.60 24000 3.63 70000 5.19 250 0.794 600 1.065 1500 1.445 4000 2.000 9000 2.62 25000 3.68 75000 5.30 260 0.804 620 1.075 1550 1.460 4100 2.020 9200 2.64 26000 3.73 80000 5.43 270 0.814 640 1.085 1600 1.475 4200 2.030 9400 2.66 27000 3.78 85000 5.55 280 0.824 660 1.100 1650 1.490 4300 2.050 9600 2.68 28000 3.82 90000 5.65 290 0.834 680 1.110 1700 1.505 4400 2.070 9800 2.70 29000 3.87 100000 5.85 DESIGN OF BEARINGS AND TRIBOLOGY 23.97 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 The value of speed factor, f n , can be obtained from Eq. (23-179b) The equivalent dynamic load for deep groove ball bearings with increased radial clearance f n ¼ m ffiffiffiffiffiffiffiffi 33 1 3 n s ¼ m ffiffiffiffiffiffiffiffi 100 3n r ð23-181bÞ For a speed factor of n ¼ 33 1 3 min, f n ¼ 1 Refer to Table 23-45 for f n of ball bearings Refer to Table 23-46 for f n of roller bearings F e ¼ P a ¼ XF r þ YF a ð23-182Þ Particular Formula TABLE 23-44 Index of dynamic stressing f L for roller bearings for use in Eq. (23-180) f L ¼ 10=3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L h =500 p L h L h L h L h L h L h L h hours f L hours f L hours f L hours f L hours f L hours f L hours f L 100 0.617 300 0.858 700 1.105 1750 1.455 4500 1.935 10000 2.46 30000 3.42 105 0.626 310 0.866 720 1.115 1800 1.470 4600 1.945 10500 2.49 31000 3.45 110 0.635 320 0.875 740 1.125 1850 1.480 4700 1.960 11000 2.53 32000 3.48 115 0.643 330 0.883 760 1.135 1900 1.490 4800 1.970 11500 2.56 33000 3.51 120 0.652 340 0.891 780 1.145 1950 1.505 4900 1.985 12000 2.59 34000 3.55 125 0.660 350 0.889 800 1.150 2000 1.515 5000 2.00 12500 2.63 35000 3.58 130 0.665 360 0.906 820 1.160 2100 1.540 5200 2.02 13000 2.66 36000 3.61 135 0.675 370 0.914 840 1.170 2200 1.560 5400 2.04 13500 2.69 37000 3.64 140 0.683 380 0.921 860 1.180 2300 1.580 5600 2.06 14000 2.72 39000 3.67 145 0.690 390 0.928 880 1.185 2400 1.600 5800 2.09 14500 2.75 39000 3.70 150 0.697 400 0.935 900 1.190 2500 1.620 6000 2.11 15000 2.77 40000 3.72 155 0.704 410 0.942 920 1.200 2600 1.640 6200 2.13 15500 2.80 41000 3.75 160 0.710 420 0.949 940 1.210 2700 1.660 6400 2.15 16000 2.83 42000 3.78 165 0.717 430 0.956 960 1.215 2800 1.675 6600 2.17 16500 2.85 43000 3.80 170 0.723 440 0.962 980 1.225 2900 1.695 6800 2.19 17000 2.88 44000 2.83 175 0.730 450 0.969 1000 1.230 3000 1.710 7000 2.21 17500 2.91 45000 3.86 180 0.736 460 0.975 1050 1.250 3100 1.730 7200 2.23 18000 2.93 46000 3.88 185 0.742 470 0.982 1100 1.270 3200 1.755 7400 2.24 18500 2.95 47000 3.91 190 0.748 480 0.994 1150 1.285 3300 1.760 7600 2.26 19000 2.98 48000 3.93 195 0.754 490 0.998 1200 1.300 3400 1.775 7800 2.28 19500 3.00 49000 3.96 200 0.760 500 1.000 1250 1.315 3500 1.795 8000 2.30 20000 3.02 50000 3.98 210 0.771 520 1.010 1300 1.330 3600 1.810 8200 2.31 21000 3.07 55000 4.10 220 0.782 540 1.025 1350 1.345 3700 1.825 8400 2.33 22000 3.11 60000 4.20 230 0.792 560 1.035 1400 1.360 3800 1.840 8608 2.35 23000 3.15 65000 4.30 240 0.802 580 1.045 1450 1.375 3900 1.850 8800 2.36 24000 3.19 70000 4.40 250 0.812 600 1.055 1500 1.390 4000 1.865 9000 2.38 25000 3.23 75000 4.50 260 0.822 620 1.065 1550 1.405 4100 1.880 9200 2.40 26000 3.27 80000 4.58 270 0.831 640 1.075 1600 1.420 4200 1.895 9400 2.41 27000 3.31 85000 4.66 280 0.840 660 1.085 1650 1.430 4300 1.905 9600 2.43 28000 3.35 90000 4.75 290 0.849 680 1.095 1700 1.445 4400 1.920 9800 2.44 29000 3.38 100000 4.90 150000 5.54 200000 6.03 23.98 CHAPTER TWENTY-THREE 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 TABLE 23-45 Speed factor f n for ball bearings for use in Eq. (23-180) f n ¼ 3 ffiffiffiffiffiffiffiffiffiffiffiffiffi 33 1 3 =n q Speed, Speed Speed, Speed Speed, Speed Speed, Speed Speed, Speed Speed, Speed n, rpm factor, f n n, rpm factor, f n n, rpm factor, f n n, rpm factor, f n n, rpm factor, f n n, rpm factor, f n 10 1.494 60 0.822 250 0.511 900 0.333 4000 0.203 15,000 0.131 11 1.447 62 0.813 260 0.504 920 0.331 4100 0.201 15,500 0.129 12 1.405 64 0.805 270 0.498 940 0.329 4200 0.199 16,000 0.128 13 1.369 66 0.797 280 0.492 960 0.326 4300 0.198 16,500 0.126 14 1.335 68 0.788 290 0.487 980 0.324 4400 0.196 17,000 0.125 15 1.305 70 0.781 300 0.481 1000 0.322 4500 0.195 17,500 0.124 16 1.277 72 0.774 310 0.476 1050 0.317 4600 0.193 18,000 0.123 17 1.252 74 0.767 320 0.471 1100 0.312 4700 0.192 18,500 0.122 18 1.225 76 0.760 330 0.466 1150 0.302 4800 0.191 19,000 0.121 19 1.206 78 0.753 340 0.461 1200 0.303 4900 0.190 19,500 0.120 20 1.186 80 0.747 350 0.457 1250 0.299 5000 0.188 20,000 0.119 21 1.166 82 0.741 360 0.453 1300 0.295 5200 0.186 21,000 0.117 22 1.148 84 0.735 370 0.448 1350 0.291 5400 0.183 22,000 0.115 23 1.132 86 0.729 380 0.444 1400 0.288 5600 0.181 23:000 0.113 24 1.116 88 0.724 390 0.441 1450 0.284 5800 0.179 24,000 0.112 25 1.100 90 0.718 400 0.437 1500 0.281 6000 0.177 25,000 0.110 26 1.089 92 0.713 410 0.433 1550 0.278 6200 0.175 26,000 0.109 27 1.071 94 0.708 420 0.430 1600 0.275 6400 0.173 27,000 0.107 28 1.060 96 0.703 430 0.426 1650 0.272 6600 0.172 28,000 0.106 29 1.048 98 0.698 440 0.423 1700 0.270 6800 0.170 29,000 0.105 30 1.036 100 0.693 450 0.420 1750 0.267 7000 0.168 30,000 0.104 31 1.025 105 0.692 460 0.417 1800 0.265 7200 0.167 32,000 0.101 32 1.014 110 0.672 470 0.414 1850 0.262 7400 0.165 34,000 0.0993 33 1.003 115 0.662 480 0.411 1900 0.260 7600 0.164 36,000 0.0975 34 0.993 120 0.652 490 0.408 1950 0.258 7800 0.162 38,000 0.0957 35 0.984 125 0.644 500 0.406 2000 0.255 8000 0.611 40,000 0.0941 36 0.975 130 0.635 520 0.400 2100 0.251 8200 0.160 42,000 0.0926 37 0.966 135 0.627 540 0.395 2200 0.247 8400 0.158 44,000 0.0912 38 0.958 140 0.620 560 0.390 2300 0.244 8600 0.157 46,000 0.0898 39 0.949 145 0.613 580 0.386 2400 0.248 8800 0.156 50,000 0.0874 40 0.941 150 0.606 600 0.382 2500 0.237 9000 0.155 41 0.933 155 0.599 620 0.378 2600 0.234 9200 0.154 42 0.926 160 0.583 640 0.374 2700 0.231 9400 0.153 43 0.919 165 0.586 660 0.370 2800 0.228 9600 0.152 44 0.912 170 0.581 680 0.366 2900 0.226 9800 0.150 45 0.905 175 0.575 700 0.363 3000 0.223 10,000 0.149 46 0.898 180 0.570 720 0.359 3100 0.221 10,500 0.147 47 0.892 185 0.565 740 0.356 3200 0.218 11,000 0.145 48 0.585 190 0.560 760 0.353 3300 0.216 11,500 0.143 49 0.880 195 0.555 780 0.350 3400 0.214 12,000 0.141 50 0.874 200 0.550 800 0.347 3500 0.212 12,500 0.139 52 0.863 210 0.541 820 0.344 3600 0.210 13,000 0.137 54 0.851 220 0.533 840 0.341 3700 0.208 13,500 0.135 56 0.841 230 0.525 860 0.339 3800 0.206 14,000 0.134 58 0.831 240 0.518 880 0.336 3900 0.205 14,500 0.132 DESIGN OF BEARINGS AND TRIBOLOGY 23.99 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 TABLE 23.46 Speed factor f n for roller bearings for us in Eq. (23-180) f n ¼ 10=3 ffiffiffiffiffiffiffiffiffiffiffiffiffi 33 1 3 =n q Speed, Speed Speed, Speed Speed, Speed Speed, Speed Speed, Speed Speed, Speed n, rpm factor, f n n, rpm factor, f n n, rpm factor, f n n, rpm factor, f n n, rpm factor, f n n, rpm factor, f n 10 1.435 60 0.838 250 0.546 900 0.372 4000 0.238 15000 0.160 11 1.395 62 0.830 260 6.540 920 0.370 4100 0.236 15500 0.158 12 1.359 64 0.822 270 0.534 940 0.367 4200 0.234 16000 0.157 13 1.326 66 0.815 280 0.528 960 0.365 4300 0.233 16500 0.156 14 1.297 68 0.807 290 0.523 980 0.363 4400 0.231 17000 0.154 15 1.271 70 0.800 300 0.517 1000 0.361 4500 0.230 17500 0.153 16 1.246 72 0.794 310 0.512 1050 0.355 4600 0.228 18000 0.152 17 1.224 74 0.787 320 0.507 1100 0.350 4700 0.227 18500 0.150 18 1.203 76 0.781 330 0.503 1150 0.346 4800 0.225 19000 0.149 19 1.184 78 0.775 340 0.498 1200 0.341 4900 0.224 19500 0.148 20 1.166 80 0.769 350 0.494 1250 0.337 5000 0.222 20000 0.147 21 1.149 82 0.763 360 0.490 1300 0.333 5200 0.220 21000 0.145 22 1.133 84 0.758 370 0.486 1350 0.329 5400 0.217 22000 0.143 23 1.118 86 0.753 380 0.482 1400 0.336 5600 0.215 23000 0.141 24 1.104 88 0.747 390 0.478 1450 0.322 5800 0.213 24000 0.139 25 1.090 90 0.742 400 0.475 1500 0.319 6000 0.211 25000 0.137 26 1.077 92 0.737 410 0.471 1550 0.316 6200 0.209 26000 0.136 27 1.065 94 0.733 420 0.467 1600 0.313 6400 0.207 27000 0.134 28 1.054 96 0.728 430 0.464 1650 0.310 6600 0.205 28000 0.133 29 1.0411 98 0.724 440 0.461 1700 0.307 6800 0.203 29000 0.131 30 1.032 100 0.719 450 0.458 1750 0.305 7000 0.201 30000 0.130 31 1.022 105 0.709 460 0.455 1800 0.302 7200 0.199 32000 0.127 32 1.012 110 0.699 470 0.452 1850 0.300 7400 0.198 34000 0.125 33 1.003 115 0.690 480 0.449 1900 0.297 7600 0.196 36000 0.123 34 0.994 120 0.681 490 0.447 1950 0.295 7800 0.195 38000 0.121 35 0.986 125 0.673 500 0.444 2000 0.293 8000 0.137 40000 0.119 36 0.977 130 0.665 520 0.439 2100 0.289 8200 0.192 42000 0.117 37 0.969 135 0.657 540 0.434 2200 0.285 8400 0.190 44000 0.116 38 0.962 140 0.650 560 0.429 2300 0.281 8600 0.189 46000 0.114 39 0.954 145 0.643 580 0.425 2400 0.274 8800 0.188 50000 0.111 40 0.947 150 0.637 600 0.420 2500 0.274 9000 0.187 41 0.940 155 0.631 620 0.416 2600 0.271 9200 0.185 42 0.933 160 0.625 640 0.412 2700 0.268 9400 0.184 43 0.927 165 0.619 660 0.408 2800 0.265 9600 0.183 44 0.920 170 0.613 680 0.405 2900 0.262 9800 0.182 45 0.914 175 0.608 700 0.401 3000 0.259 10000 0.181 46 0.908 180 0.603 720 0.398 3100 0.257 10500 0.178 47 0.902 185 0.598 740 0.395 3200 0.254 11000 0.176 48 0.896 190 0.593 760 0.391 3300 0.252 11500 0.173 49 0.891 195 0.589 780 0.388 3400 0.250 12000 0.171 50 0.896 200 0.584 800 0.385 3500 0.248 12500 0.169 52 0.875 210 0.576 820 0.383 3600 0.246 13000 0.167 54 0.865 220 0.568 840 0.380 3700 0.243 13500 0.165 56 0.856 230 0.560 860 0.377 3800 0.242 14000 0.163 58 0.847 240 0.553 880 0.375 3900 0.240 14500 0.162 23.100 CHAPTER TWENTY-THREE 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 LIFE ADJUSTMENT FACTORS An adjusted fatigue life equation for a reliability of (100-n) percent An approximate equation for adjusted factor a 1 , which accounts for reliability, R, is calculated from the Weibull distribution. The adjusted fatigue life for non-conventional materi- als and operating conditions. For values of X and Y , refer to Table 23-39 and also to bearing tables given in FAG catalogue. For values of X and Y of deep groove ball bearings with increased radial clearance, refer to Table 23-47b. L 10a ¼ a 2 a 3 L 10 ð23-183Þ where a 2 ¼ life adjustment factor for materials ¼ 3 for radial ball bearings of good quality as per AFBMA ¼ 0.2 to 2.0 for normal bearing materials ¼ 2.0 for most common material, AISI 52100 a 3 ¼ life adjustment factor for application operating conditions ¼ 1 for well and adequately lubricated bearings < 1 for other adverse lubricating conditions and temperatures. The standard does not yet include values of a 3 TABLE 23-47a Values of radial factors X and thrust factors Y for deep groove ball bearings with increase In radial clearance Normal Bearing Standard clearance Bearing clearance C3 a Bearing clearance C4 a F a F r e F a F r > e F a F r e F a F r > e F a F r e F a F r > e f o F a C o e XYXYe XYXYe XYXY 0.3 0.22 1 0 0.56 2.0 0.32 1 0 0.46 1.70 0.40 1 0 0.44 1.40 0.5 0.24 1 0 0.56 1.8 0.35 1 0 0.46 1.56 0.43 1 0 0.44 1.31 0.9 0.28 1 0 0.56 1.6 0.39 1 0 0.46 1.41 0.45 1 0 0.44 1.23 1.6 0.32 1 0 0.56 1.4 0.43 1 0 0.46 1.27 0.48 1 0 0.44 1.16 3.0 0.36 1 0 0.56 1.2 0.48 1 0 0.46 1.14 0.52 1 0 0.44 1.08 6.0 0.43 1 0 0.56 1.0 0.54 1 0 0.46 1.00 0.56 1 0 0.44 1.00 a C 3 , C 4 Standard for a radial clearance that is larger than normal. Values of factor f a are given in Table 23-47b Particular Formula DESIGN OF BEARINGS AND TRIBOLOGY 23.101 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 TABLE 23-47b Factor f o for deep groove ball bearings for use in Table 23-47a Factor f o Bore Bearing series reference number 160 60 62 63 64 00 — 12.4 12.1 11.3 — 01 — 13.0 12.2 11.1 — 02 13.9 13.9 13.1 12.1 — 03 14.3 14.3 13.1 12.2 10.9 04 14.9 13.9 13.1 12.1 11.0 05 15.4 14.5 13.8 12.4 12.1 06 15.2 14.8 13.8 13.0 12.2 07 15.6 14.8 13.8 13.1 12.1 08 15.9 15.2 14.0 13.0 12.2 09 15.9 15.4 14.1 13.0 12.1 10 16.1 15.6 14.3 13.0 12.2 11 16.1 15.4 14.3 12.9 12.2 12 16.3 15.5 14.3 13.1 12.3 13 16.4 15.7 14.3 13.2 12.3 14 16.2 15.5 14.4 13.2 12.1 15 16.4 15.7 14.7 13.2 12.2 16 16.4 15.6 14.6 13.2 12.3 17 16.4 15.7 14.7 13.1 12.3 18 16.3 15.6 14.5 13.9 12.2 19 16.5 15.7 14.4 13.9 20 16.4 15.9 14.4 13.8 21 16.3 15.8 14.3 13.7 22 16.3 15.6 14.3 13.8 24 16.4 15.9 14.8 13.5 26 16.4 15.8 14.5 13.6 28 16.4 16.0 14.8 13.6 30 16.4 16.0 15.2 13.7 32 16.4 16.0 15.2 13.9 34 16.4 15.7 15.3 13.9 36 16.3 15.6 15.3 13.9 38 16.4 15.8 15.0 14.0 40 16.3 15.6 15.3 14.1 44 16.3 15.6 15.2 14.1 48 16.4 15.8 15.2 14.2 52 16.4 15.7 15.2 56 16.4 15.9 15.3 60 16.4 15.7 64 16.4 15.9 68 16.3 15.8 72 16.4 15.9 76 16.5 15.9 TABLE 23-48 Life adjustment factor for reliability a 1 Reliability R, % L n Adjustment factor, a 1 90 L 10 1 95 L 5 0.65 96 L 4 0.53 97 L 3 0.44 98 L 2 0.33 99 L 1 0.21 Note: These values of a 1 and a 2 have to be used judiciously and designers are advised to consult manufacturer’s Catalogue 23.102 CHAPTER TWENTY-THREE 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 From Eq. (23-177a), an adjusted fatigue life equation taking into consideration adjustment factors a 1 , a 2 and a 3 , and for a failure probability of n as per ISO 281 An adjusted fatigue life equation, which accounts for variation in vibration and shock, speed, environment, etc in addition to adjustment factors a 1 , a 2 and a 3 From Eq. (23-186a), the basic equivalent load rating, which accounts for application factor K a , and adjust- ment factors a 1 , a 2 and a 3 Fig. 23-54 shows the plot of relative life vs probability of failure in percent. L 10 life (also called as B10 life or minimum life), which indicates a 10% probability of failure, i.e. 90% of the loaded bearings will survive beyond this life, is taken as reference. L 50 in Fig. 23-54 indicates median life with a 50% probability of failure, which is also known as average life. From Fig. 23-54 it can be seen that L 50 % 5L 10 , which indicates only 50% of the bearings will survive this longer life. For life curves of ball bearings as per SKF and New Departure (ND) and Needle-bearings L na ¼ a 1 a 2 a 3 C F m ¼ a 1 a 2 a 3 L ð23-184aÞ where L in millions of revolutions L hna ¼ a 1 a 2 a 3 L h ð23-184bÞ where L h in h L ¼ a 1 a 2 a 3 C K a F m ð23-185Þ where L in 10 6 revolutions K a ¼ application factor taken from Table 23-49 C ¼ K a F L a 1 a 2 a 3 1=m ð23-186Þ where L in 10 6 revolutions Refer to Fig. 23-55 Particular Formula TABLE 23-49 Load application factor K a for use in Eqs. (23-185) and (23-186) Operating conditions Applications K a Precision gearing 1.0–1.1 Commercial gearing 1.1–1.3 Applications with poor bearing seals 1.2 Smooth operation free from shock Machinery with no impact: Electric motors, machine tools, air conditioners 1–1.2 Normal operation Machinery with light impact: Air blowers, compressors, elevators, cranes, paper making machines 1.2–1.5 Operation accompanied Machinery with moderate impact: by shock and vibration Construction machines crushers, vibration screens, rolling mills 1.5–3.0 DESIGN OF BEARINGS AND TRIBOLOGY 23.103 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 L 10 L 50 1 0102030405060 Probability of failure, percent 70 80 90 100 5 10 Relative fatigue life 15 20 FIGURE 23-54 Typical life distribution in rolling bearings. (Courtesy: SKF Industries, Inc.) ND T-Needle SKF 0•2 500 1,000 2,000 3,000 5,000 Life of Bearing, Hours 10,000 20,000 50,000 0•3 0•4 0•5 0•7 Load Factor K l 1•0 1•5 2•0 2•5 FIGURE 23-55 Life curves of ball and needle bearings. 23.104 CHAPTER TWENTY-THREE 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 [...]... 10B502 12B502 15B502 17B502 20B502 25B502 30B502 35B502 40B502 45B502 50B502 55B502 60B502 65B502 70B502 75B502 80B502 85B502 90B502 95B502 100B502 105B502 110B502 120 B502 10 12 15 17 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 120 120 0TV 120 1TV 120 2TV 120 3TV 120 4TV 120 5TV 120 6TV 120 7TV 120 8TV 120 9TV 121 0TV 121 1TV 121 2TV 121 3TV 121 4TV 121 5TV 121 6TV 121 7TV 121 8TV 121 9M 122 0M 122 1M 122 2M 122 4M... 121 5TV 121 6TV 121 7TV 121 8TV 121 9M 122 0M 122 1M 122 2M 122 4M FAG 120 0E 01E 02E 120 3E 04E 05E 120 6E 07E 08E 120 9E 10E 11E 121 2E 13E 14 121 5 16 17 121 8 19 20 122 1 22 24 SKF 10 12 15 71 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 120 d 30 32 35 40 47 52 62 72 80 85 90 100 110 120 125 130 140 150 160 170 180 190 200 215 D 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 26 28 30 32 34 36 38 42... 3.4–4.0 Printing machines 4.0–4.5 Papermaking machines Wet sections Dry sections Refiners Calendars 5.0–6.0 5.0–6.0 4.5–4.6 4.0–4.5 Centrifugal casting machines 3.4–4.0 Textile machines 3.6–4.7 Machine tools Lathes, boring and milling machines Grinding, lapping, and polishing machines 2.7–4.5 2.7–4.5 Woodworking machines Milling cutters and cutter shafts Saw mills (con rods) 3.0–4.0 2.8–3.3 Machines for... cos Dpw ¼ 508 0.01 0.02 0.03 105.4 122 .9 134.5 0.01 0.02 0.03 109.7 127 .8 139.5 107.1 124 .7 136.2 105.6 123 .0 134.3 0.04 0.05 0.06 143.4 150.7 156.9 0.04 0.05 0.06 148.3 155.2 160.9 144.7 151.5 157.0 142.8 149.4 154.9 0.07 0.08 0.09 162.4 167.2 171.7 0.07 0.08 0.09 165.6 169.5 172.8 161.6 165.5 168.7 159.4 163.2 166.4 0.10 0 .12 0.14 175.7 183.0 189.4 0.10 0 .12 0.14 175.5 179.7 182.3 171.4 175.4... 6206 07 08 09 10 6211 12 13 14 6215 16 17 18 19 6220 21 22 24 6226 6228 6230 32 34 36 38 40 6244 6248 6252 6256 SKF 10 12 15 17 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 120 130 140 150 160 170 180 190 200 220 240 260 280 d 30 32 35 40 47 52 62 72 50 85 90 100 110 120 125 130 140 150 160 170 180 190 200 215 230 250 270 290 310 320 340 360 400 440 480 500 D 9 10 11 12 14 15 16 17 18 19... 1760 7.5 3000 8.0 3400 10.0 4000 12. 2 4650 15.6 6000 16.0 6950 19.3 7800 22.0 9150 22.8 10600 27.0 122 00 30.0 14000 31.0 13700 34.5 15000 39.0 17000 46.0 20900 49.0 23600 57.0 27000 64.0 30000 69.5 32500 75.0 39000 88.0 53000 120 .0 N SKF Static, Co Basic load rating capacity 61 72 90 114 176 204 240 305 355 400 475 540 620 720 710 800 830 980 1080 120 0 120 0 1370 1600 2120 N Fatigue load limit, Fn SKF... 51000 57000 N SKF Static, Co 9360 10800 127 00 17000 19000 22500 26500 33800 39000 43600 50700 58500 65000 74100 79300 88400 97500 117000 133000 143000 N SKF 12. 50 12. 50 18.00 21.20 25.00 29.00 38.00 41.50 51.00 57.00 62.00 75.00 80.00 88.00 98.00 108.00 132.00 143.00 156.00 163.00 16300 kN FAG Dynamic, C 2750 112 134 176 204 280 355 430 570 695 720 915 1120 125 0 1340 1430 1500 1700 1930 2160 2360 N... 7208B 7209B 7210B 7211B 7212B 7213B 7214B 7215B 7216B 7217B 7218B 7219B 7220B 7221B 7222B 7222B 15BA02 17BA02 20BA02 25BA02 30BA02 35BA02 40BA02 45BA02 50BA02 55BA02 60BA02 65BA02 70BA02 75BA02 80BA02 85BA02 90BA02 95BA02 100BA02 105BA02 110BA02 120 BA02 10 12 15 17 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 120 d 30 32 35 40 47 52 62 72 80 85 90 100 110 120 125 130 140 150 160 170 180... 6301 6302 6303 04 05 06 07 08 09 6310 11 12 13 14 15 16 17 18 19 20 6321 22 24 26 28 30 32 34 6336 38 40 44 SKF 10 12 15 17 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 120 130 140 150 160 170 180 190 200 220 240 d 30 37 42 47 52 62 72 80 90 100 110 120 130 140 150 160 170 180 190 200 215 225 240 260 280 300 320 340 360 380 400 420 460 500 D 11 12 13 14 15 17 19 21 23 25 27 29 31 33 35... 53.00 62.00 76.50 81.50 93.00 104.00 114.00 122 .00 125 .00 134.00 143.00 163.00 173.00 190.00 212. 00 228.00 255.00 285.00 300.00 325.00 355.00 375.00 380.00 430.00 465.00 kN FAG 8060 9750 11400 13500 15900 22500 28100 33200 41000 52700 61800 71500 81900 92300 104000 114000 124 000 133000 143000 153000 174000 182000 203000 208000 290000 251000 276000 276000 3120 00 351000 371000 377000 410000 N SKF Dynamic, . 15.2 14.0 13.0 12. 2 09 15.9 15.4 14.1 13.0 12. 1 10 16.1 15.6 14.3 13.0 12. 2 11 16.1 15.4 14.3 12. 9 12. 2 12 16.3 15.5 14.3 13.1 12. 3 13 16.4 15.7 14.3 13.2 12. 3 14 16.2 15.5 14.4 13.2 12. 1 15 16.4. — 01 — 13.0 12. 2 11.1 — 02 13.9 13.9 13.1 12. 1 — 03 14.3 14.3 13.1 12. 2 10.9 04 14.9 13.9 13.1 12. 1 11.0 05 15.4 14.5 13.8 12. 4 12. 1 06 15.2 14.8 13.8 13.0 12. 2 07 15.6 14.8 13.8 13.1 12. 1 08 15.9. 0 .127 32 1. 012 110 0.699 470 0.452 1850 0.300 7400 0.198 34000 0 .125 33 1.003 115 0.690 480 0.449 1900 0.297 7600 0.196 36000 0 .123 34 0.994 120 0.681 490 0.447 1950 0.295 7800 0.195 38000 0 .121 35