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## Q. 3.11.9

In Ex. 11–3, the minimum required load rating for 99 percent reliability, at  $x_D ={L_D}/{L_{10}}= 540 \ , \ is \ C_{10} = 6696 \ lbf = 29.8$  kN. From Table 11–2 a 02-40 mm deepgroove ball bearing would satisfy the requirement. If the bore in the application had to be 70 mm or larger (selecting a 02-70 mm deep-groove ball bearing), what is the resulting reliability?

## Verified Solution

From Table 11–2,

 Table 11–2 Dimensions and Load Ratings for Single-Row 02-Series Deep-Groove and Angular-Contact Ball Bearings Bore, mm OD, mm Width, mm Fillet Radius, mm Shoulder Diameter, mm Load Ratings, kN Deep Groove Angular Contact $d_S$ $d_H$ $C_{10}$ $C_0$ $C_{10}$ $C_0$ 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 17 470 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 26 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 1.5 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

for a 02-70 mm deep-groove ball bearing, $C_{10} = 61.8 \ \ kN =13 888$ lbf. Using Eq. (11–19)

$R\doteq 1-\left\{\frac{x_D\left(\frac{a_fF_D}{C_{10}} \right)^a-x_0 }{\theta -x_0} \right\}^b \ \ R \ge 0.90$,

recalling from Ex. 11–3 that $a_f = 1.2 \ , \ F_D = 413 \ lbf \ , \ x_0 = 0.02 \ , \left(\theta − x_0 \right) = 4.439, and \ b = 1.483$ , we can write

$R\doteq 1-\left\{\frac{\left[540\left[\frac{1.2\left(413\right) }{13 888} \right]^3-0.02 \right] }{4.439} \right\}^{1.483} =0.0999 963$
which, as expected, is much higher than 0.99 from Ex. 11–3.