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Question 11.11: The figure is a schematic drawing of a countershaft that sup......

The figure is a schematic drawing of a countershaft that supports two V-belt pulleys. The countershaft runs at 1200 rev/min and the bearings are to have a life of 60 kh at a combined reliability of 0.999. The belt tension on the loose side of pulley A is 15 percent of the tension on the tight side. Select deep-groove bearings from Table 11–2 for use at O and E, each to have a 25-mm bore, using an application factor of unity.

Manufacturer Rating Life, revolutions Weibull Parameters Rating Lives
{x}_{0} \theta b
1 90(10^{6}) 0 4.48 1.5
2 1(10^{6}) 0.02 4.459 1.483
Tables 11–2 and 11–3 are based on manufacturer 2.
Table 11-2
Dimensions and Load Ratings for Single-Row 02-Series Deep-Groove and Angular-Contact Ball Bearings
Bore, OD, Width, Fillet Radius, Shoulder Load Ratings, kN
Diameter, mm Deep Groove Angular Contact
mm mm mm mm 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 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
pr. 11.11
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The reliability of the individual bearings is R={\sqrt{0.999}}=0.9995

From statics,

\begin{array}{l l}{{R_{O}^{y}=-163.4\,{\mathrm{N}},}}&{{R_{O}^{{z}}=107\,{\mathrm{N}},}}\\ {{R_{E}^{y}=-89.2\,{\mathrm{N}},}}&{{R_{E}^{z}=-174.4\,{\mathrm{N}},}}\end{array}\begin{array}{l}{{R_{O}=195\,{\mathrm{N}}}}\\ {{R_{E}=\mathrm{196\,{\mathrm{N}}}}}\end{array}

 

x_{D}=\frac{60\,000(1200)(60)}{10^{6}}=4320

 

C_{10}=0.196\left\{\frac{4340}{0.02+4.439[\ln(1/0.9995)]^{1/1.483}}\right\}^{1/3}=8.9\,kN

A 02-25 mm deep-groove ball bearing has a basic load rating of 14.0 kN which is ample. An extra-light bearing could also be investigated.

fig. 11
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