Products
Rewards 
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Please sign up to our reward program to support us in return and take advantage of the incredible listed offers.

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY 
BUSINESS MANAGER

Advertise your business, and reach millions of students around the world.

HOLOOLY 
TABLES

All the data tables that you may search for.

HOLOOLY 
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY 
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY 
HELP DESK

Need Help? We got you covered.

Chapter 3

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?

Step-by-Step

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.