Question

g a straight (cylindrical) roller bearing is subjected to a radial load of 20 kn. the life is to be 8000 h at a speed of 950 rev/min and exhibit a reliability of 0.95. what basic load rating should be used in selecting the bearing from a catalog of manufacturer.

Answer 1

To meet a bearing life of 8000 hours at 950 rev/min with 0.95 reliability and a radial load of 20 kN, select a bearing with a basic load rating of 4.92 kN.

In order to determine the appropriate basic load rating for the roller bearing, you can use the following equation based on the bearing life equation in the context of reliability and speed:

`\[ L_(10h) = \left( (C)/(P) \right)^3 \cdot 10^6 \]`

Where:

-
`\( L_(10h) \)` is the rated bearing life in hours (8000 hours in this case),

- C is the basic load rating (what we want to find),

- P is the equivalent dynamic bearing load.

The equivalent dynamic bearing load P is given by:

`\[ P = X \cdot F_r + Y \cdot F_a \]`

Where:

-
`\( F_r \)` is the radial load (20 kN in this case),

-
`\( F_a \)` is the axial load (assuming negligible axial load,
`\( F_a = 0 \))`,

- X and Y are factors depending on the type of bearing. In this case, we will use the values provided in Table 11-6.

Given that the Weibull parameter
`(\( \theta - x_(0) \))` is 4.439 and the speed is 950 rev/min, you can find X and Y from Table 11-6.

X = 0.56

Y = 0.84

Now, rearrange the equation for P to find C:

`\[ P = X \cdot F_r + Y \cdot F_a \]`

Since
`\(F_a\)` is negligible
`(\(F_a = 0\))`:

`\[ P = X \cdot F_r \]`

Now, calculate P:

`\[ P = 0.56 \cdot 20 \]\[ P = 11.2 \, \text{kN} \]`

Next, use the formula for C:

`\[ C = \left( (L_(10h))/(10^6) \right)^(1/3) \cdot P \]`

Plug in the values:

`\[ C = \left( (8000)/(10^6) \right)^(1/3) \cdot 11.2 \]\[ C \approx 4.92 \, \text{kN} \]`

Therefore, the basic load rating C for selecting the bearing from the catalog should be approximately
`\(4.92 \, \text{kN}\)`.

The complete question is:

A straight (cylindrical) roller bearing is subjected to a radial load of 20 kN. The life is to be 8000 h at a speed of 950 rev/min and exhibit a reliability of 0.95. What basic load rating should be used in selecting the bearing from a catalog of manufacturer 2 in Table 11-6 (Weibull parameter (theta - x_{0}) = 4.439 )