An anti-friction bearing is to be heated in an oil bath at 250 degrees. The inside diameter of the bearing is 3.5". What is the bore size after heating?

When a bearing is heated, it expands due to thermal expansion. The bore size of the bearing will increase slightly as the temperature rises. The degree of expansion can be calculated using the coefficient of thermal expansion for the material of the bearing.

For most materials, the coefficient of thermal expansion can be found in engineering references, and for metals, it's typically around 6 to 10 x 10^-6 per degree Fahrenheit. Given that the original bore size is 3.5 inches, we need to apply the formula for linear expansion:

[

\Delta L = L_0 \times \alpha \times \Delta T

]

Where:

• ( \Delta L ) is the change in length (or diameter in this case),

• ( L_0 ) is the original size (3.5 inches),

• ( \alpha ) is the coefficient of thermal expansion,

• ( \Delta T ) is the temperature change in degrees Fahrenheit.

Assuming a typical coefficient (let's say 7 x 10^-6), and considering the temperature increase to 250 degrees, you can compute:

1. Determine ( \Delta T ) based on a reference temperature (for instance, room temperature is around 70