Timken rates its bearings for 3000 hours at 500 rev/min. Determine the catalog rating for a ball bearing running for 10000 hours at 1800 rev/min with a load of 4.25 kN with a reliability of 90 percent.

the catalog rating for the ball bearing is 9.73 kN

Explanation:

Given that;

Bearing Life1 = 3000 Hr

Speed of rotation1 = 500 Rev/min

Radial Load, P1 = ?

Bearing Life2 = 10000 Hr

Speed of rotation2 = 1800 Rev/min

Radial Load, P2 = 4.25 kN

first Let's find bearing life in million revolution L1

L1 =  (3000 × 500 × 60) / 10⁶

L1 = 90 millions

next we find bearing life in million revolution L2

L2 = (10000 × 1800 × 60) / 10⁶

L2 = 1080 millions

Now Using the formula

P1L1^(1/3) = P2L2^(1/3)

P1 = P2L2^(1/3) / L1^(1/3)

so we substitute

P1 = [4.25 × (1080)^1/3] / (90)^1/3

= 43.6043 / 4.4814

= 9.73 kN

Therefore the catalog rating for the ball bearing is 9.73 kN

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