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A system involves four identical ball bearings, each subjected to a radial load of 2500 N. The reliability of the system, i.e., one out of four bearings failing during the lifetime of five million revolutions, is 82%. The dynamic load carrying capacity of the bearing, so as to select it from the manufacturer’s catalogue based on 90% reliability will be
  • a)
    5248 N
  • b)
    2548 N
  • c)
    5629 N
  • d)
    3456 N
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A system involves four identical ball bearings, each subjected to a r...
P = 2500 N
Reliability of the system = 0.82
Hence reliability of each bearing = [0.82]¼
= 0.95
L10 = 9.25 million revolution
C = (9.25)⅓. X P
= (9.25) x 2500 = 5248
Hence, dynamic load carrying capacity of the bearing is = 5248 N
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Most Upvoted Answer
A system involves four identical ball bearings, each subjected to a r...
Given Information:
Radial load on each ball bearing = 2500 N
Reliability of the system = 82%
Number of ball bearings in the system = 4
Lifetime of the system = 5 million revolutions

To find:
Dynamic load carrying capacity of the bearing for 90% reliability

Solution:
Step 1: Calculation of the probability of failure of one bearing
Probability of failure of one bearing = 1 - reliability of the system
Probability of failure of one bearing = 1 - 0.82
Probability of failure of one bearing = 0.18

Step 2: Calculation of the probability of failure of all four bearings
Probability of failure of all four bearings = (0.18)^4
Probability of failure of all four bearings = 0.000104976

Step 3: Calculation of the dynamic load carrying capacity of the bearing for 90% reliability
Let X be the dynamic load carrying capacity of the bearing
Probability of failure of one bearing at X load carrying capacity = 1 - 0.9
Probability of failure of one bearing at X load carrying capacity = 0.1

From the manufacturer's catalogue, we can obtain the load carrying capacity of the bearing for 0.1 probability of failure, which is denoted by C90.

Therefore, X/C90 = (2500 N/C90)^0.67
X = C90 (2500 N/C90)^0.67

Step 4: Calculation of the dynamic load carrying capacity of the bearing for 90% reliability
Probability of failure of all four bearings at X load carrying capacity = (0.1)^4
Probability of failure of all four bearings at X load carrying capacity = 0.0001

We need to ensure that the probability of failure of all four bearings at X load carrying capacity is less than or equal to the probability of failure of all four bearings in the given system, which is 0.000104976.

Therefore, we can write the following equation:

(0.1)^4 ≤ (0.18)^4

This equation is satisfied for any value of X.

Therefore, the dynamic load carrying capacity of the bearing for 90% reliability is:

X = C90 (2500 N/C90)^0.67

Answer: Option A (5248 N)
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A system involves four identical ball bearings, each subjected to a radial load of 2500 N. The reliability of the system, i.e., one out of four bearings failing during the lifetime of five million revolutions, is 82%. The dynamic load carrying capacity of the bearing, so as to select it from the manufacturer’s catalogue based on 90% reliability will bea) 5248 Nb) 2548 Nc) 5629 Nd) 3456 NCorrect answer is option 'A'. Can you explain this answer?
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