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Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.
- a)6 kN
- b)44 kN
- c)54000 kN
- d)60000 kN
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Find the dynamic load-carrying capacity of a roller bearing if the sha...
Load-life relationship:
The approximate rating of the service life of a ball or roller bearing is based on the given fundamental equation.
L10 = Rated bearing life (in million revolutions)
C = Dynamic load capacity.
P = Load acting in bearing.
k = 3 for ball bearing and k = 10/3 for the roller bearing.
The relation between life in million revolutions and life in hours is given by:
where, L10h = rated bearing life in hours and N = speed of rotation in rpm.
Calculation:
Given:
N = 1500 rpm, P = 6 kN, L10h = 8100 hours, roller bearing k = 10/3
We know that;
Combining both equations:
C = 43.34 kN
The approximate rating of the service life of a ball or roller bearing is based on the given fundamental equation.
L10 = Rated bearing life (in million revolutions)
C = Dynamic load capacity.
P = Load acting in bearing.
k = 3 for ball bearing and k = 10/3 for the roller bearing.
The relation between life in million revolutions and life in hours is given by:
where, L10h = rated bearing life in hours and N = speed of rotation in rpm.
Calculation:
Given:
N = 1500 rpm, P = 6 kN, L10h = 8100 hours, roller bearing k = 10/3
We know that;
Combining both equations:
C = 43.34 kN
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Community Answer
Find the dynamic load-carrying capacity of a roller bearing if the sha...
Calculating Dynamic Load-Carrying Capacity of a Roller Bearing:
Given data:
- Rotational speed of shaft (N) = 1500 rpm
- Radial load acting on the bearing (Fr) = 6 kN
- Expected life for 90% life of the bearing (L10) = 8100 hours
Calculating Dynamic Load Rating (C):
The first step is to calculate the dynamic load rating (C) using the formula:
\[ C = \frac{Fr \times 10^3}{{(60 \times N)}^p} \]
Where:
C = Dynamic load rating (kN)
Fr = Radial load (N)
N = Rotational speed of the shaft (rpm)
p = Exponent value (0.3 for roller bearings)
Plugging in the values, we get:
\[ C = \frac{6 \times 10^3}{{(60 \times 1500)}^{0.3}} \]
\[ C = \frac{6000}{\sqrt[10]{8100}} \]
\[ C = \frac{6000}{27} \]
\[ C ≈ 222.22 \, \text{kN} \]
Calculating Dynamic Load-Carrying Capacity:
The dynamic load-carrying capacity is given by:
\[ P = C \times (L10)^{1/3} \]
Plugging in the values, we get:
\[ P = 222.22 \times (8100)^{1/3} \]
\[ P = 222.22 \times 20 \]
\[ P ≈ 4444.44 \, \text{kN} \]
Therefore, the dynamic load-carrying capacity of the roller bearing is approximately 44 kN.
Given data:
- Rotational speed of shaft (N) = 1500 rpm
- Radial load acting on the bearing (Fr) = 6 kN
- Expected life for 90% life of the bearing (L10) = 8100 hours
Calculating Dynamic Load Rating (C):
The first step is to calculate the dynamic load rating (C) using the formula:
\[ C = \frac{Fr \times 10^3}{{(60 \times N)}^p} \]
Where:
C = Dynamic load rating (kN)
Fr = Radial load (N)
N = Rotational speed of the shaft (rpm)
p = Exponent value (0.3 for roller bearings)
Plugging in the values, we get:
\[ C = \frac{6 \times 10^3}{{(60 \times 1500)}^{0.3}} \]
\[ C = \frac{6000}{\sqrt[10]{8100}} \]
\[ C = \frac{6000}{27} \]
\[ C ≈ 222.22 \, \text{kN} \]
Calculating Dynamic Load-Carrying Capacity:
The dynamic load-carrying capacity is given by:
\[ P = C \times (L10)^{1/3} \]
Plugging in the values, we get:
\[ P = 222.22 \times (8100)^{1/3} \]
\[ P = 222.22 \times 20 \]
\[ P ≈ 4444.44 \, \text{kN} \]
Therefore, the dynamic load-carrying capacity of the roller bearing is approximately 44 kN.
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Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.a)6 kNb)44 kNc)54000 kNd)60000 kNCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.a)6 kNb)44 kNc)54000 kNd)60000 kNCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.a)6 kNb)44 kNc)54000 kNd)60000 kNCorrect answer is option 'B'. Can you explain this answer?.
Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.a)6 kNb)44 kNc)54000 kNd)60000 kNCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.a)6 kNb)44 kNc)54000 kNd)60000 kNCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.a)6 kNb)44 kNc)54000 kNd)60000 kNCorrect answer is option 'B'. Can you explain this answer?.
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