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A ball bearing is operated on a work cycle consisting of three parts: a radial load of at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearings is 10, 000 hrs. The dynamic load carrying capacity of the bearings is
- a)11, 000 N
- b)22, 000 N
- c)33, 000 N
- d)55, 000 N
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A ball bearing is operated on a work cycle consisting of three parts:...
N = N1 + N2 + N3 = 3 x 360 = 1080 rpm
Pe = 3823 N
C = 33082 N
Most Upvoted Answer
A ball bearing is operated on a work cycle consisting of three parts:...
Calculation of Dynamic Load Carrying Capacity of Ball Bearing
Given parameters:
- Radial load of 1440 rpm for one quarter cycle
- Radial load of 5000 N at 720 rpm for one half of cycle
- Radial load of 2500 N at 1440 rpm for the remaining cycle
- Expected life of the bearings is 10,000 hrs
Step 1: Calculation of Equivalent Dynamic Load
The equivalent dynamic load (P) is calculated using the formula:
P = (X.Fr) + (Y.Fa)
Where,
X and Y are the radial and axial load factors respectively, which depend on the type of bearing and operating conditions.
Fr and Fa are the radial and axial loads respectively.
For ball bearings, the values of X and Y are given by the ISO standards as:
X = 1 for radial bearings
Y = 0.67 for radial bearings
The radial loads are given as:
Fr1 = 1440 rpm
Fr2 = 5000 N
Fr3 = 2500 N
Fa = 0 (since there is no axial load)
Therefore, the equivalent dynamic load is calculated as:
P = (X.Fr) + (Y.Fa)
= (1.0 x 1440) + (0.67 x 5000) + (1.0 x 2500)
= 8870 N
Step 2: Calculation of Dynamic Load Rating
The dynamic load rating (C) of the bearing is the load that a group of apparently identical bearings can endure for a rating life of 1 million revolutions.
The formula for dynamic load rating is given as:
C = (10^6 / L10).P
Where,
L10 is the rated life of the bearing in revolutions.
P is the equivalent dynamic load calculated in step 1.
Given, the expected life of the bearing is 10,000 hours. Therefore, the rated life of the bearing in revolutions is calculated as:
L10 = (10^6 / 60).n.Lh
Where,
n is the speed in revolutions per minute (rpm)
Lh is the expected life of the bearing in hours.
For the given parameters, n varies during the operating cycle. Therefore, the rated life is calculated as:
L10 = (10^6 / 60).[(1/4 x 1440) + (1/2 x 720) + (1/4 x 1440)].10,000
= 8.64 x 10^8 revolutions
Substituting the values of P and L10 in the formula for dynamic load rating, we get:
C = (10^6 / L10).P
= (10^6 / 8.64 x 10^8).8870
= 0.01025 x 8870
= 90.89 N
Step 3: Calculation of Dynamic Load Carrying Capacity
The dynamic load carrying capacity (Cdyn) is the load that a single bearing can endure for the rated life of 1 million revolutions.
The formula for dynamic load carrying capacity is given as:
Cdyn = (C / Fos).a1.a2.a3
Where,
Fos is the safety factor (usually taken as 1.5 to 2.5)
a1, a2, and a3 are the adjustment factors for operating conditions
Given parameters:
- Radial load of 1440 rpm for one quarter cycle
- Radial load of 5000 N at 720 rpm for one half of cycle
- Radial load of 2500 N at 1440 rpm for the remaining cycle
- Expected life of the bearings is 10,000 hrs
Step 1: Calculation of Equivalent Dynamic Load
The equivalent dynamic load (P) is calculated using the formula:
P = (X.Fr) + (Y.Fa)
Where,
X and Y are the radial and axial load factors respectively, which depend on the type of bearing and operating conditions.
Fr and Fa are the radial and axial loads respectively.
For ball bearings, the values of X and Y are given by the ISO standards as:
X = 1 for radial bearings
Y = 0.67 for radial bearings
The radial loads are given as:
Fr1 = 1440 rpm
Fr2 = 5000 N
Fr3 = 2500 N
Fa = 0 (since there is no axial load)
Therefore, the equivalent dynamic load is calculated as:
P = (X.Fr) + (Y.Fa)
= (1.0 x 1440) + (0.67 x 5000) + (1.0 x 2500)
= 8870 N
Step 2: Calculation of Dynamic Load Rating
The dynamic load rating (C) of the bearing is the load that a group of apparently identical bearings can endure for a rating life of 1 million revolutions.
The formula for dynamic load rating is given as:
C = (10^6 / L10).P
Where,
L10 is the rated life of the bearing in revolutions.
P is the equivalent dynamic load calculated in step 1.
Given, the expected life of the bearing is 10,000 hours. Therefore, the rated life of the bearing in revolutions is calculated as:
L10 = (10^6 / 60).n.Lh
Where,
n is the speed in revolutions per minute (rpm)
Lh is the expected life of the bearing in hours.
For the given parameters, n varies during the operating cycle. Therefore, the rated life is calculated as:
L10 = (10^6 / 60).[(1/4 x 1440) + (1/2 x 720) + (1/4 x 1440)].10,000
= 8.64 x 10^8 revolutions
Substituting the values of P and L10 in the formula for dynamic load rating, we get:
C = (10^6 / L10).P
= (10^6 / 8.64 x 10^8).8870
= 0.01025 x 8870
= 90.89 N
Step 3: Calculation of Dynamic Load Carrying Capacity
The dynamic load carrying capacity (Cdyn) is the load that a single bearing can endure for the rated life of 1 million revolutions.
The formula for dynamic load carrying capacity is given as:
Cdyn = (C / Fos).a1.a2.a3
Where,
Fos is the safety factor (usually taken as 1.5 to 2.5)
a1, a2, and a3 are the adjustment factors for operating conditions
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A ball bearing is operated on a work cycle consisting of three parts: a radial load of at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearings is 10, 000 hrs. The dynamic load carrying capacity of the bearings isa) 11, 000 Nb) 22, 000 Nc) 33, 000 Nd) 55, 000 NCorrect answer is option 'C'. Can you explain this answer?
Question Description
A ball bearing is operated on a work cycle consisting of three parts: a radial load of at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearings is 10, 000 hrs. The dynamic load carrying capacity of the bearings isa) 11, 000 Nb) 22, 000 Nc) 33, 000 Nd) 55, 000 NCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A ball bearing is operated on a work cycle consisting of three parts: a radial load of at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearings is 10, 000 hrs. The dynamic load carrying capacity of the bearings isa) 11, 000 Nb) 22, 000 Nc) 33, 000 Nd) 55, 000 NCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball bearing is operated on a work cycle consisting of three parts: a radial load of at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearings is 10, 000 hrs. The dynamic load carrying capacity of the bearings isa) 11, 000 Nb) 22, 000 Nc) 33, 000 Nd) 55, 000 NCorrect answer is option 'C'. Can you explain this answer?.
A ball bearing is operated on a work cycle consisting of three parts: a radial load of at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearings is 10, 000 hrs. The dynamic load carrying capacity of the bearings isa) 11, 000 Nb) 22, 000 Nc) 33, 000 Nd) 55, 000 NCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A ball bearing is operated on a work cycle consisting of three parts: a radial load of at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearings is 10, 000 hrs. The dynamic load carrying capacity of the bearings isa) 11, 000 Nb) 22, 000 Nc) 33, 000 Nd) 55, 000 NCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball bearing is operated on a work cycle consisting of three parts: a radial load of at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearings is 10, 000 hrs. The dynamic load carrying capacity of the bearings isa) 11, 000 Nb) 22, 000 Nc) 33, 000 Nd) 55, 000 NCorrect answer is option 'C'. Can you explain this answer?.
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