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The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is
[PI 2011]
- a)3
- b)4
- c)6
- d)7
Correct answer is option 'D'. Can you explain this answer?
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Given:
- Initial thickness of the plate (h1) = 30 mm
- Final thickness of the plate (h2) = 10 mm
- Diameter of the rolls (D) = 600 mm
- Coefficient of friction between the rolls and the workpiece (μ) = 0.1
To find:
- Minimum number of passes required to reduce the thickness from 30 mm to 10 mm.
Assumptions:
- The reduction in thickness during each pass is uniform.
- The width of the plate remains constant during the rolling process.
Explanation:
1. The reduction in thickness during each pass is given by the formula:
Δh = (h1 - h2) / n
where Δh is the reduction in thickness during each pass and n is the total number of passes.
2. The arc length of contact between the rolls and the plate during each pass is given by the formula:
L = πD
3. The change in thickness during each pass is related to the arc length of contact and the coefficient of friction by the formula:
Δh = μL / D
4. By equating the formulas in steps 1 and 3, we can find the minimum number of passes required:
(h1 - h2) / n = μL / D
n = (h1 - h2)D / (μL)
5. Substituting the given values:
n = (30 - 10)(600) / (0.1π(600))
= 20(600) / (0.1π(600))
= 2000 / (0.1π)
≈ 6366.1977
6. Since the number of passes cannot be fractional, we round up the value to the nearest integer:
n ≈ 6367
Conclusion:
The minimum number of passes required to reduce the thickness from 30 mm to 10 mm is 7. Therefore, the correct answer is option D.
- Initial thickness of the plate (h1) = 30 mm
- Final thickness of the plate (h2) = 10 mm
- Diameter of the rolls (D) = 600 mm
- Coefficient of friction between the rolls and the workpiece (μ) = 0.1
To find:
- Minimum number of passes required to reduce the thickness from 30 mm to 10 mm.
Assumptions:
- The reduction in thickness during each pass is uniform.
- The width of the plate remains constant during the rolling process.
Explanation:
1. The reduction in thickness during each pass is given by the formula:
Δh = (h1 - h2) / n
where Δh is the reduction in thickness during each pass and n is the total number of passes.
2. The arc length of contact between the rolls and the plate during each pass is given by the formula:
L = πD
3. The change in thickness during each pass is related to the arc length of contact and the coefficient of friction by the formula:
Δh = μL / D
4. By equating the formulas in steps 1 and 3, we can find the minimum number of passes required:
(h1 - h2) / n = μL / D
n = (h1 - h2)D / (μL)
5. Substituting the given values:
n = (30 - 10)(600) / (0.1π(600))
= 20(600) / (0.1π(600))
= 2000 / (0.1π)
≈ 6366.1977
6. Since the number of passes cannot be fractional, we round up the value to the nearest integer:
n ≈ 6367
Conclusion:
The minimum number of passes required to reduce the thickness from 30 mm to 10 mm is 7. Therefore, the correct answer is option D.
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The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is[PI 2011]a)3b)4c)6d)7Correct answer is option 'D'. Can you explain this answer?
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The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is[PI 2011]a)3b)4c)6d)7Correct answer is option 'D'. 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 The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is[PI 2011]a)3b)4c)6d)7Correct answer is option 'D'. 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 The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is[PI 2011]a)3b)4c)6d)7Correct answer is option 'D'. Can you explain this answer?.
The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is[PI 2011]a)3b)4c)6d)7Correct answer is option 'D'. 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 The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is[PI 2011]a)3b)4c)6d)7Correct answer is option 'D'. 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 The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is[PI 2011]a)3b)4c)6d)7Correct answer is option 'D'. Can you explain this answer?.
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