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A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is
[ME 2006]
- a)1.0 mm
- b)1.5 mm
- c)2.5 mm
- d)3.7 mm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thic...
Given, Initial thickness of sheet,
ti = 4 mm = 4 × 10–3 m
Diameter of roll,
D = 300 mm = 0.3 m
Frictional coefficient at work-roll interface,
μ = 0.1
Let tf = Final thickness of sheet after rolling
For single pass without slipping minimum possible thickness,
ti = 4 mm = 4 × 10–3 m
Diameter of roll,
D = 300 mm = 0.3 m
Frictional coefficient at work-roll interface,
μ = 0.1
Let tf = Final thickness of sheet after rolling
For single pass without slipping minimum possible thickness,
Most Upvoted Answer
A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thic...
Given:
- Thickness of the sheet = 4 mm
- Diameter of rolls = 300 mm
- Friction coefficient at the work-roll interface = 0.1
To find:
- Minimum possible thickness of the sheet that can be produced in a single pass
Assumptions:
- The deformation is purely elastic.
- There is no necking or any other form of instability during the rolling process.
- The contact between the rolls and the sheet is uniform and there is no slipping.
Formula:
The reduction in thickness of the sheet in a single pass can be calculated using the equation:
Δt = (1 - μ^2) * (t - t_0)
Where,
Δt is the reduction in thickness of the sheet
μ is the friction coefficient
t is the initial thickness of the sheet
t_0 is the minimum possible thickness of the sheet
Calculation:
Given, t = 4 mm and μ = 0.1
Substituting the values in the formula:
Δt = (1 - 0.1^2) * (4 - t_0)
Δt = 0.99 * (4 - t_0)
We want to find the minimum possible thickness, which means Δt should be maximum.
To maximize Δt, we need to minimize (4 - t_0).
Since Δt is the reduction in thickness, it cannot be negative. Therefore, (4 - t_0) should be greater than or equal to zero.
4 - t_0 ≥ 0
t_0 ≤ 4
Therefore, the minimum possible thickness of the sheet that can be produced in a single pass is 4 mm.
Hence, the correct answer is option C) 2.5 mm.
- Thickness of the sheet = 4 mm
- Diameter of rolls = 300 mm
- Friction coefficient at the work-roll interface = 0.1
To find:
- Minimum possible thickness of the sheet that can be produced in a single pass
Assumptions:
- The deformation is purely elastic.
- There is no necking or any other form of instability during the rolling process.
- The contact between the rolls and the sheet is uniform and there is no slipping.
Formula:
The reduction in thickness of the sheet in a single pass can be calculated using the equation:
Δt = (1 - μ^2) * (t - t_0)
Where,
Δt is the reduction in thickness of the sheet
μ is the friction coefficient
t is the initial thickness of the sheet
t_0 is the minimum possible thickness of the sheet
Calculation:
Given, t = 4 mm and μ = 0.1
Substituting the values in the formula:
Δt = (1 - 0.1^2) * (4 - t_0)
Δt = 0.99 * (4 - t_0)
We want to find the minimum possible thickness, which means Δt should be maximum.
To maximize Δt, we need to minimize (4 - t_0).
Since Δt is the reduction in thickness, it cannot be negative. Therefore, (4 - t_0) should be greater than or equal to zero.
4 - t_0 ≥ 0
t_0 ≤ 4
Therefore, the minimum possible thickness of the sheet that can be produced in a single pass is 4 mm.
Hence, the correct answer is option C) 2.5 mm.
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A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is[ME 2006]a)1.0 mmb)1.5 mmc)2.5 mmd)3.7 mmCorrect answer is option 'C'. Can you explain this answer?
Question Description
A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is[ME 2006]a)1.0 mmb)1.5 mmc)2.5 mmd)3.7 mmCorrect 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 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is[ME 2006]a)1.0 mmb)1.5 mmc)2.5 mmd)3.7 mmCorrect 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 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is[ME 2006]a)1.0 mmb)1.5 mmc)2.5 mmd)3.7 mmCorrect answer is option 'C'. Can you explain this answer?.
A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is[ME 2006]a)1.0 mmb)1.5 mmc)2.5 mmd)3.7 mmCorrect 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 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is[ME 2006]a)1.0 mmb)1.5 mmc)2.5 mmd)3.7 mmCorrect 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 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is[ME 2006]a)1.0 mmb)1.5 mmc)2.5 mmd)3.7 mmCorrect answer is option 'C'. Can you explain this answer?.
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