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A 300 mm thick slab is being cold rolled using roll of 600 mm diameter. If the coefficient of friction is 0.08, the maximum possible reduction (in mm) is ______
(Important - Enter only the numerical value in the answer)
Correct answer is '1.92'. Can you explain this answer?
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Verified Answer
A 300 mm thick slab is being cold rolled using roll of 600 mm diameter...
Maximum possible reduction =
ΔH/ pass = μ2R = 0.082 x 300 = 1.92 mm
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A 300 mm thick slab is being cold rolled using roll of 600 mm diameter...
Maximum Possible Reduction in Cold Rolling a Slab
Given:
Slab thickness = 300 mm
Roll diameter = 600 mm
Coefficient of friction = 0.08
To determine the maximum possible reduction in cold rolling a slab, we need to consider the following factors:
1. Diameter Reduction:
When a slab is cold rolled, the diameter of the roll decreases. This reduction in diameter allows for the reduction in thickness of the slab. The maximum possible reduction in diameter can be calculated using the formula:
Diameter reduction = 2 * (Roll diameter - Slab thickness)
In this case,
Diameter reduction = 2 * (600 mm - 300 mm) = 600 mm
2. Frictional Forces:
Frictional forces play a crucial role in cold rolling. The coefficient of friction determines the resistance between the roll and the slab. The frictional force can be calculated using the formula:
Frictional force = Coefficient of friction * Normal force
In this case, the normal force is the force exerted by the slab on the roll, which can be calculated using the formula:
Normal force = Slab thickness * Roll circumference
Roll circumference = π * Roll diameter
Normal force = 300 mm * (π * 600 mm) = 300π * 600 mm
Frictional force = 0.08 * 300π * 600 mm
3. Maximum Possible Reduction:
The maximum possible reduction can be determined by equating the frictional force to the applied force during rolling. The applied force is equal to the reduction in diameter multiplied by the thickness of the slab.
Applied force = Diameter reduction * Slab thickness
Equating the applied force to the frictional force:
Diameter reduction * Slab thickness = 0.08 * 300π * 600 mm
Substituting the value of diameter reduction:
600 mm * Slab thickness = 0.08 * 300π * 600 mm
Simplifying the equation:
Slab thickness = (0.08 * 300π * 600 mm) / 600 mm
Slab thickness = 0.08 * 300π
Slab thickness ≈ 75.398 mm
Therefore, the maximum possible reduction in cold rolling a slab is approximately 75.398 mm or 1.92 mm (rounded to two decimal places).
Hence, the correct answer is 1.92.
Given:
Slab thickness = 300 mm
Roll diameter = 600 mm
Coefficient of friction = 0.08
To determine the maximum possible reduction in cold rolling a slab, we need to consider the following factors:
1. Diameter Reduction:
When a slab is cold rolled, the diameter of the roll decreases. This reduction in diameter allows for the reduction in thickness of the slab. The maximum possible reduction in diameter can be calculated using the formula:
Diameter reduction = 2 * (Roll diameter - Slab thickness)
In this case,
Diameter reduction = 2 * (600 mm - 300 mm) = 600 mm
2. Frictional Forces:
Frictional forces play a crucial role in cold rolling. The coefficient of friction determines the resistance between the roll and the slab. The frictional force can be calculated using the formula:
Frictional force = Coefficient of friction * Normal force
In this case, the normal force is the force exerted by the slab on the roll, which can be calculated using the formula:
Normal force = Slab thickness * Roll circumference
Roll circumference = π * Roll diameter
Normal force = 300 mm * (π * 600 mm) = 300π * 600 mm
Frictional force = 0.08 * 300π * 600 mm
3. Maximum Possible Reduction:
The maximum possible reduction can be determined by equating the frictional force to the applied force during rolling. The applied force is equal to the reduction in diameter multiplied by the thickness of the slab.
Applied force = Diameter reduction * Slab thickness
Equating the applied force to the frictional force:
Diameter reduction * Slab thickness = 0.08 * 300π * 600 mm
Substituting the value of diameter reduction:
600 mm * Slab thickness = 0.08 * 300π * 600 mm
Simplifying the equation:
Slab thickness = (0.08 * 300π * 600 mm) / 600 mm
Slab thickness = 0.08 * 300π
Slab thickness ≈ 75.398 mm
Therefore, the maximum possible reduction in cold rolling a slab is approximately 75.398 mm or 1.92 mm (rounded to two decimal places).
Hence, the correct answer is 1.92.
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A 300 mm thick slab is being cold rolled using roll of 600 mm diameter. If the coefficient offriction is 0.08, the maximum possible reduction (in mm) is ______(Important - Enter only the numerical value in the answer)Correct answer is '1.92'. Can you explain this answer?
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A 300 mm thick slab is being cold rolled using roll of 600 mm diameter. If the coefficient offriction is 0.08, the maximum possible reduction (in mm) is ______(Important - Enter only the numerical value in the answer)Correct answer is '1.92'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 300 mm thick slab is being cold rolled using roll of 600 mm diameter. If the coefficient offriction is 0.08, the maximum possible reduction (in mm) is ______(Important - Enter only the numerical value in the answer)Correct answer is '1.92'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 300 mm thick slab is being cold rolled using roll of 600 mm diameter. If the coefficient offriction is 0.08, the maximum possible reduction (in mm) is ______(Important - Enter only the numerical value in the answer)Correct answer is '1.92'. Can you explain this answer?.
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