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In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate (under ideal rolling condition) can be atmost reduced to 20 mm in one pass, the coefficient of friction between the roll and the plate is?
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In a rolling operation using rolls of diameter 500 mm, if a 25 mm thic...
Introduction:
In a rolling operation, a plate is passed through a pair of rolls to reduce its thickness. The reduction in thickness depends on various factors, including the diameter of the rolls and the coefficient of friction between the rolls and the plate. In this case, we are given the diameter of the rolls and the maximum reduction in thickness that can be achieved in one pass. We need to determine the coefficient of friction between the roll and the plate.
Given Data:
- Diameter of rolls (D) = 500 mm
- Initial thickness of plate (t₁) = 25 mm
- Final thickness of plate (t₂) = 20 mm
Calculating the Reduction in Thickness:
The reduction in thickness in one pass can be calculated using the formula:
Reduction in thickness = t₁ - t₂
In this case, the reduction in thickness is:
Reduction in thickness = 25 mm - 20 mm = 5 mm
Calculating the Change in Diameter:
The change in diameter of the plate during the rolling operation can be calculated using the formula:
Change in diameter = 2 * Reduction in thickness
In this case, the change in diameter is:
Change in diameter = 2 * 5 mm = 10 mm
Calculating the Circumference of the Rolls:
The circumference of the rolls can be calculated using the formula:
Circumference = π * Diameter
In this case, the circumference of the rolls is:
Circumference = π * 500 mm ≈ 1570.8 mm
Calculating the Angular Change:
The angular change can be calculated using the formula:
Angular change = Change in diameter / Circumference
In this case, the angular change is:
Angular change = 10 mm / 1570.8 mm ≈ 0.0064 radians
Calculating the Coefficient of Friction:
The coefficient of friction can be calculated using the formula:
Coefficient of friction = Angular change / ln(t₁ / t₂)
In this case, the coefficient of friction is:
Coefficient of friction = 0.0064 radians / ln(25 mm / 20 mm) ≈ 0.032
Conclusion:
The coefficient of friction between the roll and the plate is approximately 0.032.
In a rolling operation, a plate is passed through a pair of rolls to reduce its thickness. The reduction in thickness depends on various factors, including the diameter of the rolls and the coefficient of friction between the rolls and the plate. In this case, we are given the diameter of the rolls and the maximum reduction in thickness that can be achieved in one pass. We need to determine the coefficient of friction between the roll and the plate.
Given Data:
- Diameter of rolls (D) = 500 mm
- Initial thickness of plate (t₁) = 25 mm
- Final thickness of plate (t₂) = 20 mm
Calculating the Reduction in Thickness:
The reduction in thickness in one pass can be calculated using the formula:
Reduction in thickness = t₁ - t₂
In this case, the reduction in thickness is:
Reduction in thickness = 25 mm - 20 mm = 5 mm
Calculating the Change in Diameter:
The change in diameter of the plate during the rolling operation can be calculated using the formula:
Change in diameter = 2 * Reduction in thickness
In this case, the change in diameter is:
Change in diameter = 2 * 5 mm = 10 mm
Calculating the Circumference of the Rolls:
The circumference of the rolls can be calculated using the formula:
Circumference = π * Diameter
In this case, the circumference of the rolls is:
Circumference = π * 500 mm ≈ 1570.8 mm
Calculating the Angular Change:
The angular change can be calculated using the formula:
Angular change = Change in diameter / Circumference
In this case, the angular change is:
Angular change = 10 mm / 1570.8 mm ≈ 0.0064 radians
Calculating the Coefficient of Friction:
The coefficient of friction can be calculated using the formula:
Coefficient of friction = Angular change / ln(t₁ / t₂)
In this case, the coefficient of friction is:
Coefficient of friction = 0.0064 radians / ln(25 mm / 20 mm) ≈ 0.032
Conclusion:
The coefficient of friction between the roll and the plate is approximately 0.032.
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In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate (under ideal rolling condition) can be atmost reduced to 20 mm in one pass, the coefficient of friction between the roll and the plate is?
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In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate (under ideal rolling condition) can be atmost reduced to 20 mm in one pass, the coefficient of friction between the roll and the plate is? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate (under ideal rolling condition) can be atmost reduced to 20 mm in one pass, the coefficient of friction between the roll and the plate is? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate (under ideal rolling condition) can be atmost reduced to 20 mm in one pass, the coefficient of friction between the roll and the plate is?.
In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate (under ideal rolling condition) can be atmost reduced to 20 mm in one pass, the coefficient of friction between the roll and the plate is? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate (under ideal rolling condition) can be atmost reduced to 20 mm in one pass, the coefficient of friction between the roll and the plate is? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate (under ideal rolling condition) can be atmost reduced to 20 mm in one pass, the coefficient of friction between the roll and the plate is?.
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