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In a rolling process, a sheet of 25 mm thickness is rolled to 20 mm thickness. Roll is of diameter 1200 mm and it rotates at 100 rpm. What is the roll strip contact length?
  • a)
    54.77 m
  • b)
    54.77 mm
  • c)
    5.477 mm
  • d)
    5477 m
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a rolling process, a sheet of 25 mm thickness is rolled to 20 mm t...
Initial thickness
h1 = 25 mm
Final thickness
h2 = 20 mm
Roll diameter = 1200 mm
Speed of rolls = 100 RPM
As we know that contact length of roll strip is given by
Where R = roll radius = 1200/2 = 600 mm
And Δh =
h1-h2 = (25 – 20) = 5 mm
Put these values we have
L = 54.77 mm
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Most Upvoted Answer
In a rolling process, a sheet of 25 mm thickness is rolled to 20 mm t...
Understanding the Rolling Process
In a rolling process, the contact length between the rolls and the material being processed is crucial for understanding the deformation and material flow.
Given Data:
- Initial Thickness (h1): 25 mm
- Final Thickness (h2): 20 mm
- Roll Diameter (D): 1200 mm
- Roll Radius (R): D/2 = 600 mm
- Roll Speed (N): 100 rpm
Contact Length Calculation:
To find the contact length (L) between the roll and the sheet during rolling, we can use the following relationship:
- The contact length can be approximated by the formula:
L = π * R * (h1 - h2) / (h1 + h2)
This formula is derived from the geometry of the rolling process, taking into account the reduction in thickness due to the rolling.
Substituting Values:
1. Calculate the average thickness:
- Average Thickness = (h1 + h2) / 2 = (25 mm + 20 mm) / 2 = 22.5 mm
2. Use the formula for contact length:
- L = π * 600 mm * (25 mm - 20 mm) / (25 mm + 20 mm)
- L = π * 600 mm * (5 mm) / (45 mm)
3. Simplifying this gives:
- L ≈ 54.77 mm
Conclusion:
Thus, the roll strip contact length during the rolling process is approximately 54.77 mm. This means that the correct answer is option 'B'.
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