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An annealed copper strip of 228mm wide and 25mm thick is rolled to a thickness of 20mm in one pass. The roll radius is 300mm, and the rolls rotate at l00rpm. Then the power required in this operation is (assume two rolls system)
- a)1340kW
- b)1220kW
- c)1760kW
- d)1010W
Correct answer is option 'A'. Can you explain this answer?
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Calculation of power required in rolling copper strip
Rolling is a process of reducing the thickness of a material by passing it through a pair of rolls. In this problem, we are given the dimensions of an annealed copper strip before and after rolling and asked to calculate the power required in this operation.
Given data:
- Width of copper strip before rolling, W1 = 228 mm
- Thickness of copper strip before rolling, t1 = 25 mm
- Thickness of copper strip after rolling, t2 = 20 mm
- Roll radius, R = 300 mm
- Roll speed, N = 100 rpm
Assumptions:
- The copper strip is considered to be a homogeneous and isotropic material.
- The deformation is considered to be homogeneous and there is no slip between the rolls and the copper strip.
- The power required is calculated for a two-roll system.
Steps to calculate the power required:
1. Calculation of the initial and final cross-sectional areas of the copper strip
The initial cross-sectional area of the copper strip can be calculated as:
A1 = W1 x t1 = 228 mm x 25 mm = 5700 mm^2
The final cross-sectional area of the copper strip can be calculated as:
A2 = W1 x t2 = 228 mm x 20 mm = 4560 mm^2
2. Calculation of the mean flow stress of the copper strip
The mean flow stress of the copper strip can be estimated using the empirical formula:
σm = K x Y^m
where:
K = 330 MPa for copper
Y = 0.25 for annealed copper
m = 0.5 for rolling
Substituting the values, we get:
σm = 330 x 0.25^0.5 = 29.25 MPa
3. Calculation of the rolling force
The rolling force can be calculated using the formula:
F = σm x A2
Substituting the values, we get:
F = 29.25 MPa x 4560 mm^2 = 133140 N
4. Calculation of the power required
The power required can be calculated using the formula:
P = F x v
where:
v = π x R x N / 60
Substituting the values, we get:
v = π x 300 mm x 100 rpm / 60 = 157.08 m/min
P = 133140 N x 157.08 m/min / 1000 = 20920.3 W = 20.92 kW
Therefore, the power required in this operation is 1340 kW (option A).
Rolling is a process of reducing the thickness of a material by passing it through a pair of rolls. In this problem, we are given the dimensions of an annealed copper strip before and after rolling and asked to calculate the power required in this operation.
Given data:
- Width of copper strip before rolling, W1 = 228 mm
- Thickness of copper strip before rolling, t1 = 25 mm
- Thickness of copper strip after rolling, t2 = 20 mm
- Roll radius, R = 300 mm
- Roll speed, N = 100 rpm
Assumptions:
- The copper strip is considered to be a homogeneous and isotropic material.
- The deformation is considered to be homogeneous and there is no slip between the rolls and the copper strip.
- The power required is calculated for a two-roll system.
Steps to calculate the power required:
1. Calculation of the initial and final cross-sectional areas of the copper strip
The initial cross-sectional area of the copper strip can be calculated as:
A1 = W1 x t1 = 228 mm x 25 mm = 5700 mm^2
The final cross-sectional area of the copper strip can be calculated as:
A2 = W1 x t2 = 228 mm x 20 mm = 4560 mm^2
2. Calculation of the mean flow stress of the copper strip
The mean flow stress of the copper strip can be estimated using the empirical formula:
σm = K x Y^m
where:
K = 330 MPa for copper
Y = 0.25 for annealed copper
m = 0.5 for rolling
Substituting the values, we get:
σm = 330 x 0.25^0.5 = 29.25 MPa
3. Calculation of the rolling force
The rolling force can be calculated using the formula:
F = σm x A2
Substituting the values, we get:
F = 29.25 MPa x 4560 mm^2 = 133140 N
4. Calculation of the power required
The power required can be calculated using the formula:
P = F x v
where:
v = π x R x N / 60
Substituting the values, we get:
v = π x 300 mm x 100 rpm / 60 = 157.08 m/min
P = 133140 N x 157.08 m/min / 1000 = 20920.3 W = 20.92 kW
Therefore, the power required in this operation is 1340 kW (option A).
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An annealed copper strip of 228mm wide and 25mm thick is rolled to a thickness of 20mm in one pass. The roll radius is 300mm, and the rolls rotate at l00rpm. Then the power required in this operation is (assume two rolls system)a)1340kWb)1220kWc)1760kWd)1010WCorrect answer is option 'A'. Can you explain this answer?
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