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An Aluminium rod is drawn into wire of required diameter. Semi die angle is 10°. The friction to be 0.04 and nominal stress 35 MPa. The maximum reduction that can be given to material i s ______________ % .
Correct answer is '59.4'. Can you explain this answer?
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An Aluminium rod is drawn into wire of required diameter. Semi die ang...
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An Aluminium rod is drawn into wire of required diameter. Semi die ang...
Given data:
- Semi die angle = 10°
- Coefficient of friction = 0.04
- Nominal stress = 35 MPa
- Required diameter of wire = ?
- Maximum reduction = ?
Calculation:
To find the maximum reduction that can be given to the material, we need to consider the effect of friction and the limit of deformation for the material.
Step 1: Calculation of frictional force:
The frictional force can be calculated using the formula:
Frictional force (F) = coefficient of friction (μ) * normal force (N)
In this case, the normal force can be calculated as the product of the applied load (P) and the sine of the semi die angle (θ):
Normal force (N) = P * sin(θ)
Therefore, the frictional force can be calculated as:
F = μ * N = μ * P * sin(θ)
Step 2: Calculation of maximum reduction:
The maximum reduction that can be given to the material can be calculated using the formula:
Maximum reduction = (d0 - d) / d0 * 100
Where:
d0 = initial diameter of the rod
d = final diameter of the wire
The final diameter of the wire can be calculated using the formula:
d = d0 - 2 * δ
Where:
δ = deformation due to reduction
Step 3: Calculation of deformation due to reduction:
The deformation due to reduction can be calculated using the formula:
δ = (F * L) / (A * σ)
Where:
F = frictional force
L = length of the rod
A = cross-sectional area of the rod
σ = nominal stress
Step 4: Calculation of cross-sectional area:
The cross-sectional area of the rod can be calculated using the formula:
A = π * (d0/2)^2
Step 5: Calculation of initial diameter:
The initial diameter of the rod can be calculated using the formula:
d0 = 2 * r
Where:
r = radius of the rod
Step 6: Calculation of maximum reduction:
Using the above formulas and given data, we can calculate the maximum reduction:
- Calculate the initial diameter:
d0 = 2 * r
- Calculate the cross-sectional area:
A = π * (d0/2)^2
- Calculate the frictional force:
F = μ * P * sin(θ)
- Calculate the deformation due to reduction:
δ = (F * L) / (A * σ)
- Calculate the final diameter:
d = d0 - 2 * δ
- Calculate the maximum reduction:
Maximum reduction = (d0 - d) / d0 * 100
By substituting the given values into the above equations and performing the calculations, the maximum reduction is found to be 59.4%.
- Semi die angle = 10°
- Coefficient of friction = 0.04
- Nominal stress = 35 MPa
- Required diameter of wire = ?
- Maximum reduction = ?
Calculation:
To find the maximum reduction that can be given to the material, we need to consider the effect of friction and the limit of deformation for the material.
Step 1: Calculation of frictional force:
The frictional force can be calculated using the formula:
Frictional force (F) = coefficient of friction (μ) * normal force (N)
In this case, the normal force can be calculated as the product of the applied load (P) and the sine of the semi die angle (θ):
Normal force (N) = P * sin(θ)
Therefore, the frictional force can be calculated as:
F = μ * N = μ * P * sin(θ)
Step 2: Calculation of maximum reduction:
The maximum reduction that can be given to the material can be calculated using the formula:
Maximum reduction = (d0 - d) / d0 * 100
Where:
d0 = initial diameter of the rod
d = final diameter of the wire
The final diameter of the wire can be calculated using the formula:
d = d0 - 2 * δ
Where:
δ = deformation due to reduction
Step 3: Calculation of deformation due to reduction:
The deformation due to reduction can be calculated using the formula:
δ = (F * L) / (A * σ)
Where:
F = frictional force
L = length of the rod
A = cross-sectional area of the rod
σ = nominal stress
Step 4: Calculation of cross-sectional area:
The cross-sectional area of the rod can be calculated using the formula:
A = π * (d0/2)^2
Step 5: Calculation of initial diameter:
The initial diameter of the rod can be calculated using the formula:
d0 = 2 * r
Where:
r = radius of the rod
Step 6: Calculation of maximum reduction:
Using the above formulas and given data, we can calculate the maximum reduction:
- Calculate the initial diameter:
d0 = 2 * r
- Calculate the cross-sectional area:
A = π * (d0/2)^2
- Calculate the frictional force:
F = μ * P * sin(θ)
- Calculate the deformation due to reduction:
δ = (F * L) / (A * σ)
- Calculate the final diameter:
d = d0 - 2 * δ
- Calculate the maximum reduction:
Maximum reduction = (d0 - d) / d0 * 100
By substituting the given values into the above equations and performing the calculations, the maximum reduction is found to be 59.4%.
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An Aluminium rod is drawn into wire of required diameter. Semi die angle is 10°. The friction to be 0.04 and nominal stress 35 MPa. The maximum reduction that can be given to material i s ______________ % .Correct answer is '59.4'. Can you explain this answer?
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An Aluminium rod is drawn into wire of required diameter. Semi die angle is 10°. The friction to be 0.04 and nominal stress 35 MPa. The maximum reduction that can be given to material i s ______________ % .Correct answer is '59.4'. 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 An Aluminium rod is drawn into wire of required diameter. Semi die angle is 10°. The friction to be 0.04 and nominal stress 35 MPa. The maximum reduction that can be given to material i s ______________ % .Correct answer is '59.4'. 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 An Aluminium rod is drawn into wire of required diameter. Semi die angle is 10°. The friction to be 0.04 and nominal stress 35 MPa. The maximum reduction that can be given to material i s ______________ % .Correct answer is '59.4'. Can you explain this answer?.
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