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A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. The working temperature of 700°C and the extrusion constant is 250 MPa. The force required for extrusion is
[ME 2003]
- a)5.44 MN
- b)2.72 MN
- c)1.36 MN
- d)0.36 MN
Correct answer is option 'B'. Can you explain this answer?
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A brass billet is to be extruded from its initial diameter of 100 mm t...
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A brass billet is to be extruded from its initial diameter of 100 mm t...
°C and the extrusion ratio is 2:1. Determine the required extrusion force if the flow stress of the brass at the working temperature is 200 MPa.
To determine the required extrusion force, we can use the following equation:
F = (K * A * L * σ) / (cos(α)^2 * η)
Where:
F = Required extrusion force
K = Extrusion constant (typically in the range of 0.7-1.0)
A = Cross-sectional area of the billet
L = Length of the billet
σ = Flow stress of the material
α = Angle of friction between the billet and the container
η = Efficiency of the extrusion process
First, let's calculate the cross-sectional area of the billet at the initial and final diameters:
Area_initial = π * (d_initial/2)^2
Area_initial = π * (100/2)^2
Area_initial = 7853.98 mm^2
Area_final = π * (d_final/2)^2
Area_final = π * (50/2)^2
Area_final = 1963.50 mm^2
Next, let's calculate the length of the billet. Since the extrusion ratio is 2:1, the length of the billet will be halved:
L = L_initial / 2
Now, let's substitute the given values into the equation to calculate the required extrusion force:
F = (K * A * L * σ) / (cos(α)^2 * η)
F = (0.7 * 7853.98 * (L_initial/2) * 200) / (cos(α)^2 * η)
Note: The angle of friction (α) and efficiency (η) are not provided in the given information, so we cannot determine their values. However, for this calculation, we can assume α = 0 (no friction) and η = 1 (perfect efficiency).
F = (0.7 * 7853.98 * (L_initial/2) * 200) / (cos(0)^2 * 1)
F = (0.7 * 7853.98 * (L_initial/2) * 200) / (1)
Simplifying the equation, we get:
F = 5492788.6 * L_initial
Therefore, the required extrusion force is 5492788.6 times the initial length of the billet.
To determine the required extrusion force, we can use the following equation:
F = (K * A * L * σ) / (cos(α)^2 * η)
Where:
F = Required extrusion force
K = Extrusion constant (typically in the range of 0.7-1.0)
A = Cross-sectional area of the billet
L = Length of the billet
σ = Flow stress of the material
α = Angle of friction between the billet and the container
η = Efficiency of the extrusion process
First, let's calculate the cross-sectional area of the billet at the initial and final diameters:
Area_initial = π * (d_initial/2)^2
Area_initial = π * (100/2)^2
Area_initial = 7853.98 mm^2
Area_final = π * (d_final/2)^2
Area_final = π * (50/2)^2
Area_final = 1963.50 mm^2
Next, let's calculate the length of the billet. Since the extrusion ratio is 2:1, the length of the billet will be halved:
L = L_initial / 2
Now, let's substitute the given values into the equation to calculate the required extrusion force:
F = (K * A * L * σ) / (cos(α)^2 * η)
F = (0.7 * 7853.98 * (L_initial/2) * 200) / (cos(α)^2 * η)
Note: The angle of friction (α) and efficiency (η) are not provided in the given information, so we cannot determine their values. However, for this calculation, we can assume α = 0 (no friction) and η = 1 (perfect efficiency).
F = (0.7 * 7853.98 * (L_initial/2) * 200) / (cos(0)^2 * 1)
F = (0.7 * 7853.98 * (L_initial/2) * 200) / (1)
Simplifying the equation, we get:
F = 5492788.6 * L_initial
Therefore, the required extrusion force is 5492788.6 times the initial length of the billet.
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A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. The working temperature of 700°C and the extrusion constant is 250 MPa. The force required for extrusion is[ME 2003]a)5.44 MNb)2.72 MNc)1.36 MNd)0.36 MNCorrect answer is option 'B'. Can you explain this answer?
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A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. The working temperature of 700°C and the extrusion constant is 250 MPa. The force required for extrusion is[ME 2003]a)5.44 MNb)2.72 MNc)1.36 MNd)0.36 MNCorrect answer is option 'B'. 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 A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. The working temperature of 700°C and the extrusion constant is 250 MPa. The force required for extrusion is[ME 2003]a)5.44 MNb)2.72 MNc)1.36 MNd)0.36 MNCorrect answer is option 'B'. 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 A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. The working temperature of 700°C and the extrusion constant is 250 MPa. The force required for extrusion is[ME 2003]a)5.44 MNb)2.72 MNc)1.36 MNd)0.36 MNCorrect answer is option 'B'. Can you explain this answer?.
A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. The working temperature of 700°C and the extrusion constant is 250 MPa. The force required for extrusion is[ME 2003]a)5.44 MNb)2.72 MNc)1.36 MNd)0.36 MNCorrect answer is option 'B'. 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 A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. The working temperature of 700°C and the extrusion constant is 250 MPa. The force required for extrusion is[ME 2003]a)5.44 MNb)2.72 MNc)1.36 MNd)0.36 MNCorrect answer is option 'B'. 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 A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. The working temperature of 700°C and the extrusion constant is 250 MPa. The force required for extrusion is[ME 2003]a)5.44 MNb)2.72 MNc)1.36 MNd)0.36 MNCorrect answer is option 'B'. Can you explain this answer?.
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