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A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.?
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A cylinder of height 60 mm and diameter 100 mm is forged at room tempe...
Problem Statement: Find the die load at the end of compression to a height of 30mm, using the slab method of analysis for a cylinder of height 60mm and diameter 100mm forged at room temperature between two flat dies. The yield strength of the work material is given as 120 N/m², and the coefficient of friction is 0.05. Assume that volume is constant after deformation. There is no sticking. Also, find the mean die pressure.
Solution:
To find the die load and mean die pressure, we can use the following steps:
Step 1: Determine the cross-sectional area of the cylinder.
The cross-sectional area of the cylinder is given by:
A = π/4 * D²
Where D = diameter of the cylinder = 100mm
Therefore, A = π/4 * 100² = 7853.98 mm²
Step 2: Determine the volume of the cylinder before deformation.
The volume of the cylinder before deformation is given by:
V1 = A * H1
Where H1 = height of the cylinder before deformation = 60mm
Therefore, V1 = 7853.98 * 60 = 471238.8 mm³
Step 3: Determine the volume of the cylinder after deformation.
The volume of the cylinder after deformation is given by:
V2 = A * H2
Where H2 = height of the cylinder after deformation = 30mm (as per the problem statement)
Therefore, V2 = 7853.98 * 30 = 235619.4 mm³
Step 4: Calculate the true strain.
The true strain is given by:
ε = ln(V1/V2)
Therefore, ε = ln(471238.8/235619.4) = 0.6931
Step 5: Calculate the true stress.
The true stress is given by:
σt = K * ε^n
Where K and n are material constants, which can be determined experimentally.
For the given material, K = 300 MPa and n = 0.15 (approximate values)
Therefore, σt = 300 * ε^0.15 = 300 * 0.6931^0.15 = 157.6 MPa
Step 6: Calculate the force required for deformation.
The force required for deformation is given by:
F = A * σt
Therefore, F = 7853.98 * 157.6 = 1237470.6 N
Step 7: Calculate the die load.
The die load is given by:
P = F / (1 - μ)
Where μ is the coefficient of friction between the workpiece and the die.
Therefore, P = 1237470.6 / (1 - 0.05) = 1302563.16 N
Step 8: Calculate the mean die pressure.
The mean die pressure is given by:
Pm = P / A
Therefore, Pm = 1302563.16 / 7853.98 = 165.7 MPa
Therefore, the die load at the end of compression to a height of 30mm is 1302563.16 N
Solution:
To find the die load and mean die pressure, we can use the following steps:
Step 1: Determine the cross-sectional area of the cylinder.
The cross-sectional area of the cylinder is given by:
A = π/4 * D²
Where D = diameter of the cylinder = 100mm
Therefore, A = π/4 * 100² = 7853.98 mm²
Step 2: Determine the volume of the cylinder before deformation.
The volume of the cylinder before deformation is given by:
V1 = A * H1
Where H1 = height of the cylinder before deformation = 60mm
Therefore, V1 = 7853.98 * 60 = 471238.8 mm³
Step 3: Determine the volume of the cylinder after deformation.
The volume of the cylinder after deformation is given by:
V2 = A * H2
Where H2 = height of the cylinder after deformation = 30mm (as per the problem statement)
Therefore, V2 = 7853.98 * 30 = 235619.4 mm³
Step 4: Calculate the true strain.
The true strain is given by:
ε = ln(V1/V2)
Therefore, ε = ln(471238.8/235619.4) = 0.6931
Step 5: Calculate the true stress.
The true stress is given by:
σt = K * ε^n
Where K and n are material constants, which can be determined experimentally.
For the given material, K = 300 MPa and n = 0.15 (approximate values)
Therefore, σt = 300 * ε^0.15 = 300 * 0.6931^0.15 = 157.6 MPa
Step 6: Calculate the force required for deformation.
The force required for deformation is given by:
F = A * σt
Therefore, F = 7853.98 * 157.6 = 1237470.6 N
Step 7: Calculate the die load.
The die load is given by:
P = F / (1 - μ)
Where μ is the coefficient of friction between the workpiece and the die.
Therefore, P = 1237470.6 / (1 - 0.05) = 1302563.16 N
Step 8: Calculate the mean die pressure.
The mean die pressure is given by:
Pm = P / A
Therefore, Pm = 1302563.16 / 7853.98 = 165.7 MPa
Therefore, the die load at the end of compression to a height of 30mm is 1302563.16 N
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A cylinder of height 60 mm and diameter 100 mm is forged at room tempe...
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A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.?
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A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.?.
A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.?.
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A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.?, a detailed solution for A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.? has been provided alongside types of A cylinder of height 60 mm and diameter 100 mm is forged at room temperature between two flat dies.find the die load at the end of compression to a height 30mm ,using slab method aof analysis.the yeild strength of the work material is given as 120 newton per metre square and the coefficient of friction is 0.05 .assume that volume is constant after deformation .there is no sticking ,also find mean die pressure.? theory, EduRev gives you an
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