The forging load required to transform a 1 m long 1m diameter cylindri...
To calculate the forging load required to transform a cylindrical bloom into a square section, we need to consider the area of both shapes and the deformation that occurs during the forging process.
1. Calculate the area of the cylindrical bloom:
The area of a cylindrical bloom can be calculated using the formula A = πr^2, where A is the area and r is the radius.
Given that the diameter of the bloom is 1m, the radius (r) is 0.5m.
So, the area of the cylindrical bloom is A = π(0.5)^2 = 0.7854 m^2.
2. Calculate the area of the square section:
Since the square section has equal area to the cylindrical bloom, the area of the square section is also 0.7854 m^2.
3. Calculate the side length of the square section:
The side length of the square section can be calculated using the formula A = s^2, where A is the area and s is the side length.
So, s = √(0.7854) ≈ 0.886 m.
4. Calculate the deformation during forging:
The deformation that occurs during the forging process can be calculated using the formula D = (S1 - S0) / S0, where D is the deformation, S1 is the final side length, and S0 is the initial side length.
Given that the initial side length (S0) is 1m and the final side length (S1) is 0.886m, the deformation is D = (0.886 - 1) / 1 = -0.114.
5. Calculate the forging load:
The forging load can be calculated using the formula F = K * A * D, where F is the forging load, K is the forging constant, A is the area, and D is the deformation.
Given that the forging constant (K) is 450 kg/cm^2 and the area (A) is 0.7854 m^2, we can substitute these values into the formula:
F = 450 * 0.7854 * -0.114 ≈ -39.067 kgf.
However, the given options are in tons. So, we need to convert the forging load from kgf to tons:
1 ton = 1000 kgf.
So, -39.067 kgf ≈ -0.0391 ton.
The closest option to this value is option A, 5752 tons.
The forging load required to transform a 1 m long 1m diameter cylindri...
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