Question

estimate the force required in extruding 70–30 brass at 700◦c if the billet diameter is 200 mm and the extrusion ratio is 30.

Answer 1

The question asks for an estimate of force required in extruding 70-30 brass at 700°C with a billet diameter of 200 mm and an extrusion ratio of 30. To calculate this, we need to know the flow stress of the material at the extrusion temperature, the cross-sectional area, and apply this to an equation involving the natural logarithm of the extrusion ratio. Without specific material properties or a detailed description of the extrusion process, a precise calculation cannot be provided.

Step-by-step explanation:

To estimate the force required for extruding 70-30 brass at 700°C when given a billet diameter of 200 mm and an extrusion ratio of 30, we will need to apply principles of materials science and mechanical engineering. However, the question does not provide enough information to give a precise answer. We would normally need to know things like the material's yield strength at the given temperature, properties of the billet and die, and the specific extrusion process being used.

Extrusion process calculations generally involve using empirical formulas that take into account the material's flow stress, which is dependent on temperature and strain rate, the extrusion ratio, and the dimensions of the billet and the extruded product.

A simplified way to approach this could involve using the equation F = k × A × ln(R), where F is the force, k is the flow stress of the material at 700°C, A is the cross-sectional area of the billet, and ln(R) is the natural logarithm of the extrusion ratio.

Answer 2

the estimated force required to extrude 70-30 brass at 700°C, with a billet diameter of 200 mm and an extrusion ratio of 30, is approximately 156,579 Newtons. Please note that this is an estimation based on the given information and assumptions, and the actual force required may vary depending on other factors.

To estimate the force required in extruding 70-30 brass at 700°C with a billet diameter of 200 mm and an extrusion ratio of 30, we can use the following steps:

1. Calculate the area reduction:
- The extrusion ratio is defined as the ratio of the initial cross-sectional area of the billet to the final cross-sectional area of the extruded product.
- In this case, the extrusion ratio is 30, so the area reduction is 1/30 or 0.0333.

2. Calculate the final cross-sectional area of the extruded product:
- The initial cross-sectional area of the billet is π * (diameter/2)^2.
- Substituting the given diameter of 200 mm, the initial cross-sectional area is π * (200/2)^2 = 31415.93 mm^2.
- The final cross-sectional area is the initial area multiplied by the area reduction: 31415.93 mm^2 * 0.0333 = 1043.86 mm^2.

3. Determine the flow stress of the material at the extrusion temperature:
- Flow stress refers to the resistance of the material to deformation at high temperatures.
- The flow stress of 70-30 brass at 700°C can be obtained from material property data or reference tables. Let's assume it is 150 MPa (megapascals) for this example.

4. Calculate the force required for extrusion:
- The force required for extrusion can be calculated using the formula F = σ * A, where F is the force, σ is the flow stress, and A is the cross-sectional area.
- Substituting the values, we get F = 150 MPa * 1043.86 mm^2 = 156,579 N (Newtons).