Chapter 18, Problem 2P

Consider the extrusion of a cylindrical billet, and compute the following.

1. Assume the starting billet to have a length of 0.3 m and a diameter of 15 cm. This is extruded into a cylindrical product that is 3 cm in diameter and 7.5 m long (a reduction ratio of 25). Neglecting the areas on the two ends, compute the ratio between the product surface area (wraparound cylinder) and the surface area of the starting billet.
2. How would this ratio change if the product were a square with the same cross�sectional area as that of the 3�cm�diameter circle?
3. Consider a cylinder�to�cylinder extrusion with a reduction ratio of R. Derive a general expression of the relative surface areas of product to billet as a function of R. (Hint: Start with a cylinder with length and diameter both equal to 1 unit. Because the final area will be 1/R times the original, the final length will be R units, and the final diameter will be proportional to 1/ R).
4. If the final product had a more complex cross�sectional shape than a cylinder. Would the final area be greater than or less than that computed in part c?
5. Relate your preceding answers to a consideration of lubrication during large�reduction extrusion operations.