Grade 12General Physics
An aluminum extrusion process is simulated numerically with a computer. In this process, a punch pushes an aluminum billet of diameter D through a die of smaller diameter d. In the computer simulation, what is the maximum punch velocity Vp so that the net dynamic force (predicted by the simulation) acting on the aluminum during extrusion is at most 5% of the force due to deformation of the aluminum? Evaluate for a specific case where D = 0.10 m, d = 0.02 m, and the density of aluminum is ? = 2700 kg/m3.
The force due to deformation of the aluminum during extrusion is given by
Hint:
The extrusion of the aluminum through the die is analogous to fluid flowing through a pipe which transitions from a larger diameter to a smaller diameter (e.g. water flowing through a fireman’s hose). The net dynamic force acting on the fluid is the net force required to accelerate the fluid, which occurs when the velocity of the fluid increases as it flows from the larger diameter section to the smaller diameter section (due to conservation of mass).
