In most rolling mills, the metal rods are coiled by pushing them through a pipe that has a corkscrew-like shape, called the laying pipe. The goal of this project is to model the wear distribution along a laying pipe and to find the shape of the pipe that has the least wear. A lower and better distributed wear extends the life of the pipe and reduces the down time of the mill, thus increasing the productivity.

Given specific boundary conditions on the geometry of the pipe, we derived a shape dependent expression for wear from the forces involved. In finding the optimal shape that reduces the wear, we plan on using techniques such as calculus of variations, optimal control, and numerical methods to solve the differential equations involved.