Optimal Open-Loop Ram Velocity Profiles for Isothermal Forging: A Variational Approach

Abstract

This paper considers the problem of selecting the ram velocity profile in an isothermal forging, to best obtain a desired material microstructure. This is to be accomplished by tracking a prescribed strain rate profile. A weighting function, reflecting the rate at which the microstructure is transforming, describes the relative importance of different parts of the billet. Finding the optimal solution generally requires a search over an infinite-dimensional function space. However, for a certain class of forgings the task reduces to solving a single ordinary differential equation. The result is a globally optimal and unique ram velocity profile. The method is demonstrated for the simulated forging of a TiAl turbine disk.