Control of Transient Thermal Response During Sequential Open-Die Forging: A Trajectory Optimization Approach

A trajectory optimization approach is applied to the design of a sequence of open-die forging operations in order to control the transient thermal response of a large titanium alloy billet. The amount of time the billet is soaked in furnace prior to each successive forging operation is optimized to minimize the total process time while simultaneously satisfying constraints on the maximum and minimum values of the billet’s temperature distribution to avoid microstructural defects during forging. The results indicate that a “differential” heating profile is the most effective at meeting these design goals.