Model reduction and process control of thermomechanical behaviour of non‐linear material deformation

Abstract

AbstractThis paper describes a design procedure for metal forming processes by using the controllable subspace of the full system. The velocity profile of the moving die is designed using the reduced order system. The metal forming processes are simulated using non‐linear finite element methods based on the rigid viscoplastic flow formulation. The balanced model reduction technique is applied to reduce the full state space model to a reduced order model that retains the controllable subspace of the thermomechanical system. The linear quadratic regulator theory with output tracking is used as an off‐line design tool to design the die velocity schedule. The process design is carried out to maintain the strain rate of the critical portion of the billet at a desired value. The procedure for designing the process parameters is demonstrated using two case studies.