MODEL-REDUCTION AND PROCESS-CONTROL OF THERMOMECHANICAL BEHAVIOR OF NONLINEAR MATERIAL DEFORMATION

This paper describes a design procedure for metal forming processes by using the controllable subspace of the full system. The velocity prof ile 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 m odel to a reduced order model that retains the controllable subspace o f the thermomechanical system. The linear quadratic regulator theory w ith output tracking is used as an off-line design tool to design the d ie velocity schedule. The process design is carried out to maintain th e strain rate of the critical portion of the billet at a desired value . The procedure for designing the process parameters is demonstrated u sing two case studies.