Process Modelling and Control in Metal Forming

In this paper, the state space modelling of metal forming and off-line design of process variables are addressed. A reduced order approach is used to develop state equations for the non-linear finite element model of deformation processes. The influence of optimally designed process variables is studied using the variance in strain-rates and input power as performance measures. The state variables include the forging die contact nodal velocities and nodal velocities of selected elements within the billet. The control input is the ram velocity which is found using the Linear Quadratic Regulator (LQR) theory to maintain desired strain-rates in the selected finite elements. The condensation techniques required to build the state space model and the results obtained from controlling various bulk deformation processes are discussed with examples.