Dynamic optimization of induction heat-up and surface hardening processes on complex spatial domains

This contribution deals with the dynamic optimization of induction heat-up and surface hardening processes for workpieces with complex shapes. Suitable optimal control problems are formulated and tackled by using the formal Lagrangian technique in terms of a first optimize then discretize approach. The numerical solution of the optimality conditions is carried out by using the gradient algorithm in combination with FEM software. The approach is illustrated both for an axisymmetrical workpiece and a gear wheel with complex and non-convex geometry.