NUMERICAL OPTIMIZATION OF THE PLASTO-HYDRODYNAMIC DRAWING OF NARROW STRIPS

Initial developments in plasto-hydrodynamic drawing were for circular cross section wires, which has previously been modelled. In this proce ss the deformation of the wire is achieved by pulling the wire through a stepped cavity filled with a viscous fluid. Hydrodynamic action gen erates surface shears and compressive stresses in the material of suff icient magnitude to produce plastic deformation, even though the small est bore size of the hydrodynamic pressure head is larger than the und eformed diameter of the wire. Both process and model have been extende d to a rectangular section strip the results of which have previously been published. In this study a finite difference computer model of th e process has been submitted to the process of numerical multi-dimensi onal optimisation. The Newtonian, strain hardening, computer model of the process is formed into a merit function, the order of the optimisa tion problem is seen to be reduced by the use of ratio's. This functio n was then supplied to the optimisation code. The optimisation code us es the direct search algorithm of Hooke and Jeeves [1]. This method us es a pattern vector in n-dimensional Euclidean space to explore the lo cal region about the current search point before moving in the directi on of the computed pattern vector. The method has been proven to have good valley following properties. Multiple applications of the optimis ation code were made from different initial points in space to overcom e any occurrence of multi-modality, which was speculated upon by Rohde [2] in his study of optimum step profiles for stepped slider bearing profiles. Emphasis has been placed on the geometrical configuration of the stepped cavity. The fluid properties are approximately those of a generic form of polyethylene, with strip properties of commercially a vailable soft copper, fluid and material properties were constant thro ughout the study. The results show significantly different optimum cav ity configurations and performance surfaces for different velocities.