Keywords: forging simulation, multi-objective optimisation, genetic algorithms.

Forging is a complex nonlinear process. Simulation based on the finite element method has been an ongoing research field in metal forming. Optimal forging design considering geometric, material and process properties of cold and hot operations have been presented in the literature [1,2,3,4].

Metal forming optimisation is a typical multi-objective problem with possible conflicting relationships within the objective functions. Previous studies on metal forming optimisation consider the weight coefficients approach to solve multi-objective problems by using a single-objective functional which combines multiple objective functions into one [2,4]. Nevertheless, it is difficult to make sure whether the solution achieved is an optimal one.

The objective of the present work is to design a novel multi-objective optimisation model for multi-stage hot forging processes. The optimisation methodology considers a genetic algorithm supported by an elitist strategy. Individuals are evaluated for each objective function and a Pareto like iterative procedure will be considered finding optimised solutions. Near-optimal solutions are found managing the drawing of a Pareto front. The obtained Pareto optimal solutions offer designers the capability to trade-off solutions at various dimensions such as parameter level, objective level and inter-stage level.

The design example consists of a two-stage forging process applied to a pre-heated billet made of AISI 1018 steel. The goal of the design example is to search for a preform die shape, an initial work-piece temperature and stroke lengths for each stage that will produce after forging a flashless cross-sectional H-shaped axisymmetric product with complete die fill. Two sets of design variables are addressed: shape design and process variables. Common objective functions are the minimisation of the forging load, the control of the forged shape and the material microstructure. Pareto optimal solutions are determined and the validation of the method is performed based on the visualization of the search space and the convergence to the near Pareto front with a good spread of solutions. Performance comparison with a single objective function confirms the methodology proposed by the new optimisation approach.

1

Z. Xinhai, Z. Guoqun, W. Guangchun, W. Tonghai, "Optimal preform die design through controlling deformation uniformity in metal forging", J. Mater. Sci. Technol., 18(5), 465-467, 2002.

2

C.F. Castro, C.A.C. António, L.C. Sousa, "Optimisation of shape and process parameters in metal forging using genetic algorithms", J. Mat. Proc. Tech., 146, 356-364, 2004. doi:10.1016/j.jmatprotec.2003.11.027

3

G. Zhao, X. Ma, X. Zhao, R.V. Grandhi, "Studies on optimization of metal forming processes using sensitivity analysis methods", J. Mat. Proc. Tech., 147, 217-228, 2004. doi:10.1016/j.jmatprotec.2003.12.018

4

C.C. António, C.F. Castro, L.C. Sousa, "Eliminating forging defects using genetic algorithms", Mater. Manuf. Process., 20, 509-522, 2005. doi:10.1081/AMP-200053557

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