Keywords: metal forming processes, hot forging, die design, optimisation, genetic algorithms, finite element method.

The computational modelling of forging is now well established. Within the last 20 years the finite element method has become a powerful technique to simulate metal forming processes. Nowadays, optimisation techniques play a crucial role to improve a given metal-forming process and its final product. The so-called inverse techniques developed for optimisation problems allow the calculation of the optimal solution using as entry parameters the specifications of the final product. Then it calculates the design parameters that produce the required final product [1].

This paper presents a study of non-isothermal forging process optimisation. A design space is defined in terms of basically two kinds of variables: shape geometry parameters and process parameters not related with shape, such as material temperatures or friction coefficients. An evolutionary genetic algorithm [2,3] is proposed to optimise die geometry and work-piece temperature of a two-stage forging process with preform and final operations.

An inverse optimisation problem begins with the request of a prescribed final product. The process variables are established and the design vector is considered with an interval of allowable values for each variable. The developed algorithm discretizes independently each interval and the binary code format for each variable is defined. The gathering of the binary encoding of all variables of the design vector will constitute an individual. Then it will be possible to select randomly an individual associated to a particular design vector.

The iterative process can be described as follows:

(i)

An initial population is randomly generated. For each individual of the population an independent numerical simulation of the two-stage forging direct problem is performed. Each forging simulation will produce a forged piece with an associated fitness function value.

(ii)

A new population of solutions is generated from the previous one using the genetic operators: Selection, Crossover, Elimination/Substitution and Mutation.

(iii)

For each individual of the population an independent numerical simulation of the two-stage forging direct problem is performed. Each forging simulation will produce a forged piece with an associated fitness function value.

(iv)

The optimisation program checks if the stopping criteria are satisfied. If the convergence conditions are not satisfied, the iterative process continues from (ii); if the convergence conditions are satisfied the design objectives are met and the iterative process stops.

The developed method is applied to a two-stage forging example of a pre-heated billet of aluminium alloy AL6016T6. The shape of the preform tool geometry is discretized using B-spline functions. The displacements of selected control points of the B-spline curve are the shape design parameters defined in the design parameter vector. The considered process variable is the initial temperature of the work-piece. The temperature of the work-piece will change along the forging process due to shear stress, die velocity and friction, among others, and its maximum value strongly influences the quality of the final product.

The presented case considers a multi-objective optimisation of the process parameters aiming the reduction of the difference between the realized and the prescribed final forged shape under minimal energy consumption, restricting the maximum temperature. The optimised product is very close to the desired one accounting for material/energy savings using the optimised design.

1

L. Fourment, J-L Chenot, "Optimal design for non-steady-state metal forming processes-1 shape optimization method", Int. J. Numer. Methods Engineering, 39(1), 33-50, 1996. doi:10.1002/(SICI)1097-0207(19960115)39:1<33::AID-NME844>3.0.CO;2-Z

2

K. DeJong, "Evolutionary computation: Recent developments and open issues", in Evolutionary Algorithms in Engineering Computer Science EUROGEN99, John Wiley & Sons Ltd, Chichester, 43-54, 1999.

3

C.F. Castro, C.A.C. António, L.C. Sousa, "Optimization of shape and process parameters in metal forging processes using genetic algorithms", Journal of Materials Processing Technology, 146, 356-364, 2004. doi:10.1016/j.jmatprotec.2003.11.027

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)