An integrated FEM and ANN methodology for metal-formed product design

https://doi.org/10.1016/j.engappai.2008.04.001Get rights and content

Abstract

In the traditional metal-formed product development paradigm, the design of metal-formed product and tooling is usually based on heuristic know-how and experiences, which are generally obtained through long years of apprenticeship and skilled craftsmanship. The uncertainties in product and tooling design often lead to late design changes. The emergence of finite element method (FEM) provides a solution to verify the designs before they are physically implemented. Since the design of product and tooling is affected by many factors and there are many design variables to be considered, the combination of those variables comes out with various design alternatives. It is thus not pragmatic to simulate all the designs to find out the best solution as the coupled simulation of non-linear plastic flow of billet material and tooling deformation is very time-consuming. This research is aimed to develop an integrated methodology based on FEM simulation and artificial neural network (ANN) to approximate the functions of design parameters and evaluate the performance of designs in such a way that the optimal design can be identified. To realize this objective, an integrated FEM and ANN methodology is developed. In this methodology, the FEM simulation is first used to create training cases for the ANN(s), and the well-trained ANN(s) is used to predict the performance of the design. In addition, the methodology framework and implementation procedure are presented. To validate the developed technique, a case study is employed. The results show that the developed methodology performs well in estimation and evaluation of the design.

Introduction

In metal forming processes, tooling is subjected to compressive force and dynamic stress. The dynamic stress is repeated for each production shot and causes tooling fatigue failure. To have a long service tooling and produce quality product, the tooling design is critical as it is determined by various design parameters related to forming process, tooling itself, deformed part and the equipment used. Tooling fabrication, on the other hand, is a costly and non-trivial process, which usually involves a lot of processes, machines and raw materials. The design of tooling must thus be extensively verified before they are physically realized. In traditional metal-formed product development paradigm, the design of tooling and product is based on experience which is obtained through expensive and time-consuming trial-and-error; late design changes are always needed. This kind of product development paradigm often leads to high development cost and long time-to-market. Therefore, the extensive evaluation of tooling design solution and optimization is of importance. It could ensure “right design the first time” and reduce the trial-and-error in workshop.

To realize this objective, numerical simulation and modelling is one of the powerful tools to address the issue. Many researches have been conducted to apply the finite element method (FEM) in product design and development. To name a few, Yang et al. integrated CAD, CAE and rapid prototyping technology to analyse and visualize the hot forging process in order to eliminate the defects at the corner and at a refined local region (Yang et al., 2002). Spider forging was used as a case study. In this research, the rigid-plastic deformation of the deformation body was first analysed by FEM, and the workpieces at different forming stages were then fabricated by laminated object manufacturing (LOM) to study the formation of product defect. Fujikawa applied the FE simulation to study the design parameters for the crankshaft forging process (Fujikawa, 2000). Eight factors concerning the material filling performance, forming load and the material quantity were selected. In order to reduce the number of simulations, orthogonal array was employed to determine the critical design combination. By using his proposed approach, he claimed that the development cost could be reduced by 40% when compared with the conventional trial-and-error approach. To support the design of the whole metal-forming system, Fu et al. proposed a simulation-based approach to assessing the design of metal-forming system (Fu et al., 2006). Based on their study, an integrated simulation framework for supporting metal-forming system design was proposed and various design factors relating to the quality of metal-formed product were articulated. The design index was also proposed to evaluate the performance of different forming system designs and finally the optimal design was identified. Furthermore, he and his colleagues developed a methodology for die life assessment through identification of stress concentration region and the stress level for prediction of tooling fatigue life (Tong et al., 2005). They used a case study of bevel gear forging to test and verify the procedure and its robustness.

By using the FEM simulation to support the design solution generation in metal-forming product development, a critical issue is the infinite design alternatives via the configuration of different design variables relating to metal-formed part design, process determination and process parameter settings, tooling design and material properties selection. To simulate all the design alternatives, it would be very difficult, if not impossible, as the coupled simulation of tooling deformation and billet plastic flow is very time-consuming. On the other hand, if only the selected design scenarios are simulated, how to select those scenarios from the whole design space is also an issue as the traditional design of experiment (DoE) would not help a lot. Therefore, an interesting research topic has been raised up: how to integrate the FEM simulation with artificial neural network (ANN) to significantly reduce the simulations, but not at the cost of losing the design space which should be explored in searching for the optimal design solution? This paper is to address this issue.

The ANN is a computational network that attempts to simulate the process that occurs in the human brain and nervous system during pattern recognition, information filtering and functional control (Hagan et al., 1996). It uses an inductive approach to generalize the input–output relationships to approximate the desired functions; such specific capability is helpful when the case is difficult to derive a mathematical model. This uniqueness decides its promising applications in product design and development, especially for metal-formed product development as the relationship of the performance and behaviour of the designed forming system with its design parameters is very difficult to be represented as an explicit mathematical model. This raises an interesting research topic on how to employ the ANN to help product design and development. Currently, many researches have been conducted. Sterjovski et al. introduced three ANNs to predict the impact toughness of heat treated pressure vessel steel, hardness of pipeline and fitting steels after welding, and the hot ductility and hot strength of microalloyed steels in continuous casting process (Sterjovski et al., 2005). Their ANN's prediction results were verified with actual experiments with good agreement. Xing et al. presented a method to blend a smooth surface by using ANN (Yuan et al., 2002). They used 9857 point coordinates on the neighbouring surfaces as training data, 2500 point coordinates inside the blending surface were computed by ANN. The surface built by ANN approach was comparable with the surface built by NURBS approach. In addition, Fuh et al. employed ANN in estimation of plastic injection moulding production cost (Fuh et al., 2004). Nineteen cost-related factors were identified and historical cost data were collected to train up the ANN. They found that the estimation could be more accurate by using different ANN's structures for different cost range. Vassilopoulos et al. used ANN to generalize the experimental data and approximate the relationship between design parameters (orientation angle of the fibres, stress ratio, the maximum applied stress and the amplitude of applied stress) and the fatigue life of multidirectional composite laminates (Vassilopoulos et al., 2007). In their study, only 50% of experimental data was enough to model the fatigue life characteristics of the material. Raj et al. made use of the advantages of FEM and ANN to model the hot upsetting, hot extrusion and metal cutting processes (Hans Raj et al., 2000). Different process parameter configurations were simulated by FEM. The ANN was used to approximate the function based on FEM results. The process load was estimated by presenting the required process parameters to the ANN. They raised a new ANN application in the automatic selection of tools and real-time monitoring of tool wear. Lorenzo et al. applied ANN to predict ductile fracture in cold forming operation. Five variables (effective strain, tangential stress, effective stress, maximum principle stress and mean stress) at the critical regions of workpiece in five forming steps were predicted by FEM, and those variables were then inputted to the ANN for estimating the occurrence of ductile fracture (Di Lorenzo et al., 2006). Ohdar and Pasha used ANN to control the sinter-forged density of metal power preform. The density was identified as a function of compacting pressure, sintering temperature and percent reduction. Forty-six sets experimental data under difference process parameters were collected. Thirty-six of them were used as training samples, while remaining 10 sets data were used to test the performance of ANN. The testing result showed that the error was no more than 0.42% (Ohdar and Pasha, 2003). Ko et al. utilized ANN to evaluate the design in multi-stage metal-forming to avoid ductile fracture. In their study, a cold heading process was optimized to demonstrate and validate their proposed design method (Ko et al., 1998). Furthermore, Kim and Kim utilized FEM to simulate the metal forming behaviours with different billet dimension and tooling design for the production of rib-web product and cylindrical pulley, respectively (Kim and Kim, 2000). They made use of the ANN's function approximation ability to find the optimum design to eliminate the under-filling defect of the rib-web product and enhance the dimensional accuracy of the cylindrical pulley.

The above monolithic researches have shown that ANN has promising and potential applications in industries. However, there is a lack of extensive researches on developing a methodology to integrate the ANN and FEM for product design and development. This paper attempts to conduct a research in this niche area by integrating the ANN and FEM simulation to support the metal-formed product design.

In this research, a framework on the integrating FEM simulation and ANN methodology to find the desired parameter configuration and optimal design solution is first proposed. The methodology utilizing the FEM to predict the mechanical behaviours of design and employing the ANN to approximate the non-linear relationship between the design parameters and the mechanical behaviours of the designed forming system is developed. To illustrate the detailed procedure and processes, a case study is used to implement the developed methodology. The results show the proposed methodology could estimate the performances of different design solutions and identify the best one.

Section snippets

Methodology

When optimizing design parameters, it is impractical to simulate all the design combinations. The integrated FEM and ANNs methodology proposed in this research can predict the design behaviours based on the limited simulation of design scenarios and identify the optimal design from the whole design space. Fig. 1 presents the framework of the methodology for product design and development.

From Fig. 1, it can be seen that the preliminary design is conducted firstly. For metal-formed product

Case study

To illustrate the integrated FEM and ANN methodology and how it is used to predict the mechanical behaviours of a metal-forming system, a radial metal-forming product is used as a case study. Fig. 5(a) and (b) show the geometry and dimension of the formed part and punch, respectively. Fig. 5(c) shows the die assembly.

Conclusions

In the traditional product development paradigm, product design parameters are determined by experience. Even with the emergence of FEM simulation technology, it cannot easily find the best design as it is impossible to conduct all the simulation for any given point in the design space. In metal forming, a forming system usually involves a lot of design parameters. A subtle change of any parameter will constitute a new design scenario and a new simulation is needed to explore its behaviours and

Acknowledgements

The authors would like to thank the grant support with the project of ITS/028/07 from the Innovation and Technology Commission of Hong Kong Government and the project of G-YF67 from the Hong Kong Polytechnic University to support this research.

References (18)

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