an integrated fem and ann methodology for metal-formed product design

8/12/2019 An Integrated FEM and ANN Methodology for Metal-Formed Product Design.

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

W.L. Chan, M.W. Fu, J. Lu

Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

a r t i c l e i n f o

Article history:

Received 25 August 2007

Received in revised form

11 March 2008

Accepted 1 April 2008Available online 2 June 2008

Keywords:

FEM simulation

Artificial neural network

Metal forming

Metal-formed product design

Die design

Design solution evaluation

a b s t r a c t

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 andtooling 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.

& 2008 Elsevier Ltd. All rights reserved.

1. 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 extensivelyverified 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) tostudy 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 sim-

ulations, 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

ARTICLE IN PRESS

Contents lists available atScienceDirect

journal homepage: www.elsevier.com/locate/engappai

Engineering Applications of Artificial Intelligence

0952-1976/$ - see front matter & 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engappai.2008.04.001

Corresponding author. Tel.: +852 27665527.

E-mail address: [email protected] (M.W. Fu).

Engineering Applications of Artificial Intelligence 21 (2008) 1170 1181
http://www.sciencedirect.com/science/journal/eaaihttp://www.elsevier.com/locate/engappaihttp://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.engappai.2008.04.001mailto:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.engappai.2008.04.001http://www.elsevier.com/locate/engappaihttp://www.sciencedirect.com/science/journal/eaai


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parameter configuration, and tooling geometry. To evaluate the

preliminary design based on design performance and productionefficiency, design criteria are needed. The design criteria include

the amount and distribution of stress, strain and deformation

loading, etc. Among all the design parameters related to product,tooling and process, the critical design parameters are selected

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Find ANNs structurewith lowest error

1). Select training casesfrom OA

representation

3). FEM analysis

2). CAD model

ANN

Model 1

ANN

Model 2

ANN

Model n

Designparametercombination

1.) Define design

2.) Define criticaldesign parameters

parameters anddesign criteria

Modify design

parameter(s)?

Acceptable result?No

Add training caseto re-train the ANNs

FEMValidation

Consistent?

ToolingFacbrication

Yes

No

Possible design

parameter

combination(s)

Acceptable result?No

Mechanical

Behavior 1

Mechanical

Behavior n

Mechanical

Behavior 2+

Cut the performance surfacegraph by the corresponding

trimming plan at the definedperformance level

Define required

performances level

Performancesurface graphs

Assembly all the remainingperformance surface graph

Yes

Yes

Lower designrequirement (s)?

No

Yes

Re-design

the product

No

Yes

Redesignthe product

-

Full factorial design

in pre-defined level

Preliminary design

Training case generation

Well trained ANN models

Training ANNs

Approach 1: Direct ANNs output

Approach 2: Output

Approach 2: post-process

Approach 1Start Here!

Approach 2

Start Here!

Approach 1 Approach 2

Fig. 1. Integrated FEM and ANN framework.

W.L. Chan et al. / Engineering Applications of Artificial Intelligence 21 (2008) 117011811172


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and their variation range is determined. The critical design

parameters will generate different design scenarios through the

combination and configuration of these critical design para-

meters. The training cases can then be selected among those

combinations by using an appropriate orthogonal array (Ross,

1996). The geometry of training case is modelled in CAD systems

while the mechanical performances are simulated by CAE

systems. The design parameter combinations of the training casesand its corresponding FEM results are used as the sources to train

up different ANNs for different mechanical performances estima-

tion purpose. Since many ANNs configurations can be successfully

trained, the number of validation cases is used to find the

appropriate configuration with lowest average error for each ANN.

The average error of the validation cases is determined by

average error

Pni1jri;a ri;e=ri;aj 100%i

n (1)

where ri,a and ri,e are the actual and estimated results of the ith

validation case, respectively, andn is the number of the validation

cases.

Once the ANNs have been well trained, there are two

approaches to utilize them to yield the optimized design con-figuration, as shown in Fig. 1. For the first approach, the mec-

hanical performance estimation can be directly obtained from the

corresponding ANN by inputting a design parameter combination.

Different design parameter combinations can be explored to find

the satisfactory mechanical performances estimated by ANNs.

For the second approach, the ANNs are used to generate the

corresponding performance surface graph which represents the

estimated mechanical performance for the full factorial design. As

shown inFig. 2, theX-Yplan of the surface graph indicates all the

design parameter combination in pre-defined level, which is an

example of theX-Yplan of the performance surface graph with six

design parameters in three levels. The letters fromatoerepresent

the design parameters from 1 to 6 respectively, while the numbers

1 to 3 designate the level of the corresponding parameter. Forexample,d2 represents the second level of the design parameter 4.

Each design parameter combination is allocated anX-Ycoordinate.

The design parameter combination ofa1,b1,c1,d1,e1,f1 is located

at the original. The position of each combination is arranged to

make the neighbour combinations only varying one level of a

parameter so as to form a smooth surface. The Z-axis of the

surface graph indicates the estimated mechanical behaviour

performance. Fig. 3 shows an example of performance surface

graph. After different performance surfaces are formed, they are

used to find the possible design scenarios. As shown in Fig. 4, the

performance surfaces are generated by ANNs and the trimming

plan is set at the critical mechanical behaviour level in the

corresponding performance surface. The trimming plan is em-

ployed to cut the performance surfaces, the remaining surface

shows all the possible design scenarios which can fulfill the

corresponding mechanical performance requirements. Finally, the

remaining surfaces are assembled. The overlapping region shows

the possible design scenarios that can meet all the defined design

requirements. Usually, if more performance surfaces are used

(more design requirements), the overlapping area of the as-

sembled remaining surfaces will be decreased. This implies that

less number of possible design scenarios meet all the design

requirements.

For the above both approaches, if the results estimated by

ANNs are accepted, the model will be validated by FEM. If the

results are consistent, the design solution is accepted. Otherwise,

that model will become a training case for the ANNs in order to

make the ANNs more knowledgeable. After that, another

suggested solution from the upgraded ANNs can be obtained

and validated by FEM simulation again. If there is none of

the results estimated by ANNs can fulfil the design require-

ments, the product has to be re-designed, different product and

tooling geometry parameters and process parameters should be

considered.

In this design framework, the first approach is more direct

to check the mechanical performances with defined design

parameter combination. It is more convenient to optimize

design with only few requirements. For the second approach,

it has to go through some post-processing procedure. How-ever, it can easily find all the possible optimal results in the case

which has a lot of design requirements. Both the proposed

approaches are more effective to yield an optimal design as the

number of time consuming FEM simulation can be reduced

significantly.

2.1. CAE simulation

CAE simulation technology utilizes finite element technique to

reveal the mechanical behaviours of forming systems. To simulate

a forming system, the geometry of each die component and the

workpiece are modelled in CAD system. The finished CAD models

are then converted to a data exchange format such as STL, IGES,and STEP in such a way that they can be imported to CAE systems

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Fig. 2. X-Yplan of the performance graph (six parameters in three level).

Fig. 3. Performance surface graph.

W.L. Chan et al. / Engineering Applications of Artificial Intelligence 21 (2008) 11701181 1173


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for simulation. Before the model is analysed, pre-processing is

needed, which includes nine steps.

(1) input and assemble the components;

(2) define the model deformation type (rigid, elastic or plastic

body);

(3) select element type, mesh density and meshing;

(4) set material properties for the model;

(5) set initial and boundary conditions (e.g. temperature, friction,

symmetry, etc.);

(6) define tooling motion;

(7) set the number of simulation step;

(8) define termination conditions;

(9) set the value for convergence criteria.

With all the above settings, the model can be simulated. The

simulation results can then be obtained in post-processing stage.

2.2. Design parameters and evaluation criteria

For the tooling design, there are two critical criteria to evaluate

its performance, namely the maximum deformation load and

maximum von Mises effective stress. The deformation load not

only determines the die stress but also the size of the forming

machine, which is further related to the production cost. The level

of deformation load is related to the billet design, process

determination, part geometry, tooling structure and the billet

material properties. Most of the tooling failure is caused by tooling

fatigue, which is further determined by cycle stress located at the

stress concentrated region (Fu et al., 2006). von Mises effective

stress is the combined representation of stress components sij.

Therefore, it can be used to evaluate the tooling fatigue life cycle.

Based on the stress simulation results, material properties, the

geometry of the tooling and the part and design requirements, the

critical design parameters and its variable range can be defined.

3. Case study

To illustrate the integrated FEM and ANN methodology andhow 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.

3.1. Simulation models

All the components geometry in Fig. 5 were modelled by a

commercial CAD system, viz., Pro/E, and then exported to a CAE

simulation system, DEFORM 3D system. The punch and billet

were considered as elastic and plastic bodies, respectively. The

punch material is M2, which is high alloyed, high speed tool steel

with Youngs modulus of 250 GPa and Poisson ratio of 0.3. The

billet material is AISI 1016. In addition, the tetrahedral element is

used for meshing. The punch is meshed into 20,000 elements and

the billet model is 16,000 elements.

Through simulation, the simulation results are available. Fig. 6

shows the deformation load variation in the entire forming

process. The stress level of the punch at the most severe stress

concentration region is critical to qualify the die fatigue life of the

system. Fig. 7 illustrates the stress concentration at the second

radius corner with the maximum stress.

3.2. Orthogonal array

In the conventional application of ANN, the training cases are

from historical or experimental data (Fuh et al., 2004;Ohdar and

Pasha, 2003). The training data range may be limited. It may not

accurately predict the result beyond the training data range. The

training cases of this paper, however, are generated by FEM

simulation. The parameter combinations can be designed accord-

ing to the study. In this case study, six variable design parameters

were defined based on the simulation results in Section 3.1; they

are shown in Fig. 8. If the five levels of each parameter were

studied, there were 15,625 combinations in total. The criteria to

select the training cases are the data range should be wider than

required and well distributed. Therefore, the orthogonal array is

employed which would suggest using less simulation to find outthe relationship between parameters (Ko et al., 1998). L25

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Fig. 4. Trimming and assemble process of the performance surface graphs.



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Fig. 5. Die structure: (a) punch design; (b) part design and (c) die assembly.

Fig. 6. Deformation load: (a) section of the deformed part and (b) the variation of deformation load.

Fig. 7. The maximum stress location and distribution: (a) stress distribution at the last forming step and (b) maximum stress variation.



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orthogonal array was used as reference to select the combination

as training case for the ANNs.

There are 25 design combinations in the selected L25

orthogonal array. Some parameters combinations were conflicted

each other in this case study. Therefore, these combinations have

been modified. In order to reduce the computation time, a quarterof model was simulated for each case. All the parameter

combinations of the training case and the corresponding simula-

tion results are shown inTable 1.

3.3. Network training and testing

The ANNs were built and trained in Matlab environment. The

training process adjusts the weight of each neuron to an

appropriate value. There are many available training algorithms,

but the most popular one is the error back-propagation algorithm

(Hagan et al., 1996;Sterjovski et al., 2005;Yuan et al., 2002;Fuh

et al., 2004;Vassilopoulos et al., 2007;Fonseca et al., 2003) and it

was used in this study. There is no strict rule for design of the ANNstructure. However, the number of neurons in the hidden layers is

critical to determine the complexity level of the function. If the

desired function has a large number of inflection points, more

number of neurons in the hidden layer is needed ( Hagan et al.,

1996), but it also needs more number of training cycle to be

converged. Termination criteria are 50,000 training cycles or 0.001

mean square error (mse). The mse is calculated as

mse 1

Q

XQ

k1

ek2 1

Q

XQ

k1

tk ak2 (2)

whereQis total number of training case, t(k) represents the kth

training cases target error while a(k) represents the kth trainings

actual output Matlab.

Random weighing was set for the first learning cycles. The

learning rate was set as 0.01. The learning rate plays an important

role for the learning algorithm. In general, a larger value results in

the fast convergence. But the algorithm becomes unstable that

may cause the increase of error. On the other hand, a smaller value

can yield a more accuracy result, but longer time to converge

(Matlab; Bai et al., 2007). In this research, different networkconfigurations with difference number of hidden layers and

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Fig. 8. Design parameters: (a) part parameters; (b) punch parameters and (c) local illustration of punch.

Table 1

The detail design combinations and corresponding results of the training cases

Trained design parameters Results

Parameters 1 2 3 4 5 6 Max. load (N) Punch-eff. stress (MPa)

Case 1 0 1 13 40 1 20 4,36,000 2820

Case 2 0 2.75 3.25 42.5 0.5 22.5 4,40,000 3250

Case 3 0 4.5 6.5 45 0 25 3,96,000 2750

Case 4 5 6.25 6.5 47.5 0.5 27.5 3,48,000 2410

Case 5 7.5 8 0 50 1 30 3,29,000 2340

Case 6 2.5 2.75 6.5 45 0.5 30 4,53,000 3160

Case 7 5 2.75 9.25 47.5 1 20 3,95,000 2820

Case 8 10 4.5 9.25 50 1 22.5 3,08,000 2080

Case 9 7.5 6.25 9.25 40 0.5 25 3,68,000 2370

Case 10 10 8 0 42.5 0 27.5 3,13,000 2020

Case 11 2.5 1 13 50 0.5 27.5 3,96,000 2990

Case 12 5 2.75 9.25 40 0 30 3,76,000 2540

Case 13 0 1 13 42.5 0.5 20 4,35,000 2920

Case 14 5 6.25 0 45 1 22.5 3,56,000 2350

Case 15 5 8 3.25 47.5 1 25 3,50,000 2510

Case 16 2.5 4.5 9.25 42.5 1 25 3,32,000 2280

Case 17 0 1 13 45 1 27.5 5,14,000 3320

Case 18 7.5 4.5 9.25 47.5 0.5 30 2,96,000 2000Case 19 7.5 6.25 3.25 50 0 20 3,44,000 2320

Case 20 7.5 8 6.5 40 0.5 22.5 3,31,000 2150

Case 21 2.5 1 13 47.5 0 22.5 3,85,000 2770

Case 22 2.5 2.75 0 50 0.5 25 4,11,000 2940

Case 23 10 4.5 3.25 40 1 27.5 3,54,000 2330

Case 24 10 6.25 6.5 42.5 1 30 3,35,000 2350

Case 25 10 8 0 45 -0.5 20 3,32,000 2290



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neurons have been tested and validated with eight validation

cases as shown in Table 2. Those combinations did not fall into the

full-factorial table with same number of design parameter and its

level of the training case (six parameters with five levels). To

evaluate which network configuration is the preferred one, Eq. (1)

is used to find their average error for comparison. Among different

tested configurations, the smallest average errors were 7.75% and

8.75% for the ANN model in terms of the von Mises effective stressprediction and load prediction, respectively. Fig. 9 shows the

configuration of ANN to estimate the effective stress, while Fig. 10

shows the configuration of ANN to estimate the deformation load.

The first model consists of three hidden layers; the first hidden

layer is composed of five neurons while the each of others is

composed of 10 neurons. The second model consists of three

hidden layers. The first layer is composed of 10 neurons while the

each of other layer was composed of 40 neurons. In both models,

all neurons in hidden layers used transfer function of hyperbolic

tangent sigmoid:

fx ex ex

ex ex (3)

The output layer used the following linear function:

fx x (4)

3.4. Estimation of mechanical performances

In order to demonstrate the ANNss ability to generalize the

training data, the ANNs direct output method (the approach one

as stated in Section 2) was used to estimate the deformation load

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Table 2

Validation cases and results

Design combinations Results

Parameter 1 2 3 4 5 6 Max. load

(N) (FEM)

Max. load

(N) (ANN)

Max. load

error (%)

Punch-eff.

stress (MPa) (FEM)

Punch-eff.

stress (MPa) (ANN)

Max. stress

error (%)

Case 1 0 8 3 50 1 25 3,16,000 3,62,000 14.56 2320 2440 5.17

Case 2 0 2 5 40 0.5 20 4,33,000 4,43,000 2.31 2670 2840 6.37

Case 3 2 3 8 45 0 30 3,76,000 4,60,000 22.34 2590 3150 21.62

Case 4 3 4 5 48 1 23 3,87,000 3,93,000 1.55 2630 2660 1.14

Case 5 4 5 6 42 0 26 3,21,000 3,43,000 6.85 2140 2400 12.15

Case 6 5 3 8 42 0.5 25 3,97,000 3,66,000 7.81 2800 2650 5.36

Case 7 8 5 3 46 1 25 3,87,000 3,43,000 11.37 2700 2450 9.26

Case 8 10 8 0 45 1 24 3,15,000 3,25,000 3.17 2220 2240 0.90

Average error: 8.75 Average error: 7.75

Fig. 9. ANN structure for evaluating the maximum von Mises effective stress of the punch.

Fig. 10. ANN structure for evaluating the forming load of the punch.



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and the effective stress of the input design parameter combina-

tion. The FEMs and ANNs results with varying the level of only

one parameter, and the combinations which did not fall into the

full-factorial table with same number of design parameter and its

level of the training case (six parameters with five levels) are

compared. Figs. 1116 show the comparison of the FEMs and

ANNs results about the effective stress and deformation load,

respectively. The result shows the ANNs prediction gave asatisfactory agreement with the FEMs result.

3.5. Estimation of desired design parameter combinations

The well-trained ANNs were used to estimate the mechanical

performances of the potential combinations, which could fulfil the

pre-defined design criteria, viz., the maximum von Mises effective

stress is less than 2.5 GPa and the deformation load is less than

350 kN. Firstly, a three-level combination table was generated and

shown inFig. 2. This combination table was used to form the X-Y

plane for the surface graph. Each stress and deformation load

results were estimated by the well-trained ANNs. These results

would be represented by the Z-axis coordinate for the corre-

sponding combination. The formed performance surface graphsare shown inFig. 17.

In order to find all the possible combinations, plans at the

2.5 GPa stress level and 350 kN loading level were set in the

corresponding graph as shown in Fig. 18. The plane cuts off

the upper surface in each graph and the lower surface is retained.

The section of the remaining stress and load surface were then

assembled. The area of the overlap regions as shown in Fig. 19,

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10

1

2

3

4

5

Von Mises Effective Stress

Validation (Parameter 1)

VonMisesEffectiv

eStress

(GPA)

Parameter Level

FEM

ANNs

0

100

200

300

400

500

600

700

Load Validation (Parameter 1)

Load(kN)

Parameter Level

FEM

ANNs

2 3 4 5 1 2 3 4 5

Fig. 11. Comparison of FEMs and ANNs results with different level of parameter 1.

10

1

2

3

4

5



VonMisesEffectiveStress

(GPA)

Parameter Level

FEM

ANN

0

100

200

300

400

500

600700


Load(kN)

Parameter Level

FEM

ANN

2 3 4 5 1 2 3 4 5


10

1

2

3

4

5

Von Mises Effective StressValidation (Parameter 3)


(GPA)

Parameter Level

FEM

ANNs

0

100

200

300

400

500

600

700


Load(kN)

FEM

ANNs

2 3 4 5 1

Parameter Level

2 3 4 5




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which indicate the suggested combinations and could meet

both design criteria, viz. stress was less than 2.5GPa and the

loading was less than 350 kN. Some of the suggested combina-

tions, however, were unachievable due to the conflict of

parameter configuration and they were thus eliminated. The

design scenarios close to the contour of the overlapping section

are the marginal cases, which may not meet the design

requirements. Therefore, it is conservative to choose the cases

at the centre of overlapping section or far away from the contour.

Fig. 20shows the remaining suggested solutions and four selected

validation cases. The result shows the good agreement with theFEM result as shown inTable 3. Among the four cases, case 4 has

the largest error with 5.73% for deformation load estimation

and 7.22% for von Mises effective stress estimation. The ave-

rage error for the estimation of maximum deformation load is

2.55%, while the average error for the estimation of maximum

stress is 2.99%. When comparing the estimation accuracy with

Section 3.4, it can be found the validation agreement in this

approach is better. This is because all the combinations in the

performance surface graph fall into the full-factorial table

with the same number of design parameter and its level of the

training case (six parameters with five levels). Those combina-

tions (input pattern) are more favourable to be recognized by thewell-trained ANNs.

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10

1

2

3

4

5



VonMisesE

ffectiveStress

(G

PA)

Parameter Level

FEM

ANNs

0

100

200

300

400

500

Load(kN)

FEM

ANNs


2 3 4 5 1

Parameter Level

2 3 4 5


10

1

2

3

4

5



VonMisesEffectiveStre

ss

(GPA)

Parameter Level

FEMANN

0

100

200

300

400

500

600

700


Load(kN)

FEMANN

2 3 4 5 1

Parameter Level

2 3 4 5


10.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5




(GPA)

Parameter Level

FEM

ANNs

0

100

200

300

400

500

600

700


Load(kN)

Parameter Level

FEM

ANNs

2 3 4 5 1 2 3 4 5




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4. 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 thebest 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

performance. It is not pragmatic to find the optimal solutionthrough one-by-one simulation. To address this issue, the

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Fig. 18. Trimming plan and the remaining surfaces: (a) stress level surface graph and (b) load level surface graph.

Fig. 17. Design criteria representation: (a) stress performance surface graph and (b) load performance surface graph.

Fig. 19. The retained sections after trimming: (a) loading level surface graph; (b) stress level surface graph and (c) overlap section.



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integrated FEM and ANN methodology developed in this research

can effectively find out the highly non-linear relationship between

the design parameters and the mechanical behaviours of the

design. In this research, two design approaches were proposed to

evaluate the design and find the desired design parameter

combination. To verify the developed methodology, a case study

was presented to validate the performance of ANN and demon-

strate the implementation procedure. All the validation results

show the estimation of ANN can achieve satisfactory level,

especially the estimation of combinations which fall into the

full-factorial table with the same number of design parameter and

level of the training case. The developed design and optimization

methodology helps evaluate the quality of design at the up-front

of design stage and thus can greatly reduce the simulation time

and make it possible to search for the optimal design in the whole

design space.

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.

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ARTICLE IN PRESS

Fig. 20. The remaining suggested combination and the selected validation case.

Table 3

Validation case results in the overlapping region

Design configurations Results

Parameter 1 2 3 4 5 6 FEM-max.

load (N)

ANN-max.

load (N)

Max. load

error (%)

FEM-max.

stress (MPa)

ANN-max.

stress (MPa)

Max. stress

error (MPa)

Case 1 0 8 6.5 40 1 25 3,29,000 3,31,000 0.61 2260 2300 1.77

Case 2 5 4.5 0 50 0 30 3,40,000 3,50,000 2.94 2390 2340 2.09

Case 3 10 4.5 0 45 1 25 3,31,000 3,34,000 0.91 2330 2310 0.86

Case 4 10 8 0 40 1 20 3,14,000 3,32,000 5.73 1940 2080 7.22

Average error: 2.55 Average error: 2.99


an integrated fem and ann methodology for metal-formed product design

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