an integrated fem and ann methodology for metal-formed product design
TRANSCRIPT
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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
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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
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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.
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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.
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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
Von Mises Effective Stress
Validation (Parameter 2)
VonMisesEffectiveStress
(GPA)
Parameter Level
FEM
ANN
0
100
200
300
400
500
600700
Load Validation (Parameter 2)
Load(kN)
Parameter Level
FEM
ANN
2 3 4 5 1 2 3 4 5
Fig. 12. Comparison of FEMs and ANNs results with different level of parameter 2.
10
1
2
3
4
5
Von Mises Effective StressValidation (Parameter 3)
VonMisesEffectiveStress
(GPA)
Parameter Level
FEM
ANNs
0
100
200
300
400
500
600
700
Load Validation (Parameter 3)
Load(kN)
FEM
ANNs
2 3 4 5 1
Parameter Level
2 3 4 5
Fig. 13. Comparison of FEMs and ANNs results with different level of parameter 3.
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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
Von Mises Effective Stress
Validation (Parameter 4)
VonMisesE
ffectiveStress
(G
PA)
Parameter Level
FEM
ANNs
0
100
200
300
400
500
Load(kN)
FEM
ANNs
Load Validation (Parameter 4)
2 3 4 5 1
Parameter Level
2 3 4 5
Fig. 14. Comparison of FEMs and ANNs results with different level of parameter 4.
10
1
2
3
4
5
Von Mises Effective Stress
Validation (Parameter 5)
VonMisesEffectiveStre
ss
(GPA)
Parameter Level
FEMANN
0
100
200
300
400
500
600
700
Load Validation (Parameter 5)
Load(kN)
FEMANN
2 3 4 5 1
Parameter Level
2 3 4 5
Fig. 15. Comparison of FEMs and ANNs results with different level of parameter 5.
10.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Von Mises Effective Stress
Validation (Parameter 6)
VonMisesEffectiveStress
(GPA)
Parameter Level
FEM
ANNs
0
100
200
300
400
500
600
700
Load Validation (Parameter 6)
Load(kN)
Parameter Level
FEM
ANNs
2 3 4 5 1 2 3 4 5
Fig. 16. Comparison of FEMs and ANNs results with different level of parameter 6.
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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.
References
Bai, H., Kwong, C.K., Tsim, Y.C., 2007. Process modelling and optimization usingartificial neural networks and gradient search method. International Journal ofAdvanced Manufacturing Technology 31, 790796.
Di Lorenzo, R., Ingarao, G., Micari, F., 2006. On the use of artificial intelligence toolsfor fracture forecast in cold forming operations. Journal of Materials ProcessingTechnology 177, 315318.
Fonseca, D.J., Navaresse, D.O., Moynihan, G.P., 2003. Simulation metamodelingthrough artificial neural networks. Engineering Applications of ArtificialIntelligence 16, 177183.
Fu, M.W., Yong, M.S., Tong, K.K., Muramatsu, T., 2006. A methodology forevaluation of metal forming system design and performance via CAEsimulation. International Journal of Production Research 44, 10751092.
Fuh, J.Y., Zhang, Y.F., Nee, A.Y.C., Fu, M.W., 2004. Computer-aided Injection MoldDesign and Manufacture. Marcel Dekker, NewYork ISBN: 0-824-75314-3.
Fujikawa, S., 2000. Application of CAE for hot-forging of automotive components.Journal of Materials Processing Technology 98, 176181.
Hagan, M.T., Demuth, H.B., Beale, M., 1996. Neural Network Design. PWS Pub.ISBN:0-534-94332-2.
Hans Raj, K., Sharma, R.S., Srivastava, S., Patvardhan, C., 2000. Modeling ofmanufacturing processes with ANNs for intelligent manufacturing. Interna-tional Journal of Machine Tools & Manufacture 40, 851868.
Kim, D.J., Kim, B.M., 2000. Application of neural network and FEM for metalforming processes. International Journal of Machine Tools & Manufacture 40,911925.
Ko, D.C., Kim, D.H., Kim, B.M., Choi, J.C., 1998. Methodology of perform designconsidering workability in metal forming by the artificial neural network andTaguchi method. Journal of Materials Processing Technology 8081, 487492.
Matlab Neural Network Toolbox Users Guide Version 5.
Ohdar, R.K., Pasha, S., 2003. Prediction of process parameters of metal powderperform forging using artificial neural network (ANN). Journal of MaterialsProcessing Technology 132, 227234.
Ross, P.J., 1996. Taguchi Techniques for Quality Engineering: Loss Function,Orthogonal Experiments, Parameter and Tolerance Design, second ed.McGraw-Hill, NewYork ISBN:0-070-53958-8.
Sterjovski, Z., Nolan, D., Carpenter, K.R., Dunne, D.P., Norrish, J., 2005. Artificialnetworks for modeling the mechanical properties of steels in variousapplications. Journal of Materials Processing Technology 170, 536544.
Tong, K.K., Yong, M.S., Fu, M.W., Muramatsu, T., Goh, C.S., Zhang, S.X., 2005. CAEenabled methodology for die fatigue life analysis and improvement. Interna-tional Journal of Production Research 43, 131146.
Vassilopoulos, A.P., Georgopoulos, E.F., Dionysopoulos, V., 2007. Artificial neuralnetworks in spectrum fatigue life prediction of composite materials. Interna-tional Journal of Fatigue 29, 2029.
Yang, D.Y., Ahn, D.G., Lee, C.H., Park, C.H., Kim, T.J., 2002. Integration of CAD/CAM/CAE/RP for the development of metal forming process. Journal of MaterialsProcessing Technology 125126, 2634.
Xing, Yuan, Jiang, Hangfan, Wang, Yu, 2002. A neural network approach to surfaceblending based on digitized points. Journal of Materials Processing Technology120, 7679.
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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
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