26-07-2012, 02:44 PM
OPTIMIZATION OF OPERATING PARAMETERS FOR EDM PROCESS BASED ON THE TAGUCHI METHOD AND ARTIFICIAL NEURAL NETWORK
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Abstract:
In this paper the complexity of electrical discharge machining process which is very difficult to
determine optimal cutting parameters for improving cutting performance has been reported. Optimization of
operating parameters is an important step in machining, particularly for operating unconventional machining
procedure like EDM.
A suitable selection of machining parameters for the electrical discharge machining process relies
heavily on the operators’ technologies and experience because of their numerous and diverse range. Machining
parameters tables provided by the machine tool builder can not meet the operators’ requirements, since for an
arbitrary desired machining time for a particular job, they do not provide the optimal machining conditions. An
approach to determine parameters setting is proposed. Based on the Taguchi parameter design method and the
analysis of variance, the significant factors affecting the machining performance such as total machining time,
oversize and taper for a hole machined by EDM process, are determined.
Artificial neural networks are highly flexible modeling tools with an ability to learn the mapping
between input variables and output feature spaces. The superiority of using artificial neural networks in
modeling machining processes make easier to model the EDM process with dimensional input and output
spaces. On the basis of the developed neural network model, for a required total machining time, oversize and
taper the corresponding process parameters to be set in EDM by using the developed and trained ANN are
determined.
1. Introduction:
Electrical Discharge Machining (EDM) was first introduced in the 1940's as a crude device used to cut broken
machining tools from expensive in-process parts. Since that time EDM has become a sophisticated and
indispensable technology, revolutionizing the tool, die, and mold making industries, and making significant
inroads into the production of highly accurate, intricate and difficult to machine production parts.
In electrical discharge machining, it is important to select machining parameters for achieving optimal
machining performance. Usually, the desired machining parameters are determined based on experience or
handbook values. However, this does not ensure that the selected machining parameters result in optimal or near
optimal machining performance for that particular electrical discharge machine and environment. In earlier
work to solve this task, Lin, Wang, Yan, Tarng [2] used the Taguchi method with fuzzy logic as an efficient
approach to determine the optimal machining parameters in the electrical discharge machining process.
The Taguchi method can optimize performance characteristics through the settings of process parameters and
reduce the sensitivity of the system performance to sources of variation. As a result, the Taguchi method has
become a powerful tool in the design of experiment methods [2]. However, most published Taguchi applications
to date have been concerned with the optimization of a single performance characteristic. Handling the more
demanding multiple performance characteristics is still an interesting research problem [2].
By means of orthogonal array with the grey relational analysis the optimization procedure for
determining the optimal machining parameters with the multiple performance characteristics in the EDM
ISSN: 0975-5462 6880
A.Thillaivannan et. al. / International Journal of Engineering Science and Technology
Vol. 2(12), 2010, 6880-6888
process can be greatly simplified [3]. As a result, the method developed in this study is very suitable for
practical use in a machine shop.
In the past decade, neural networks have been shown to be the highly flexible modeling tools with
capabilities on learning the mathematical mapping between input variables and output features for nonlinear
systems [6]. Also, the superior performances of neural networks for modeling machining processes have been
published elsewhere. In these, multi-layer Perceptions based on back-propagation (BP) technique have been
employed for monitoring and modeling the reported processes.
Wang, Gelgele, Yi Wang, Yuan and Fang developed a hybrid artificial neural network and genetic
algorithm methodology for modeling and optimization of electro-discharge machining [7]. The hybridization
approach is aimed not only at exploiting the strong capabilities of the two tools, but also at solving
manufacturing problems that are not amenable for modeling using traditional methods. Based on an
experimental data, the model was tested with satisfactory results. The developed methodology with the model is
highly beneficial to manufacturing industries, such as aerospace, automobile and tool making industries.
A better process model is established based on neural networks by comparing the predictions from
different models under the effect of change of polarity between the electrode and the work materials in the EDM
process. Initially, pertinent process variables affecting the MRR, namely the polarity of the electrode, the
discharge time, the peak current, and the materials of both the tool and the workpiece, were screened by making
use of Taguchi method on design of experiments [8]. The DOE experimental data were later used for training
the various process models. Finally, more experimental verification on the established process models was
conducted, and comparisons among the models, including a statistical process model, were analyzed.
2. Problem Formulation
2.1 Design Variables
The formulation of an optimization problem begins with identifying the underlying design variables,
which are primarily varied during the optimization process. In this paper current and feed are considered as
design variables.
2.2 Constraints
The constraints represent some functional relationship among the design variables and other design
satisfying certain physical phenomenon and certain resource are greater than or equal to, a resource value. In
this paper, oversize and taper of the EDM hole are considered as constraints.
2.3 Objective function
The objective function can be of two kinds. Either the objective function is to be minimized or it has to
be maximized. In this paper, minimization of total machining time is considered as objective function.
3. Experimental equipment and design
An EDM machine, developed by SPARKONIX (I) LTD. was used as the experimental machine. The
work material, electrode and the other machining conditions were as follows (1) Workpiece (anode), Stainless
Steel 340C; (2) Electrode (cathode), Tungsten Ø 1.6mm; (3) Dielectric fluid, Kerosene; (4) Workpiece height,
50mm; (5) Workpiece length, 100mm.
A total of two machining parameters (current and feed) were chosen for the controlling factors and
each parameters have levels as shown in Table 1.
Table 1 Process parameters and their levels
PARAMETERS LEVELS
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6
CURRENT
(A)
1
2
3
4
5
6
FEED
(mm/min)
0.28
0.2825
0.2875
0.29
-
-
ISSN: 0975-5462 6881
A.Thillaivannan et. al. / International Journal of Engineering Science and Technology
Vol. 2(12), 2010, 6880-6888
The machining results after the EDM process under the designed machining conditions are evaluated in
terms of the following measured machining performance: (1) total machining time (min); (2) oversize (mm); (3)
taper (mm).
4. Solution Methodology
Taguchi Method is a new engineering design optimization methodology that improves the quality of
existing products and processes and simultaneously reduces their costs very rapidly, with minimum engineering
resources and development man-hours. The Taguchi Method achieves this by making the product or process
performance "insensitive" to variations in factors such as materials, manufacturing equipment, workmanship and
operating conditions.
Neural networks are developed using the current understanding of the biological nervous system. The
key to the development of a neural network in the domain of engineering design and group technology is its
ability to store a large set of patterns as memories that can be recalled. During recall this memory can be excited
with a key pattern containing a part of information about a particular member of a stored pattern set. The
particular pattern set can be recalled through the association of the key pattern and the information memorized.
Neural networks have learning and generalization abilities. They are able to learn the correlation between input
examples and the expected outcome, and more importantly, to generalize the relationship.
4.1 Taguchi Method
Experimental design methods [9] were developed originally by Fisher [10]. However, classical
experimental design methods are too complex and not easy to use. Furthermore, a large number of experiments
have to be carried out as the number of the process parameters increases. To solve this important task, the
Taguchi method uses a special design of orthogonal array to study the entire parameter space with only a small
number of experiments. The experimental results are then transformed into a signal-to-noise (S/N) ratio. The
S/N ratio can be used to measure the deviation of the performance characteristics from the desired values.
Usually, there are three categories of performance characteristics in the analysis of the S/N ratio: the lower-thebetter,
the higher-the-better, and the nominal-the-better. Regardless of the category of the performance
characteristic, a larger S/N ratio corresponds to better performance characteristic. Therefore, the optimal level of
the process parameters is the level with the highest S/N ratio. Furthermore, a statistical analysis of variance
(ANOVA) is performed to identify the process parameters that are statistically significant. The optimal
combination of the process parameters can then be predicted based on the above analysis.
4.1.1 Parameters and their Levels:
The process parameters of the EDM taken up for experiment and their levels for the optimization based
of Taguchi method are given below in the Table 2
Table 2 Parameters and their levels for Taguchi method
PARAMETERS
LEVELS
Level 1 Level 2 Level 3
CURRENT
2
4
6
FEED
0.28
0.2875
0.29
4.1.2 Selection of Orthogonal Array
By knowing the parameters and their corresponding levels we can chose a standard OA, based on the
Degrees of freedom.
4.1.2.1 Degrees of freedom
We know, the number of D.O.F. for
a factor = Number of levels – 1
The number of D.O.F. for Current = 3 – 1 = 2 The number of D.O.F. for Feed = 3 – 1 = 2
Since there is no interaction between current and feed, the total degrees of freedom is
ISSN: 0975-5462 6882
A.Thillaivannan et. al. / International Journal of Engineering Science and Technology
Vol. 2(12), 2010, 6880-6888
2+ 2 = 4.
4.1.2.2 Orthogonal Array
A three-level L9 OA is selected for conducting the experiment, because in our consideration we have
each 3 level for both the factors current and feed. Hence we should pick a OA from a three-level OA and in that
L9 OA is selected because the total D.O.F is 4 which is less than the D.O.F. of the selected L9 OA which is (No.
of trials – 1) 8.
The table 3 below shows the standard L9 OA:
Table 3 L9 Orthogonal array
Sl.
No
A
Current
B
Feed
C D Total
machining
time (a)
min
Total
machining
time (b)
min
Total
machining
time ©
min
Total
machining
time (Avg.)
min
S/N
ratio
N
1 1 1 1 1 31.26 31.32 31.47 31.35 -29.92
2 1 2 2 2 42.35 41.46 39.91 41.24 -32.31
3 1 3 3 3 42.82 40.38 41.93 41.71 -32.41
4 2 1 2 3 15.85 15.73 15.64 15.75 -23.94
5 2 2 3 1 16.71 15.65 14.23 15.53 -23.84
6 2 3 1 2 15.83 15.56 15.65 15.68 -23.91
7 3 1 3 2 18.25 18.58 19.33 18.72 -25.45
8 3 2 1 3 16.23 16.76 16.48 16.42 -24.34
9 3 3 2 1 16.52 16.33 16.05 16.3 -24.24
The numbers in the current (A), column are nothing but the levels of Current. Similarly for feed (B)
and column C and D are the interactions between the factors, in our case since there are no interactions between
the factors columns C and D are just dummy columns i.e. it has no influence on the experiment.
The performance characteristic i.e. total machining time are taken from the experiment conducted for
every set of current and feed making a total of 9 trials.
4.2 Artificial Neural Network
An artificial neural network is an information-processing system that has certain performance
characteristics in common with biological neural networks. Artificial neural networks have been developed as
generalizations of mathematical models of human cognition or neural biology, based on the assumptions that:
1. Information processing occurs at many simple elements called neurons.
2. Signals are passed between neurons over connection links.
3. Each connection link has an associated weight, which, in a typical neural net, multiplies the signal
transmitted.
4. Each neuron applies an activation function (usually nonlinear) to its net input (sum of weighted input signals)
to determine its output signal.
In the past decades, numerous studies have been reported on the development of neural networks based
on different architectures. Basically, one can characterize neural networks by its important features, such as the
architecture, the activation functions, and the learning algorithms. Each category of the neural networks would
have its own input output characteristics, and therefore it can only be applied for modeling some specific
processes. In this work, ANN is employed for modeling and determination of optimal parameters for the EDM
process.
4.2.1 Architecture
Neural networks are in general categorized by their architecture. The number of hidden layers is critical
for the convergence rate at the stage of training the network parameters. Empirically speaking, one hidden layer
T = 212.77 T1= 240.36
ISSN: 0975-5462 6883
A.Thillaivannan et. al. / International Journal of Engineering Science and Technology
Vol. 2(12), 2010, 6880-6888
should be sufficient in the multi-layered networks because the number of neurons is typically assumed to be
dominant in the networks. In other words, the number of neurons must be determined by an optimization
method. In this work, a multi-layer backpropagation network is adopted to model the EDM process. To be in
particular, a four layer BP network with 6,14,18,2 neurons in each of the respective layers. This particular
configuration gives the output values, which are nearer to the target set values with very little error.
MATLAB® software, which is a high-performance language for technical computing, is used for
modeling and developing of neural network.
4.2.2 Activation Functions
The connections among the neurons are made by signal links designated by corresponding weightings.
Each individual neuron is represented by an internal state, namely the activation, which is functionally
dependent of the inputs. In general, the Sigmoid functions (S-shaped curves), such as logistic functions and
hyperbolic tangent functions, are adopted for representing the activation. In the networks, a neuron sends its
activation to the other neurons for information exchange via signal links. In this work, two different functions
for activation have been employed. They are Linear transfer function and Tan-sigmoid transfer function, in
which the former is used for the output layer and the latter is used for the all hidden layers.
4.2.3 Algorithm
There are many variations of the backpropagation algorithm. The simplest implementation of
backpropagation learning updates the network weights and biases in the direction in which the performance
function decreases most rapidly - the negative of the gradient. One iteration of this algorithm can be written as
Xk+1 = Xk – αk gk
where Xk+1 is a vector of current weights and biases, Xk is the current gradient, and gk is the learning
rate.
There are two different ways in which this algorithm can be implemented: incremental mode and batch
mode. In the incremental mode, the gradient is computed and the weights are updated after each input is applied
to the network. In the batch mode all of the inputs are applied to the network before the weights are updated.
4.2.4 Training
There are two backpropagation training algorithms: gradient descent, and gradient descent with
momentum.These two methods are often too slow for practical problems. There are several high performance
algorithms that can converge from ten to one hundred times faster than the algorithms mentioned above. All of
the faster algorithms operate in the batch mode.
These faster algorithms fall into two main categories. The first category uses heuristic techniques,
which were developed from an analysis of the performance of the standard steepest descent algorithm. One
heuristic modification is the momentum technique. There are two more heuristic techniques: variable learning
rate backpropagation and resilient backpropagation.
ISSN: 0975-5462 6884
A.Thillaivannan et. al. / International Journal of Engineering Science and Technology
Vol. 2(12), 2010, 6880-6888
4.2.4.1 Resilient Backpropagation
Multilayer networks typically use sigmoid transfer functions in the hidden layers. These functions are
often called "squashing" functions, since they compress an infinite input range into a finite output range.
Sigmoid functions are characterized by the fact that their slope must approach zero as the input gets large. This
causes a problem when using steepest descent to train a multilayer network with sigmoid functions, since the
gradient can have a very small magnitude; and therefore, cause small changes in the weights and biases, even
though the weights and biases are far from their optimal values.
The purpose of the resilient backpropagation training algorithm is to eliminate these harmful effects of
the magnitudes of the partial derivatives. In this work, resilient BP network is used.