Influence of optimization techniques and nano surface coating materials on microstructure of iron-nickel-chromium alloy using wire EDM process

The experiment performance has been conducted on wire EDM as shown in Figure 1. It has brass wire with the diameter of 0.25 mm as cutting tool, deionized water consider to dielectric medium at constant atmospheric temperature. The flow chart diagram of the optimization techniques is shown in Figure 2. Three input variables as pulse on time (T_on), pulse off time (T_off) and wire feed (WT) has been used for machining on iron-nickel-chromium alloy and measured output performance as surface roughness (SR) and material removal rate (MRR). The experimental work has been optimized L27 orthogonal array by Mintab software to get error less input and output as shown in Table 2. The Table 3 shows three levels of input parameters. The L27 orthogonal array has been conducted in 3 × 3 level. The below equation shows S/N ratio (single to noise) input parameter.

Fig. 1

Fig. 2

The optimized output parameter founded in S/N ratio has been employed to conduct the input variables. The surface roughness and material removal rate has been predicted by Taguchi method to get minimum error and more accuracy.

Taguchi Method has been applied to experimental design through method employed orthogonal array to manage the process affecting parameters and their levels. It probably has to conduct all possible combination such as factorial design, Taguchi method combination test pair. These allow for collecting the data to find factors affecting the most output with least possible experimentations, which has been saving resource and time. ANOVA (analysis of variables) on the data collected to be used choosing new parameters for performance characterizes optimized. In order to find the study parameters, cause and effect diagram to determine potential parameters that affect machining characteristics (SR and MRR) was constructed. From the cause and effect diagram and literature review of wire EDM, we were choosing three input parameter for this investigation. In this investigation, L₂₇ orthogonal array was with three control factors, that is, pulse on time, pulse off time and wire feed. Signal to noise ratio was obtained by using Minitab software. SR considered as lower is better (LB) and MRR considered as higher is better (HB) for determining optimized machining parameters. The loss function logarithmic transformation can be used to calculate S/N ratio.

Back propagation is a special type of neural network and it is also named as back propagation error method. It is mostly used for multi layered neural networks. In artificial neural network, one of the methods is back propagation neural network used to calculate gradient descent that is needed to calculate the weight of the network. This method uses a derivative of the squared error function with respect to the weights of the network. The back propagation neural network, otherwise backward propagation error method, mainly look for error function, even then having the minimum value of weight space is known as rule or gradient descent. The weights that can minimize the error function are then considered to be a solution.

BPNN is a feed forward neural network. Back-propagation, an abbreviation for “backward propagation of errors” is a common method of training ANN. In 1986, Rumelhart et al. had described a new supervised learning procedure known as back propagation neural network (BPNN), which is used for linear as well as non-linear classification. From a desired output, the network learns from many inputs. In BPNN, the errors are back propagated to the input layer. BPNN is a supervised algorithm in which error difference between the desired output and calculated output is back propagated. The procedure is repeated during learning to minimize the error by adjusting the weights through the back propagation of error. As a result of weight adjustments, hidden units set their weights to represent important features of the task domain. It has the capability to establish the connection between HVS parameter values and FIS output values by adjusting the neural network weights and bias before and after embedding watermark. Owning to use of neural network, watermark can be extracted without the host signal, and therefore, reduce the boundary in practical applications.

BPNN consists of three layers: 1) input layer, 2) hidden layer, and 3) output layer. The number of hidden layers, and the number of hidden units in each hidden layer depends upon the complexity of the problem as shown in Figure 3.

Fig. 3

During this step, error is calculated by difference between the targeted output and actual output of each output unit. This error is back propagated to the previous layer, that is, hidden layer. For each unit in the hidden layer N, error at that node is calculated. In a similar way, error at each node of previous hidden layer, that is, N-1 is calculated. These calculated errors are used to correct the weights so that the error at each output unit is minimized. Forward and backward steps are repeated until the error is minimized up to the expected level. The training algorithm of back propagation includes four stages: 1. initialization of weights, 2. feed forward, 3. back propagation of errors, 4. updating the weights and biases. The bias acts like weights on the connection from units whose output is always 1. During initialization of weights, some arbitrary values are given initially to give some output by feed forwarding through the layers. So, the difference between the obtained and actual values is calculated as error and back propagated. High initial weight will result in 90 a faster learning rate. But weights may oscillate. If initial weights are too small, then learning rate will be slow (Table 5). For best results, initial weights may be considered between −0.5 to 0.5 or −1 to 1. In back propagation method first, the output of hidden layer is calculated by the formula: Hi=f(∑wijXi−aj)j=1,2,…,l {H_i} = f\left( {\sum {{w_{ij}}{X_i} - {a_j}} } \right)j = 1,2, \ldots ,l where and f represent the output of hidden layer and the incentive function of neurons, l is the neuron number of hidden layer, n is the neuron number of the input layer, is the weight factor between input-layer and hidden layer, is threshold value. The next step is to predict the output values by using the formula: Ok=∑Hiwik−bkk=1,2,…,m {O_k} = \sum {{H_i}{w_{ik}} - {b_k}k = 1,2, \ldots ,m} where is threshold value, m is the neuron number of the output layer. Then, according to the prediction error calculated by the difference between the predicted output and the expected output, weight factor and threshold value can be updated as follows: ωij=ωij+ηHi(1−Hi)X(i)∑ωikeiki=1,2,…,n:j=1,2,…,l \matrix{{{\omega _{ij}} = {\omega _{ij}} + \eta {H_i}\left( {1 - {H_i}} \right)X\left( i \right)\sum {{\omega _{ik}}{e_{ik}}} } \hfill \cr {i = 1,2, \ldots ,n:j = 1,2, \ldots ,l} \hfill \cr } ωij=ωik+ηHiek j= 1,2,…,m {\omega _{ij}} = {\omega _{ik}} + \eta {H_i}{e_k}\,j = \,1,2, \ldots ,m a1=aj+ηHi(1−Hi)x(i)∑ωikekj=1,2,…,l {a_1} = {a_j} + \eta {H_i}\left( {1 - {H_i}} \right)x\left( i \right)\sum {{\omega _{ik}}{e_k}j = 1,2, \ldots ,l} bk=bk+ek k=1,2,…,m {b_k} = {b_k} + {e_k}\,k = 1,2, \ldots ,m

One of the more popular activation functions for backpropagation networks is the sigmoid, a real function sc: IR → (0, 1) defined by the expression. The constant c can be selected arbitrarily and its reciprocal 1/c is called the temperature parameter in stochastic neural networks. An alternative to the sigmoid is the symmetrical sigmoid S(x).

Generally, there are two types of learning methods as follows: 1. sequential learning or pre-pattern method, 2. batch learning or pre-epoch method. In sequential learning, a given input pattern is broadcasted forward and then the error is calculated and back propagated, the weights are reorganized until we get the targeted output. In batch learning, the weights are reorganized only after the entire set of training network has been offered to the network. Thus, the weights are updated after every epoch.

Due to changes in network environment, in a dynamic environment in need of an optimization algorithms, which learn from the experimental results and find the optimum solution to the end user. So many soft computing techniques are evolved such as artificial neural network, fuzzy logic system, and genetic algorithms, as shown in Figure 4.

Fig. 4

To minimize output errors in fuzzy modelling system, it needs trial steps and auxiliary calculation for adjusting the fuzzy membership functions. Because there are no proper methods to convert the human idea into the knowledge part of the fuzzy system, which leads the system output inadaptability nature. In the case of artificial neural network, it having good adaptability of output based on the input parameters and it also support the non-linear correlation between the input and output parameters. To improve the performance combining the advantages of both FIS and ANN, it is called as ANFIS. This ANFIS supports the knowledge and adaption features.

Jang combines the advantages of fuzzy interference system (FIS) with artificial neural network (ANN) and named as adaptive neuro fuzzy interference system (ANFIS), which consists of multi-layer approaches. ANFIS consists of fuzzification, rule, normalization, defuzzification and output layers, as shown in the figure.

Jang developed network system (ANFIS) as a rule based system and it learns/decides the rules from the training data. Two different types of methods are used in FIS such as Mamdani and Takagi-Sugeon-Kang (TSK). In our system, we use the TSK approach to derive the optimized results. Here rules are mainly focusing on the input output relationship such as if this is the input parameter then what will be the output; simply if-then rules are used for correlating the input and output values.

The values of p, q and r constant that can be evaluated during the training process based on the training data. Next step is to form fuzzy rules by combining these functions by the ANFIS. In this layer, it receives input from the external source and it assigns the member function to all the input values based on the weights. This is an adaptive layer so based on the input fuzzy set assign a member function to each input values: O11=μXi(a) f or i = 1,2,…n O_1^1 = {\mu _{Xi}}\left( a \right)\,f\,or\,i\, = \,1,2, \ldots n

Layer 2 – rule layer

In this model, there are two type of rules can be applied by the system such as AND and OR rule. Our proposed work adopts the AND rule to provide the relative strength information about input values, considered as firepower of all the fuzzy rules. Product of all the input membership value is considered as output of this layer.

Layer 3 – normalization layer

Third layer is a Normalized layer. This is to normalize all the firing strength based on each rule's weight to all the rules’ weights.

It can be calculated as: Oi3=wi O_i^3 = wi

Layer 4 – defuzzification

Defuzzification is an adaptive layer, which uses the first order function to form f_i = p_ix + q_iy + k_i. The derived output this layer is in the form of: Oi4=wifi=wi(pix+qiy+ki. O_i^4 = {w_i}{f_i} = {w_i}\left( {{p_i}x + {q_i}y + {k_i}} \right..

Layer 5 – output layer

This is an output layer. From this layer, we get the final output of this network by sum of all the input layers by using the formula: Oi5=fi=Σwifi=Σ[wi(pix+qiy+ki]. O_i^5 = fi = \Sigma {w_i}{f_i} = \Sigma \left[ {{w_i}\left( {{p_i}x + {q_i}y + {k_i}} \right.} \right].

Finally, by having ANFIS, the input values are mapped with output values to get the optimized results. This method follows the values that are grouped into two set such as training data and checking data. In ANFIS, a combination of the back propagation and least square methods are used to train the input values. The result of the training data is prediction of error in a minimized manner.

The Taguchi model was used for the optimization of signal response. The performance output, surface roughness (SR) was the type “lower the better” and material removal rate was the type “higher the better”. The S/N ratio was examined by loss function logarithmic transformation, which was given by Xiong [29] as shown in the following equation: SNratio=|−10log10[1n∑i=1nyi2] {S \over N}ratio = | - 10{{log}_{10}}[ {{1 \over n}\sum\limits_{i = 1}^n {y_i^2} } ]

The ANOVA model was conducted using the MINITAB-19 software in order to examine the significant input parameters. The three types of parameters were the deciding factor of WDM: pulse on time, pulse off time, wire feed as shown in Figure 5(a) & 5(b). Higher F value and lower P value mention the importance degree of every input parameter on material removal rate and surface roughness of hybrid treated iron-nickel-chromium alloy at 95% confidence level as shown in Table 6 and 7.

Fig. 5

The BPNN gives better performance. Hence, we were required to develop confidence level and overall best fit model performance, as shown in Figure 6. For that, we had to input parameter in ANFIS. The figure shows the ANFIS model simulation results in the form of graphical rules. It is noted that the performance output probability was maximum by varying input parameters and also by applying the if-then rules:

If (pulse on time is low) and (wire feed is low) and (signal to noise ratio is high), then (surface roughness is high).

If (pulse on time is moderate) and (wire feed is moderate) and (signal to noise ratio is high), then (surface roughness is high).

If (pulse on time is moderate) and (wire feed is low) and (signal to noise ratio is high), then (surface roughness is high).

If (pulse on time is moderate) and (wire feed is low) and (signal to noise ratio is moderate) then (surface roughness is high).

If (pulse on time is high) and (wire feed is moderate) and (signal to noise ratio is high), then (surface roughness is high).

If (pulse on time is high) and (wire feed is low) and (signal to noise ratio is high), then (surface roughness is high).

Fig. 6

The Figure 7 shows that the correlation of the input parameters to output performance of wire EDM. From this, we can clearly concluded that the output performance as material removal rate was high when the pulse on time and wire feed became maximum and also surface roughness was high while the pulse on time and wire feed became minimum. Similarly, the pulse off time was minimum the performance output as material removal rate became high and surface roughness was less. The BPNN error calculation methods were implemented at the output parameters such as experimentation output parameters value (EOP) and prediction of back propagation neural network output parameters (BPOP), as shown in Table 8 (a) and 8 (b).

Fig. 7

The graph shows the details of the predicted value obtained by Taguchi, back propagation neural network, fuzzy logic system modelling and hybrid ANFIS model. To investigate the scattering about the agreement line (45 degrees line), one line was plotted in the range within the 2% error and then two more lines, which was Taguchi, BPNN and fuzzy logic, were over, then the range of 4,6,12% error was conceived. It was calculated that the predicted value accommodated by Taguchi, BPNN model and fuzzy model generated over the range 99% of accuracy, which obtained the reliability of models as shown in Table 9. The hybrid ANFIS model dominated the Taguchi, BPNN model and fuzzy logic model, and the reason of the maximum of hybrid ANFIS model predicted values were plotted on the agreement line.

While in case of Taguchi, BPNN and fuzzy modelling, some more predicted values were crossing the 2% of error, as shown in Figure 8. Consequently, the Taguchi, BPNN and fuzzy models were dominated by the hybrid ANFIS model. The Taguchi gives the largest mean error predicted value, which was 4.56% followed by fuzzy logic within the mean error 2.78%; BPNN model gave 1.52% mean error and hybrid ANFIS employed mean error of 0.5%. ANFIS Taguchi hybrid algorithm is made to be optimized and develop advantages, while it can solve nonlinear functions and approximation problems. In addition, the hybrid algorithm is a flexible and robust tool that can engage predictive and confidence interval prediction 99.79% in hybrid ANFIS model. It is very close to the actual value (Table 10).

Fig. 8

The analysis of metallurgical and mechanical properties of iron-nickel-chromium alloy and hybrid treated iron-nickel-chromium alloy was carried out after machining in wire EDM. Ganapathy Srinivasan et.al [24] investigated the hybrid treated iron-nickel-chromium alloy before machining; it had deposition compound layer form as presence of Mo_xN, Fe_xN, CrN, Ni_XN, and thin FCC M phase. That layer produced compressive residual stress on the material surface. The Figure 9 (a) and (b) shows the SEM analysis of iron-nickel-chromium alloy before and after machining in wire EDM. Figure 9(a) clearly shows the formation of recast layer on the surface of the material. The recast layer was formed as shrinkage of melted material and rapid solidification that induced tensile residual and high thermal stress, which produced micro cracks on surface [25]. Y.S Tarng et. al [26] observed that the recast layer lead to changes of microstructure as an austenite (√/− Fe). This phase was not observed in the material before machining. The tensile residual stress of recast layer increased the effect of maximum shear stress, which lead to indentation depth and plastic deformation [27]. These affect the mechanical properties of material after machining. Figure 9 (c) shows that the SEM analysis of hybrid treated iron-nickel-chromium alloy after machining in wire EDM same machining parameters. It clearly shows that no evidence was found regarding the formation of recast layer on the surface after machining. This effect is believed to be due to the fact that the tensile and thermal stress effect was balanced by the presence of compressive residual stress in hybrid treated material [28]. And also the crack propagation and micro holes were not noted in the machined surface. Due to this reason, there were no significant changes in the mechanical properties.

Fig. 9