Prediction of Forces during Drilling of Composite Laminates Using Artificial Neural Network: A New Approach

Drilling of fiber-reinforced plastics (FRP’s) is an inevitable machining operation, because it facilitates assembly of several components by means of mechanical fastening. But, drilling of FRP leads to delamination which results in reduced life and efficiency of the FRP part. The delamination that induced during drilling is directly affected by the thrust force and torque. In the present research endeavour, four different types of drill point geometries have been used for making of holes in two different types of composite laminates. The drilling of composite laminate has been conducted at three different levels of spindle speed and feed rate. A new artificial neural network (ANN) approach has been proposed to predict the drilling-induced thrust force and torque. The values of thrust force and torque predicted by the proposed ANN models are in close agreement with the experimental values.


INTRODUCTION
The use of FRP's has increased to a great extent over the last few years due to their exceptional physical and mechanical properties such as, high strength to weight ratio, high impact resistance, excellent corrosion resistance and ease of manufacturing [1,2].The use of these materials has grown in the field of aerospace, aircrafts, automobiles etc. where they have replaced many conventional materials.Generally, primary production of FRP leads to near-net shape product.But, sometimes the product has to be made in parts due to the intricacy in the product design.Thus drilling of FRP's is inevitable as it facilitates the assembly of FRP parts by means of mechanical fastening [3][4][5].However, the damageinduced during drilling is one of the major challenges that cannot be completely avoided.It has been found that the thrust force and torque produced during drilling directly affect the drilling-induced damage [6,7].It has been stated that high cutting speed and feed rate results in higher values of thrust force and delamination [8,9].El-Sonbaty et al. [10] found that both the thrust force and torque increases with drill diameter and feed rate.The effect of tool geometry on the thrust force and torque has also been investigated [11].The thrust force generated during drilling was identified as the root cause for the occurrence of delamination.Hence, the models for critical thrust force were developed using linear elastic fracture mechanics [12,13].A near-linear relationship was found between the delamination factor and average thrust force during drilling of carbon fiber-reinforced plastic (CFRP) composite [14].On the contrary, it has been reported that it is not only the thrust force that influences the drilling-induced damage; torque also plays significant role [15].
A number of predictive models were developed to predict the critical thrust force during drilling of FRP's [16][17][18].Hocheng and Tsao [19,20] proposed an analytical approach to predict the critical thrust force for different drill point geometries.It was found that the core drill offers the highest critical feed rate followed by candle stick drill, saw drill, step drill and the traditional twist drill.The mathematical models to predict the thrust force, torque and delamination during drilling of composite laminates have also been developed [21,22].Various predictive models have been developed, but the need of the hour is to develop more generic models is an area of paramount importance.Hence, ANN predictive models are used to solve complex and non-linear problems, thus saving time and cost of conducting the experiments.Mishra et al. [23] developed an ANN model to predict the drilling-induced damage during drilling of glass fiber-reinforced plastic (GFRP) composites.Latha and Senthilkumar [24] developed a neural network model based on back propagation algorithm to predict the delamination factor during the drilling of GFRP laminates.Athijayamani et al. [25] developed an ANN and a regression model to predict the thrust force and torque during drilling of natural fiberreinforced hybrid composites.The results revealed that the ANN models are better than the regression models in predicting thrust force and torque.In order to develop the ANN models, the number of neurons in hidden layer and the values of learning rate and momentum factor are found using hit and trial method.Therefore, in the present research initiative, a new ANN approach in context of drilling of composite laminates has been suggested to find the number of neurons in the hidden layer and the values of momentum factor and learning rate.

Preparation of composite specimen
Composite laminates of 4 mm thickness were prepared using hand lay-up technique.Araldite LY556 along with hardener HY 951was used as resin.Two different types of GFRP laminates were fabricated, namely, unidirectional GFRP and [(0/90)/0]s GFRP laminates.

Drilling setup
Drilling of the developed GFRP laminates was conducted on a radial drilling machine using solid carbide drills.Four different types of drill point geometries (4-facet, 8facet, Jo and parabolic drill) of 4 and 8mm diameter was used for making of holes in the developed laminates.Three different levels of spindle speed (750, 1500 and 2250 rpm) and feed rate (10, 15 and 20 mm/min) were used to conduct the drilling experiments.

Measurements
Four-component piezoelectric drill dynamometer (Make: Kistler, Type: 9272) was used to record the thrust force and torque signals.The dynamometer is attached to the charge meters (Make: Kistler, Type: 5015) and the output of the charge meters is supplied as an input to the personal computer using an analogue/ digital card.

ARTIFICIAL NEURAL NETWORKS: AN INTRODUCTION
An ANN is a computational technique which is inspired by biological neural network system.An ANN is a fast, efficient, accurate and cost effective process-modeling tool.The working principle of an ANN is similar to the human brain.The neurons transmit the information from one to another through synaptic weights of the links [26].
A general symbol of neuron consisting of processing nodes and synaptic connections is shown in Figure 1.

Figure 1. General symbol of an artificial neuron
The weight (w ij ) associated with the link is multiplied with the input signal (x i ) transmitted through that link to calculate the weighted function.The net input function is calculated by adding the weighted function with a bias b.The bias is much like a weight, except that it has a constant input of 1.The net activation input for j th neuron is given by: Where, w ij is the weight of link connecting neuron j to i, and x i is the input of i th neuron.Finally, the net input is passed through the transfer function , which produces the scalar output .The neuron output is given by; The function f = (net j ) is referred to as activation function.There are different activation functions like, uni-polar sigmoid function, bi-polar sigmoid function, pure linear etc.The ANN can be trained from a set of training data to find the solution of complex non-linear problems in which the output parameter is depends on one or more input parameters.The predictive models developed on the basis of ANNs are more generic in nature.Moreover, any number of input parameters can be considered without knowing the interrelationship among them.The network is built directly from the experimental data by its self-organizing capabilities.ANN can be easily applied to solve the problems difficult to solve or cannot be solved using mathematical techniques [27].
The working of a neural network is shown in Figure 2. Conceptually, the working principle of a neural network is similar to the mechanical feedback servo control system.A neural network can be trained to perform a particular function by adjusting the values of the connections (weights) between the elements.Generally, neural networks are adjusted, or trained, so that a particular input leads to a specific target output.The difference between the output and the target is called error.The training of the network is stopped when the network output matches the target, or reached the maximum number of iterations, or reached the minimum acceptable error value.

APPLICATION OF ARTIFICIAL NEURAL NETWORKS: A NEW APPROACH
Most of the engineering problems are modeled using neural networks with one hidden layer.Generally, hit and trial method is used to find the number of neurons in the hidden layer and the values of momentum factor and learning rate.Moreover, the ANN is trained for minimum error and the resulting ANN is tested using the test data.In the present research initiative, it is proposed that the ANN should be trained for three different approaches to fit the requirements.

First approach
The training error should be reduced and then the testing should be done.The training error is given by: ( ) where, p is the total number of training pairs.

Second approach
The overall mean percentage error during the testing of test data should be minimized.The mean percentage error (MPE) is given by; ( ) target output 100 target where, Q is the total number of test data pairs.

Third approach
The maximum percentage error Max_PE should be reduced during the testing of test data pairs.Max_PE = maximum {error_percent} (5) where, {error_percent} is a set consisting of percentage error for each test data input.
Here, {error_percent} = {p 1 , p 2 ... p q } and ( ) target output 100 target q q q q P − = × , for q = 1, 2, 3 ... Q When a set of new data is presented to the trained neural network the second and third approach is very important in order to reduce the error.It is sometimes difficult to train and design the ANN for a particular problem as it takes much time to decide the number of neurons in hidden layer and the values of learning rate and momentum factor.Hence, a new approach has been proposed to design the ANN with one hidden layer.The training phase is based on error back propagation algorithm.The proposed procedure helps to find the number of neurons in a hidden layer and the values of momentum factor and learning rate for three different approaches.The principal steps involved in this new ANN approach are as follows: Step 1: Initialize the number of neurons in hidden layer (J), learning rate (η), momentum factor (α), maximum number of epochs η max and the minimum acceptable error E max .
Step 2: Specify the maximum number of neurons in hidden layer (J max ), the maximum learning rate (η max ) and the maximum momentum factor α max .The new ANN approach is presented with the help of a flow chart as shown in Figure 3.

PREDICTIVE MODELLING OF THRUST FORCE AND TORQUE USING NEW ANN APPROACH
A code based on proposed algorithm was written in MATLAB.Three layer network architectures were used to predict the thrust force and torque as shown in Figure 4.
The numbers of neurons in input layer is six.Five for the number of input variables (material, drill point geometry, drill diameter, feed rate and spindle speed) and one for bias.The modelling of thrust force and torque was carried out one at a time.Hence, the output layer consists of one neuron corresponding to one output variable.It is worthy to note that the training of the ANN for one output leads to less complexities and better results.
Assuming that the activation function used in the hidden and the outer layer is sigmoidal, the outputs of the hidden and outer layer were calculated using the following equation: ( ) Initially, a pilot running of the program was done by varying the neurons of hidden layer from four to fifty using 0.1 as value for the learning rate and 0.9 for the momentum factor.This was done in order to obtain the idea of the neurons in the hidden layer.The number of neurons in the hidden layer was finally varied from 10 to 45.The learning rate was kept low and was varied from 0.05 to 3 at intervals of 0.025.The momentum factor was varied between 0.7 and 0.9 at intervals of 0.05.
The data sets were first normalized and a sigmoidal function was used as an activation function.The number of iterations used was 15000.The weights were randomly chosen and were kept below 1, both in the input and the hidden layers.First, 130 data sets were chosen randomly for the purpose of training the algorithm, whereas the remaining 14 data sets were used to test the program.

PREDICTION OF THRUST FORCE AND TORQUE
Using the new ANN approach, the modelling was done for both the thrust force and torque.The number of hidden layers and the values of momentum factor and the learning rate were calculated for all the three approaches (first approach: minimum error in training, second approach: minimum mean percentage error during testing, and third approach: minimum-maximum percentage error during testing).The details of the developed ANN models for thrust force and torque are shown in Table 1.
The results obtained from the developed thrust force model based on three different approaches of ANN application, as shown in Figure 5.The model fails during testing when the non-linearity in the data is more and the error during training is minimum.
The results obtained from the thrust force model, which was based on the second approach, have shown exceptional compliance with the experimental values, as can be seen in Figure 5.The results of the thrust force model presented in Table 2 clearly indicate that the second approach is better in copmarison with the other two approaches in terms of predicting drilling-induced thrust force.The results obtained from the developed torque model based on three different ANN approaches is shown in Figure 6.It is quite clear from the figure that the torque model based on the second approach gives better results.The results presented in Table 3 also indicate that the second approach is better than the other two approaches in predicting drilling-induced torque.

CONCLUSION
In the present research endeavour, the drilling of unidirectional GFRP and [(0/90)/0]s GFRP laminates were conducted using four different carbide drills of 4 and 8mm diameter at three different levels of spindle speed and feed rate.A new ANN approach (first approach: minimum error in training, second approach: minimum mean percentage error during testing, and third approach: minimum-maximum percentage error during testing) has been proposed to develop the predictive thrust force and torque models.The suggested new ANN approach can be easily used to find the number of neurons in a hidden layer and the values of momentum factor and learning rate.The cumbersome hit and trial method used to find the parametric values of the neural network can be avoided if the proposed ANN approach is used to solve the problem.The testing of the developed models using test data reveals that the thrust force and torque model based on the second ANN approach, i.e. minimum mean percentage error is better than the other two approaches.The three approaches suggested are realistic in nature and can be used to develop ANN models for different engineering problems.Furthermore, the predictive force models can be utilized commercially to save time and cost.Further increase in data sets may lead to a better predictive model.

Figure 2 .
Figure 2. Working principle of a neural network

Step 3 :
Initially, set minimum error during training (ET), minimum mean percentage error during testing (Min_MPE) and minimu-maximum percentage error during testing (Min_Max_PE) is equal to infinity.Step 4: Train the ANN for J neurons in hidden layer, learning rate (η) and momentum factor (α) till the network reached the maximum number of epochs (η max ) or the minimum acceptable error value (E max ).Compute the training error.Step 5: If, training error is less than ET than set ET as training error and record J, η and α along with weights on connection to the hidden layer V and weights on connections to the hidden layer of the output layer W. Step 6: Calculate the outputs for the test data with the trained ANN.Step 7: Calculate the MPE and (Max_MPE) for the test data.Step 8: If, MPE < Min_MPE then set Min_MPE = MPE and record J, η, α, V and W. Step 9: If, Max_PE < Min_Max_PE then set Min_Max_PE = Max_PE and record J, η, α, V and W. Step 10: If, α < α max then α = α + Δα and go to Step 4 else go to Step 11.Note: Δα is a small increment in the momentum factor.Step 11: If, η < η max then η = η + Δη and go to Step 4 else go to Step 12. Note: Δη is a small increment in the learning rate.Step 12: If, J < J max then J = J+1 and go to Step 4 else go to Step 13.Step 13: Display the values recorded in Step 5, 8 and 9.

Figure 6 .Figure 8 .
Figure 6.Experimental and predicted values of thrust force for test data sets