Surface Roughness Prediction Techniques for CNC Turning

MATERIALS AND METHODS

The work material used for the present investigation is aluminum alloy 6082 cylindrical work pieces. The chemical composition and physical properties of the material used in this study is given in Table 1, 2.

Multiple Regression Model
This study uses statistical multiple regression model for prediction of surface roughness in machining of aluminum alloys, which is used to determine the correlation between a criterion variable and a combination of predicted variables. It can be used to analyze data from any of the major quantitative research designs such as fundamental comparative, correctional and experimental. This method is also able to handle interval ordinal or categorical data and provides estimates both of the magnitude and statistical significance of the relationships between variables (Gall et al., 1996). Therefore, multiple regression analysis will be helpful to predict the criterion variable finish surface roughness via predictor variables, such as spindle speed, feed and depth of cut.

Multiple Repression Prediction Model: Formulation
The proposed second order model equation is:

(1)

Where, Y is the estimated response and X₁, X₂ and X₃ are the spindle speed, feed rate, depth of cut, because these are the controllable machining parameters. They can be used to predict the surface roughness which will influence the product quality, where the coefficients β₀, β₁, β_{2-------------} β₉ are to be estimated. To test the developed model, analysis of variance (ANOVA) is used to investigate and model the relationship between a response variable and one or more independent variables. The independent variables are qualitative (categorical) and no assumption is made about the nature of the relationship (that is, the model does not include coefficients for variables). In order to judge the accuracy of the multiple regression prediction model, percentage deviation (Ø) and the average percentage deviation were used and defined as:

(2)

Where:

φi	= Percentage deviation of single sample data
Rai	= Actual Ra measured by Profilometer
	= Predicted Ra generated by multiple regression

Table 1:	Chemical composition of Aluminum Alloy 6082

Table 2:	Physical properties of Aluminum alloy 6082

	= Average percentage deviation of all sample data
n	= Size of the sample data

This method would test the average percentage deviation of measured R_a and predicted R_a as well as its ability to evaluate the prediction of this model.

Artificial Neural Network Model
Artificial neural networks, which are simplified models of the biological neuron system, is a massively parallel distributing processing system made up of highly interconnected neural computing elements or processing units which are called neurons. Neural networks are built by connecting these neurons together by weighted inter connections. Determination of these weights i.e., training, is the most significant task. In supervised learning the network is trained to learn a mapping from certain inputs to given outputs. An example of supervised learning is the back propagation method for Multi-Layer Perceptron (MLP) networks (Boothroyd and Winston, 1989; Ozel and Karpat, 2002). Multi-layer means the addition of one or more hidden layers in between the input and output layers. In the network each neuron receives total input from all of the neurons in the preceding layer as follows:

(3)

Where:

A neuron in the network produces its output (Out_j) by processing the net input through an activation (Transfer) function f, such as tangent parabolic function given as:

(4)

Table 3:	Machining parameters and their levels

Table 4:	Experimental Lay out and results of the experimental data

Experimental Details
The experiments were conducted according to full factorial design. The three cutting parameters selected for the present investigation are cutting speed (V), feed (f) and depth (d) of cut. Since the considered variables are multi-level variables and their outcome effects are not linearly related, it has been decided to use three level tests for each factor. The machining parameters used and their levels are shown in Table 3.

All the experiments were conducted on CNC Turning Lathe with the following specifications: Swing Over the Bed: 150 mm, Swing Over Cross Slide: 50 mm, Distance Between Centers: 300 mm, Spindle Power 1 HP, Spindle Speed (step less): 0-3000 rpm, Spindle Bore: 21 mm, Spindle Taper: MT3, Tailstock Taper: MT2, the Tool Holder used for Turning operation was a WIDAX tool holder SDJCR 1212 11F3 and the tool material used for the study was Carbide Cutting Tool.

The average surface roughness (R_a) which is mostly used in industrial environments is taken up for the present study. The roughness was measured number of times and averaged. The average surface roughness is the integral absolute value of the height of the roughness profile over the evaluation length and was represented by the following equation.

(5)

Where:

The surface roughness was measured by using Surtronic 3⁺ stylus type instrument manufactured by Taylor Hobson with the following specifications. Traverse Speed: 1 mm sec^-1, Cut-off values 0.25, 0.80 and 2.50 mm, Display LCD matrix, Battery Alcaline 600 measurements of 4 mm measurement length. The surfaces are cleaned and positioned using a V-block before each measurement. The design matrix (Myers and Montgomery, 1995) and experimental results are shown in Table 4. The experiments were repeated three times and average value was taken up for multiple regression model.

RESULTS AND DISCUSSION

Regression Analysis
The second order multiple regression model for the surface roughness (R_a, μm) is developed as a function of cutting parameters such as cutting speed (V), federate (f) and depth of cut (d). From the experimental data for surface roughness, the regression equation was developed and is given as:

(6)

This analysis is carried out at a significance level of 5% i.e., confidence level of 95%. From the analysis of Table 5 it is evident that, the F-calculated value is greater than the F-table value (F_{0.05, 9, 17} = 2.49) and hence the second order developed model is quite ample.

The capability of the multiple regression Coefficients for second order model was found to be as 0.851. This shows that the second order model can explain the variation to the extent of 85.1% and P value is less than 0.05 hence model is significant.

Residual Plots for Ra
The regression model is used for determining the residuals of each individual experimental run. The difference between the measured values and predicted values are called residuals. The residuals are calculated and ranked in ascending order. The normal probabilities of residuals are shown in Fig. 1 . The normal probability plot is used to vary the normality assumption. As shown in Fig. 1 , the data are spread roughly along the straight line. Hence it can be concluded that the data are normally distributed (Shew and Kwong, 2002).

Figure 2 shows the residuals against the observation order. Figure 2 is used to show the correlation between the residuals. From the Fig. 2 it is emphasized that a tendency to have runs of positive and negative residuals indicates the existence of a certain correlation. Also the plot shows that the residuals are distributed evenly in both positive and negative along the run. Hence the data can be said to be independent.

Figure 3 indicates the residuals versus fitted values, which shows only the maximum variation of -1 to 1.5 mm in surface roughness between the measured and the fitted values. This plot does not reveal any obvious pattern and hence the fitted model is ample.

The performance of the developed model was tested using three experimental data which were never used in the modeling process. The results predicted by the multiple regression were compared with the measured values and also average percentage deviation () was calculated and presented in the Table 6.

Fig. 1:	Normal probability plot of the residuals (Response is Ra)

Fig. 2:	Residual versus order of the data (Response is Ra)

Fig. 3:	Residuals versus the fitted values (Response is Ra)

Artificial Neural Network Model
The optimal neural network architecture used in this study is shown in Fig. 4 it was designed using NEURO SOLUTIONS 5.0. The network consists of one input, two hidden and one out put layer. Hidden layers have eight neurons each, where as the input and output layers have three and one neuron, respectively.

Table 5:	ANOVA for the response function

Table 6:	Comparison of the predicted and measured results as a percentage deviation (using Multiple Regression)
Avg. deviation: 8.76%

Fig. 4:	Neural network architecture designed

Since surface roughness prediction in terms of cutting speed, feed and depth of cut was the main interest in this research, neurons in the input layer as shown in Fig. 4 corresponding to the cutting speed, feed and depth of cut the output layer corresponds to surface roughness.

Generation of Training Data
To calculate the connection weights, a set of desired network output values are needed. Desired output values are called the training data set. The training data set in this study was created using full factorial design in the design of experiments (DOE). The surface roughness values corresponding to the training data were measured at different locations and average value was taken. This is the most common experimental design. A three level full factorial design creates 3ⁿ training data, where n is the number of variables (n = 3). In this study 3³ = 27 training data were used. The range of process variables are shown in Table 3.

Network Training
Calculation of weights to the variables is called network training. The weights are given quasi-random, intelligently chosen initial values. They are then iteratively updated until convergence takes place i.e. minimize the Mean Square Error (MSE) between the network prediction and training data set as shown below.

Table 7:	Comparison of the predicted and measured results as a percentage deviation (Using artificial neural network model)
Avg. deviation: 0.9853%

Fig. 5:	Desired out put and actual network output

The learning rate [step size 1.0, momentum 0.7] selected and the training process takes place for 50,000 training iterations. The MSE calculated for training data is 0.0003.

The Fig. 5 shows the measured output i.e. measured Surface Roughness and network predicted Surface Roughness.

Neural Network Testing
Once the weights are adjusted the performance of the trained network should be tested using three experimental data which were never used in the training process. The results predicted by the network were compared with the measured values and percentage deviation (Ø) has been calculated and shown in the Table 7.

CONCLUSIONS

Using full factorial design in the design of experiment, the machining parameters which are influencing the surface roughness on the machining of Al Alloys has been modeled using Multiple Regression and Artificial Neural Networks.

ACKNOWLEDGMENTS

The Authors are thankful to the Hon`ble Chairman Dr. M. Santhi Ramudu,Managing Director Mr. M. Sivaram, Rajeev Gandhi memorial College of Eng and Technology, Nandyal and Head of the Mechanical Engineering Department for providing the facilities to carry out the research work.