4.4 Modeling of Cutting Performance of Coated Carbide Tool in Dry and
4.4.1 Design of Experiments and Prediction of Surface Roughness by
The simplest and most common type of factorial design is one that uses the two levels of each factor i.e. a 2n factorial design. Here the three parameters speed, feed and depth of cut are used to study their effects quantitatively on surface roughness and tool life. In order to investigate the main effect of these three factors, total 23 = 8 experiments were carried out as per factorial design of experiments considering two levels (High and Low) of each of the three factors. The high and low levels of process parameters for the coated carbide tool are as follows.
Cutting speed: 150–300 m/min Feed: 0.1–0.32 mm/rev
Depth of cut: 1–3 mm.
The main effect of a factor is the change in response produced by a change in the level of the factor. The parameter which has higher effect on the surface roughness value should have more representation in the dataset to be used. The effect of factor for an input variable can be evaluated as [Dieter, 1991]
responses at high levels responses at low levels Effect of a factor
half the number of runs in the experiment
= − (4.8)
The total number of experiments is decided by the effect of factor. In order to compute the effect of each process parameter initially factorial design of 8 experiments are carried out. Factor with least influence is assigned level 2. The levels of other factors are taken in proportion to their effect, and additional experiments are performed to represent these levels in the data set. For example, if the influence levels for depth of cut, feed, and cutting speed come out to be 2, 3 and 5 respectively, then one additional level of feed and three additional levels of cutting speed have to be generated. Thus for feed, one value in the middle of range should be chosen and other process parameters corresponding to this may be taken at random. Similarly, in the case of cutting speed, three additional levels should be chosen to have a total of five equally spaced levels in the range. Thus, initial training dataset of 23 should be increased by one level of feed and three levels of cutting speed, making the training data set to be 12. If the magnitude of effect of factor is less than one fifth of the magnitude of effect of most influential parameter, the factor is considered insignificant and is eliminated from the consideration. All these data sets are used to train the neural network.
The size of testing data set is very important from the point of view of reliability of the network. A guideline regarding this has been provided in [Kohli and Dixit, 2005]. The method to decide the minimum number of testing data in a network is as follows. Supposing that in the validation data, the percentage of data having an error greater than a prescribed value ispf. The network is always fitted in such way so that in no prediction, the error is more than the prescribed value. For a testing data size of k, the probability that in this dataset, all of the predictions fall within the limit is given by
0 1 100
k
pf
P = − . (4.9) Using this expression, one can find the testing dataset size k, if P0 and p f are known. For example, let us suppose that requirement is that, in general, 75% of the time the prediction error should come out to be less than the prescribed value and that the probability that a network will have poorer predictive capability is 0.1.
Then, putting p = 25 and Pf 0 = 0.1 into the expression at Equation 4.9 gives k = 8.
Hence, in the present work, eight random testing datasets were chosen for testing the NN models.
In a properly fitted neural network, the network gives nearly equal training and testing errors. The network parameters are arranged to achieve higher accuracy. The error measures used to assess the performance of fitted neural network are presented below.
Let Raiis the experimentally observed value of surface roughness, and ˆRaiis the neural network predicted value of surface roughness.
Absolute error in prediction for ith data =(Rai−Raˆ i) (4.10)
(ˆ )
Percentage fractional error in prediction for ith data (or % deviation) i i 100
i
Ra Ra
Ra
= − ×
(4.11)
Mean square error 2
1
1 ˆ
( ) n ( i i)
i
MSE Ra Ra
n =
= − (4.12) Root mean square fractional error,
2 1 2
( ˆ )
( errf ) n i i
i i
Ra Ra
RMS = nRa
= − (4.13)
Effective error = max of [RMSerrf of training data, RMSerrf of testing data] (4.14) Table 4.1 and Table 4.2 represent the training and testing data set for air-cooled turning for the prediction of surface finish. Altogether, there are 21 data for training and 8 data for testing. The network was trained using TRAINLM function in MATLAB. The activation function was LOGSIG. The best trained network gives
the RMS errors in training and testing as 5.89% and 14.80% respectively. The maximum effective percentage deviation was found to be 24.52 %. Out of total 29 data, only 2 data were found to have error more than 20%. Considering the inherent statistical variation in machining, 20% deviation in prediction may be deemed acceptable.
Similarly, Table 4.3 and Table 4.4 represent the training and testing data sets for dry turning for the prediction of surface finish.Here also, total 21 data were used for training and 8 data for testing. The RMS errors in training and testing were found to be 3.55% and 12.26% respectively. The maximum effective percentage deviation was found to be 17.47%, i.e. less than 20%.
To assess the performance of a predictive model in the presence of statistical deviations, hypothesis testing may be employed. In this work, hypothesis testing has been carried out. Before describing the results of the hypothesis testing for the present work, a brief description of the hypothesis testing is provided below.
Many a times, some results are strongly believed to be true. But after taking a sample, it is noticed that data of one sample does not wholly tally with the results.
The difference is due to (i) the original belief being wrong and (ii) the sample being slightly one sided. Tests are, therefore, needed to distinguish between the two possibilities. These tests tell about the likely possibilities and reveal whether or not the difference can be due to chance elements. If the difference is not due to chance elements, it is significant, and therefore these tests are called test of significance.
The whole procedure is known as testing of hypothesis. A hypothesis is a statement supposed to be true till it is proved false. It may be based on previous experience or derived theoretically. First, a statistician forms a research hypothesis. Then he derives a statement, which is the opposite of the research hypothesis. The approach here is to set up an assumption that there is no contradiction between the believed results and the sample results and the difference can be described solely to chance.
Such a hypothesis is called a null hypothesis (H0).
Table 4.1. Training data set for prediction of surface roughness in turning of mild steel with coated carbide tool during air-cooled turning
v m/min
f mm/rev
d mm
Ra (µm)
148 0.10 1.0 2.17
149 0.10 3.0 2.15
145 0.32 1.0 4.30
149 0.32 3.0 4.81
327 0.10 1.0 1.86
320 0.10 3.0 3.38
327 0.32 1.0 3.82
320 0.32 3.0 4.26
211 0.10 1.1 2.32
273 0.12 1.1 2.16
229 0.20 1.3 2.23
272 0.24 1.5 2.86
269 0.28 1.6 3.83
207 0.32 1.7 3.99
165 0.10 1.8 2.43
207 0.12 1.9 2.36
240 0.14 2.0 2.63
202 0.20 2.2 4.49
290 0.12 2.9 2.55
211 0.14 1.1 1.62
204 0.16 2.2 2.65
Table 4.2. Testing data set for prediction of surface roughness in turning of mild steel with coated carbide tool during air-cooled turning
v m/min
f mm/rev
d mm
Ra (µm) 245 0.12 3.0 2.60 250 0.14 1.2 2.38 179 0.20 1.4 2.27 232 0.24 2.5 3.46 268 0.28 2.6 3.47 162 0.32 2.7 4.70 185 0.10 2.8 2.55 270 0.16 1.2 1.93
Table 4.3: Training data set for prediction of surface roughness in turning of mild steel with coated carbide tool during dry turning
v m/min
f mm/rev
d mm
Ra (µm) 145 0.10 1.0 3.63 158 0.10 3.0 2.44 145 0.32 1.0 4.58 158 0.32 3.0 4.78 303 0.10 1.0 2.36 305 0.10 3.0 2.34 285 0.32 1.0 3.56 289 0.32 3.0 4.02 167 0.10 1.1 2.47 273 0.12 1.1 2.15 225 0.20 1.3 1.97 280 0.24 1.5 3.16 261 0.28 1.6 3.37 215 0.32 1.7 4.38 160 0.10 1.8 2.69 197 0.12 1.9 2.86 255 0.14 2.0 2.87 201 0.20 2.4 3.73 291 0.12 2.9 2.84 197 0.14 1.1 2.38 203 0.16 2.2 2.85
Table 4.4: Testing data set for prediction of surface roughness in turning of mild steel with coated carbide tool during dry turning
v m/min
f mm/rev
d mm
Ra
(µm) 247 0.12 3.0 2.72 254 0.14 1.2 2.19 183 0.20 1.4 3.53 247 0.24 2.5 2.67 272 0.28 2.6 3.35 166 0.32 2.7 5.34 209 0.10 2.8 2.32 259 0.16 1.2 2.07
Here, a test of hypothesis using Student’s t-test at 95% confidence level was carried out for the assessment of prediction accuracy of surface finish. Generally,
Student’s t-test is used when the size of sample is less than 30. The main application of t-distribution is to test if the sample mean (x) differs significantly from the hypothetical value of population mean (µ) and to test the significance of the difference between two sample means. In the present work, some replicate experiments were carried out for both the dry and air-cooled turning. Each replicate experiment was carried out for 5-6 passes and the surface roughness values were than used in student’s t-test calculation. The result showed that prediction accuracy up to 15% is sufficient at 95% confidence level [Appendix A].
The trained networks were used to generate some contour plots of surface roughness. Figure 4.3 and Figure 4.4 show the contour plot of surface roughness for dry turning and air-cooled turning. In each case, (a), (b) and (c) depict the contour for 3 depths of cut viz. 1 mm, 2 mm and 3 mm. It is seen that in general the surface roughness in air-cooled turning is lesser compared to the dry turning. During air- cooled turning at 1 mm depth of cut, ISO grade N7 (1.6 µm) surface finish could be achieved. Comparing both Figures 4.3 and 4.4, it is observed that surface roughness increases at low speed and at moderate feed of 0.2 mm/rev. However, the surface roughness decreases as speed increases. During dry turning, the surface finish is found to be better as compared to air-cooled turning at high speed. It has also been noticed that increase in depth of cut has slight influence in increasing the surface roughness. The interaction of speed and feed affects the surface finish significantly.
From both the figures, it can be concluded that coated carbide tool can be used at high feed to obtain a reasonable surface finish.
Fig. 4.3.CLA surface roughness (micron) Fig. 4.4.CLA surface roughness (micron) for different depths of cut in turning of mild for different depth of cut in turning of steel with coated carbide tool for dry turning mild steel with coated carbide tool for air-cooled turning