The model B referred width of the cut parameter is not separated from the ANOVA even if it not significant. The width of the cut parameter is not significant in influencing
the surface roughness during machining is done. Separation of insignificant factor does not affect the calculation and the mathematical model because of the different
average error of 3.8 compared with 3.3 if not saperated unsignificant factor. This is proved by small changes R square values 0.8316 and the adjusted R-square 0.7685
compared R-squared 0.8133 and adjusted R-squared 0.7718 after separation.
4.4 Development of a Mathematical Model of Surface Roughness
The estimation of surface roughness with takes all the components of the interaction that influencing the result. The mathematical model for surface roughness is obtained
through the linear equation, see equation 4.1. Ra = 0.758328 – 0.0045 x Vc + 1.600156 x fz – 0.00706 x ae Equation 4.1
The differences error of surface roughness is by looking at the difference between the result of mathematical model compared with the experimental data in the table 4.3.
The average error obtained was 9 .
Table 4.3: Surface Roughness value
Vc mmin
fz mmtooth
ae mm Experimental
Ra Mathematical
Model Ra Error
100 0.15
2 0.499091
0.53376687 7
125 0.15
5 0.373333
0.399970585 7
125 0.1
2 0.30375
0.341143005 12
125 0.1
8 0.27625
0.298782525 8
100 0.1
5 0.455556
0.43257881 5
125 0.2
2 0.5025
0.501158645
56
150 0.2
5 0.36
0.36736236 2
125 0.15
5 0.481667
0.399970585 17
150 0.15
8 0.224444
0.2661743 19
150 0.15
2 0.315
0.30853478 2
125 0.15
5 0.48875
0.399970585 18
100 0.2
5 0.561667
0.59259445 6
4.5 Clarification Model for the Surface Roughness
Normal plot for residuals basically to look for patterns that indicate something other than noise is present Anderson and Whitcomb, 2005. The error of Normal probability
for surface roughness measurement in the experiment is shown in figure 4.1. The distribution of deviations is seem minimum where all measurements obtained from the
experiment is closed to the straight line that indicating the line is a true value. The tendency plot point bend down to the left and pull the right side of the curve shows
that the left and right ends of the distribution is smaller error than expected, that the actual error not as large as expected value Montgomery 2009. Because the trends of
the plot are basically has a small deviation from the model prediction.
57
Figure 4.1: Normal Plot Graph
The distribution of errors is in normal state after removing some data that has a high error in experiments. There are five data from the experiment has been ignored in this
analysis because the data has an error will affected to the analysis that have will be made. Figure 4.2 shows the effect of the model on each experiment with using distance
cook graph. From the figure 4.2 found that there are no defect in the calculation after five removing five experiments that have an error, where all the data distance is less
than the probability 0.25 and with no isolated points is formed. Montgomery, peck, and Vining 2001 say that the way to interpret Cook’s distance is “the squared
Euclidean distance…that the vector of fitted values moves when the ith observation is deleted”.
N or
ma l
p ro
ba bility
Internally Studentized Residuals
58
Figure 4.2: Cook’s Distance graph
The mathematical models built from the ANOVA are made to calculate the range of error that exists during experiments. The error of surface roughness is calculated with
compared the data experimental data obtained from the experiments with actual data get from the substitutions parameter value into mathematical model. Experimental data
compared between measured and calculated are shown in Figure 4.4. The Comparative results have a small error range between the experimental and the model with an
average value of 0.002 or 9 of error. It is competitive when compared with the previous research with an error of 8.3 by Shahrom et al. 2013. According to Hills
and Trucano 1999, for the predicted uncertainty in the model parameters, the experimental error, and an additional acceptable error of ±10 of the model’s mean
predictions. The error occur in this experiment is quite smaller when compared to the 15 error obtained by Brezocnik et al. 2004 using genetic programming techniques.
Run Number C
ook D is
ta nc
e
59
Figure 4.3: Predicted versus Actual graph
Figure 4.4: comparison between the results of the surface roughness between the experimental and model, the average error of 9
Experiment Model
Actual P
red ict
ed
60
4.6 The factors influencing surface roughness
