DEVELOPMENT OF EMPIRICAL MODEL FOR PREDICTION OF SURFACE ROUGHNESS USING REGRESSION
In this present work, the important challenge is to manufacture high quality and low cost products within the stipulated time. The quality is one of the major factors of the product which depends upon the surface roughness and hence the surface roughness placed an important role in product manufacturing. Hence, an Empirical model is proposed for prediction of surface roughness in machining processes at given cutting conditions. The model considers the following working parameters spindle speed, feed, depth of cut, number of flutes and overhang of the tool. For a given work-tool combination, the range of cutting conditions are selected from different cutting condition variables. The experiments were conducted based on the principle of Factorial Design of Experiment (DOE) method with mixed level. After conducting experiments, surface roughness values are measured. Then these experimental results are used to develop an Empirical model for prediction of surface roughness by using Multiple Regression method. In this the Artificial Intelligence based neural network modelling approach is presented for the prediction of surface roughness of Aluminium Alloy products machined on CNC End Milling using High speed steel tool. Trails were made with different combinations of step size and momentum to select the best learning parameter. The best network structure with least Mean Square Error (MSE) was selected among the several networks. The multiple regression models, which are most widely used as prediction methods, are considered to be compared with the developed Artificial Neural Network (ANN) model performance.
In this present work, the important challenge is to manufacture high quality and low cost products within the stipulated time. The quality is one of the major factors of the product which depends upon the surface roughness and hence the surface roughness placed an important role in product manufacturing. Hence, an Empirical model is proposed for prediction of surface roughness in machining processes at given cutting conditions. The model considers the following working parameters spindle speed, feed, depth of cut, number of flutes and overhang of the tool. For a given work-tool combination, the range of cutting conditions are selected from different cutting condition variables. The experiments were conducted based on the principle of Factorial Design of Experiment (DOE) method with mixed level. After conducting experiments, surface roughness values are measured. Then these experimental results are used to develop an Empirical model for prediction of surface roughness by using Multiple Regression method. In this the Artificial Intelligence based neural network modelling approach is presented for the prediction of surface roughness of Aluminium Alloy products machined on CNC End Milling using High speed steel tool. Trails were made with different combinations of step size and momentum to select the best learning parameter. The best network structure with least Mean Square Error (MSE) was selected among the several networks. The multiple regression models, which are most widely used as prediction methods, are considered to be compared with the developed Artificial Neural Network (ANN) model performance.
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International Journal of Advances in Engineering & Technology, Nov. 2013.<br />
©IJAET ISSN: 22311963<br />
Table 4. Regression Analysis: In Ra Vs. v, f ,nf ,vnf ,vol ,fol, nfol<br />
Modified Regression Analysis with interaction terms<br />
Ra = -5.46+0.0108v+0.0789f-10.2nf-0.000816vnf-<br />
0.000285vol-0.00200fol+0.394nfol<br />
Predictor Coef SE Coef T P<br />
Constant -5.456 1.530 -3.57 0.001<br />
V 0.010813 0.001771 6.11 0.000<br />
F 0.07890 0.01996 3.95 0.000<br />
NF -10.246 1.032 -9.93 0.000<br />
Vnf -0.0008164 0.0001850 -4.41 0.000<br />
Vol -0.00028543 0.00005142 -5.55 0.000<br />
Fol -0.0019967 0.0006114 -3.27 0.002<br />
Nfol 0.39447 0.02828 13.95 0.000<br />
S=0.523343 R-Sq=89.6% R-Sq(adj)=87.8%<br />
Analysis of Variance:<br />
Source DF SS MS F P<br />
Regression 7 94.889 13.556 49.49<br />
0.001<br />
Residual error 40 10.956 0.274<br />
Total 47 105.845<br />
The values predicted by first order and second order multiple regression models are tabulated in Table<br />
5. The percentage deviation is computed between the experimental values and predicted values for the<br />
train data and results are tabulated in Table 5.<br />
S.<br />
No<br />
Experime<br />
ntal<br />
Ra<br />
Table 5. Experimental & Regression Model Values<br />
First Order<br />
Multiple<br />
Regression<br />
Ra<br />
Second<br />
Order<br />
Multiple<br />
Regression<br />
Ra<br />
S.<br />
No<br />
Experime<br />
ntal<br />
Ra<br />
First Order<br />
Multiple<br />
Regression<br />
Ra<br />
Second Order<br />
Multiple<br />
Regression Ra<br />
1 1.747 2.27 1.48 25 4.777 3.34 5.34<br />
2 1.537 2.39 1.48 26 4.773 3.46 5.34<br />
3 1.717 3.51 2.21 27 7.087 4.58 6.06<br />
4 1.563 3.39 2.21 28 6.31 4.46 6.06<br />
5 1.46 1.82 1.08 29 3.947 2.89 4.12<br />
6 1.513 1.93 1.08 30 4.403 3.00 4.12<br />
7 1.677 3.05 1.80 31 5.393 4.01 4.84<br />
8 1.653 2.94 1.80 32 5.75 4.12 4.84<br />
9 0.823 1.48 0.67 33 3.213 2.55 2.90<br />
10 0.587 1.36 0.67 34 2.797 2.43 2.90<br />
11 1.623 2.60 1.40 35 2.707 3.67 3.62<br />
12 1.657 2.48 1.40 36 2.54 3.55 3.62<br />
13 2.497 2.03 1.99 37 2.04 3.10 1.90<br />
14 2.49 1.91 1.99 38 2.353 2.98 1.90<br />
15 3 3.03 3.51 39 2.847 4.10 3.42<br />
16 4.07 3.15 3.51 40 3.167 4.22 3.42<br />
17 1.58 1.46 2.30 41 1.21 2.64 1.39<br />
18 1.5 1.57 2.30 42 0.97 2.52 1.39<br />
19 4.193 2.58 3.82 43 2.437 3.76 2.91<br />
20 4.057 2.69 3.82 44 2.73 3.64 2.91<br />
21 2.55 1.00 2.61 45 0.947 2.18 0.89<br />
22 2.493 1.12 2.61 46 1.257 2.07 0.89<br />
23 3.86 2.24 4.13 47 2.86 3.19 2.41<br />
24 4.26 2.12 4.13 48 3.203 3.30 2.41<br />
Percentage Deviation 47.40 16.833<br />
2046 Vol. 6, Issue 5, pp. 2041-2052
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