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Optimization of process parameters in drilling EDM of Inconel x-750 using RSM and desirability function.

INTRODUCTION

Recently manufacturing industries are confronting trials from these advanced materials viz. super alloys, ceramics, and composites, that are hard and tough to machine, needing high precision, surface quality that increases machining cost. To encounter these trials, non-conventional machining process is being retained to achieve higher metal removal rate with better surface finish and larger dimensional accuracy, alongside less tool wear. Electric Discharge Machining (EDM), a non-conventional process, has an expansive requests in automotive, defense, aerospace and micro system industries plays an excellent role in the development of least cost products with more reliable.

Many attempts had been made for modelling of EDM process and investigation of the process performance to improve the surface quality and MRR are still challenging problems, which gives a better MRR, at the cost of a slightly higher tool wear [1], [2] and [3].

Anil Kumar et al [4] studied the influence of peak current, Pulse on time, duty factor, and concentration of silicon abrasive powder in dielectric fluid on MRR and Surface Roughness. The experiments were performed using EN-24 tool steel and the optimum parameter combinations were discussed. Copper rod was used as electrode and holes were drilled on tool steel plates.

Some of the important parameters that influence the quality of profile/hole cut using EDM are peak current (IP), voltage (V), gap distance (GAP), pulse on time ([T.sub.ON]) and pulse off time ([T.sub.OFF]). Many researchers have analyzed the impact of these parameters on surface finish, material removal rate (MRR), tool wear rate (TWR) and over cut (OC). Almost all the researchers have assumed the peak current and voltage between tool and work piece as static, i.e., deterministic [5], [6] and [7].

Priyesh N. Santoki et al [8] studied the influences of EDM parameters on Overcut. In their work different types of tool materials were analyzed and it was found that copper tool has low wear rate than silver and Graphite tool. Also the experimental results indicate that the current significantly affects the OC followed by pulse on time & pulse off time.

V.B. Chaudhari et al. [9] investigated the effects of electrical process parameters on the performances of die-sinking electrical discharge machining with two types of dielectric medium i) Oxygen and Air (Dry EDM), ii) Kerosene on Incoloy 800, the input parameters were optimized using Taguchi L9 orthogonal Array and it was resulted that MRR is more for EDM using kerosene as dielectric as compared to dry EDM.

S. Dhanabalan et al [10] studied the influence of process parameters on form tolerances such as cylindricity, circularity, perpendicularity, and parallelism. It was found that pulse on time and current have significant effect on MRR and TWR and pulse off time have significant effect on form tolerances and it was also found that the circular electrodes produces uniform spark density from its circumference which gives better form tolerances, whereas hexagonal and square electrodes give poor form tolerances.

Dinesh Kumar et al. [11] investigated the polarity conditions (straight and reverse) in smart ZNC EDM Machine on hastelloy steel by using sintered tool electrode of material copper tungsten (CuW). The effects of input parameters i.e. polarity, tool electrode material, peak current, pulse on time, duty cycle and gap voltage on the overcut was analyzed using analysis of variance. It was found that reverse polarity with powder metallurgy tool electrode yields maximum value of [T.sub.ON] time and the average value of duty cycle and gap voltage gives the better result for overcut in this study.

O. Yilmaz et al [12] investigated fast hole drilling EDM on Inconel 718 and Ti6Al4V. A series of experiments were carried out using single and multi-channel tubular electrodes made of brass and copper materials. The experimental results revealed that the single-channel electrode has comparatively better material removal rate and lower electrode wear ratio.

Jeswani [13] had chosen water as dielectric. The Experiments were conducted by comparing the performances of kerosene and distilled water over the pulse energy range 72-288 mJ. Machining in distilled water resulted in a higher MRR and a lower wear ratio than in kerosene.

It is inferred from the literature that no credible work has been accomplished on form tolerances in EDM of Inconel x-750. Also achieving, optimal performance is very difficult as there are many process parameters that determine the output characteristics. In the present work, IP, [T.sub.ON], [T.sub.OFF] and GV are considered as the process parameters and optimized for better MRR, TWR and form tolerances. In most of the earlier researches, only single objective optimization is performed. In this work, an attempt is made to optimize, MRR, TWR and form tolerances simultaneously.

Experimental Details:

The experiments were carried out on an EDM DRILLING machine of the type SD 350 ZNC manufactured by Oscar EDM Ltd. The main objective of this work is to obtain minimum tool wear rate, maximum material removal rate and form tolerances such as circularity and cylindricity within acceptable range. The photograph of machining zone is shown in Fig. 1. The size of the work piece is 110mm x 50mm x 10mm thickness plate. In this work, through holes of size 3mm diameter is drilled in all the experiments using copper electrode. Distilled water is used as dielectric medium.

[FIGURE 1 OMITTED]

A. Workpiece Selected:

The work piece material used in this investigation is the Inconel Alloy x-750, a corrosion and oxidation resistant material with good tensile and creep properties at elevated temperatures. This alloy has been adopted for a wide variety of applications, mainly in the nuclear and aerospace industries. The chemical composition of Inconel x-750 is shown in Table 1.

B. Parameters and its levels:

The Selected process variables were varied up to five levels and full factorial central composite design (CCD) based response surface methodology was adopted to design the experiments. T able 2 shows the process variables and its levels used for designing the experiment. The selection of factors was based on the preliminary experiments by one factor at a time approach.

Before experimentation, the work piece top surface was flattened using a surface grinding machine. The work piece and electrode were weighted before and after the machining by using electronic weigh-balance. Refer to (1) and (2) to calculate the material removal rate and tool wear rate. Fig. 2 and 3 shows the photograph of work piece and electrode weighed before machining.

MRR (g/min) = Initial Weight-Final Weight/Machining time (1)

TWR (g/min) = Initial Weight-Final Weight/Machining time (2)

The photograph of work piece and electrode weighed before machining are shown in Fig. 2 (a) and 2 (b). The form tolerance such as circularity and cylindricity was measured by using co-ordinate measuring machine (CMM) and it is shown in Fig. 3.

C. Design of Experiments:

The full factorial central composite design based RSM approach of Minitab software recommended 31 runs/experiments as shown in Table 3. Experiments were conducted as per the central composite design RSM design combination of parameters and the responses material removal rate, tool wear rate and form tolerances are measured

[FIGURE 2a OMITTED]

[FIGURE 2b OMITTED]

[FIGURE 3 OMITTED]

Mathematical model:

In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The main idea of RSM is to use a set of designed experiments to obtain an optimal response. Central composite design can be implemented to estimate a second-degree polynomial model, which is still only an approximation at best. In this work, response surface modelling (RSM) is utilized for determining the relations between the various EDM process parameters with the various machining criteria and exploring the effect of these process parameters on the responses, i.e. the material removal rate, tool wear rate, circularity and cylindricity and it is shown in (5), (6), (7) and (8). In order to study the effects of the EDM parameters on the above mentioned machining criteria, second order polynomial response surface mathematical models can be developed. In the general case, the response surface is described in the below mentioned form (3).

y = [[beta].sub.0] + [summation] [[beta].sub.i] [X.sub.i] + [summation] [[beta].sub.ii] [X.sub.i.sup.2] + [summation] [[beta].sub.ij] [X.sub.i] [X.sub.j] ..., (3)

Where, Y is the corresponding response, e.g. the MRR, TWR, Circularity and Cylindricity produced by the various process variables of EDM and the xi (1, 2, ..., n) are coded levels of n quantitative process variables, the terms [[beta].sub.0], [[beta].sub.i], [[beta].sub.ii] and [[beta].sub.ij] are the second order regression coefficients. The second term under the summation sign of this polynomial equation is attributable to linear effect, whereas the third term corresponds to the higher-order effects; the fourth term of the equation includes the interactive effects of the process parameters.

Applying the least square technique, the values of these coefficients can be estimated by using the observations collected (Y1, Y2,.....Yn) through the design points (n). This equation can be rewritten according to the five variables in the coded form (4).

[Y.sub.u] = [[b.sub.o], [[b.sub.1], [X.sub.1] + [b.sub.2] [X.sub.2] + [b.sub.3] [X.sub.3] + [b.sub.4] [X.sub.4] + [b.sub.5] [X.sub.5] + [b.sub.11] [X.sub.1.sup.2] + [b.sub.22] [X.sub.2.sup.2] + [b.sub.33] [X.sub.3.sup.2] + [b.sub.44] [X.sup.4.sub.2] + [b.sub.55] [X.sub.5.sup.2] + [b.sub.12] [X.sub.1][X.sub.2] + [b.sub.13] [X.sub.1] [X.sub.3] + [b.sub.14] [X.sub.1] [X.sub.4] + [b.sub.15] [X.sub.1] [X.sub.5] + [b.sub.23] [X.sub.2] [X.sub.3] + [b.sub.24] [X.sub.2] [X.sub.4] + [b.sub.34] [X.sub.3] [X.sub.4] + [b.sub.35] [X.sub.3] [X.sub.5] + [b.sub.45] [X.sub.4] [X.sub.5] (4)

MRR = 0.074271 + 0.002883 A + 0.006350 B -0.004000 C - 0.003900 D - 0.006837 [A.sup.2] - 0.007487 [B.sup.2] - 0.002262 [C.sup.2] + 0.006488 [D.sup.2] + 0.002663 (A x D) + 0.009063 (B x C) - 0.013888 (B x D) - 0.006213 (C x D) (5)

TWR = 0.024238 - 0.001442 A + 0.001983 B -0.000283 C - 0.000833 D - 0.000266 [A.sup.2] - 0.001316 [B.sup.2] 0.000779 [D.sup.2] + 0.002800 (A x B) - 0.001563 (A x C) - 0.001663 (A x D) - 0.000950 (B x D) + 0.003638 (C x D)(6)

Circularity = 0.035143 - 0.004458 A -0.008042 B + 0.002292 C + 0.000458 D + 0.005412 [A.sup.2] + 0.000662 [B.sup.2] 0.001338 [C.sup.2] + 0.001162 [D.sup.2] + 0.001812 (A x C) - 0.003438 (A x D) - 0.002312 (B x C) - 0.001063 (B x D) 0.000813(C x D) (7)

Cylindricity = 0.040286 - 0.007083 A -0.017083 B + 0.006750 C + 0.001250 D + 0.010241 [A.sup.2] + 0.002241 [B.sup.2] 0.005009 [C.sup.2] +0.002741 [D.sup.2] + 0.004125 (A x C) - 0.006875 (A x D) - 0.003875 (B x C) - 0.002875 (B x D) 0.002375 (C x D) (8)

RESULTS AND DISCUSSION

The Minitab statistical package was used to analyze the experimental data and response parameters. The analysis of variance has been performed to check the adequacy of the proposed model as well as the significance of individual parameters at 95% confidence level. T able (4-8) shows the regression coefficients for MRR, TWR, Circularity and Cylindricity and corresponding P-values. If P value is less than 0.005 the factor is known as significant factor if it is 0.0000 means it is known as most significant factor.

The results from the T able 4 shows that discharge current, pulse on time, pulse off time, gap voltage, some of square terms and the interaction terms are significant for MRR. The multiple regression coefficients for MRR was found to be 98.22%.

The results from the T able 5 shows that discharge current, pulse on time, pulse off time, gap voltage, some of square terms and the interaction terms has significant effects on TWR. The multiple regression coefficients for tool wear rate was found to be 99.07%.

From the Table 6 it was inferred that discharge current, pulse on time, pulse off time, some of square terms and the interaction terms has significant effects on Circularity. The multiple regression coefficients for Circularity was found to be 98.08%.

From the Table 7 it was observed that discharge current, pulse on time, pulse off time, some of square terms and the interaction terms has significant effects on Cylindricity. The multiple regression coefficients for Circularity was found to be 98.23%.

To verify whether the proposed model actually describe the experimental data, the multiple regression coefficient were computed. The multiple regression coefficients for MRR, TWR, Circularity and Cylindricity were found to be 98.22%, 99.07%, 98.08% and 98.23% respectively. On the basis of the high values of regression coefficients, it can be said that the second order model are adequate in representing the process. Surface plot for the responses were obtained considering the significant parameters and most significant parameters and the remaining parameters were kept constant because their influence is not more on the responses.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Fig. 4 shows the surface plot for MRR Vs pulse on time and pulse off time and it was inferred that increase in MRR with increase in pulse on time, due to the fact discharge energy is increased. So the machining efficiency is high which results in high MRR. Pulse off time is inversely proportional to MRR. As the Pulse off time increases MRR decreases.

Whereas Fig. 5 shows the surface plot for MRR Vs pulse on time and gap voltage and it was observed that increase in MRR with increase in pulse on time, due to the fact discharge energy is increased .But as pulse on time increases, MRR is more and debris is larger which in turn reduces gap between tool and work piece. This leads to short circuiting which results in reduction in MRR. MRR generally increases with increase in gap voltage, this is due to the fact that at higher gap voltage, energy per pulse increases, which results in high machining efficiency which in turn leads to high MRR.

[FIGURE 6 OMITTED]

Fig. 6 shows the surface plot of MRR with respect to gap voltage and pulse off time. MRR generally increases with increase in gap voltage, this is due to the fact that at higher gap voltage, energy per pulse is high , which results in high machining efficiency which in turn leads to high MRR. The MRR generally decreases with increase in pulse off time.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

Fig. 7 shows the surface plot of TWR varying with respect to discharge current and pulse on time. It was observed from the figure that at low pulse on time, TWR is more. This is due the fact longer machining time is required to make a hole. TWR increases continuously from 1A to 5A. This is because at low discharge current low thermal energy is produced, as discharge current increase this in there is increase in thermal energy, which causes larger tool wear.

Fig. 8 shows the surface plot of TWR varying with respect to discharge current and pulse off time. TWR increases continuously from 1A to 5A. This is because at low discharge current less thermal energy is produced, as discharge current increases this in turn increases thermal energy, which causes larger tool wear. TWR decrease with increase in pulse off time due to continuous decrease in thermal energy with an increase in pulse off time.

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

Fig. 9 shows the surface plot of TWR varying with respect to discharge current and gap voltage. It is observed that as discharge current increases, TWR rapidly increases. This is due to fact at high discharge current tool wears quickly due to high discharge energy. However with increase in gap voltage TWR increases.

Fig. 10 shows the surface plot of TWR varying with respect to gap voltage and pulse off time. TWR decrease with increase in pulse off time due to continuous decrease in thermal energy with increase in pulse off time. However with increase in gap voltage TWR increases. This is due to the fact that at higher gap voltage, energy per pulse increases, which results in high machining efficiency which in turn leads to larger tool wear.

The surface plots for the form tolerance such as circularity are plotted by considering the significant factors and it is shown in Fig 11-13.

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

Fig. 11 shows the variation of circularity Vs discharge current and pulse off time, circularity of the hole decreases with increase in pulse off time. Circularity increases with increase in discharge current due to high thermal energy produced.

Fig. 12 shows the variation of circularity Vs discharge current and gap voltage, circularity of the hole increases with increase in discharge current and voltage. This is due to fact high thermal energy is produced which affects the accuracy of the hole.

[FIGURE 13 OMITTED]

Fig. 13 shows the variation of circularity Vs pulse on time and pulse off time. It is observed that at low pulse on time circularity is high due to larger machining time, as pulse on time increases circularity decreases. Circularity of the hole decreases with increase in pulse off time.

The surface plots for the form tolerance such as cylindricity are plotted by considering the significant factors and it is shown in Fig. 14-16.

[FIGURE 14 OMITTED]

[FIGURE 15 OMITTED]

Fig. 14 shows the variation of cylindricity Vs discharge current and pulse off time, cylindricity of the hole decreases with increase in pulse off time. Cylindricity increases with increase in discharge current due to high thermal energy produced.

Fig. 15 shows the variation of cylindricity Vs discharge current and gap voltage, circularity of the hole increases with increase in discharge current and voltage. This is due to fact high thermal energy is produced which affects the accuracy of the hole.

[FIGURE 16 OMITTED]

Fig. 16 shows the variation of cylindricity Vs pulse on time and pulse off time. It is observed that at low pulse on time cylindricity is high due to larger machining time, as pulse on time increases cylindricity decreases. Cylindricity of the hole decreases with increase in pulse off time.

Many designed experiments involve determining optimal conditions that will produce the "best" value for the response. Depending on the design type (factorial, response surface, or mixture), the operating conditions that can be controlled may include one or more of the following design variables: factors, components, process variables, or amount variables. Response Optimizer provides an optimal solution for the input variable combinations and an optimization plot. The optimization plot is interactive and the input variable settings on the plot can be adjusted to search for more desirable solutions. The optimal combination of the parameters is obtained through desirability function approach by using Response Optimizer plot and it is shown in Fig 17.

[FIGURE 17 OMITTED]

The above graph shows optimum value for the EDM Drilling process among the DOE combination. The optimized value is indicated in square bracket at the top of the Fig. 17. The optimum value is taken between the low and high range of process parameters value. The optimal parameter combination for better output response on Inconel x-750 is as follows,

Ip = 2 amp, [T.sub.ON] = 24[micro]s, T off = 9[micro]s and V = 3 volt.

Conclusions:

Experiments were conducted on hole drilling EDM to optimize the process parameters to achieve better performance. Based on the experiments and subsequent analysis, it is concluded that the discharge current, pulse on time, pulse off time, gap voltage, some of square terms and the interaction terms are significant for MRR and TWR. Whereas discharge current, pulse on time, pulse off time, some of square terms and the interaction terms has significant effects on Circularity and Cylindricity. The limitation of this research is, certain responses are inversely proportional. Hence, only trade-off solutions can be obtained. This research will help the researchers and industries for developing a knowledge base and predict the responses without further experimentation for Inconel x-750.

ACKNOWLEDGMENT

The authors would like to thank the support of Precision Wirecut Machine Tools Limited, Coimbatore for permitting us to conduct the experimental work. We are also grateful to all the staff members for their guidance and expert comments in respect to our queries and problems.

REFERENCES

[1.] Kuppan, P., A. Rajadurai and S. Narayanan, 2008. "Influence of EDM process parameters in deep hole drilling of Inconel 718", International Journal of Advanced Manufacturing Technology, 38: 74-84.

[2.] Wasim Akram, Kulbhushan Bhagat, 2014. "Investigation Into the Effect of EDM Parameters on Tool Wear Rate during Machining of AISI-1045 steel", International Journal of Engineering Research and Genetic Science, 2(1): 21-29.

[3.] Saeed Daneshmand, Ehsan Farahmand kahrizi, Esmail Abedi, M. Mir Abdolhosseini, 2013. "Influence of Machining Parameters on Electro Discharge Machining of NiTi Shape Memory Alloys"; International Electrochemical Science, 8: 3095-3104.

[4.] Yih-fong Tzeng, Fu-chen Chen, 2007. "Multi-objective optimization of high-speed electrical discharge machining process using a Taguchi fuzzy-based approach", Materials and Design, 28: 1159-1168.

[5.] Tomadi, S.H., M.A. Hassan, Z. Hamedon, 2009. "Analysis of the Influence of EDM parameters on Surface Quality, Material Removal Rate and Electrode Wear of Tungsten Carbide", International Multi Conference of Engineers and Computer Scientists, II: 978-988.

[6.] Arunbharathi, R., P. Ashokavarthanan and K. Manojmathew, 2014. "Experimental investigation of process parameters in wire electrical discharge machining by response surface methodology on IS2062 steel", International Journal of Applied Mechanics and Materials, 550: 53-61.

[7.] Natarajan, N. and R.M. Arunachalam, 2011. "Experimental investigations and optimization of process parameters in micro-EDM with multiple performance characteristics", International Journal of Experimental Design and Process Optimization, 2(4): 336-356.

[8.] Priyesh, N., Santoki, Prof. Ashwin P. Bhabhor, 2015. "Parametric Study for overcut using EDM with tool of Graphite, Copper & Silver", International Journal of Innovative and Emerging Research in Engineering, 2(3): 31-38.

[9.] Chaudhari, V.B., S.S. Soni, A.B. Pandey, 2014. "Parametric Study of Incoloy 800(Super Alloy) in Dry EDM", International Journal of Advance Research In Science And Engineering, 3: 382-389.

[10.] Dhanabalan, S., K. Sivakumar, C. Sathiya Narayanan, 2014. "Analysis of Form Tolerances in Electrical Discharge Machining Process for Inconel 718 and 625", Materials and Manufacturing Processes, 29: 253259.

[11.] DineshKumar, Naveen Beri, AnilKumar, 2011. "Study of Overcut During Electric Discharge Machining of Hastelloy Steel With Different Electrodes Using the Taguchi Method", International Journal of Advanced Engineering Technology, II: 306-312.

[12.] Oguzhan Yilmaz, M. Ali Okka, 2010. "Effect of Single and Multi-Channel electrodes application on EDM fast hole drilling performance", International Journal Advance Manufacturing Technology, 51: 185-194.

[13.] Jeswani, M.L., 1981. "Effects of the addition of graphite powder to kerosene used as the dielectric fluid in electrical discharge machining", Wear, 70: 133-139.

(1) Arunbharathi, R., (2) Ashoka Varthanan, P., (3) Karthick, B, (4) Sathish Kumar, P.

(1) Assistant Professor, Department of Mechanical Engineering, Sri Krishna College of Engineering and Technology, Coimbatore, Tamilnadu, India - 641008.

(2) Professor and Head, Department of Mechanical Engineering, Sri Krishna College of Engineering and Technology, Coimbatore, Tamilnadu, India - 641008.

(3) & (4) PG Scholar, Department of Mechanical Engineering, Sri Krishna College of Engineering and Technology, Coimbatore, Tamilnadu, India - 641008.

Received 25 January 2016; Accepted 28 April 2016; Available 5 May 2016

Address For Correspondence:

Arunbharathi. R, Assistant Professor, Department of Mechanical Engineering, Sri Krishna College of Engineering and Technology, Coimbatore, Tamilnadu, India - 641008.

E-mail: arunbharathi@skcet.ac.in
Table I: Chemical Composition Of Inconel X-750

Ni      Co      Cr      Fe     Si      Mn

70.00   1.00    15.50   7.00   0.50    1.00

C       Al      Ti      Cu     S       Nb+Ta

0.080   0.700   2.500   0.50   0.010   0.95

Table II: Choosen Levels Of Process Parameters

                                   Levels
Parameters              Units
                                   -2   -1   0    1    2

Discharge current (A)   A          1    2    3    4    5
Pulse-on time (B)       [micro]s   20   21   22   23   24
Pulse-off time (C)      [micro]s   5    6    7    8    9
Gap voltage (D)         V          2    3    4    5    6

Table III: Experimental Results

      Discharge     Pulse on   Pulse off   Gap
      current (A)   time (B)   time (C)    voltage
Run                                        (D)

      A             [micro]s   [micro]s    V

1     4             21         8           3
2     3             22         7           4
3     4             21         6           5
4     3             22         7           6
5     3             22         7           2
6     2             21         8           3
7     4             23         6           5
8     3             22         7           4
9     3             22         7           4
10    2             23         8           5
11    2             21         6           3
12    4             21         8           5
13    4             21         6           3
14    3             20         7           4
15    2             23         8           3
16    3             22         9           4
17    2             23         6           3
18    4             23         8           5
19    5             22         7           4
20    4             23         8           3
21    2             21         8           5
22    3             22         7           4
23    3             24         7           4
24    3             22         5           4
25    2             23         6           5
26    3             22         7           4
27    3             22         7           4
28    4             23         6           3
29    3             22         7           4
30    1             22         7           4
31    2             21         6           5

Run   MRR      TWR       Circularity   Cylindricity
      (g/min)  (g/min)   (mm)          (mm)

1     0.0434   0.0118    0.055         0.080
2     0.0739   0.0239    0.035         0.040
3     0.0947   0.0117    0.037         0.046
4     0.0915   0.0193    0.042         0.052
5     0.1075   0.0229    0.038         0.048
6     0.0394   0.0200    0.053         0.074
7     0.0599   0.0204    0.022         0.012
8     0.0715   0.0247    0.035         0.040
9     0.0765   0.0242    0.037         0.040
10    0.0462   0.0270    0.036         0.044
11    0.0519   0.0247    0.044         0.056
12    0.0548   0.0160    0.046         0.068
13    0.0561   0.0224    0.039         0.046
14    0.0327   0.0151    0.054         0.082
15    0.0974   0.0205    0.034         0.038
16    0.0555   0.0236    0.033         0.034
17    0.0797   0.0253    0.036         0.038
18    0.0598   0.0232    0.028         0.022
19    0.0477   0.0209    0.048         0.072
20    0.1032   0.0225    0.035         0.042
21    0.0421   0.0313    0.062         0.092
22    0.0729   0.0245    0.036         0.040
23    0.0545   0.0228    0.022         0.014
24    0.0735   0.0242    0.027         0.004
25    0.0485   0.0180    0.042         0.052
26    0.0739   0.0242    0.034         0.040
27    0.0759   0.0244    0.035         0.042
28    0.0760   0.0343    0.030         0.024
29    0.0753   0.0244    0.034         0.040
30    0.0447   0.0254    0.066         0.088
31    0.0795   0.0211    0.056         0.084

Table IV: Estimated Regression Coefficients For Mrr

Term       Coefficient   SE- coefficient   T-value   P-value

Constant   0.074271      0.000995          74.639    0.000
A          0.002883      0.000537          5.365     0.000
B          0.006350      0.000537          11.816    0.000
C          -0.004000     0.000537          -7.443    0.000
D          -0.003900     0.000537          -7.257    0.000
A2         -0.006837     0.000492          -13.886   0.000
B2         -0.007487     0.000492          -15.207   0.000
C2         -0.002262     0.000492          -4.594    0.000
D2         0.006488      0.000492          13.179    0.000
AD         0.002663      0.000658          4.045     0.001
BC         0.009063      0.000658          13.769    0.000
BD         -0.013888     0.000658          -21.100   0.000
CD         -0.006213     0.000658          -9.439    0.000

S = 0.00263273           R-Sq = 98.93 %    R-Sq(adj) = 98.22 %

Table V: Estimated Regression Coefficients For Twr

Term       Coefficient   SE- coefficient   T-value   P-value

Constant   0.024238      0.000148          163.389   0.000
A          -0.001442     0.000093          -15.528   0.000
B          0.001983      0.000093          21.363    0.000
C          -0.000283     0.000093          -3.052    0.007
D          -0.000833     0.000093          -8.976    0.000
A2         -0.000266     0.000085          -3.151    0.006
B2         -0.001316     0.000085          -15.567   0.000
D2         -0.000779     0.000085          -9.211    0.000
AB         0.002800      0.000114          24.625    0.000
AC         -0.001563     0.000114          -13.742   0.000
AD         -0.001663     0.000114          -14.621   0.000
BD         -0.000950     0.000114          -8.355    0.000
CD         0.003638      0.000114          31.990    0.000

S = 0.000454823          R-Sq = 99.44 %    R-Sq(adj) = 99.07 %

Table VI: Estimated Regression Coefficients For Circularity

Term        Coefficient   SE- coefficient   T-value   P-value

Constant    0.035143      0.000568          61.92     0.000
A           -0.004458     0.000307          -14.54    0.000
B           -0.008042     0.000307          -26.23    0.000
C           0.002292      0.000307          7.48      0.000
D           0.000458      0.000307          1.50      0.153
[A.sup.2]   0.005412      0.000281          19.27     0.000
[B.sup.2]   0.000662      0.000281          2.36      0.031
[C.sup.2]   -0.001338     0.000281          -4.76     0.000
[D.sup.2]   0.001162      0.000281          4.14      0.001
AC          0.001812      0.000375          4.83      0.000
AD          -0.003438     0.000375          -9.16     0.000
BC          -0.002312     0.000375          -6.16     0.000
BD          -0.001063     0.000375          -2.83     0.012
CD          -0.000813     0.000375          -2.16     0.045
S = 0.001510169           R-Sq = 98.91 %    R-Sq(adj) = 98.08 %

Table VII: Estimated Regression Coefficients For Cylindricity

Term        Coefficient   SE- coefficient   T-value   P-value

Constant    0.040286      0.001135          35.489    0.000
A           -0.007083     0.000613          -11.554   0.000
B           -0.017083     0.000613          -27.866   0.000
C           0.006750      0.000613          11.010    0.000
D           0.001250      0.000613          2.039     0.057
[A.sup.2]   0.010241      0.000562          18.234    0.000
[B.sup.2]   0.002241      0.000562          3.990     0.001
[C.sup.2]   -0.005009     0.000562          -8.918    0.000
[D.sup.2]   0.002741      0.000562          4.880     0.000
AC          0.004125      0.000751          5.494     0.000
AD          -0.006875     0.000751          -9.156    0.000
BC          -0.003875     0.000751          -5.161    0.000
BD          -0.002875     0.000751          -3.829    0.001
CD          -0.002375     0.000751          -3.163    0.006
S = 0.00300338            R-Sq = 99.00 %    R-Sq(adj) = 98.23 %
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Author:Arunbharathi, R.; Ashoka, Varthanan P.; Karthick, B.; Sathish, Kumar P.
Publication:Advances in Natural and Applied Sciences
Date:May 15, 2016
Words:5155
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