The percentage contribution of different process variables on OC is presented in Figure 4.5 and it can be seen in this case A, C, D, AB, AC, AD, BC, BD, CD, A^2, B^2, C^2, D^2 are significant model terms. Voltage has a significant effect on OC followed by pulse on duration and pulse off duration.
Figure 4. 4: Percentage contribution of process variables
95.238 10.581 2.143 2.143 11.905 4.286 20.119 2.976 23.333 1.905 6.500 2.309 7.195 Model A-Voltage C-Pulse on duration D-Pulse off duration AB AC AD BC BD CD B^2
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The Analysis of variance summary indicates that the quadric model is statistically significant for OC and linear terms of voltage, pulse on duration and pulse off duration, interaction terms of voltage, peak current and pulse on duration and square terms of peak current, pulse on duration and pulse off duration are significant model terms. Hence, analysis of OC is extended for these terms only. The three dimensional surface plots for the OC with respect to the significant process parameters are shown in Figures (4.6-4.10). In each of these graphs, two machining parameters are varied while the other two parameters are held constant as its middle value. The interaction effect of voltage and current on OC in the form of 3D surface graph at constant pulse on duration of 30µs and pulse off duration of 40µs is represented in Figure 4.6 using design expert software and response surface methodology. From this Figure, it is observed that maximum OC was obtained at the highest current (32 ampere) and highest voltage (40V) combination. The minimum OC was obtained at the highest current (32 amps) and lowest voltage (30V) combination. It can be observed from these graphs that there is significant amount of curvature indicating non-linearity in the variation. It also points towards significant contribution from the interaction of the machining parameters. It is observed that OC increases with increase in current and the voltage. There is significant decrease in OC with increase in current, however with increase in voltage there is slight increase in OC. As for as the current is concerned, more current means more energy available per spark. This higher energy available per spark leads to melting of more material per spark and hence high overcut effect.
Figure 4. 5: Interaction effect of Voltage and Peak current on OC
At constant peak current of 20 ampere and pulse off duration of 45µs, the interaction effect of voltage and pulse on duration on OC is represented in Figure 4.7. It is observed that maximum OC was found at the highest voltage of (40V) and lowest pulse on
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duration of 20µs.The minimum OC was obtained at the lowest voltage (30V) and the highest pulse on duration of (40µs) combination. It indicates significant contribution from the interaction of the machining parameters. It is interesting to note that OC first increases with increase in voltage and the pulse on duration and then decreases. There is a significant increase in OC with increase in voltage however with increase in pulse on duration initially there is increase in OC then reduction on further increment of pulse on duration.
Figure 4. 6: Interaction effect of Voltage and Pulse on duration on OC
On observing the interaction effect of voltage and pulse off duration on OC at constant peak current of 20 ampere and pulse on duration of 30µs is demonstrated in Figure 4.8 it can be seen that maximum OC (0.210µm) was obtained at the highest voltage (40V) and lowest pulse off duration (30µs) combination. The minimum OC (0.149 µm) was determined at the lowest pulse off duration (30µs) and lowest voltage (30V) combination. Furthermore, with the increase in voltage and pulse off duration the value of OC increases initially and then decreases at higher levels of voltage and pulse off duration settings. It is observed that there is substantial increase in OC with increase in voltage and pulse off duration.
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Figure 4. 7: Interaction effect of Voltage and Pulse off duration on OC
Figure 4.9 shows the interaction effect of peak current and pulse on duration on OC at constant voltage of 30 V and pulse off duration of 45µs. The maximum OC value of (0.210µm) was obtained at the highest voltage (40V) and lowest pulse off duration (30µs) combination similarly the minimum OC (0.149 µm) was obtained at the lowest pulse off duration (30µs) and lowest voltage (30 V) combination. Moreover, with the increase in voltage and pulse off duration the value of OC increases initially and then decreases at higher levels of voltage and pulse off duration settings. It is observed that there is significant increase in OC with increase in voltage and pulse off duration.
Figure 4. 8: Interaction effect of Peak current and Pulse on duration on OC
Figure 4.10 illustrates the interaction plot of peak current and pulse off duration on OC constant voltage of 35V and pulse on duration of 30µs. From this Figure, it is observed that maximum OC was gained at the lowest peak current of (8 ampere) and highest pulse off duration of 60µs.The minimum OC was achieved at the lowest peak current of
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(8ampere) and lowest pulse off duration of (30µs) combination. Moreover, OC first increases with increase in voltage and the pulse on duration and then decreases. There is a significant increase in OC with increase in current however with increase in pulse off duration initially there is increase in OC.
Figure 4. 9: Interaction effect of Peak current and Pulse off duration on OC
The effect of pulse on duration and pulse off duration on OC at constant voltage of 35V and peak current of 20 amperes is represented in Figure 4.10. Additionally, it is observed that maximum OC was achieved at the lowest pulse on duration of (20µs) and highest pulse off duration of 60µs.The minimum OC was attained at the highest pulse on duration of 40µs and lowest pulse off duration of (30µs) combination. However, OC first increases with increase in pulse off duration and the pulse on duration and then decreases. There is a significant increase in OC with increase in pulse on duration nevertheless with increase in pulse off duration initially there is increase in OC but later onwards it starts decreasing.
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The reduced model for RCL after backward elimination process is demonstrated in Table 4.6 in ―Appendix 2‖ and the model F-value of 11.53 indicates that the model is significant. There is only a 0.01% chance that an F-value this large could occur due to noise. The percentage contribution of different process variables on RCL is presented in Figure 4.11.
Figure 4. 11: Percentage contribution of process variables
From Figure 4.12, it is observed that maximum RCL was obtained at the highest pulse on duration of (40µs) and highest pulse off duration of 60µs.The minimum RCL was obtained at the highest pulse on duration of 40µs and lowest pulse off duration of (30µs) combination. It is seen that RCL decreases with increase in pulse off duration and with the increase in pulse on duration it also decreases. There is a noteworthy increase in RCL with increase in pulse on duration however with increase in pulse off duration initially there is increase in RCL but later onwards it starts decreasing.
70.614 40.853 5.487 7.096 8.127 17.137 Model A-Voltage
D-Pulse off duration CD
A^2 B^2
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Figure 4. 12: Interaction effect of Pulse on duration and Pulse off duration on RCL
Table 4.7 shows the truncated model for TA after backward elimination process and is presented in ―Appendix 3‖ it can be seen the model F-value of 2699.29 infers the model is significant. The percentage contribution of different process variables on RCL is presented in Figure 4.14 and it can be seen in this case A, B, C, D, AB, AD, BC, BD, CD, A^2, B^2, C^2, D^2 are significant model terms. Peak current has a significant effect on TA followed by pulse off duration, pulse on duration and voltage.
Figure 4.14: Percentage contribution of process variables
It can be observed from Table 4.17 that the interaction terms AB and BC have maximum influence on TA as compared to other interaction terms. Hence interaction plots for only AB and BC have been considered. The interaction effect of peak current and Voltage on TA in the form of 3D surface graph at constant pulse on duration of 30µs and pulse off
99.951 4.961 23.33 12.525 14.194 17.436 2.505 12.868 1.473 2.554 0.241 0.378 1.572 2.603 Model A-Voltage B-Peak current C-Pulse on duration D-Pulse off duration AB AD BC BD CD A^2 B^2 C^2 D^2
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duration of 45µs is represented in Figure 4.15. From this Figure, it is observed that maximum TA (3.03951°) was obtained at the highest peak current of 32A and lowest voltage of (30V) combination. The minimum TA (1.5419°) was obtained at the lowest peak current of 8A and highest voltage (40V) combination. Furthermore, with the increase in voltage and peak current the value of TA increases initially and then decreases at higher levels of voltage and peak current settings. It is observed that there is significant increase in TA with increase in voltage and peak current.
Figure 4.15: Interaction effect of Voltage and Peak current on TA
Figure 4.16: Interaction effect of Pulse on duration and Peak current on TA
From Figure 4.16, it is observed that maximum TA (2.634°) was achieved at the highest peak current of 32A and the lowest pulse on duration (20µs) combination. The minimum TA (0.860°) was obtained at the least peak current of 8A and maximum pulse on duration (40µs) combination. Furthermore, with the increase in pulse on duration and peak current the value of TA increases initially and then decreases at higher levels of pulse on
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duration and peak current settings. It is observed that there is significant increase in TA with increase in pulse on duration and peak current. Based on Equation 4.5, the effect of input parameters on values of MRR, OC, RCL and TA has been evaluated by computing the values of various constants in Tables (4.4 - 4.7).
The mathematical models of MRR, OC, RCL and TA can be expressed in coded form as follows: 0 .6 4 7 5 0 .0 2 7 5 * 0 .0 2 5 4 * 0 .0 4 4 * 0 .0 3 1 6 * 0 .0 3 0 * 0 .0 4 5 0 * ( 4 .6 ) M R R A C D A C A D B D 0 .2 1 4 0 .0 1 2 * 0 .0 0 6 7 * 0 .0 0 6 7 * 0 .0 1 0 * 0 .0 0 5 * 0 .0 1 8 * 2 2 2 2 0 .0 0 8 * 0 .0 1 9 * 0 .0 0 6 * 0 .0 0 6 * 0 .0 2 3 * 0 . 0 1 1 * 0.0 1 *2 ( 4.7 ) O C A C D A B A C A D B C B D C D A B C D 2 2 9 2 .5 2 8 1 3 .5 9 9 * 4 .9 8 4 * 6 .0 1 2 * 1 3 .86 6 * 2 0 .1 3 5* ( 4.8 ) R C L A D C D A B 1 .5 2 0 3 0 .2 3 7 * 0 .5 1 3 * 0 .3 7 6 * 0 .4 0 0 * 0 .4 7 1 * 0 .1 7 8 * 2 2 2 2 0 .4 0 4 * 0 .1 3 7 * 0 .1 8 0 * 0 .1 37 * 0 .17 2 * 0 .3 4 9 * 0 .4 5 *3 ( 4 .9) T A A B C D A B A D B C B D C D A B C D