The results of the experimental response obtained during the manufacturing process of the anklefoot prosthesis with Aluminum 6061 material with a combination of cutting parameters are shown in Table 5. Analysis of Variance (ANOVA) discusses the effect of milling parameters on machining time. Furthermore, regression analysis was used to build a mathematical model between the factors and the resulting responses. The practicality of the mathematical model is tested using the regression coefficient [17]. Finally, the machining parameters are optimized to obtain a combination of cutting parameters with minimum machining time [18].
Table 5. Time Machining Test Results
Run

Real Values

Experimental Results

Spindle Speed (Rpm)

Feed Rate (mm/min)

Step Over (mm)

Toolpath Strategy

Time Machining (minute)

1

6500

600

0.15

Flowline

475

2

7500

600

0.15

Flowline

475

3

6500

800

0.15

Flowline

453

4

7500

800

0.15

Flowline

453

5

7000

700

0.1

Raster

589

6

7000

700

0.2

Raster

462

7

7000

700

0.1

Scallop

578

8

7000

700

0.2

Scallop

457

9

6500

700

0.15

Raster

505

10

7500

700

0.15

Raster

505

11

6500

700

0.15

Scallop

497

12

7500

700

0.15

Scallop

497

13

7000

600

0.1

Flowline

565

14

7000

800

0.1

Flowline

525

15

7000

600

0.2

Flowline

431

16

7000

800

0.2

Flowline

431

17

6500

700

0.1

Flowline

543

18

7500

700

0.1

Flowline

543

19

6500

700

0.2

Flowline

440

20

7500

700

0.2

Flowline

440

21

7000

600

0.15

Raster

533

22

7000

800

0.15

Raster

533

23

7000

600

0.15

Scallop

524

24

7000

800

0.15

Scallop

476

25

7000

700

0.15

Flowline

474

26

7000

700

0.15

Flowline

474

27

7000

700

0.15

Flowline

474

3.1 Analysis of Variance (ANOVA)
The effect of machining parameters (spindle speed, feed rate, step over, and toolpath strategy) on machining time was analyzed using analysis of variance (ANOVA). Furthermore, the mathematical model that has been determined is tested for significance by means if the significance level was α = 0.05, then the confidence level was 95%. This analysis says that the response is significant if the Pvalue is less than 0.05. The results of the ANOVA analysis are presented in Table 6 [20][21]. The results of the ANOVA show that the feed rate (B), the step over (C), the toolpath strategy (D), products C2, products D2, and the twolevel interaction effect on B x D have significant impacts on the machining time of anklefoot prosthesis. Step Over (C) with PValue 0.000 has the most impact on machining time.
Table 6. Analysis of Variance of Time Machining of AnkleFoot Prosthesis
3.2 Regression Equations
The response surface method (RSM) performs mathematical modeling and analysis to analyze the relationship between several variable parameters and responses. The experimental response is used to construct a mathematical model for the milling process of the anklefoot prosthesis [21,22]. The quadratic model of time machining was made based on experimental results using Minitab 19 software. The following equation expresses the model:
y = α1 + α2*x1 + α3*x2 + α4*x3 + α5*x4 + α6*x12 + α7*x22 + α8*x32 + α9*x42 +
α10*x1*x2 + α11*x1*x3 + α12*x1*x4 + α13*x2*x3 + α14*x2*x4 + α15*x3*x4 (1)
Where y is the machining time, x1 is the spindle speed, x2 is the feed rate, x3 is the step over, x4 is the toolpath strategy, and α is the regression coefficient. The quadratic model based on formula (1) is stated as follows:
y = α1 + α2*A + α3*B + α4*C + α5*D + α6*A2 + α7*B2 + α8*C2 + α9*D2 + α10*A*B +
α11*A*C + α12*A*D + α13*B*C + α14*B*D + α15*C*D (2)
The machining time mathematical model is obtained by RSM using the experimental results to change the parameters in formula (2) as follows:
Time Machining = 474 + 0.00 *A – 11.00*B – 56.83*C – 8.17*D – 5.83*A2 + 0.17*B2 +
16.42*C2 + 35.42*D2 – 0.00*A*B – 0.00*A*C – 0.00*A*D +
10.00*B*C – 12.00*B*D + 1.50*C*D
The coefficient R2 describes the level of fit of the data with the model. The model is meaningful if the value of R2 is close to 1. In this study, the value of R2 = 97.67% for machining time is close to 1. Therefore, it can be concluded that the mathematical model of machining time is reliable. In addition, graphical methods can be used to test whether the presented model is feasible or not, as shown in Figure 3. In order to determine that the residual model is normally distributed, the probability plot of the residual graph is used [22]. The model is said to be good if the residuals are normally distributed, which then becomes the main requirement for further testing. In this study, the results showed that the residuals were normally distributed
Furthermore, the calculation of the residual vs. machining time graph is used to determine whether the model function is feasible. The model is said to be feasible if the residual vs. machining time graph is random and follows a linear line pattern [17]. This shows that the calculated machining time value does not affect the residual value. This study shows that it is randomly distributed because the graph does not have a specific pattern. Furthermore, the results of the exact residual test from this study also obtained a graph with points that spread along the zero axis so that the residual data can be said to be identical. Based on the charts obtained, it can be concluded that this model meets the residual assumption.
3.3 Effect of Machining Parameters on Time Machining
A threedimensional response surface graph is presented in Figure 4 to Figure 9 to clearly show the relationship between the various milling parameters and machining time in manufacturing anklefoot prostheses. Based on the 3D plot graph, it can be seen that the interaction between machining parameters between spindle speed (A) and feed rate (B) in Figure 4, the interaction between spindle speed (A) and step over (C) in Figure 5, the interaction between spindle speed (A) and toolpath strategy (D) in Figure 6, the interaction between feed rate (B) and step over (C) in Figure 7 and the interaction between step over (C) and toolpath strategy (D) in Figure 9 does not have a statistically significant effect on machining time. However, behind that, the interaction between feed rate (B) and toolpath strategy (D) in Figure 8 has a statistically significant effect on machining time.
Based on Figure 4, minimum machining time can be obtained through a combination of minimum spindle speed (A) and maximum feed rate (B). Figure 5 shows that the smallest machining time can be obtained by combining machining parameters with maximum spindle speed (A) and maximum step over (C). Figure 6 shows the minimum machining time can be obtained through a combination of minimum spindle speed (A) and medium toolpath strategy (flowline). Next, Figure 7 shows that the minimum machining time can be obtained by combining the maximum feed rate (B) and maximum step over (C). Figure 8 shows that the minimum machining time can be obtained by combining the maximum feed rate (B) and medium toolpath strategy (D). The next 3D plot in Figure 9, which shows the interaction between the minimum step over (C) and the medium level of the toolpath strategy (flowline), which affects the machining time
It can be seen from the above Figure 4 to Figure 9 that based on the interaction between the two factors, the spindle speed and feed rate (AxB), the spindle speed and step over (AxC), the spindle speed and toolpath strategy (AxD), the feed rate and step over (BxC), the feed rate and toolpath strategy (BxD), and the step over and toolpath strategy (CxD) for the effect of machining time. The results from the threedimensional response surface plot above are almost the same as those obtained from the analysis of variance
3.4 Optimization of Cutting Conditions
The lower the predicted expected value, the better the time machining. In general, the lower the spindle speed, the higher the feed rate, and the higher the stepover with the toolpath strategy type of flowline will result in minimum machining time. Based on the analyzed structure, the minimum machining time in processing the anklefoot prosthesis is 424.4601 minutes, according to Figure 10. In addition, as shown in Table 7, for machining time, the desirability value is 1.0000. Therefore, the total average machining time is 494.5185 minutes. Therefore, compared with the optimized results, the machining time of the anklefoot prosthetic is shorter, and the machining time of the obtained anklefoot prosthetic manufacturing is better.
Table 7. RSM Optimization Results for Responses
Response

Spindle Speed (rpm)

Feed rate (m/min)

Step Over (mm)

Toolpath Strategy

Predicted

Desirability

Machining Time

6500

800

0.2

Flowline

424.4601

1.0000
