Improvement By Genetic Algorithm In Finding The Optimum Surface Finish When End Milling Ti64 Using Sntr Coated Tools

Improvement by Genetic Algorithm in Finding the Optimum Surface Finish When End Milling Ti64 using SNTR coated tools A.S Mohrunia , S. Sharif, M.Y. Noordinb A .Novliantaa Faculty of Engineering, Sriwijaya University, Indralaya, 30662 OI-Indonesia E-mail : [email protected]

ABSTRACT In this works, surface roughness for end milling of Ti-6Al-4V under wet conditions were optimized. Genetic algorithm (AG) was used for finding the optimum cutting conditions such as cutting speed (V), feed per tooth (fz), and radial rake angle (γo). The optimized results were compared to that had been generated using response surface methodology (RSM). It has been proven that AG-results showed more accurate than RSM-results which have been validated using data taken according to the design of experiments (DOE). Keywords: Surface Roughness, End Milling, Titanium Alloys, Genetic Algorithm, Response Surface Methodology

Introduction Titanium alloys are used widely known as difficult to cut materials, especially at higher cutting speeds, due to their several inherent properties. Among the titanium alloys, Ti-6Al-4V is the most widely used in the aerospace, chemical and ship building industry because of their superior mechanical properties, heat and corrosions resistance, so it has been chosen as the workpiece in this study.[1]. Due their low machinability of the alloy under study, selecting the machining conditions and parameters is crucial. According to the past reports, the range of feeds and cutting speeds which provide a satisfactory tool performance is very limited. On the other hand, adequate tool, coating, geometry and cutting flow materials should be used [2]. The study of [3] has pioneered in finding of the optimum cutting conditions for machining processes using response surface methodology, which are followed by [4][5]. After that, [6]-[8] have begun with the researches using titanium alloy as workpiece. Recently, it has begun to explore the study using non-conventional algorithm in [9][11]. Furthermore, according to the previous studies, there is no researcher employed genetic algorithm in searching the optimum cutting conditions for machining of aerospace

materials. Base on these facts, it is necessary to take part in contribution of providing such lack in information

Procedure of Experiments MAHO 700S CNC machining center for side milling operation was used. The grade K-30 solid carbide end mill cutters, with PVD Supernitride coated which were prepared with different radial rake angle according to DOE, were used for experimentation. Surface roughness of the machined surface was measured using portable Taylor Hobson Surftronic +3. Before conducting the measurement, the instrument was calibrated using a standard specimen roughness delivered to ensure the consistency and accuracy of surface roughness values. . There are three cutting parameters used in this study, such as cutting speed, feed rate, and radial rake angle. Machining conditions used in this optimization study for each cutting parameters are : • Cutting speed V : 130 - 160 m/min. • Feed rate fz : 0,03 - 0,07 mm/teeth. • Radial rake angle : 7 - 13o

Cutting parameters such as cutting speed, feed rate, and radial rake angle are coded using transformed equation (1) according to circumstance of limitation of the milling machine.

x=

ln xn − ln xn0 ln xn1 − ln xn0

(1)

x the coded variable of any factor

Where corresponding to its natural is xn, xn1 is the natural value at the +1 level and xn0 is the natural value of the factor corresponding to the base or zero level. The level of independent variables and coding identification are shows in Table 1. Table 1. Levels of independent variables for end milling Ti6Al4V Level in coded form Independent Variable

-α

-1

0

1

α

V (mm. min −1 ) x1

124.5 3

130

144.2 2

160

167.03

fz (mm.tooth −1 ) x 2

0.025

0 .03

0.046

0 .07

0.083

γο (°) x3

6.2

7.0

9.5

1 3.0

14.8

Research Methodology The mathematical model used in this study is 2nd CCD surface roughness model. Genetic algorithm result compared to the response surface methodology. The mathematical model shown by equation (2) 2 Ў2 = -1.0014 – 0.085531x1 + 0.43082x2 - 0.070215x1 + 2 0.057597x2 -0.016614x1x3 0.020616x2x3 0.0752385x12 + 0.0787339x1x2 (2) Thus model is valid for end milling of titanium alloy, Ti-6Al-4V using Supernitride coated carbide tools under wet conditions with the following range of respective cutting speed (V, fz, and γ) : 130 ≤ V ≤ 160 m/min; 0.03 ≤ fz ≤ 0.07 mm/teeth; 7 ≤ γ ≤ 13 (o) for std order 1 to std order 24. 2nd order CCD surface roughness model also used for std order 13 to std order 24 with the following range of respective cutting speed (V, fz, and γ) : 124.53 ≤ V ≤ 167.03 m/min; 0.025 ≤ fz ≤ 0.083 mm/teeth; 6.2 ≤ γ ≤ 14.8 (o).

Genetic Algorithm (AG) inspired from biological evolution where the evolution is the method of searching among en enormous number possibilities for solutions. AG is the algorithm of searching base on selection and genetic mechanism. The solution found by Genetic Algorithm is coded to binary numbers called chromosomes. The fitness value of each chromosome evaluated by an objective function. Selected individuals are then reproduced, the selecting usually in pairs through the application of genetic operator. These operators are applied to copulate of individuals with a given probability, and result in new offspring. The offspring from reproduction are then evaluated by mutation and elitism probability, and then these new individuals are prime for the next generation. Selection, reproduction and evaluation processes are repeated until some termination criteria are achieved. The flow chart of AG method is showed by figure 1. To solve the problem in this optimization study, it’s important to pick out the following parameters that take crucial part of AG, such as population size, maximum number of generation, total string length, crossover probability, mutation probability, and elitism probability. It’s important to acquire the best solutions. To solve the problem in this optimization study, it’s important to pick out the following parameters that take crucial part of GA, such as population size, maximum number of generation, total string length, crossover probability, mutation probability, and elitism probability. It’s important to acquire the best solutions. Parameters used in this study using GA that must determine are [13]: • Population size = 80 • Maximum generation = 15 • Crossover probability (Pc) = 0.45 • Mutation probability (Pm) = 0.25 • Elitism probability (Pe) = 0.5

Initial Population Gen =0

Evaluate Solution

Gen=gen+1

Reproduction

Crossover No

Mutation

14

Axial

-1.1412

0

0

0,320

15

Axial

1.1412

0

0

0,272

16

Axial

1.1412

0

0

0,288

17

Axial

0

-1.1412

0

0,230

18

Axial

0

-1.1412

0

0,234

19

Axial

0

1.1412

0

0,640

20

Axial

0

1.1412

0

0,696

21

Axial

0

0

-1.1412

0,361

22

Axial

0

0

-1.1412

0,360

23

Axial

0

0

1.1412

0,368

24

Axial

0

0

1.1412

0,360

Table 3 shows the optimization result of RSM and AG, and then compared to find out root mean square error (RMSE) of RSM and AG method.

Termination yes

Table 3: The optimization result for RSM and GA

Stop Figure 1: Genetic algorithm flow chart

Results and Discussion Surface roughness experimental result for Supernitride coated solid carbide tools showed by table 2. This result used for validate the comparison between Response Surface Methodology and Genetic Algorithm. Table 2: Surface roughness result for Supernitride coated solid carbide tools

Std Order

Experimenta l Ra

RSM Ra

AG Ra

1

0,284

0,282

0,284

2

0,196

0,193

0,197

3

0,668

0,639

0,635

4

0,624

0,600

0,617

5

0,280

0,282

0,280

6

0,190

0,193

0,190

7

0,612

0,639

0,612

8

0,576

0,600

0,576

9

0,329

0,380

0,346

10

0,416

0,380

0,415

Std Oder

Type

V (m/min)

fz (mm/ tooth)

γ (⁰)

Ra (µm)

11

0,352

0,380

0,352

1

Factorial

-1

-1

-1

0,284

12

0,400

0,380

0,403

2

Factorial

1

-1

-1

0,196

13

0,344

0,360

0,362

3

Factorial

-1

1

-1

0,668

14

0,320

0,360

0,361

4

Factorial

1

1

-1

0,624

15

0,272

0,282

0,283

5

Factorial

-1

-1

1

0,280

16

0,288

0,282

0,285

6

Factorial

1

-1

1

0,190

17

0,230

0,224

0,224

7

Factorial

-1

1

1

0,612

8

Factorial

1

1

1

0,576

18

0,234

0,224

0,225

9

Center

0

0

0

0,329

19

0,640

0,758

0,641

10

Center

0

0

0

0,416

20

0,696

0,758

0,696

11

Center

0

0

0

0,352

21

0,361

0,367

0,368

12

Center

0

0

0

0,400

22

0,360

0,367

0,368

13

Axial

-1.1412

0

0

0,344

23

0,368

0,367

0,368

24

0,360

0,367

0,368

17 18

Table 4: The Optimization Result for RSM

19

NO

V (m/min)

fz (mm/tooth )

1

160,00

0,030000

8,3130

0,19298

2

160,00

0,030000

0,19298

3

160,00

0,030000

9,3537 12,822 0

4

160,00

0,030000

0,19298

5

160,00

0,030000

6

160,00

0,030000

7

160,00

0,030000

11,0570 10,990 0 10,447 0 10,416 0

8

160,00

0,030000

9

160,00

10

160,00

γ (0)

Ra (µm)

0,19298

1 2 3 4 5 6 7 8 9 10

V (m/min) 132,906315 158,559030 9 130,977652 9 146,016759 3 131,377499 6 159,802941 3 134,125845 7 145,543298 2 158,268258 6

11

153,709782 155,151448 3

12

156,813422

13

124,526509

14

124,526509 167,027957 1 166,733424 7

15 16

0,02545413 2 0,02549252 9 0,07356909 5 0,07815443 5

9,54293385 5 9,54293385 5 9,54293385 5 9,54293385 5

0,224 0,225 0,641 0,696

RMSE comparison of RSM and GA about experimental data from the previous research showed by Table 4. Table 6: Comparison between Response Surface Methodology validate with experimental result Std Orde r

Experime n tal Ra

RSM Ra

AG Ra

Estimated Error RSM

Estimated Error AG

0,19298

1

0,284

0,282

0,284

4,03254E-06

1,86539E-07

0,19298

2

0,196

0,193

0,197

9,13705E-06

1,05855E-06

0,19298

3

0,668

0,639

0,635

0,000818617

0,001059942

0,030000

7,9021 12,920 0

0,19298

4

0,624

0,600

0,617

0,000599008

4,79605E-05

0,030000

9,0691

0,19298

5

0,280

0,282

0,280

3,96759E-06

3,17621E-08

6

0,190

0,193

0,190

8,86399E-06

6,29325E-05

7

0,612

0,639

0,612

0,000750131

5,12766E-08

8

0,576

0,600

0,576

0,000553443

1,69157E-07

9

0,329

0,380

0,346

0,002605034

0,000300692

10

0,416

0,380

0,415

0,001293155

1,37661E-06

11

0,352

0,380

0,352

0,000786215

5,11355E-08

12

0,400

0,380

0,403

0,00039842

7,9734E-06

13

0,344

0,360

0,362

0,00026509

0,00031128

0,19298

Table 5 : The Optimization Result for AG NO

20

144,234973 6 144,234973 6 144,234973 6 144,234973 6

fz (mm/tooth) 0,03163089 4 0,03033763 1 0,06957743 2 0,06989131 5 0,03062453 5 0,03076269 1 0,06761216 4 0,06591816 6 0,04618864 3 0,05190277 9 0,04603766 6 0,05141653 1 0,04616723 0,04600321 7 0,046193011 0,046

γ (0) 7,24614747 9 7,02737840 5 8,16452547 5

Ra (µm) 0,284 0,197 0,635

9,53713297

0,617

14

0,320

0,360

0,361

0,001622606

0,001657032

9,623519611 9,65539131 4 12,6585162 7 12,4248268 8 9,56871480 6 10,4244459 9 9,54573594 2 10,3526380 1

0,280

15

0,272

0,282

0,283

0,000101215

0,000124301

0,190

16

0,288

0,282

0,285

3,52771E-05

1,21589E-05

0,612

17

0,230

0,224

0,224

3,43118E-05

3,16323E-05

0,576

18

0,234

0,224

0,225

9,71729E-05

8,8526E-05

19

0,640

0,758

0,641

0,013947146

9,31132E-07

20

0,696

0,758

0,696

0,003856166

4,19497E-08

21

0,361

0,367

0,368

4,05103E-05

4,48784E-05

22

0,360

0,367

0,368

5,42398E-05

5,97878E-05

23

0,368

0,367

0,368

4,03517E-07

9,05191E-08

9,54 9,55385571 9 9,54293385 5 9,54293385 5

0,362

24

0,360

0,367

0,368

5,42398E-05

5,92767E-05

0,346 0,415 0,352 0,403

0,361

Mean Square Error

0,0011641

0,000161348

0,283

RMSE

0,034118912

0,0127023

0,285

The result from Table 4. shows that Genetic Algorithm is better than response Surface Methodology. It can be seen from RMSE from RSM and AG method. Comparison of RSM and AG method about experimental data showed by Figure 2.

Figure 2: Comparison of RSM and AG method validate out with experimental result.

Based on the results above, optimum combination of cutting conditions such as cutting speed, feed rate, and radial rake angle for achieving minimum surface roughness value for machining Ti-6Al-4V, can be found by AG method.

Conclusions Overall performance of optimizing the cutting conditions using genetic algorithm has shown slightly better results than those using response surface methodology. This can be recognized from the root mean squared error (RMSE) of AG which is 0,0127023, when compared to the RMSE of RSM 0,034118912. Additionally AG showed also more precise than RSM in finding of the minimum surface roughness value. Genetic algorithm can accomplish the optimization of surface roughness in machining of aerospace materials with adequate accuracy, which is required in industry.. The optimum cutting condition found using genetic algorithm is as follows : cutting speeds V = 159,8 m/min, feed per tooth fz = 0,0307mm/tooth and radial rake angle γ0 = 9,6550.

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