1. Introduction

Plasma arc cutting technology is one in which nitrogen, oxygen and compressed air are used to generate a plasma jet and then different type of materials such as nonferrous metal, stainless steel and others materials can be cut. During the plasma cutting process a source of heat is an electric arc generated by a plasma torch. The focus of manufacturers using plasma cutting process is optimization of productivity and the required quality of products made by plasma cutting. Both of these aspects are dependent on the appropriate choice of the process parameters. Plasma arc current, type gas, plasma gas pressure (plasma gas mass flow rate), cutting speed are parameters which have important effect on the quality characteristics. The effect of process parameters on the quality of the high tolerance plasma arc cutting of a 5 mm commercially pure titanium sheet was investigated in [1]. Authors concluded that the quality characteristics of the cutting edge of high tolerance plasma arc cutting of commercially pure titanium from a geometrical point of view need to be integrated with the considerations on the functional requirements for the cutting edge and on economical considerations that are partially correlated to microstructural modifications occurred at the cutting edge. A high tolerance plasma arc cutting system was used to cut plates of a 15 mm thick mild steel [2] and the arc voltage and cutting speed, plasma gas flow rate, shield gas flow rate and shield gas mixture are included in the analysis and their effects on kerf position and shape are evaluated.

It was shown that very good quality can be achieved for all the sides by varying the cutting speed and the arc voltage only. The effect of cutting speed and plasma gas pressure in plasma cutting of a 5 mm thick low alloy steel was analysed in [3]. It was shown that good quality cuts can be produced at the cutting speed from 400 to 700 mm/min and at the plasma gas pressure from 4 to 5 bar. Numerical method [4] and [5], genetic algorithms [6], statistical techniques [7] are common for the machining processes models. A new control strategy for plasma arc cutting was developed by [8] and this algorithm reduced the complexity of the nonlinear system modelling and achieved a real-time and online control for the cutting process by combining the advantages of fuzzy control and PID neural network control.

The regression analysis was used in [9] for the development of empirical models able to describe the effect of the process parameters on the cut quality in plasma arc cutting of a 15 mm thick mild steel sheets. It was found that the surface roughness and the kerf taper angle are mainly affected by the cutting height, whereas the heat affected zone is mainly influenced by the cutting current.

Investigation on the optimization and the effect of process parameters on material removal rate and surface roughness parameters during plasma arc cutting of EN31 steel using Taguchi method with grey relational analysis was presented in [10]. Also, analysis of variance was performed to get the contribution of each process parameters on the performance characteristics and it was observed that gas pressure is significant process parameters that affects the response.

The aim of this paper are to determine the effect and optimization of process parameters (cutting speed and plasma gas pressure) on surface roughness, kerf with and cut perpendicularity in plasma arc cutting of stainless steel a 5 mm thick using Grey relational analysis coupled with Taguchi method.

2. Experimental procedure

2.1. Test material, plasma cutting system and measuring equipment

The test material used in this experiment are X5CrNi18-10 steel plates. This steel belongs to austenitic stainless steel group. The chemical composition and mechanical properties of this steel are given in Tables 1 and 2.

Cutting of test samples was performed using the HiFocus 280i neo plasma device. HiFocus technology is based on the plasma cutting principle with narrowed and stabilized plasma arc. Narrowing and stabilizing the plasma arc is achieved by using a smaller diameter nozzle, increased plasma gas rotation, and the additional application of the rotary gas to the plasma arc through a non-potential coaxial nozzle.

Measurement of surface roughness was performed on the Mitutoyo SJ-210 measuring device. The surface roughness parameter Rz was measured at five different places along the cut edge. The Mitutoyo TM-505 microscope was used to measure the cut perpendicularity and kerf width, which were measured at 9 different places along the edge of the cut.

2.2. Design of experiments

In this paper, a full experiment plan was used. Cutting speed and plasma gas pressure are varied for this experiment. other process parameters were constant. A total of 9 samples were sampled for each combination of cutting speed and plasma gas pressure (Fig. 1).

In this experiment, there are two cutting parameters at three levels each. The cutting parameters levels are shown in the Table 3. Other constant parameters like current, voltage, nozzle distance from workpiece, types of plasma and secondary gas are shown in the Table 4.

The experimental layout for Taguchi L9 ([3.sup.2]) orthogonal array is shown in Table 5.

3. Results and discussions

The aim of this paper is to determine the optimal plasma cutting parameters for minimizing surface roughness, kerf width and cut perpendicularity. The mean values of the surface roughness parameter Rz, kerf width and cut perpendicularity are given in Table 6.

3.1 Effect of input parameters on the analyzed quality characteristics

In plasma cutting of termally cut materials, the most significant impact on the quality of the cut surface is the combination of input parameter. In this case, effect of cutting speed and plasma gas pressure on the roughness of the cut surface, cut perpendicularity and kerf width are analyzed.

From Fig. 2. can be seen:

* When cutting speed increases from 2000 to 2500 mm/min, the surface roughness decreases rapidly. Increasing the speed from 2500 to 3000 mm / min does not have a significant impact on surface roughness.

* When plasma gas pressure increases from 6 to 8 bar, the surface roughness increases. Increasing plasma gas pressure from 8 to 10 bar, roughness decreases.

From Fig. 3. can be seen:

* When cutting speed increases from 2000 to 2500 mm/min, the cut perpendicularity decreases. Increasing the speed from 2500 to 3000 mm / min, cut perpendicularity increases.

* When plasma gas pressure increases from 6 to 8 bar, the cut perpendicularity decreases. Increasing plasma gas pressure from 8 to 10 bar, cut perpendicularity increases.

From Fig. 4. can be seen:

* When cutting speed increases, kerf width decreases.

* When plasma gas pressure increases, kerf width also increases.

3.2 Grey Relational Analysis

Gray relational analysis is used for optimization multi-response characteristics. Optimization of such complicated characteristics can be converted into optimization single-response characteristic based on calculating Grey Relational Grade (GRG).

In this case, there are three response characteristics that should be minimzed. These are, the surface roughness parameter Rz, cut perpendicularity and kerf width.

The first step in the grey relational analysis is that the experimental results are normalized in the range between 0 and 1. All of three quality characteristics are required to be minimized, so smaller-is-better approach is used. This criterion can be expressed as:

[x.sub.i](k) = max [y.sub.i](k) - [y.sub.i](k)/max [y.sub.i](k) - min [y.sub.i](k) (1)

where, [y.sub.i](k) is the i-th eksperimental result for the k-th process responses, max [y.sub.i](k) is the largest value of [y.sub.i](k), min [y.sub.i](k) is the smallest value of [y.sub.i](k), and [x.sub.i](k) is the normalized value of [y.sub.i](k).

The normalized values of surface roughness, cut perpendicularity and kerf width calculated by (1) are shown in Table 7. After normalization, the deviation sequence was calculated by (2) and given in Table 7.

[[DELTA].sub.0i](k) = [absolute value of [x.sub.0](k) - [x.sub.i](k)] (2)

where, [[DELTA].sub.0i](k) is difference of the absolute value between [x.sub.0](k) and [x.sub.i](k). [x.sub.0](k) is the reference sequence of the k-th process response.

The next step is to determine grey relational coefficient based on normalized values of responses. The grey relational coefficients (GRC) can be calculated as:

[[xi].sub.i](k) = [[DELTA].sub.min] + [sigma][[DELTA].sub.max]/[[DELTA].sub.0i] + [sigma][[DELTA].sub.max] (3)

where, [[DELTA].sub.min] denotes smallest value of [[DELTA].sub.0i](k), [[DELTA].sub.max] denotes largest value of [[DELTA].sub.0i](k), and [sigma] is a distinguishing coefficient. Its value can be chosen in the range of 0 to 1. Generally, this coefficient has value of 0,5.

Average value of the Grey relational coefficients for all responses determine the Grey relational grade (GRG). Grey relational grade can be calculated by (4).

[[gamma].sub.i] = 1/n [n.summation over (k=1)] [[xi].sub.i](k) (4)

where, [[xi].sub.i](k) is the Grey relational coefficient of k-th process response in i-th eksperiment and n is the number of process responses.

The calculated values of Grey relational coefficient and Grey relational grade are given in Table 8.

The higher value of Grey relational grade represents that the corresponding process reponses are close to the optimal condition. In this case, it is experiment number 8 with the best combination of process parameters for surface roughness, cut perpendicularity and kerf width among 9 experiments.

The means of the Grey relational grade for each level of cutting speed and plasma gas pressure are given in Table 9. According to the results shown in Table 9, the cutting speed has the most significant effect in reducing surface roughness, cut perpendicularity and kerf width.

Fig. 5. shows the response graph for mean Grey relational grade from which the optimal combination of cutting parameters can be determined. This is the combination of parameters for which the highest mean Grey relational grade are obtained. Therefore, optimal plasma cutting parameters for X5CrNi18-10 stainless steel plates with respect to surface roughness, cut perpendicularity and kerf width are, cutting speed of V = 2500 mm/min and plasma gas pressure of p = 8 bar.

4. Conclusion

In this study, the Grey relational analysis was applied for optimization of the parameters of the plasma cutting process. Stainless steel X5CrNi18-10 plates with thickness of 5 mm were cut using different cutting speed and plasma gas pressure. Three output process parameters, surface roughness, cut perpendicularity and kerf width, were monitored. The optimal plasma cutting parameters are: cutting speed V = 2500 mm/min and plasma gas pressure p = 8 bar. The same parameters are recommended by the manufacturer of cutting equipment.

However, the author's recommendation is that a lower plasma gas pressure (p = 6 bar) can be used at the same cutting speed of 2500 mm/min, as the cut quality remains the same and lower production costs are achieved. In both cases (plasma gas pressure, p = 6 bar and p = 8 bar) the cuts belong to the same quality class according to EN ISO 9013.

The experimental result showed that the cutting speed has the most significant effect in reducing surface roughness, cut perpendicularity and kerf width.

The proposal for future research is that other input parameters (current, type of plasma gas, nozzle distance, etc.) are varied besides the cutting speed and the plasma gas pressure, and then to analyse the influence of these parameters on the cut quality for different thickness of material.

DOI: 10.2507/28th.daaam.proceedings.149

5. Acknowledgments

The authors acknowledge the project (Modern machining processes) was financially supported by the Ministry of Education, Science and Youth of Sarajevo Canton.

6. References

[1] Gariboldi, E. & Previtali, B. (2005). High tolerance plasma arc cutting of commercially pure titanium. Journal of Materials Processing Technology, 160, (2005) 77-89, ISSN 0924-0136

[2] Bini, R.; Colosimo, B.M.; Kutlu, A.E. & Monno, M. (2008). Experimental study of the features of the kerf generated by a 200A high tolerance plasma arc cutting system. Journal of Materials Processing Technology, 196, (2008) 345355, ISSN 0924-0136

[3] Begic, D.; Kulenovic, M.; Cekic, A. & Dedic, E. (2012). Some experimental studies on plasma cutting quality of low alloy steel, Annals of DAAAM for 2012 & Proceedings of the 23rd International DAAAM Symposium, Vol.23, No.1, Vienna, Austria, ISSN 2304-1382, ISBN 978-3-901509-91-9, Katalinic, B. (Ed.), pp. 0183-0186, DAAAM International Vienna, Vienna

[4] Freton, P.; Gonzalez, J.J.; Gleizes, A.; Camy Peyret, F.; Caillibotte, G. & Delzenne, M. (2002). Numerical and experimental study of plasma cutting torch. Journal of Physics D: Applied Physics, 35, 2 (2002) 115-131, ISSN 1361-6463

[5] Begic-Hajdarevic, D. & Bijelonja, I. (2014). Experimental and numerical investigation of temperature distribution and hole geometry during laser drilling process. Procedia Engineering, 100, (2014) 384-393, ISSN 1877-7058

[6] Ficko, M. & Palcic, I. (2013). Designing a layout using the modified triangle method, and genetic algorithms. International Journal of Simulation Modelling, 12, 4 (2014), 237-251, ISSN 1726-4529

[7] Begic-Hajdarevic, D.; Vucijak, B.; Pasic, M. & Bijelonja, I. (2017). Analysis of the influence of cutting parameters on surface roughness in laser cutting process of tungsten alloy using control charts. Tehnicki vjesnik - Technical Gazette, 24, Suppl. 2 (2017) 339-344, ISSN 1848-6339

[8] Deli, J. & Bo, Y. (2011). An intelligent control strategy for plasma arc cutting technology. Journal of Manufacturing Processes 13 (2011) 1-7, ISSN 1526-6125

[9] Salonitis, K. & Vatousianos, S. (2012). Experimental Investigation of the Plasma Arc Cutting Process. Procedia CIRP 3 (2012) 287 - 292, ISSN 2212-8271

[10] Kumar Das, M.; Kumar, K.; Barman, T. & Sahoo, P. (2014). Optimization of process parameters in plasma arc cutting of EN 31 steel based on MRR and multiple roughness characteristics using grey relational analysis. Procedia Materials Science, 5 (2014), 1550-1559, ISSN 2211-8128.

Caption: Fig. 1. Test samples

Caption: Fig. 2. Effect of cutting speed and plasma gas pressure on surface roughness

Caption: Fig. 3. Effect of cutting speed and plasma gas pressure on cut perpendicularity

Caption: Fig. 4. Effect of cutting speed and plasma gas pressure on kerf width

Caption: Fig. 5. Response graph for mean Grey relational grades with selected optimal cutting parameters

Table 1. Chemical composition of X5CrNi18-10 steel

                       Chemical composition (percentages by mass)
Steel name    Steel
              number         C                Si              Mn

X5CrNi18-10   1.4301   [less than or    [less than or    [less than or
                       equal to]0,07    equal to]1,00    equal to]2,00

                       Chemical composition (percentages by mass)
Steel name
               P max.         S              N         Cr         Ni

X5CrNi18-10    0,045    [less than or    0,12-0,22   17-19,5   8,5-11,5
                       equal to]0,030

Table 2. Mehanical properties of X5CrNi18-10 steel

                         Maximum       Minimum 0,2 % proof
Steel name    Steel    hardness HB   strength, [R.sub.p0,2]
              number                      N/[mm.sup.2]

X5CrNi18-10   1.4301       215                 190

              Tensile strength,
Steel name       [R.sub.m]
               N/[mm.sup.2]

X5CrNi18-10       500-700

Table 3. Cutting parameters and their levels

Simbol    Cutting parameter           Level
                                 1      2      3

A           Cutting speed      2000    2500   3000
              V, mm/min
B        Plasma gas pressure     6      8      10
               p, bar

Table 4. constant cutting parameters

Constant parameter          Value

Current                     60 A
Voltage                     140 V
Nozzle distance             4 mm
Material thickness          5 mm
Plasma gas           [N.sub.2]/[H.sub.2]
Secondary gas             [N.sub.2]

Table 5. Ortogonal array L9 ([3.sup.2]) of the experimental run

Exp.         A                  B
No.    Cutting speed   Plasma gas pressure

1.           1                  1
2.           1                  2
3.           1                  3
4.           2                  1
5.           2                  2
6.           2                  3
7.           3                  1
8.           3                  2
9.           3                  3

Table 6. Experimental results

           A           B         Mean height           Cut
        Cutting    Plasma gas   of the profile   perpendicularity
Exp.     speed      pressure     Rz, [micro]m      u, [micro]m
No.    V, mm/min     p, bar

1.       2000          6            15,996            615,11
2.       2000          8            13,756            514,05
3.       2000          10           9,861             527,81
4.       2500          6            8,192             424,82
5.       2500          8            10,572            411,00
6.       2500          10           11,851            421,59
7.       3000          6            9,365             812,74
8.       3000          8            10,272            426,77
9.       3000          10           11,022            503,23

       Kerf width
Exp.   a, [micro]m
No.

1.       1991,1
2.       2055,5
3.       1971,4
4.       1934,2
5.       1990,7
6.       1954,4
7.       1871,4
8.       1834,1
9.       1962,8

Table 7. Normalized values and deviation sequences of responses

Exp.     Normalized values         Deviation sequences
No.         of responses            [[DELTA].sub.0i](k)

         Rz        u       a       Rz       u       a

1.        0      0,492   0,291     1      0,508   0,709
2.      0,287    0,743     0     0,713    0,257     1
3.      0,786    0,709   0,380   0,214    0,291   0,620
4.        1      0,966   0,548     0      0,034   0,452
5.      0,695      1     0,293   0,305      0     0,707
6.      0,531    0,974   0,457   0,469    0,026   0,543
7.      0,850      0     0,832   0,150      1     0,168
8.      0,733    0,961     1     0,267    0,039     0
9.      0,637    0,770   0,419   0,363    0,230   0,581

Table 8. Grey relational coefficients and Grey relational grades

Exp.       Grey relational          Grey relational
No.           coefficient         grade [[gamma].sub.i]

         Rz        u       a     [[gamma].sub.i]   Rank

1.      0,333    0,496   0,414        0,414         9
2.      0,412    0,661   0,333        0,469         8
3.      0,700    0,632   0,446        0,593         6
4.        1      0,936   0,525        0,820         2
5.      0,621      1     0,414        0,678         3
6.      0,516    0,950   0,479        0,648         4
7.      0,769    0,333   0,748        0,617         5
8.      0,652    0,927     1          0,860         1
9.      0,580    0,685   0,462        0,576         7

Table 9. Response table for the mean Grey relational grade

Level    Cutting parameters

          A: Cutting speed    B: Plasma gas pressure

1              0,492                  0,617
2              0,715                  0,669
3              0,684                  0,606
A              0,223                  0,063
Rank             1                      2

Total mean of Grey relational grade = 0,6305