Process Capability and Average Roughness in Abrasive Water Jet Cutting Process of Stainless Steel

Process capability analysis is frequently employed to evaluate if a product or a process can meet the customer’s requirement. In general, process capability analysis can be represented by using the process capability index. Until now, the process capability index was frequently used for manufacturing processes with quantitative characteristics. However, for a process with qualitative characteristic like cutting surface, the data’s type and single specification caused limitations of using the process capability index. Taguchi developed a surface quality by abrasive water jet cutting or quadratic quality loss function to address such issues. In this study, we intend to construct a measurable index which incorporates the process capability index philosophy concept to analyze the process capability with the consideration of the qualitative surface roughness. The manufacturers can employ the proposed index to self-assess the process capability. The objective of this study was to examine the effects of abrasive water jet machining variables like cutting speed of the stainless steel material. The roughness of the varied surface through the cut depth was also measured and determined as a process capability index of 3 zones machined surface. Keywords-abrasive water jet cutting; process capability; cutting speed; surface roughness; stainless steel


INTRODUCTION
The abrasive water jet (AWJ) cutting technique is one of the most rapidly improving technological methods of cutting materials.In this cutting technique, a thin, high velocity water jet accelerates abrasive particles that are directed through an abrasive water jet nozzle at the material to be cut.AWJ is one of the most widely used technological methods.The advantages of AWJ cutting include the possibility of cutting almost all materials e.g.Titanium, Aluminum, the absence of thermal distortion, high flexibility, small cutting forces and being environmentally friendly.Due to these capacities, this cutting technique is more cost-effective than traditional and non-traditional machining processes [1][2][3][4][5][6][7][8][9].The mechanism and rate of material removal during the AWJ cut depends on both the type of abrasive and the range of process parameters.A considerable number of studies have investigated the effects of cutting velocity, spreading distance, water pressure, abrasive grain size and other factors on the surface roughness [6][7][8][9][10][11][12].Thus, it is necessary to have a deeper knowledge of the optimal conditions of operation, which will allow us to ensure a good surface roughness.A large amount of research effort has been made, in recent years, to understand the AWJ process and improve its cutting performance such as the depth of cut and surface finish for various materials [11][12].Researchers used granite samples for their experimental studies and investigated the effect of process parameters on rock cutting.It was found that entraining of abrasive particles increase the cutting capability of water jets and increases of water jet pressure allow obtaining deeper cut depths.Process capability analysis (PCA) [13][14][15][16] is frequently employed by the manufacturers to evaluate if the capability of process can meet the customer's requirement.Process Capability Indices (PCIs) are a quantitative measurement of the process capability in most manufacturing industries.PCIs, such as Cp and Cpk are commonly used for most manufactures [15][16], can frequently measure the process capability for the quantitative response for example surface roughness.Authors in [15] evaluate the related scale of the process mean with the tolerance specification (i.e. the difference between the upper tolerance limit and the lower tolerance limit).Cp evaluates the related scale of the specification's tolerance with process's tolerance.While Cpk simultaneously, evaluates the centering degree and the dispersion degree.These PCIs will make some adjustments if there are necessary particulars like the unilateral specification.For the quantitative type, the theories on PCA and PCIs are well developed in [15][16][17] but qualitative data type may exist during the manufacturing environment, e.g. the production parts, pistons, gears, the integrated circuit manufacturing, so, the process capability analysis for qualitative data will be an important issue to study.However, most studies only focus on the PCA application for the quantitative response data, and the qualitative response data is seldom mentioned [16][17].
Several difficulties can be mentioned as: (i) the target of the qualitative data may lead to unobvious centering evaluation, e.g. the target will be set as zero defect, (ii) the limitation of the unilateral specification, especially only the upper specification exists, e.g. the defect rate may be less than 1% and (iii) the quantitative data utilizes the process mean (µ) and process deviation (σ) to compute the PCIs, however, the qualitative data cannot directly utilize them to compute the PCIs.

III. EXPERIMENTAL RESULTS AND DISCUSSION
A. Surface Roughness of the cut surface After machining operations by AWJ cutting process, the cut surface was monitored by optic microscope and is presented in Figure 3 which shows the very good surface cut of the upper edge beginning of the cut (zone 1) and the bad surface machined in the lower edge, ending of the cut (zone 3).In this zone there is a presence of the striation marks (Figure 3(b)).Obtained photographs were analyzed and edited with the use of image manipulation software.Cut surfaces were divided in two zones; upper zone (beginning of the cut with no visible presence of machining marks), and lower zone, (ending of the cut with visible machining marks) as shown in Figure 3(b).Lines outlining machining marks and showing their approximate curve angle were added.For the surface cut with the highest cutting speed V equal to 250mm/min, numerous grooves and elevations in the lower zone are clearly visible marks (Figure 3(b)).With decrease in the cutting speed an improvement of surface quality in its lower part can be observed.For the lowest used cutting speed, machining marks are fewer and faintly visible.It can be observed that the width of the zone with visible machining marks and their curve angle increases with the growth in cutting speed.The presence of machining marks in the lower part of cut surfaces is linked to the decrease in kinetic energy of abrasive particles in AWJ.
After machining by AWJ cutting process, with different cutting speeds, we measured the surface average roughness Ra in three zones (see Figure 4).Table III presents Ra of the all work pieces, in the three zones.It was observed that the sensitivity of measured parameters is directly related to both cutting speed and distance from upper cut edge.With the increase in cutting speed V, a degradation of surface quality defined by analyzed parameters for zone 2 and zone 1 planes was observed (Figures 3 and 5).
Based on the analysis of Table III and Figure 5, it can be stated that the cutting speed V, has a significant influence on the surface roughness of the cut surfaces.Also, the distance from the upper cut surface edge directly affects surface quality and measurement results.In the area where AWJ enters the cut material, decrease in cutting speed by around 20% (from V=250mm/min to 200mm/min) results in drop of roughness parameter by approximately 14% in zone 3. Further decrease of the cutting speed to 150mm/min (decrease by approximately 40%) results in surface roughness parameters dropping by 26% in zone 3. A downward trend can also be seen when analyzing the measurement results taken in the center of cut surfaces.However, this time the drop is more significant by 20% for the medium cutting speed and 40% for the lowest used cutting speed.In the lower part of the studied cut surfaces the sharpest growth in values of measured parameters can be seen for the highest used cutting speed of 250mm/min.For the lower cutting speeds, 150mm/min, the increase in roughness is not as intense when compared to the values observed for the upper, parts of cut surfaces (zone 1).This can be caused by the drop in the kinetic energy of abrasive water jet being less intense for lower cutting speeds.In this part of the surface, biggest increases in surface quality can be achieved by using the lowest researched cutting speed of 150mm/min.Figure 5 shows an excellent surface roughness of the machined surface in the zone 1, and a bad surface quality in the zone 3, for cutting speed of 250mm/min.

A. Process Capability
Process capability Cp and PCI Cpk are considered shortterm potential capability measures for a process.In Six sigma, we want to describe processes quality in terms of sigma because this gives us an easy way to talk about how capable different processes are by using a common mathematical framework.In other words, it allows us to compare, for      V. CONCLUSION In this study, we constructed a quantitative measurement PCI for the qualitative response of the surface roughness.The quantitative measurements are based on the Taguchi's quality function philosophy and PCI concept.It is a ratio deriving from the customer's quality loss with respect to the actual process's quality loss.By employing the proposed PCI, the manufacturers can assess and meet the customer's requirement.The analysis of the machined surface by AWJC process extracted the following conclusions: • Edge quality of the cut surface is a function of cutting speed.
• With decrease in cutting speed, cut surface quality visibly improves, which is most clearly noticeable for the lower part of examined cut surfaces.The difference in the measured value of Ra parameter is about 26% between the highest and lowest researched cutting speeds, in favor of the latter.
• Cut surfaces are characterized by the occurrence of two zones.In the first zone, there are no visible machining marks.In the second one, machining marks can be easily observed.The second zone width and the visibility of machining marks is closely related to the cutting speed.
• Results of this research can have a practical use in determining surface roughness parameters best suited to adequately evaluate cut surfaces of elements machined with the use of AWJ.
• This process will produce conforming products, in zone 1 and zone 2, as long as it remains in statistical control.
• The process capability report for Ra in zone 3, gives a bad or not adequate process in this zone, So, a new process must be chosen.

Fig. 3 .
Fig. 3. Photograph of machined surface after AWJ Cutting (a) Good surface at low cutting speed, (b) Coarse surface at high cutting speed.

Fig. 4 .
Fig. 4.Measurement zones of Ra of the machined surface.

Fig. 7 .
Fig. 7.Process capability report for Ra in zone 2 of the cut surface.

Fig. 8 .
Fig. 8.Process capability report for Ra in zone 3 of the cut surface.

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