# Fuzzy MCDM Methodology for Analysis of Fibre Laser Cutting Process
## 2 Materials and Methods  
### Experimental Research  
A plate with a thickness of 3 mm made of S235 steel was used for cutting specimens. S235 is low carbon structural steel known for its versatility in different engineering and construction applications. It is used for responsible welded structures without risk of brittle fracture. In addition to good weldability, it also has good cold-forming properties. Structural applications of S235 steel include boiler tanks, oil tanks, storage containers, condensers, rods, pins, levers, holders, etc. The chemical composition and mechanical properties of S235 steel are given in Tables 1 and 2, respectively. The experiment was conducted using a GWEKE fibre laser-cutting machine with the maximal power of 2 kW. During the cutting process, laser power was set at 2 kW, while oxygen with a purity of 99.95% (3.5 grade) was supplied coaxially with a conical nozzle of 1.2 mm hole diameter. The distance between the sheet and the cutting head was set at 1 mm. The Box-Behnken experimental design was adopted to define 13 alternative laser cutting conditions by changing process parameters at three levels: focus position (\(f\) = 1, 1.5, 2 mm), cutting speed (\(v\) = 1.8, 2.7, 3.6 m/min) and oxygen pressure (\(p\) = 0.75, 0.85, 0.95 bar). In previous research, in the context of the application of MCDM in laser cutting, other authors considered different criteria such as kerf width [25; 28; 30], material removal rate [25; 30], surface roughness [26; 28; 30], heat-affected zone [26; 30], machining time [26], kerf taper [28] and emission rate and carbonization [25]. In the present study, the multi-criteria analysis of the fibre laser cutting process considered the following criteria: kerf width on a straight cut, kerf width on a curved cut (radius of 30 mm), surface roughness and surface productivity. Kerf width is a very important kerf geometry characteristic for contour cutting technologies [5]. Also, given that kerf geometry depends on the cut profile [31], and that kerf width is closely related to the dimensional accuracy of cut features (positive or negative), i.e., adjustments of the offsets, kerf widths on a straight and on a curved cut were considered as criteria in the framework of the MCDM. On the other hand, surface roughness is one of the most important quality indicators for assessment of the cut surface, while surface productivity, as an indicator of material removal rate, is an important criterion to manufacturers. It should be noted that cross attachment, which is probably the most important quality criterion, was omitted from the MCDM matrix because no combination of parameters in the experiment resulted in cross formation. Likewise, due to the high negative correlation between linear specific energy, which is a useful indicator of cutting efficiency in terms of eco-friendly technology criteria [32], and surface productivity, this criterion was also omitted. Finally, economical aspects in fibre laser cutting using oxygen were not considered because of negligible influence of resulting assist gas flows, which are considerably lower than in the case of laser fusion cutting. Surface roughness, in terms of average maximum height of the profile (\(R_{z}\)), was measured three times along the cut edge at the middle of the sheet thickness using a Marsurf XR 1 surface roughness tester. The surface roughness parameter \(R_{z}\) is very important in defining cut quality categories according to the ISO 9013 standard [33]. Three measurements of kerf width on a straight cut and three measurements of kerf width on a curved cut were obtained optically using the optical coordinate measuring machine (CMM) DeMeet 443. Surface productivity is one of the productivity indicators in contour cutting, defined as the produced cut surface in unit time. It can be estimated as the product of the sheet thickness and the cutting speed. The investigated experimental space, along with the used measurement systems, are given in Figure 1.