The work pieces used in the experiments were as-received 0.8 mm thick AISI316L stainless sheets (0₂₂Cr₁₇Ni₁₂Mo₂). Laser cutting experiments were conducted using a 1 kW continuous wave (cw) IPG YLR-1000-SM ytterbium single-mode fiber laser with 1.07 μm wavelength, a TEM00 beam intensity distribution, and a 14 μm delivery fiber core diameter. The beam has an M2 of 1.1. After the delivery optical fiber, the laser beam was collimated to a 3 mm diameter and focused using a lens of 7.5 inch focal length. The laser beam spot size at focus was measured to be 62 μm. During laser cutting experiments the laser power was varied between 800 and 1000 W and the cutting speed between 10 and 30 mm/s. Focal position was varied between 5 mm below the work piece surface, and 13 mm above the surface.

A Practice laser cutting head with a coaxial conical nozzle and a 0.8 mm exit hole diameter was used. The nozzle standoff from the work piece was varied between 1 and 2 mm. The work piece was placed on a CNC x-y table below the stationary laser beam as shown in Figure 2. Ar gas was used with the regulator gas pressure set between 1.0 and 2.0 bar. The laser cut samples were analyzed by using an optical microscopy.

There is a coaxial conical nozzle and a 0.8 mm exit hole diameter inside normal cutting head. Normal nozzle does not have a throat, while supersonic nozzle should have a throat near the end of gas outlet. So the supersonic nozzle was modified from normal cutting nozzle. There is a chamfer at the end of its exit hole which could be shown in Figure 3. The diameter dc is 1.76 mm, and diameter do is 2.26 mm and LO is 2.0 mm.

There are four controlling factors in this optimization algorithm experiment. Table 1 shows their levels in details used in experimentation.

Table 2 shows the standard L4³ test schedule which was used in laser cutting with normal nozzle as well as supersonic nozzle.

In this optimization algorithm, roughness, which could be measured by using a LSM 700 3D Laser Scanning Microscope on the cutting section of each sample, is considered as the index of evaluation of the analysis by synthesis. According to specific circumstance, the calculation formula shows below.

In Formula (1), i stands for test piece number; T_i stands for roughness; T_max stands for the maximum roughness; T_min stands for the minimize roughness; K_i stands for synthesize analysis score of each sample.

Range analysis can be used to calculate the range R, using mathematical statistics to work out, in each collar of orthogonal table; and the primary and secondary relationship of every factor could be based on its value. According to the value of the range, people can look for reasonable combining parameters of fiber cutting machine. The calculation formula shows below.

In Formula (2), subscript j stands for level of the optimization algorithm; k stands for impacting factor of the optimization algorithm. ΔR equals to the Maximum among I, II, III in K collar minus the Minimum among I, II, III in K collar inside Table 3.

(1) Analyzing datum inside Table 2, the 8th test sample seems the best one, to which its level combing is A₃B₂C₁D₃; the 6th test sample seems the worst one, to which its level combing is A₂B₃C₁D₂.

(2) The primary and secondary relationship of 4 factors in Table 3 and Figure 4 shows their rank order: D → B → A → C. Factor D could be found that its impact dominated among the four factors. A, B and C factors’ effect seems that there was so little difference between them.

(1) Analyzing datum inside Table 4, the 2th test sample seems the best one, to which its level combing is A₁B₂C₂D₂; the 7th test sample seems the worst one, to which its level combing is A₃B₁C₃D₂. But, its score can compare with average score under the condition of using 0.8 mm normal nozzle.

(2) The primary and secondary relationship of 4 factors in Table 5 and Figure 5 shows their rank order: A → B → C → D. Factor A could be found that its impact dominated among the four factors. B, C factors’ effect seems that there was so little difference between them. Factor D’s effect seems stable and inconspicuous under the condition of using supersonic nozzle.