Laser cutting is a fairly new technology that allows metals to be cut with extreme precision. The laser beam is typically 0.2 mm in diameter with a power of 1-10 kW. Depending on the application of the laser cutter a selection of different gases are used in conjunction with the cutting.
When cutting with oxygen, material is burned and vaporized when heated by the laser beam to ignition temperature. The reaction between the oxygen and the metal creates additional energy in the form of heat, supporting the cutting process. These exothermic reactions explain why oxygen can penetrate thick and reflective material; however, they need to be controlled, since violent reactions can occur and not only reduce cut quality but affect workplace safety.
Laser system
Laser cutting for shaping and separating work pieces into parts of desired geometry is one of the most widespread tasks of laser material processing. For certain well defined applications, e.g. cutting metal sheet using CO2-lasers, suppliers of laser cutting machines provide a comprehensive database for process parameters. However, in general new customized cutting processes have to be individually optimized with respect to the targeted geometry and the material to be cut while taking into account the equipment to be used. Since laser cutting processes are often governed by a multitude of parameters, some of which interacting with each other, the optimization of a process is determined by a high degree of complexity. As a consequence, the optimization of an industrial laser process might be a time consuming and cost intensive task, particularly in case simplified methods such as the one-factor at a time approach are applied. In addition, possible interactions of different factors might remain partly unconsidered if such intuitive approaches are chosen. In this paper, we present an optimization study of laser cutting of stainless steel using a design of experiments.
The purpose of the paper is to find a model using DOE based also on the influence of the laser parameters to the output parameter Rz. This study was realized on a laser system Mazak Super Turbo-X 48, Mk2, 1800W, CO2, to cut alloy steel with thickness 3 mm using O2 as assisting gas.
To investigate the influence of roughness a model has been created for dependence upon the cutting parameters. Attempts to measure surface roughness were performed on work-piece of alloy steel. The measured parameter of surface roughness were Rz in μm and was measured on a Mitutoyo SV-C 600 measuring tool and Surfpak-SV 1.500 software for analyse.
Pre-Experimental Test
On the laser cutting process, feed rate is the most important parameter terms of productivity operation (a higher feed rate means a higher economic efficiency). To accurately determine the levels of variation for the factorial experiment was performed an OFAT experiments were only the feed rate v [mm/min] was varied and surface roughness Rz [µm] was measured.
The other parameters of the laser cutting machine were kept constant and their values were set according to recommendations of the machine programming book and laser operators.
No.
64
63
62
65
66
67
v
[mm/min]
800
1500
3000
3400
4000
4500
Rz [µm]
m. top.
10,3
4.98
4,64
4,48
m.top
picture
For the parameters witch remain constant was choosed the followings value:
nozzle size: 1,2 [mm];
nozzle focus NF=-1 [mm];
gap offset NW=1[mm];
assist gas pressure p=0,6 [bar];
laser power P=1400 [W];
laser frequency F=600 [Hz];
laser duty R=100[%].
In table 1 is shown the roughness value by cutting alloy steel, OLC45, with thickness 3mm for different cutting speeds.
Software CurveExpert Professional 1.5.0
Using the CurveExpert Professional 1.5.0 software, fig.2, with input data from table 1 was find some regression functions witch approximate the roughness Rz[μm] variation by cutting speed v[mm/min]. From the proposed functions was selected the regression function with the bigger scor(996 points) and witch aproximate better the roughness Rz[μm] variation by cutting speed v[mm/min]. The choosing model was the Heat Capacity model, fig.3.
Regression function definition for a confidence interval of 95%, it is shown below:
(1)
were:
a = -9.213397808106344E-02
b = 1.544881813181382E-04
c = -1.889470471354003E-08
The obtained function can be used to calculate the roughness value for a specified feed rate or calculate the required feed rate to achieve a certain surface roughness.
To cut alloy steel, OLC45, with thickness 3 mm, the laser sistem manufacturer, Mazak, suggests a maximum cutting speed of v=3000[mm/min] and the other cutting parameters have the values:
nozzle size: 1,2 [mm];
nozzle focus NF=-1 [mm];
gap offset NW=1[mm];
assist gas pressure p=0,6 [bar];
laser power P=1400 [W];
laser frequency F=1000 [Hz];
laser duty R=100[%].
Regression function
The laser sistem manufacturer gives no indication of surface quality achieved and also gives no indication how the cutting parameters should be modified to achieve a surface roughness imposed by the design or by standard classes.
At low feed rate (ex. 800 mm/min) appear melted craters on the cutting surface, in the lower workpiece (tabel 1, sample 64) because there is a surplus of energy. At feed rates between 1500[mm/min] and 4000[mm/min] surface defects disappear and surface roughness decreases as feed rates increases. The minimum value of surface roughness (Rz =4,48 [µm]) is obtain for a feed rate 4088[mm/min].
The experiment shows that at the maximum feed rate suggested from laser system manufacturer v=3000[mm/min] the surface roughness is valoarea Rz=4,98 [µm], and at a feed rate v=4000[mm/min], witch is with 33,33% higher than the maximum speed sugested from laser system manufacturer, the surface roughness has the value Rz=4,48 [µm]. We can see that at this feed rate higher than that indicated by the tool manufacturer(tabel 1, sample 66) cut quality is very good and the surface roughness value has improved by 11,16%.
At feed rates higher that 4000[mm/min] craters appear on the lower part of the workpiece(tabel 1, sample 67), because the laser beam is fluctuanting. Beam inconsistency is due to oxides occuring in the cutting area. These oxides are reflective and redirects photons randomly. Some of them will be directed outside the cutting area and will have no effect on the cut. The other will be in cutting area were creates more enrgy, which create melting material on the bottom edge and instantaneous oxidation with formation of oxides bags.
FACTORIAL DESIGN - DOE
A series of experiments have been performed under the experimental plan to analyze the influence of the process parameters on roughness parameters and to obtain a complex relationship to show roughness variation according to these parameters. Each output value of measured roughness is the average of the five passes of pick-up.
The experimental tests were based on 25 factorial plan. Such experiments or studies are called factorial experiments because we are interested in the effects of two or more factors on the response variable.
In factorial experiments, the data can be split into sub-samples corresponding to each possible combination of levels of the different factors. The effects of the factors can be analyzed by comparing the different sub-samples appropriately. In this section, we introduce some terminology and define a model for factorial experiments.
Experimental data
A
B
C
D
E
Std
Run
presiune
putere
frecventa
randament
viteza
R1
4
1
0.2
1800
500
90
3000
13.947
7
2
0.6
1800
800
90
3000
11.966
10
3
0.2
1500
500
100
3000
7.193
15
4
0.6
1800
800
100
3000
10.451
3
5
0.6
1800
500
90
3000
14,024
21
6
0.6
1500
800
90
3500
6.394
20
7
0.2
1800
500
90
3500
9.786
5
8
0.6
1500
800
90
3000
13.672
26
9
0.2
1500
500
100
3500
6.457
29
10
0.6
1500
800
100
3500
5.386
13
11
0.6
1500
800
100
3000
11.599
6
12
0.2
1500
800
90
3000
8.326
1
13
0.6
1500
500
90
3000
7.373
18
14
0.2
1500
500
90
3500
10.215
30
15
0.2
1500
800
100
3500
7.247
27
16
0.6
1800
500
100
3500
5.549
19
17
0.6
1800
500
90
3500
12.368
31
18
0.6
1800
800
100
3500
09. Jul
25
19
0.6
1500
500
100
3500
6.699
24
20
0.2
1800
800
90
3500
15.296
2
21
0.2
1500
500
90
3000
10.474
16
22
0.2
1800
800
100
3000
18.035
22
23
0.2
1500
800
90
3500
8.446
23
24
0.6
1800
800
90
3500
8.616
12
25
0.2
1800
500
100
3000
15.233
14
26
0.2
1500
800
100
3000
13.044
32
27
0.2
1800
800
100
3500
17.625
11
28
0.6
1800
500
100
3000
9.646
17
29
0.6
1500
500
90
3500
12.095
28
30
0.2
1800
500
100
3500
20.052
9
31
0.6
1500
500
100
3000
12.502
8
32
0.2
1800
800
90
3000
15.53
Analyse of results
For obtaining the mathematical model of the experimental results obtained an experiment 25 plan was performed using the software Design - Expert, fig.4.
Design of Experiments (DOE) techniques for studying the factors that may affect a product or process in order to identify significant factors and optimize designs. The software also expands upon standard methods to provide the proper analysis treatment for interval and right censored data - offering a major breakthrough for reliability-related analyses.
The design of the experiment
To find the model and study the influence factors was used an Factorial model with response Rz and was ignored the 3FI interactions, fig. 5.
Model choice
To analyze the response no transformation it is needed because the ratio of max to min is 3.72299 and it is lower than 10. Introducing the experimental data in the software the recommended regression model that matched the data was the polynomial regression.
Thus, the following equation was derived by the software:
(2)
Applying the ANOVA analyze on the roughness model derived we can obtain the influence of each parameter and the adequacy of the model. The summary of the analyze is shown in table 3.
The data correspond for a degree of reliability P=95%, (α= 0.5) and the value of Fisher test shows that the model is significant and in this case the gas pressure, power and interaction gas pressure with power are significant model terms.
In figure 6 there is represented the influence of the gas pressure p and power P on the surface roughness that are the most significant factors in this sequence.
Analyse of ANOVA
Response 1 Rz
ANOVA for selected factorial model
Source
Sum of
Squares
df
Mean
Square
F
Value
p-value
Prob > F
Model
309,5490559
9
34,39433954
5,397268912
0.0006
significant
A- gas pressure
56,1270125
1
56,1270125
8,807628922
0.0071
significant
B- power
102,2021045
1
102,2021045
16,03787858
0.0006
significant
C- frequency
3,108771125
1
3,108771125
0,487838231
0.4922
D- efficiency
0,000648
1
0,000648
0,000101686
0.9920
E- feed rate
25,97402813
1
25,97402813
4,075926923
0.0558
AB
81,332258
1
81,332258
12,76291604
0.0017
significant
AD
20,4608045
1
20,4608045
3,210774375
0.0869
AE
7,521381125
1
7,521381125
1,180278995
0.2891
CE
12,822048
1
12,822048
2,012076463
0.1701
Residual
140,1959921
22
6,372545097
Cor Total
449,745048
31
The influence of the main factors
The next step was the optimization of factors for a minimum roughness. Also we choose a maximum feed rate and a minimum gas pressure for a better profitability. The optimization result is shown in figure 7 and we see that we get the better desirability for the model at maximum feed rate and minimum gas pressure.
Contour plot of Desirability
The figure 8 shown the point prediction for parameter Rz for the feed rate-gas pressure interaction. As we wish we have a predicted roughness Rz= 6,963 at a feed rate v=3500mm/min and a gas pressure p =0,6 bar.
Point prediction
Conclusions and intentions
The main conclusions drawn from the paper are:
The mathematical model derived from the experiment is significant;
The ANOVA analyze performed assures the reliability of the models indicating a good significance of the factors at a degree of reliability P=95%;
With this model we can find for any value of Rz the right combination of laser machine parameters.
