28-12-2012, 06:07 PM
ANALYSIS OF THE HEAT AFFECTED ZONE IN CO2 LASER CUTTING OF STAINLESS STEEL
ANALYSIS OF THE HEAT.pdf (Size: 432.79 KB / Downloads: 32)
ABSTRACT
This paper presents an investigation into the effect of the laser cutting
parameters on the heat affected zone in CO2 laser cutting of AISI 304 stainless
steel. The mathematical model for the heat affected zone was expressed as a
function of the laser cutting parameters such as the laser power, cutting speed,
assist gas pressure and focus position using the artificial neural network. To
obtain experimental database for the artificial neural network training, laser
cutting experiment was planned as per Taguchi’s L27 orthogonal array with three
levels for each of the cutting parameter. Using the 27 experimental data sets, the
artificial neural network was trained with gradient descent with momentum
algorithm and the average absolute percentage error was 2.33%. The testing
accuracy was then verified with 6 extra experimental data sets and the average
predicting error was 6.46%. Statistically assessed as adequate, the artificial
neural network model was then used to investigate the effect of the laser cutting
parameters on the heat affected zone. To analyze the main and interaction effect
of the laser cutting parameters on the heat affected zone, 2-D and 3-D plots were
generated. The analysis revealed that the cutting speed had maximum influence
on the heat affected zone followed by the laser power, focus position and assist
gas pressure. Finally, using the Monte Carlo method the optimal laser cutting
parameter values that minimize the heat affected zone were identified.
Introduction
Among various advanced machining processes, laser cutting is one of the most
widely used thermal-based processes applied for processing a wide variety of materials. In
laser cutting the material is melted or evaporated by focusing the laser beam on the workpiece
surface. It is a high energy-density process that works quickly on complex shapes, is
applicable to any type of material, generates no mechanical stress on the workpiece, reduces
waste, provides ecologically clean technology, and has the ability to do work in the micro
range [1]. Numerous additional advantages such as convenience of operation, high precision,
small heat affected zone (HAZ), minimum deformity, low level of noise, flexibility.
Mathematical modeling
To perform the analysis of the effect of the laser cutting parameters on the width of HAZ, an
accurate mathematical model is needed. Through the mathematical model, any experimental
result of the width of HAZ with any combination of laser cutting parameters can be estimated.
Although the regression models are very promising for practical applications, they are of
limited applicability and reliability in laser cutting modeling. It was shown that artificial neural
networks (ANNs), which are based on matrix-vector multiplications combined with non-linear
(activation) functions, offer better data fitting capability than regression models for complex
processes with many non-linearities and interactions such as CO2 laser cutting [12]. ANNs are
able to learn the key information patterns within multidimensional information domain and can
be used in modeling of complex physical phenomena [13]. Therefore, the width of HAZ
predictive model was developed using ANN on the basis of experimental results.
ANN model design
To establish a mathematical relationship between the width of HAZ and the laser
cutting parameters a multilayer feed forward type ANN was selected [14]. Four neurons at the
input layer (for each of the laser cutting parameter), one neuron at the output layer for
calculating the width HAZ and only one hidden layer were used to define ANN architecture.
Single hidden layer ANN model was chosen, because it is widely reported that this
architecture can be trained to approximate most functions arbitrarily well [15, 16].
Considering the total number of connection weights in the ANN architecture and biases of the
hidden and output neurons, as well as the available number of data for training, it was decided
that the number of hidden neurons should be four (fig. 2).
ANN model validation
There is a variety of statistical performance measures for evaluating the ANN
performance. To test the prediction capability of the developed model, the trained ANN was
initially tested by presenting 27 input data patterns, which were employed for the training
purpose. For each input pattern, the predicted value of the width of HAZ was compared with
the respective experimentally measured value, and the statistical method of absolute
percentage error (APE), as one of the most stringent criteria, was used.
Main effect plots
Initially, the effect of the laser cutting parameters on the width of HAZ was
analyzed by changing one parameter at a time, while keeping all other parameters constant at
center level - level 2 (fig. 3). From fig. 3(a) it can be seen that the increase in the laser power
results in an increase in the width of HAZ for the laser power range from 1.6 to 1.9 kW. This
is due to the increase of thermal energy that is absorbed in material as the laser power
increases. These findings are in agreement with the previously reported results [7, 11].
However, using the laser power above 1.9 kW, the effect of the laser power on the
width of HAZ is opposite, i. e. with an increase in the laser power the width of HAZ tends to
decrease. This trend could be confirmed by similar findings in the literature [11]. These
opposite effects of the laser power could be explained by considering the interaction effect of
the laser power with other parameters. For example, as explained by Mathew et al. [9], there
exists an optimum region of the laser power to cutting speed ratio where the width of HAZ is
minimal. As shown in fig. 3(b) with an increase in the cutting speed the width of HAZ
decreases non-linearly. As the cutting speed is increased, the interaction time between laser
beam and material is reduced and hence the width of HAZ is reduced. Similar conclusions
were made in the earlier studies [7, 9, 11]. From fig. 3© it can be seen that the width of HAZ
decreases linearly with increasing assist gas pressure. This positive influence on the width of
HAZ can be attributed to the efficient cooling effects of the assist gas. In the case of the focus
position, fig. 3(d), suggests that focusing the laser beam deep into the bulk of material is
beneficial for minimizing the width of HAZ. When the focus position is close to the back
surface of the sheet, the kerf width becomes wider so that nitrogen more effectively ejects the
molten material, minimizing heat penetration into the material i. e. minimizing the the HAZ.
Interaction effect plots
In order to determine the interaction effects of the laser cutting parameters on the
width of HAZ, 3-D surface plots were generated considering two parameters at a time, while
the third and fourth parameter were kept constant at center level. Since there are six possible
two-way interactions (P and v, P and p, P and f, v and p, v and f and p and f), six 3-D plots
were generated (fig. 4) using the ANN model.
Figure 4(a) shows the width of HAZ as a function of the laser power and the cutting
speed. The interaction is expressed by the difference between the relatively smaller influence
of the laser power when using high cutting speed, and the big influence of the laser power
when using low cutting speed. As shown in fig. 4(b), the effect of the assist gas pressure on
the width of HAZ is variable and depends on the laser power level.
Generally, an increase in the assist gas pressure reduces the width of HAZ. However,
at low power level, high assist gas pressure increases the width of HAZ. This effect may be
attributed to the role the assist gas plays in heat transport through the thickness of the workpiece
and to the rise in flow turbulence and less effective cooling at high pressure [19]. Focusing the
laser beam up to the half of material thickness (–1.5 mm) and using high laser power results in
high width of HAZ, fig. ©. On the other hand, focusing the laser beam deep into the bulk of
material (2.5 mm) and using high laser power (in the range from 1.9 to 2 kW) decreases the
width of HAZ. This effect is also noticeable when using laser power of 1.6 kW and by shifting
the focus position in positive direction towards the workpiece surface (about –2 mm).