Modelling and evaluation factors to macrogeometrical quality at abrasive waterjet cutting.
Hloch, Sergej ; Fabian, Stanislav ; Radvanska, Agata 等
Abstract: The paper deals with experimental work and evaluation of
the abrasive waterjet factors influence on stainless steel and cast
aluminium macrogeometrical quality according to full factorial design.
Full factorial design was used as a statistical method to study effects
of independent factors: pressure, abrasive mass flow rate, traverse
feed, J/T abbreviation and depth to impact the taper as a dependent
variable. Obtained multiple inverse logarithmic regression equations
after analysis of variance give the level quality as a function of the
process parameters. Key words: abrasive waterjet, perpendicular
deflection, factor analysis, macrogeometrical evaluation
1. Introduction
Along with the development of technology, the scientists and the
technologists in the field of manufacturing are facing more and more
challenging problems. The demand for the highest accuracy and surface
finish, the challenge to produce critical surfaces and complex shapes
has necessitated for the use of non-traditional machining techniques.
The use of such non-traditional machining techniques is found to be the
best option for manufacturing complex dies and aerospace components with
the required high precision and accuracy. Competition and scientific
progress requires introduction of technologies that perform challenging
claims of modern production in automation field, from economy,
environmental and energy efficiency point of view. Abrasive waterjet
cutting represents all of these claims. The abrasive waterjet cutting
technique is considered to be a flexible tool in the processing of a
wide range of materials without time loss by tool changing and with
minimal risk to occupational safety, health and environment (Radvanska,
2003).
Nowadays the AWJ technology represents cold precise, computer
controlled shape cutting without any strain. These attributes poses this
technology to the position of permanent use in the future, that
represents excellent perspective for expansion in volume sectors,
especially there, where the materials with excellent utility properties
are used. Abrasive waterjet technology can be used for machining
aerospace materials like titanium alloys, composites and carbides.
Abrasive waterjet technology has greatly altered the tooling and
manufacturing industry, resulting in the dramatic improvement in
accuracy, quality, and productivity. Presently, the abrasive waterjet
cutting process is being used for many applications. However, such
techniques are not favorably nourished due to the difficulties and
complexities involved in setting their process factors that enter the
cutting process. The nature of the mechanisms involved in the domain of
AWJ machining is still not well understood but is essential for AWJ
control improvement. In spite of great research effort and good
knowledge in the field of abrasive waterjet machining there is a number
of unexplained factors. One of them is process factors influence on work
piece surface quality.
2. Related and previous works
The number of scientific papers concerning the evaluation of
macrogeometrical features of abrasive waterjet cutting are available
(Hashish, 1984); (Hires, 2004); (Annoni & Monno, 2001); (Annoni et
al., 2001). The objective is to determine the final shape of the kerf walls which is a function of the geometric characteristic of the
abrasive waterjet tool and its quality factors. The taper geometry
directly depends on the shape of the jet, which is not similar to shape
of a fixed geometry tool. In fact, due to hydrodynamic characteristics
of the jet, geometry is significantly influenced by pressure, water
orifice diameter, abrasive parameter and mixing parameter. These factors
influence the qualitative characteristics of the tool, the speed and
kinetic energy of the stream. Through cutting factors, created tool hits
the workpiece the at upper erosion base (Fig. 1), where erosion process
begins (Blagodarny, et al. 2003). These factors create surface as an
area of working movement trajectory of abrasive waterjet. The
specificity of such material machining is in the fact that there are
used particles with more edges; that are oriented at random in the
liquid phase of waterjet (Junkar, 2002). This random position and
different shape of abrasive particles causes irregular removal mechanism
of material. Another specificity of abrasive waterjet tool is that it
consists of three phases (Lebar & Junkar, 2004). The updated model
(Fig. 2) contains new factors--traverse direction and abrasive feeding
direction. The influence of these factors has not been exactly explained
yet. It is assumed that these factors cause the asymmetry roughness
values due to the feeding direction of solid phase, distribution of
abrasive particles in the waterjet, and traverse direction.
[FIGURE 1 OMITTED]
As can be seen from the model of AWJ cutting, one of the
macrogeometry features of AWJ cutting is perpendicular deflection and
kerf. Perpendicular deflection means the constriction of the walls at
the abrasive waterjet cutting. This method of cutting by floppy tool
erodes material that causes the deflections and deformations of the
workpiece. Taper is defined as a difference between the top and the
bottom profile of the cut (Fig.2). Figure 2 displays four common forms
of taper generated by abrasive waterjet. Basic types of the
perpendicular deflection are:
--V-shape deflection--formed if cutting section is wider on upper
erosion base than in lower erosion base. V-shape deflection is formed as
a consequence of stream erosion on the upper zone of the workpiece. Also
rebound of the stream can cause the erosion of the kerf side. At the
top, the taper is formed by high traverse feed cutting, and this
macrogeometrical feature is typical for very thin material as it is
shown on Figure 2, where is the example of V-taper of the kerf on 4 mm
thick stainless steel.
--Reverse taper--such deflection is caused mainly by low traverse
feed.
--Barrel taper--is typical for thick materials (Fig. 2).
--Ideal (zero) taper--can be achieved by specific factor
combination.
[FIGURE 2 OMITTED]
Also, the "combination taper" can be found, where two of
the above mentioned taper types may combine.
The deflection can be caused by following factors:
--Standoff--the distance between the nozzle and the top of the
target material.
--Material properties--mainly hardness, thickness, chemical and
physical composition.
--Traverse feed.
--Quality of the tool, exiting the mixing tube.
--Quality of abrasive and abrasive mass flow rate.
Type and magnitude of the perpendicular deflection is influenced
mainly by material thickness, its hardness or machinability.
Perpendicular deflection and kerf width belongs to the basic
macrogeometrical features of the surface machined by abrasive waterjet
technology. Magnitude of the deflection predetermines the necessity for
the further cut surface treatment and hence total utilisation of the
material. It also determines the size of the material allowance for the
further machining. This raises the total production cost with low
material utilisation with extended of the production process that
decreases its competitiveness. That is why the effort for deflection
phenomenon reduction is highly required.
3. Problem definition
Abrasive water jet machined surfaces exhibit the texture typical
for machining with high energy density beam processing. The surface
quality is superior in the upper region and poor in the lower zone with
pronounced texture marks called striations (Bohacik & Hloch, 2003).
The optimization of abrasive waterjet technology process parameter
has been accelerated because of the need for improvements in surface
quality. Moreover, the process features change drastically with
machining factors entering the abrasive waterjet cutting process. The
elaboration of the mathematical model with process factors (pressure,
abrasive mass flow rate, traverse rate, nozzle diameter, and traverse
direction) and output variables (perpendicular deflection) is a
difficult task.
The taper geometry directly depends on the shape of the jet, which
is not similar to the shape of a fixed geometry tool. In fact, due to
hydrodynamic characteristics of the jet, the geometry is significantly
influenced by pressure, water orifice diameter, abrasive parameter and
mixing parameter. These factors influence the qualitative
characteristics of the tool, the speed, kinetic energy of the stream.
Through cutting parameters, created tool hits the workpiece the at upper
erosion base, where erosion process begins. These facts confirm that
abrasive waterjet cutting is more difficult process and can not be
expressed by classic experimental schemes. Technologic process of
abrasive machining in real objects is in the most of cases very dynamic
and stochastic process. Analytic process identification seems to be
ineffective and of low practical use. By its application, it is not
possible to achieve the completed model of the process--the influence of
certain parameters are neglected, in some of the factors there are not
known the exact values, they are variable in time and most often, the
intuition is applied to determine them (Gombar, 2005).
For such classic experimental design, some routine is needed and it
is not effective from the time point of view. On the other hand, the
mathematical statistical methods (Design of Experiments) enable the
statistic model design outsourcing from the great amount of independent
variables (Fabian & Hloch, 2005).
[FIGURE 3 OMITTED]
4. Problem solution--experimental set up and method
To evaluate the cutting process of abrasive waterjet, the influence
of process parameters (pressure, traverse speed, abrasive mass flow rate
and J/T abbreviation) on the quality of abrasive waterjet cutting
surfaces is analyzed by application of design of experiments. The
analysis of variance is performed in order to identify which selected
process parameters and their interaction variables influence
significantly the cutting quality of kerf and taper (Fabian & Hloch,
2005). In order to investigate the influence of abrasive waterjet
process factors on taper--macrogeometrical cutting quality, full
factorial design for five independent variables has been designed. Full
factorial analysis was used to obtain the combination of values that can
optimize the response, which allows one to design a minimal number of
experimental runs (Gombar, 2005), (Blagodarny, et al. 2003).
y = f([D.sub.v]/[D.sub.a], [m.sub.a], p, v, h) (1)
Among the many process variables that influence the cutting
results, four have been selected and considered as factors in the
experimental phase. Five factors--independent variables submitted for
the analysis in the factorial design of each constituent at levels [-1;
+1] are listed in the Table 1.
The experimental cuts have been performed in a random sequence, in
order to reduce the effect of any possible error. A [2.sup.5] full
factorial analysis has been used with 3 replicates at the centre point,
leading to the total number of 32 experiments. Considering the four
levels of the [x.sub.1], [x.sub.2], [x.sub.3], [x.sub.4], [x.sub.5] and
variables -1 and 1, the designed matrix is 32-obsevations for dependent
variable perpendicular deflection. The graphical interpretations of
factorial design are illustrated in the Figure 3, 4. Samples series A
have been made with independent variable--factor J/T at high level
0.14/1.2 (+1) and samples series B at lowest level of J/T abbreviation.
The behavior of the presented system can be described by the nonlinear polynomial logarithmic equation (2), which includes all interaction
terms regardless of their significance:
log y = [b.sub.0] log [x.sub.0] + [b.sub.1] log [x.sub.1] [b.sub.2]
log [x.sub.2] [b.sub.3] log [x.sub.3] [b.sub.4] log [x.sub.4] [b.sub.5]
log [x.sub.5] (2)
Where [??] is the average perpendicular deflection response,
[x.sub.1], [x.sub.2], [x.sub.3], [x.sub.4], [x.sub.5], are independent
variables, b0 is coefficient constant for offset term, [b.sub.1],
[b.sub.2], [b.sub.3], [b.sub.4], [b.sub.5], are coefficients constant
for linear effects and [b.sub.12], [b.sub.21], [b.sub.31],...,
[b.sub.12345] are coefficients constant for interactions effects. The
model evaluates the effect of each independent variable to a response
y--perpendicular deflection. The experiments were carried out based on
the analysis using Statistica 7.0 and Matlab to estimate the responses
of the dependent variable.
4.1 Experimental set up
A two dimensional abrasive waterjet machine Wating, was used in
this work with following specification: work table x-axis 2000 mm,
y-axis 3000 mm, z-axis discrete motion, with maximum traverse rate 250
mm x [min.sup.-1]. The high-pressure intensifier pump the Ingersoll-Rand
Streamline model was used with maximum pressure of 380 MPa. As a cutting
head an AutolineTM from Ingersoll-Rand has been used. The mechanical
properties and chemical composition of the workpiece with austenitic composition is shown in Table 2. The properties of each sample are:
length 35 mm, width 8 mm, and height 10 mm. Abrasive machining
conditions used in this study are listed in the Table 2.
4.2 Samples preparation
According to experimental methodology of graphic presentation (Fig.
2,3) each cut has been replicated three times; yielding total of 48
cuts. For investigation of the influence of the traverse rate the
samples created for this purpose have been cut in two directions
+180[degrees] and -180[degrees] (Fig. 4). Traverse direction has been
added to the experiment to explain the significance with connection of
the selected factors. As a target material stainless steel AISI 304 has
been used for experimental cutting of the samples.
The stainless steel has been chosen as a target material for few
reasons: material is very attractive, because of its resistance to
corrosion; it can provide significant value creation for the end user
when considering all of the important attributes and how they help to
bring reliability, performance, and safety to industry and the consumer;
the material average annual increase in use is almost 7%, it is well
above aluminium and aluminium alloys [12]; stainless exhibits a
remarkable range of mechanical properties.
[FIGURE 4 OMITTED]
4.3 Measurement procedure
A universal microscope UMM 200 CARL ZEISS JENA has been used for
measurement of perpendicular deflection. For the measurement of the kerf
width and has been used a digital offset centreline digimatic callipers Mitutoyo 573-102-10 to calculate the kerf with 0.01 mm measurement
precision. The measurement procedure consisted of measurements of
variable dependents: width of upper erosion base yueb and width of lower
erosion base [y.sub.1eb].
[FIGURE 5 OMITTED]
Quadratic means of upper and lower erosion base width, that has
been found out, by measuring at five equidistant points along the kerfs
are shown in the Fig. 4. Marginal zones have been excluded from the
evaluation process. Experimental graphic dependence describes the taper
characteristics of 10 mm thick stainless steel.
5. Statistical evaluation and regression diagnostics
The quantitative description of the conditions effects on
perpendicular deflection has been performed. Response surface
methodology is an empirical modeling technique used to evaluate the
relationship between a set of controllable experimental
factors--independent variables and observed results--dependent variable
[lambda]. The experimental results were analyzed using the analysis of
variance. The normality of experimental measured data has been tested
according to Shapiro-Wilkson parametrical test criteria for its good
power properties in comparison with a wide range of alternative tests.
Shapiro-Wilkson test proved that 31 out of 32 experiments (repeated
measurements) did not exceed the critical value W[alpha] = 0.788 for n =
6 and [alpha] = 0.05, respectively probability value p is out of range,
as preferred significance level [alpha], hence we can accept the null
hypothesis of normal distribution measurements repeatability. 31 out of
32 repeated measurements have normal Gauss distribution what enables to
use parametrical Grubbs test of measurement remoteness. For the rest of
experiments it was necessary to apply the Dixon's non-parametric
test of remote measurements presence. The equation 3 shows the
correlation matrix and the estimation of regression function coefficient
vector:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The regression coefficients and equations obtained from analysis of
variance gives the level of significance of variable parameters tested
according to Student's t-test. The critical value then is:
[t.sub.1-[alpha]/2(f) = [t.sub.0.0975] (f = 26) = 2.0027 (4)
Obtained regression coefficients that showed no statistical
significance has been rejected from the following evaluation. Total
regression variability size of dependent variable y is expressed by
following equation:
[s.sup.2.sub.y] = [n.summation over (i=1)][([y.sub.i] -
[bar.y]).sup.2] = 0.0154 (5)
5.1 Regression diagnostics
Testing of model adequacy has been done by Fisher-Snedecor; F-test,
where testing criterion F = 3.3266 and critical value is
[F.sub.1-[alpha]([f.sub.1],[f.sub.2]) =
[F.sub.0.95]([f.sub.1]=31,[f.sub.2]=27) = 1.89561.
Since F > [F.sub.1-[alpha]([f.sub.1],[f.sub.2]), we can reject
[H.sub.0] hypothesis, hence regression function describes variability of
measured values. The regression equation is designed adequate. Figure 7
displays the residual values that show heteroskedasticity, disordered
set of values, that means that during the measurement of dependent
variable, has not been observed.
[FIGURE 7 OMITTED]
Figure 8 shows the normal probability plot of residual values.
Computed reliability value for Shapiro-Wilkson test of normality p =
0.53835 and value of W criteria is W = 0.97139. According to inequality
[W.sub.[alpha]] [greater than or equal to] W, we can accept [H.sub.0]
hypothesis of residual values probability.
[FIGURE 8 OMITTED]
The regression equation obtained from analysis of variance gives
the level of average roughness as a function of independent variables:
J/T abbreviation, abrasive mass flow rate, pressure, traverse feed, and
material thickness. All terms regarding their significance are included
in the following inverse logarithmic equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where [??] is the response, that is kerf width [[micro]m] and v is
traverse feed, h--thickness of material, [m.sub.a]--abrasive mass flow
rate, p--pressure, [D.sub.v]/[D.sub.A]--J/T abbreviation are evaluated
independent variables (Tab.1). According to the equation (4) factors
[x.sub.5], [x.sub.4], have positive effect and factors [x.sub.2],
[x.sub.3], [x.sub.1] have negative effect. Considering their negative
effect, factors [x.sub.2], [x.sub.3], [x.sub.1] are situated on the
denominator of the equation (5). On the other hand, the kerf width with
the increase of number values of the independent variables having
negative effects. These results can be hereinafter interpreted in the
Pareto Chart, which graphically displays the magnitudes of the effects
from the results obtained.
The effects are sorted from largest to smallest. The Pareto chart
shows that material thickness is an important factor affecting the
average roughness. The significance of independent variables is
interpreted in the Pareto chart of standardized effects for variable Ra.
Fig. 9 graphically displays the influence magnitudes of the effects,
which are sorted from largest to smallest, from obtained results. The
most important factors affecting the stainless steel experimental
material kerf with--macrogeometrical quality are [x.sub.5]--material
thickness, [x.sub.3]--pressure [x.sub.1]--J/T abbreviation,
[x.sub.4]--traverse speed and [x.sub.2]--abrasive mass flow rate which
is closely under the critical value 2.0027. From that reason the
mentioned non significance evaluated independent variable--abrasive mass
flow rate was included to the final equation (5).
The model (5) has been checked by several criteria. The fit of the
model has been expressed by the coefficient of determination [R.sup.2] =
0.8134 which was found to be for equation indicating 81.34% for the
model of the variability in the response can be explained by the models.
The value also indicates that only 18.66% of the total variation is not
explained by the model. This shows that equation is a model suitable for
describing the response of the average roughness. The adjusted
determination coefficient [R.sub.adj] = 0.88134 is high to advocate the
high significance of the model. A higher value of the correlation
coefficient R = 85.32% justifies a good correlation among the
independent variables. This indicates good agreement between the
experimental and predicted values of average roughness. Statistical
significance of correlation coefficient [r.sub.y,x1,x2,x3,x4,x5] =
96.23%.
Regression equation has been tested by the Fisher's
statistical test for analysis of variance. Statistical testing of the
model has been tested by the Fisher's statistical test for analysis
of variance. The F value is the ratio of the mean square due to
regression to the mean square due to the real error. Generally, the
calculated F-value equation (3) exceeds the critical value
[F.sub.1-[alpha]]([f.sub.1], [f.sub.2] =
[F.sub.0.95]([f.sub.1]=6,[f.sub.2]=25) = 3.8348418.
F = [y.sup.2]x1,x2,x3,x4,x5/1 - [y.sup.2] x1,x2,x3,x4,x5 x N - q -
1/q = 52.198 (7)
6 Results and discussion
The significance of independent variables is interpreted in the
charts (Fig. 10) that show the factors significance in percent
expression of regression coefficients. As can be seen, the most
important factors affecting the kerf width--the macro geometrical
quality feature, from controllable factors is pressure [x.sub.3] with
percent portion of 13%, on the second position of factor significance is
J/T abbreviation with percent portion of 12%, traverse speed--[x.sub.3]
(11%) and abrasive mass flow rate (7%). As can be seen from the figure
the most significant factor that affects the kerf width and the
perpendicular deflection is material thickness. This factor is
uncontrollable but it is important to know the influence of that
independent variable in connection with the controllable factor that
enters the abrasive waterjet machining process. The increase in the
number of impacting particles at lower traverse rates contributes to the
improved surface finish. Increasing the pump pressure the average
roughness improves, but the factor is not significant according to
Figure 8.
The material thickness is also important in context with the
mechanical properties of the target material. The harder the material is
the significance of the material thickness grows up. This statement
agrees with additional experiment results where the cast aluminium has
been used as a target material. At the experiment where the target
material stainless steel has been used, the pressure as an evaluated
factor has been more significant because the pressure is responsible for
the kinetic energy of the abrasive waterjet. The right part of the
Figure 10 shows percent significance of evaluated factors and
significance of the absolute member. As can be seen, the significance of
absolute member is less than the sum of the all independent variables.
It can be assumed that absolute member significance, is 42% in percent,
is high due to neglecting the material properties influence. This
suggests that new experiments will be needed. The following figure
displays the Pareto charts of the factors significance in upper erosion
base and the lower erosion base. The left side of the picture shows the
influence of the abrasive waterjet factors to kerf width or the Pareto
chart characterising the AWJ tool that hits the upper surface of the
target material. As can be seen, the most significant factor that
influences the kerf width is J/T abbreviation, the second is traverse
feed and pressure. Abrasive mass flow rate is not significant in such
case. The right part of the Figure 11 shows the Pareto chart of the
factor significance in depth of 10 mm. As can be seen, the behaviour of
the evaluated independent variables has changed dramatically. The most
significant factor affecting the kerf in the depth of 10 mm is pressure,
traverse speed and abrasive mass flow rate. The significance of J/T
abbreviation is weaker than the critical value. The factors significance
changes due to absorption of the kinetic energy of the waterjet by the
target material. That is why the significance of the pressure, traverse
feed and abrasive mass flow rate has increased.
The Figure 12 closely describes the abrasive waterjet factors
behaviour as the target material thickness changes. As can be seen from
the Figure 12 the significance of the pressure, abrasive mass flow rate
and traverse speed rises as the depth of the target material increases.
[FIGURE 12 OMITTED]
The following Figure 13 shows plot of marginal means and
confidential limits (95%), for independent variables pressure, traverse
feed and material thickness.
[FIGURE 13 OMITTED]
Marginal means plots show predicted macrogeometrical quality
feature kerf width as a function of independent variable--factors.
Pressure is situated on the upper x axis, material thickness is situated
on the lower x axis and traverse speed is expressed as a line pattern
with the low factor level (on graph in blue colour) and high factor
level is expressed by the red line pattern. As can be seen from the
plots of marginal means the most important factor affecting the kerf
width is material thickness what is evident on the right side of the
Figure 13. Also the significance of the traverse feed increases as the
thickness of the machined material rises. At the upper erosion base,
where machining by abrasive waterjet begins its action, the pressure is
almost constant as can be seen on the left side of the Figure 13. An
increase of the pressure, in general, improves surface quality.
Increasing the pressure causes the increase of the abrasive water jet
kinetic energy [10]. From fluid mechanics point of view, the primary
factor in the hydroabrasive cutting process is the water stream
velocity, and it strongly depends on pressure and diameter of the
diamond orifice and diameter of the focusing tube. The following Figure
14 shows plots of marginal means for independent variables pressure,
abrasive mass flow rate and traverse feed. Pressure is situated on upper
x axis, abrasive mass flow rate is situated on lower x axis and traverse
speed is expressed as a line pattern with the low factor level (on graph
in blue colour) and high factor level is expressed by red line pattern.
[FIGURE 14 OMITTED]
The traverse rate is more sensitive factor then abrasive mass flow
rate. With the speed increase of abrasive cutting head the kerf width
increase. The lower the speed is, the longer abrasive waterjet remains
at the upper erosion base location, thus having prolonged period to
erode the workpiece.
The following section deals with the influence of the selected
factors to perpendicular deflection evaluated through factor analysis
where four independent variables were submitted--J/T abbreviation,
pressure, abrasive mass flow rate and traverse speed. The following
figure displays the Pareto chart of the factors significance on
perpendicular deflection at abrasive waterjet machining of the
austenitic stainless steel. As can be seen, the dominating factor that
causes the higher deflection is pressure. Lower pressure of the pump
causes the low kinetic energy of the final tool that enters the cutting
process. The kinetic energy is absorbed by the material and hence the
perpendicular deflection rises. The second significant factor is ratio
of the nozzle and the focusing tube diameters--J/T abbreviation. This
factor relates with size and active length of cutting tool. The impact
of J/T abbreviation is shown on Figure 15. The important fact is that
J/T abbreviation with level -1 (0.1/1) creates more coherent stream.
Therefore the surface quality improves with higher pressure and smaller
diameter because an abrasive water jet disposes higher energy
concentrated to smaller area of the workpiece.
Experimental data have been tested according to Cochran's
test. The regression coefficients and equations obtained from the
analysis of variance give the level of significance of variable
parameters tested according to Student's t-test. All regression
coefficients show statistical significance (Fig. 15). The model,
expressed by following equation, was generated by multiple nonlinear
regressions of the data and is a function of the significant variables
(eq.8):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
Where: y[lambda] is the response--perpendicular deflection.
Following Figure 16 shows profiles of predicted values and desirability.
[FIGURE 16 OMITTED]
As can be seen in Figure 16 the perpendicular deflection increases
as the diameter of focusing tube and traverse feed increase and with
decreasing of abrasive mass flow rate and pressure. Graphical
interpretations of the statistically evaluated results and their
significance are on following Figure 17 and Figure 18 in percent
expression.
[FIGURE 17 OMITTED]
The traverse rate is more sensitive factor in comparison with
abrasive mass flow rate. With the increasing speed of abrasive cutting
head the taper increases. The smaller speed is, the abrasive waterjet
remains for longer time at the upper erosion base location, and then the
stream can erode the work piece for longer period. Material thickness is
the most important factor. Material thickness as a factor in not
controllable, but it is necessary to know its function.
[FIGURE 18 OMITTED]
Experimental graphic dependence describes the taper characteristics
of 10 mm thick stainless steel. In the graph, the influence of J/T
abbreviation as a process factor is evident. The smaller the diameter of
water orifice is, the higher is the speed of water jet. This improves
the macrogeometrical quality characteristics of cutting surface. The
diameter of cutting tool is crucial. This phenomenon is connected to
energetic potential of the stream. These characteristics are changing
dramatically depending on the depth (Fig. 18), consequently on kinetic
energy absorption by workpiece due to hydrodynamic friction of abrasive
waterjet. Figure 17 and 18 shows the percent proportion derived from
regression coefficient of examined process parameters influence in upper
erosion base and lower erosion base by factorial analysis. With an
increase in the abrasive mass flow rate, the quality of surface--taper
characteristics improves. But according to planned level conditions of
this factor the range of abrasive mass flow rate is 300 g.[min.sup.-1]
up to 500 g.[min.sup.-1]. From this reason, high abrasive mass flow
rates influence the perpendicular deflection is less significant. As the
abrasive mass flow rate increases, the speed of the abrasive water jet
decreases. The higher the mass-flow rate is, the higher is the number of
abrasive particles that must share the kinetic energy of the water jet.
It is assumed that at low values of the factor [x.sub.2], the particles
do not collide one with another. They hit the material with a maximum
velocity and maximum possible kinetic energy. The final result is that
the abrasive mass flow rate is of weaker influence in comparison with
hydrodynamics factors, pressure and J/T abbreviation.
In additional experiments two factors--pressure and traverse feed
have been followed. In Figure 19 and 20 the dependence of the two
factors on perpendicular deflection is shown at cutting the 10, 15 and
20 mm thick stainless steel. It is apparent that the influence of the
pressure is linear in the pressure range 310 to 350 MPa, as it is shown
on Figure 20.
[FIGURE 19 OMITTED]
[FIGURE 20 OMITTED]
7. Conclusion
The analysis has pointed out that variable independent factors
influence the morphology of the cutting surface in terms of macro
cutting quality--kerf width and perpendicular deflection of the target
material--stainless steel AISI 304 and cast aluminium. It has been found
that the influence of selected factors is variable related to different
depths. Obtained inverse logarithmic regression equations after analysis
of variance give the level quality as a function of the process factors.
Upon ascertainment by full factorial design can be pronounced following
conclusions. With an increase in the abrasive mass flow rate, the
quality of surface--taper characteristics improves. Material thickness
and traverse rate and their interaction as have been proved previously
have most significant effect to the perpendicular deflection. The most
important factors influencing the cutting quality of aluminium are
pressure configuration of water orifice and focusing tube diameters and
abrasive mass flow rate. The different influence of evaluated abrasive
waterjet factors in upper erosion base where cutting process begins and
on lower erosion base has been found. The most predominate factor in
shallow depths of workpiece is J/T abbreviation and traverse feed.
Increasing the material thickness the factor influence is changing. The
factors significance changes due to absorption of the kinetic energy of
the waterjet stream by the target material. That is why the significance
of the pressure, traverse feed and abrasive mass flow rate enhanced.
Increasing the feed rate the taper will be V-shaped type and in lower
traverse feed the taper will be an inverse V-shaped. At the cutting of
the cast aluminium it has been observed that dominant parameters
influencing macrogeometrical quality are hydrodynamic factors--pressure
and J/T abbreviation. These factors directly determine quality of the
tool--high-speed waterjet. This means that the quality of AWJ tool
influences the kerf. The more focused the nozzle is the weaker the taper
will be exhibited.
8. References
Annoni, M., Monno M. A lower limit for the feed rate in AWJ
precision machining. In. BHR Group 2000 Jetting Technology, p. 285-295,
ISBN 1 86058 253 2.
Blagodarny, V.; Hloch, S. & Ragan, E, Design of experiments of
stainless steel abrasive waterjet macrogeometrical cutting quality. In:
Mechanical Engineering Technologies. vol. 11, no. 4/72 (2004), p.
116-119, 1310-3946.
Blagodarny, V.; Hloch, S. & Kmec, J. Planovanie experimentov
vplyvu technologickych parametrov vodneho luca na kvalitu obrobenej
plochy, 5. Vedecka konferencia s medzinarodnou ucastou: Informatika a
algoritmy 2002, ISBN 80-88941-21-0,
Chen, F.L.; Siores, E. The effect of cutting jet variation on
striation formation in abrasive water jet cutting. International Journal
of Machine Tools & Manufacture 41 (2001) 1479-1486.
Coray, P., S.; Jurisevic, B.; Junkar, M. & Heiniger, K. C.
Measurements on 5:1 Scale Abrasive Water Jet Cutting Head Models. In:
Proceedings of the 6th International Conference on Management of
Innovative Technologies MIT'2003--post-conference edition.
Ljubljana: University of Ljubljana. 2003. s. 87-102.
Fabian, S.; Hloch, S. Prispevok k technickym moznostiam zvysovania
kvality produktov technologie vysokorychlostneho hydroabrazivneho prudu.
In: AT&P journal. 1335-2237 : XII, 2005. 66-68. (strany 66-68, 2005)
Gombar M., Ing. Tvorba statistickeho modelu drsnosti obrobeneho
povrchu s vyuzitim Matlab. In Vyrobne inzinierstvo. (s. 14-17) 2006.
Hashish, M. Machining of Hard Materials with Abrasive-Suspension
Jets, Proceedings of the 9th American Waterjet Conference, (Dearbom,
Michigan, August 23-26, 1997), pp. 267-280.
Hires, O. The study of cutting surfaces quality. In: Funkcne
povrchy 2004: Trencin, 27.-28. maj 2004. Trencin: Trencianska
univerzita, 2004. ISBN 80-8075-021-1.
Hloch, S.; Fabian, S.; & Rimar, M.: Design of Experiments
Applied on Abrasive Waterjet Factors Sensitivity Identification. In:
Nonconventional Technologies Review. 1454-3087 2005. 119-126.
Hloch, S: Evaluation of abrasive waterjet factors influencing the
surface quality. In: Transactions of the Universities of Kosice. c. 2
(2005), s. 12-21. ISSN 1335-2334.
Jurisevic, B.; Coray, P. S.; Heiniger, K. C., & Junkar, M. Tool
Formation Process in Abrasive Water Jet Machining. In: Proc. of the 6th
International Conference on Management of Innovative Technologies
MIT'2003 University of Ljubljana. 2003.
Kramar, D.; Vengust, I. & Butala, P. Computer Numerical Control for Abrasive Waterjet Cutting Process Identification and Modeling. In:
Proceedings of the 6th International Conference on Management of
Innovative Technologies MIT'2003--post-conference edition.
Ljubljana: University of Ljubljana. 2003. s. 157-163.
Radvanska, A. FMEA risk assessment of abrasive waterjet cutting.
In. proc. New trends in the operation of production technology 2003. FVT TU Kosice with the seat in Presov, Otto, A. Stainless Steel--A Material
for Architectural Visions, Krupp
Thyssen Nirosta GmbH, Krefeld, Germany, Presentation on the
occasion of the Symposium Stainless Steel in Architecture on 15th June
2000 in Berlin organized by Euro Inox Brussels (Belgium) and
Informationsstelle Edelstahl Rostfrei, Dusseldorf (Germany).
Valicek, J.; Madr, V.; Drzdik, M.; Lupt k, M.; & Slivecka, L.
Method of the determination of superposition relation of changes in
surface geometry to mechanical parameters of material due to corrosion.
In. Acta Mechanica Slovaca. 3-A/2005. ISSN 1335-2393. p.171-176.
ValiSek, J.; Sodomka, L.; M dr, V.; Lupt k, M. & SliveSka, L.
Nondestructive testing with direct evaluation of changes in
physical-mathematical properties of materials. In. proc. Defektoskopie
2005. Brno University of Technology. 2005 ISBN 80-214-3053-2, p.
245-250.
Vie, G. Cutting hard rock with abrasive-entrained waterjet at
moderate Pressures, Fluidyne Corporation, Auburn, Washington 98002,
Weule, H., Suchy, U. Mixing head for abrasive-water-jet cutting
with an annular driving jet. Jetting technology, BHR group limited,
Cromwell Press, Trowbridge, Wiltshire, UK 2000, ISBN 1-86058-253-2,
Wilkins, Ch. Waterjet cutting: The other "Non
traditional" process. EDM Today, September/October 2003 Issue,
Yanaida, K. Flow Characteristics of Water Jets. In: Coles N G,
Barrall J S (eds.)1974 Proceedings of the 2nd International Symposium of
Jet Cutting Technology, BHRA
This Publication has to be referred as: Hloch, S.; Fabian, S.;
Radvanska, A.; Gombar, M. & Valicek, J.(2006). Modelling and
evaluation factors to macrogeometrical quality at abrasive waterjet
cutting, Chapter 22 in DAAAM International Scientific Book 2006, B.
Katalinic (Ed.), Published by DAAAM International, ISBN 3-901509-47-X,
ISSN 1726-9687, Vienna, Austria
DOI: 10.2507/daaam.scibook.2006.22
Authors' data: Ing., PhD. Hloch S.[ergej] *, doc. Ing. PhD.
Fabian S.[tanislav] *, Ing., PhD. Radvanska A.[gata] *, Ing. Gombar
M.[iroslav] **, Ing. Ph.D. Valicek J.[an] ***, * Faculty of
Manufacturing Technologies of Kosice, Slovak Republic, ** Department of
Natural Sciences and Technical Disciplines, University of Presov, Slovak
Republic, *** Institute of Physics, Mining and Geological Faculty,
VSB-Technical University of Ostrava, 708 33, Czech Republic,
hloch.sergej@fvt.sk, fabian.stanislav@fvt.sk, radvanska.agata@fvt.sk,
mirek@unipo.sk, valicek.jan@seznam.cz
Table 1. Coded independent variables at defined levels
Factors Factor level
N Var. Terminology and dimension -1 +1
1 [x.sub.1] J/T abbreviation [mm] 0.2/1 0.14/1.2
2 [x.sub.2] Abrasive mass flow rate 200 500
[g.[min.sup.-1]]
3 [x.sub.3] Pressure [MPa] 200 350
4 [x.sub.4] Traverse feed [mm.[min.sup.-1]] 70 120
5 [x.sub.5] Thickness [mm] 1 9
Table 2. Experimental set up
Variable factors Values Constant factors Values
Pressure p [MPa] 200/350 Standoff 3 mm
Traverse rate v 70/120 Abrasive material Barton Garnet
[mm.[min.sup.-1]] Mesh 80
J/T abbreviation 0.14/1.2; Cutting head Autoline [TM]
0.1/1
Abrasive mass 200/500 Material thickness 10 mm
flow rate
[g.[min.sup.-1]]
Target material: Stainless steel AISI 304--Chemical Properties and
Physical Aspects
% C max % Mn max % P max % S max % Si max % Cr max % Ni
0.07 2.0 0.045 0.03 1 18/20 8/10
Tensile Slip Limit Strength
Strength Rm Rp 0,2% Tensibility max.
[N.[mm.sup.-2]] [N.[mm.sup.-2]] min. % HRB Structure
540/680 195 45 88 austenitic
System characteristics of Ingersoll Rand Streamline Pump
Double
Intensifier type effect Water pressure (max) 380 MPa
Intensifier power 50 kW Intensification ratio 20:01
Oil pressure (max) 20 MPa Accumulator volume 2 1
Number of cuts: 48 (16 cuts Number of measurements: 576
with 3 replications)
Fig. 9. Pareto chart displaying the depth as the most sufficient
factor that affects the perpendicular deflection at waterjet cutting
h [mm] 16,87719
p [MPa] 3,97979
Dv/Da [mm/mm] 3,40101
v [mm.[min.sup.-1]] 3,13541
[m.sub.a][g.[m.sup.-1] 1,90729
Note: Table made from bar graph.
Fig. 10. Percent evaluation of selected factors influence on
perpendicular deflection
h [mm] 57%
Dv/Da [mm/mm] 12%
[m.sub.a][g.[min.sup.-1]] 7%
p [Mpa] 13%
v[mm.[min.sup.-1]] 11%
[m.sub.a][g.[min.sup.-1]] 4%
p [Mpa] 8%
v[mm.[min.sup.-1]] 6%
h [mm] 33%
abs.clen 42%
Dv/Da [mm/mm] 7%
Note: Table made from pie chart.
Fig. 11 Pareto charts show that depth was found to be the most
significant factor that affects the perpendicular deflection at
waterjet
(1)J/T abbreviation [mm] -19,0739
(4)Traverse feed [mm.[[min.sup.-1]] 5,186621
(3)Pressure [MPa] -3,0917
(2) Abrasive mass flow rate (g.[min.sup.-1]] -1,94287
(3)Pressure [MPa] -8,59285
(4)Traverse feed [mm.[[min.sup.-1]] 5,591991
(2) Abrasive mass flow rate (g.[min.sup.-1]] -3,92629
(1)J/T abbreviation [mm] -,290836
Note: Table made from bar graph.
Fig. 15. Pareto chart and graph with percent portion of the factors
influence on perpendicular deflection
(3)Pressure [MPa] -6,3444
(1)J/T abbreviation [mm] 6,162503
(4)Traverse feed [mm.[[min.sup.-1]] 3,061318
(2) Abrasive mass flow rate (g.[min.sup.-1]] -2,72053
Note: Table made from bar graph.
[(J/T).sub.a] [mm/mm] 33%
[M.sub.a] [g.[min.sup.-1]] 14%
p [MPa] 35%
[s.sub.t] [mm.[min.sup.-1]] 18%
Note: Table made from pie chart.
