%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Experimental Results} \label{chap:results}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
In this chapter, the results obtained from the two sets of experiments (Tests~A and~B)
described in Section~\ref{sec:procedure} are presented. The raw data from the various
sensors, acquired with the three acquisition boards and stored in the personal
computer, were processed with computer programs produced with \mbox{MATLAB} (software
from \mbox{The MathWorks}).


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Test A---Variation of Cutting Conditions and Materials}
\label{sec:results_test_A}

This section presents the resultant cutting forces, measured temperatures, and
acoustic emission (AE) signals generated during the cutting tests described in
Section~\ref{sec:procedure_test_A} for the cutting conditions shown in
Tables~\ref{tab:speed_feed} and~\ref{tab:width} and for the four work materials
080A15, 080M40, 304S15, and \mbox{6082-T6}. The first part is dedicated to the
cutting force results; the second part shows the temperature results from the upper
embedded thermocouple; whereas the third part is dedicated to both energy and
frequency characteristics of the AE emissions.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Cutting Forces} \label{sec:results_forces}

The plots shown in
Figures~\mbox{\ref{fig:[forces][speed]}--\ref{fig:[forces][6082-T6][width]}} present
the variation of the tangential force ($F_\mr{X}$) and feed force ($F_\mr{Y}$) for
different cutting conditions and work materials. Since, for a given work material and
cutting condition, each test was repeated at least twice, where three readings of 16384
samples where acquired, resulting in a minimum of six readings, the following data
processing technique was conducted: for each of the six readings, the mean of each
16384 samples was firstly computed; afterwards, the mean of the means of the six
readings was calculated, representing each point shown on the plots (the length of the
error bars represents two standard deviations).

Figure~\ref{fig:[forces][speed]} shows the variation of $F_\mr{X}$ and $F_\mr{Y}$ with
cutting speed ($V$) for feed rates ($t_1$) of 0.02 and \mbox{0.1 mm$/$rev} and constant
width of cut (\mbox{$w = 1.2$ mm}). It can be observe that, in most cases, both cutting
forces $F_\mr{X}$ and $F_\mr{Y}$ decrease slightly with increasing $V$. It can also be
observed that the tangential force $F_\mr{X}$ is always higher than the feed force
$F_\mr{Y}$. However, since these trends were not consistent for all tested conditions,
each plot is described separately. The description of the variation of the cutting
forces with $V$ for \mbox{$t_1 = 0.02$ mm$/$rev} and for the four work materials is
described next:
\begin{description}

   \item [080A15 (Figure~\ref{fig:[forces][speed]}a)] $F_\mr{X}$ and $F_\mr{Y}$ appear
   to remain roughly constant for speeds higher than 100~m$/$min. However, between 75
   and 100~m$/$min, both $F_\mr{X}$ and $F_\mr{Y}$ exhibit an abrupt increase in
   amplitude.

   \item [080M40 (Figure~\ref{fig:[forces][speed]}c)]
   Although, $F_\mr{X}$ remains approximately constant, $F_\mr{Y}$ shows an increase
   with increasing $V$, contradicting the general trend observed in the other cases.
   However, the data is reasonably scattered.

   \item [304S15 (Figure~\ref{fig:[forces][speed]}e)]
   Both cutting forces appear to decrease slightly with increasing $V$, although the
   data is very scattered.

   \item [6082-T6 (Figure~\ref{fig:[forces][speed]}g)]
   Both $F_\mr{X}$ and $F_\mr{Y}$ appear to decrease with increasing $V$. However,
   between 75 and 100~m$/$min, a small increase in both cutting forces is observed.
   Above 200~m$/$min an increase in $F_\mr{Y}$ is also observed.

\end{description}
Next, the variation of the cutting forces with $V$ for \mbox{$t_1 = 0.1$ mm$/$rev} is
described:
\begin{description}

   \item [080A15 (Figure~\ref{fig:[forces][speed]}b)]
   $F_\mr{X}$ and $F_\mr{Y}$ appear to increase in the 50--75~m$/$min speed range, to
   decrease between 75 and 150~m$/$min, and to remain more or less constant above
   150~m$/$min.

   \item [080M40 (Figure~\ref{fig:[forces][speed]}d)]
   $F_\mr{X}$ and $F_\mr{Y}$ are observed to rapidly increase in the 50--75~m$/$min
   speed range and then to decrease smoothly above 75~m$/$min.

   \item [304S15 (Figure~\ref{fig:[forces][speed]}f)]
   Both cutting forces are observed to decrease with increasing $V$.

   \item [6082-T6 (Figure~\ref{fig:[forces][speed]}h)]
   Both cutting forces are observed to decrease with increasing $V$, although, between
   75 and 100~m$/$min, a small increase is observed.

\end{description}

Figure~\ref{fig:[forces][feed]} shows the variation of the cutting forces with $t_1$
for \mbox{$V = 75$} and 200~m$/$min, and \mbox{$w = 1.2$ mm}. Both cutting forces are
observed to increase strongly with increasing $t_1$. The relationship between
$F_\mr{X}$ and $t_1$ can be represented by a straight line with positive slope and a
quasi-zero intercept. However, it can be observed that, in same cases, at high feed
rates, the slope of the relationship between $F_\mr{X}$ and $t_1$ lowers with
increasing $t_1$, which is most visible in Figures~\ref{fig:[forces][feed]}a and
\ref{fig:[forces][feed]}b. In all cases, $F_\mr{Y}$ is observed to increase with $t_1$,
although its rate of increase decreases for higher $t_1$ values. Moreover, it can also
be observed that $F_\mr{X}$ is 1.25--2 times higher than $F_\mr{Y}$.

Figures~\mbox{\ref{fig:[forces][080A15][width]}--\ref{fig:[forces][6082-T6][width]}} show
the variation of the cutting forces with $w$ for four different combinations of $V$ (75
and 200~m$/$min) and $t_1$ (0.02 and 0.1~mm$/$rev). For all combinations of $V$ and $t_1$,
it can be concluded that the relationship between both cutting forces and $w$ falls very
closely on a straight line with positive slope, i.e.\ $F_\mr{X}$ and $F_\mr{Y}$ are almost
directly proportional to $w$.

\clearpage

\begin{figure}[p]
   \center{\includegraphics{[forces][speed].eps}}
   \caption[Variation of cutting forces with cutting speed.]
   {Variation of cutting forces with cutting speed.
   (a)~080A15, \mbox{$t_1 = 0.02$ mm$/$rev}. (b)~080A15, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~080M40, \mbox{$t_1 = 0.02$ mm$/$rev}. (d)~080M40, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (e)~304S15, \mbox{$t_1 = 0.02$ mm$/$rev}. (f)~304S15, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (g)~6082-T6, \mbox{$t_1 = 0.02$ mm$/$rev}. (h)~6082-T6, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[forces][speed]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[forces][feed].eps}}
   \caption[Variation of cutting forces with feed rate.]
   {Variation of cutting forces with feed rate.
   (a)~080A15, \mbox{$V = 75$ m$/$min}. (b)~080A15, \mbox{$V = 200$ m$/$min}.
   (c)~080M40, \mbox{$V = 75$ m$/$min}. (d)~080M40, \mbox{$V = 200$ m$/$min}.
   (e)~304S15, \mbox{$V = 75$ m$/$min}. (f)~304S15, \mbox{$V = 200$ m$/$min}.
   (g)~6082-T6, \mbox{$V = 75$ m$/$min}. (h)~6082-T6, \mbox{$V = 200$ m$/$min}.}
   \label{fig:[forces][feed]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[forces][080A15][width].eps}}
   \caption[Variation of cutting forces with width of cut; work material 080A15.]
   {Variation of cutting forces with width of cut; work material 080A15.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[forces][080A15][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[forces][080M40][width].eps}}
   \caption[Variation of cutting forces with width of cut; work material 080M40.]
   {Variation of cutting forces with width of cut; work material 080M40.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[forces][080M40][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[forces][stainless][width].eps}}
   \caption[Variation of cutting forces with width of cut; work material 304S15.]
   {Variation of cutting forces with width of cut; work material 304S15.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[forces][304S15][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[forces][aluminium][width].eps}}
   \caption[Variation of cutting forces with width of cut; work material 6082-T6.]
   {Variation of cutting forces with width of cut; work material 6082-T6.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[forces][6082-T6][width]}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage
\subsection{Temperature} \label{sec:results_temp}

The plots shown in
Figures~\mbox{\ref{fig:[temp][speed]}--\ref{fig:[temp][6082-T6][width]}} show the
temperature variation measured by thermocouple $T_1$ for different cutting conditions
and work materials, as described in Section~\ref{sec:procedure_test_A}. For each
cutting condition and work material, each test was conducted at least twice, during
which three reading of 200 samples were acquired, resulting in a minimum of six
readings. Subsequently, each set of 200 samples was divided into 20 sets of 10 samples,
and the mean of each set of 10 samples was computed, resulting in a minimum of 60 mean
values. The temperature was taken as the maximum value found among these 60 mean
values.

Figure~\ref{fig:[temp][speed]} shows the variation of $T_1$ with $V$ for \mbox{$t_1 =
0.02$} and 0.1~mm$/$rev, and \mbox{$w = 1.2$ mm}. It can be observed that, generally,
$T_1$ increases slightly with $V$; however, since this trend is not observed for all
conditions, each case is described individually. When {$t_1 = 0.02$ mm$/$rev}:
\begin{description}

   \item [080A15 (Figure~\ref{fig:[temp][speed]}a)]
   Temperature $T_1$ increases with $V$ up to 150~m$/$min, above which $T_1$ becomes
   constant with further increase of $V$.

   \item [080M40 (Figure~\ref{fig:[forces][speed]}c)]
   Temperature $T_1$ increases more or less linearly with $V$.

   \item [304S15 (Figure~\ref{fig:[forces][speed]}e)]
   Temperature $T_1$ remains more or less constant with varying $V$.

   \item [6082-T6 (Figure~\ref{fig:[forces][speed]}g)]
   Temperature $T_1$ remains more or less constant with varying $V$.

\end{description}
When {$t_1 = 0.1$ mm$/$rev}:
\begin{description}

   \item [080A15 (Figure~\ref{fig:[temp][speed]}b)]
   Temperature $T_1$ increases with $V$ up to 75~m$/$min, above which $T_1$ becomes
   constant with further increase of $V$.

   \item [080M40 (Figure~\ref{fig:[forces][speed]}d)]
   Temperature $T_1$ increases with $V$ up to 100~m$/$min, above which $T_1$ becomes
   constant with further increase of $V$.

   \item [304S15 (Figure~\ref{fig:[forces][speed]}f)]
   Temperature $T_1$ remains more or less constant with varying $V$.

   \item [6082-T6 (Figure~\ref{fig:[forces][speed]}h)]
   Temperature $T_1$ increases with $V$ up to 100~m$/$min, above which $T_1$ becomes
   constant with further increase of $V$.

\end{description}

Figure~\ref{fig:[temp][feed]} shows the variation of $T_1$ with $t_1$ for \mbox{$V = 75$}
and 200~m$/$min, and \mbox{$w = 1.2$ mm}. Generally, $T_1$ is observed to increase more or
less linearly with increasing $t_1$.

Figures~\mbox{\ref{fig:[temp][080A15][width]}--\ref{fig:[temp][6082-T6][width]}} show, for
four different combinations of $V$ (75 and 200~m$/$min) and $t_1$ (0.02 and 0.1~mm$/$rev),
the variation of $T_1$ with $w$. In most cases, $T_1$ can be observed to increase linearly
with $w$. However, exceptions can be observed for work material 080M40: when {$V = 75$
m$/$min} and \mbox{$t_1 = 0.02$ mm$/$rev} (Figure~\ref{fig:[temp][080M40][width]}a),
\mbox{$V = 200$ m$/$min} and \mbox{$t_1 = 0.02$ mm$/$rev}
(Figure~\ref{fig:[temp][080M40][width]}c), and \mbox{$V = 200$ m$/$min} and \mbox{$t_1 =
0.1$ mm$/$rev} (Figure~\ref{fig:[temp][080M40][width]}d), $T_1$ increases quite
considerably with $w$ bellow $w = $~0.6~mm, above which $T_1$ increases with $w$ with a
lower rate of increase.

\clearpage

\begin{figure}[p]
   \center{\includegraphics{[temp][speed].eps}}
   \caption[Variation of temperature $T_1$ with cutting speed.]
   {Variation of temperature $T_1$ with cutting speed.
   (a)~080A15, \mbox{$t_1 = 0.02$ mm$/$rev}. (b)~080A15, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~080M40, \mbox{$t_1 = 0.02$ mm$/$rev}. (d)~080M40, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (e)~304S15, \mbox{$t_1 = 0.02$ mm$/$rev}. (f)~304S15, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (g)~6082-T6, \mbox{$t_1 = 0.02$ mm$/$rev}. (h)~6082-T6, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[temp][speed]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[temp][feed].eps}}
   \caption[Variation of temperature $T_1$ with feed rate.]
   {Variation of temperature $T_1$ with feed rate.
   (a)~080A15, \mbox{$V = 75$ m$/$min}. (b)~080A15, \mbox{$V = 200$ m$/$min}.
   (c)~080M40, \mbox{$V = 75$ m$/$min}. (d)~080M40, \mbox{$V = 200$ m$/$min}.
   (e)~304S15, \mbox{$V = 75$ m$/$min}. (f)~304S15, \mbox{$V = 200$ m$/$min}.
   (g)~6082-T6, \mbox{$V = 75$ m$/$min}. (h)~6082-T6, \mbox{$V = 200$ m$/$min}.}
   \label{fig:[temp][feed]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[temp][080A15][width].eps}}
   \caption[Variation of temperature $T_1$ with width of cut; work material 080A15.]
   {Variation of temperature $T_1$ with width of cut; work material 080A15.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[temp][080A15][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[temp][080M40][width].eps}}
   \caption[Variation of temperature $T_1$ with width of cut; work material 080M40.]
   {Variation of temperature $T_1$ with width of cut; work material 080M40.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[temp][080M40][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[temp][stainless][width].eps}}
   \caption[Variation of temperature $T_1$ with width of cut; work material 304S15.]
   {Variation of temperature $T_1$ with width of cut; work material 304S15.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[temp][304S15][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[temp][aluminium][width].eps}}
   \caption[Variation of temperature $T_1$ with width of cut; work material 6082-T6.]
   {Variation of temperature $T_1$ with width of cut; work material 6082-T6.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[temp][6082-T6][width]}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage
\subsection{Acoustic Emission}  \label{sec:results_ae}

The plots shown in
Figures~\mbox{\ref{fig:[mode][speed]}--\ref{fig:[mode][6082-T6][width]}} show the
variation of the energy and frequency content of the AE emissions for different cutting
conditions and work materials. As described in Section~\ref{sec:procedure_test_A}, for
each cutting condition and material, each cutting test was conducted at least twice,
during which three readings of 8388608 samples were acquired. Subsequently, each set of
8388608 was divided into 8 subsets of 1048576 samples, resulting, effectively, in 48
sets of 1048576 samples, which were further analysed in the following ways:
\begin{description}

   \item [Energy analysis] Primarily, each set of 1048576 samples was full-wave rectified,
   followed by its low-pass filtering (1000~Hz cut-off frequency). Afterwards, the
   probability density function of the data set was computed in order to obtain the value
   where the distribution reaches its maximum, the mode ($I_\mr{mode}$). Since the mode is
   also defined as the most common value of a data set, as already referred in
   Section~\ref{sec:ae_theory}, the mode is less sensitive to outlying values that the
   mean. The example of a raw AE signal presented in Figure~\ref{fig:[080M40][time]} shows a
   typical Test~A continuous-type AE signal superimposed by two large bursts; a higher
   value of the root mean square of the AE signals ($I_\mr{RMS}$) was obtained comparatively
   to the value of $I_\mr{mode}$, indicating that the effect of the unwanted outlying bursts
   were disregarded in the calculation of $I_\mr{mode}$. In order to obtain the points
   represented in the plots shown in
   Figures~\mbox{\ref{fig:[mode][speed]}--\ref{fig:[mode][6082-T6][width]}}, the mean of
   each 48 $I_\mr{mode}$ values were calculated (the length of the error bars represents
   two standard deviations).

   \item [Frequency analysis] First of all, the FFT (Section~\ref{sec:ae_theory}) of each
   1048576 data set was computed. Afterwards, the spectrum was divided into 256 bands
   between 100 and 500~kHz, and then the values falling within each band were added
   together, resulting in a spectral data set of 256 elements, as shown in
   Figure~\ref{fig:[080M40][spectrum]}. By observation of the AE spectra, it was concluded
   that changes at the higher frequency range would not be significantly detected when
   compared to changes at the lower frequency range, since most energy of the spectra was
   around the \mbox{100--200 kHz} frequency range (Figure~\ref{fig:[080M40][spectrum]}
   and~\ref{fig:[304S15][spectrum]}a). Therefore, it was decided to compute each frequency
   power spectrum in relation to a predetermined reference spectrum, i.e.\ the reference
   spectrum shown in Figure~\ref{fig:[080M40][spectrum]}; this was achieved by dividing
   the 256 points of all the frequency spectra by the reference spectrum. As demonstrated
   by the example shown in Figure~\ref{fig:[304S15][spectrum]}b, similar significance is
   observed for all frequencies when the spectrum is relative to the reference.
   Subsequently, the frequency value that divides the spectrum into two parts of equal
   energy, the mean frequency ($f_\mr{mean}$, as defined in Section~\ref{sec:ae_theory}),
   was calculated for all 48 spectra of each cutting condition and work material. In order
   to obtain the points represented in the plots shown in
   Figures~\mbox{\ref{fig:[freq][speed]}--\ref{fig:[freq][6082-T6][width]}}, the mean of
   each 48 $f_\mr{mean}$ values was computed (the
   length of the error bars represents two standard deviations).

\end{description}
\begin{figure}[h]
   \center{\includegraphics{[TIME][200][0.1][1.2][080M40].eps}}
   \caption[Example of AE time series.]
   {Example of a 0.01~s AE time series. (work material 080M40, \mbox{$V = 200$ m$/$min},
   \mbox{$t_1 = 0.1$ mm$/$rev, $w = 1.2$ mm}).}
   \label{fig:[080M40][time]}
\end{figure}
\begin{figure}[h]
   \center{\includegraphics{[SPECTRUM][200][0.1][1.2][080M40].eps}}
   \caption[Example of AE power spectrum.]
   {Example of AE power spectrum (work material 080M40, \mbox{$V = 200$ m$/$min},
   \mbox{$t_1 = 0.1$ mm$/$rev, $w = 1.2$ mm}). This power spectrum will be used
   as a reference for frequency domain calculations.}
   \label{fig:[080M40][spectrum]}
\end{figure}
\begin{figure}[h]
   \center{\includegraphics{[SPECTRUM][200][0.1][1.2][stainless].eps}}
   \caption[Example of AE power spectrum.]
   {Example of AE power spectrum (work material 304S15, \mbox{$V = 200$ m$/$min},
   \mbox{$t_1 = 0.1$ mm$/$rev, $w = 1.2$ mm}). (a)~Original spectrum.
   (b)~Original Spectrum divided by the reference spectrum shown
   in Figure~\ref{fig:[080M40][spectrum]}.}
   \label{fig:[304S15][spectrum]}
\end{figure}


Figure~\ref{fig:[mode][speed]} shows the variation of $I_\mr{mode}$ with $V$ for
\mbox{$t_1 = 0.02$} and 0.1~mm$/$rev, and \mbox{$w = 1.2$ mm}. It can be observed
that $I_\mr{mode}$ is strongly dependent on $V$ because $I_\mr{mode}$ increases
almost exponentially with increasing $V$. However, for the lower $t_1$ values
(0.02~mm$/$rev), $I_\mr{mode}$ increases more quickly than when \mbox{$t_1 = 0.1$
mm$/$rev}.

Figure~\ref{fig:[mode][feed]} shows the variation of $I_\mr{mode}$ with $t_1$ for
\mbox{$V = 75$} and 200~m$/$min, and \mbox{$w = 1.2$ mm}. In most cases it can be
stated that $I_\mr{mode}$ decreases slightly or remains constant with increasing $t_1$.
However, since these trends are not observed in all cases, each plot is described
separately; for \mbox{$V = 75$ m$/$min}:
\begin{description}

   \item [080A15 (Figure~\ref{fig:[mode][feed]}a)]
   The value of $I_\mr{mode}$ remains more or less constant in the \mbox{0.01--0.06
   mm$/$rev} range, and it increases slightly with $t_1$ above 0.06~mm$/$rev.

   \item [080M40 (Figure~\ref{fig:[mode][feed]}c)]
   Between 0.01 and 0.02~mm$/$rev, $I_\mr{mode}$ increases with $t_1$, between 0.02 and
   0.1~mm$/$rev, it decreases with $t_1$, and above 0.1~mm$/$rev, $I_\mr{mode}$ remains
   more or less constant with increasing $t_1$.

   \item [304S15 (Figure~\ref{fig:[mode][feed]}e)]
   The value of $I_\mr{mode}$ remains approximately constant with increasing $t_1$.

   \item [6082-T6 (Figure~\ref{fig:[mode][feed]}g)]
   Below 0.04~mm$/$rev, $I_\mr{mode}$ decreases abruptly with $t_1$, and above
   0.04~mm$/$rev, $I_\mr{mode}$ remains approximately constant but with a tendency to
   increase.

\end{description}
When \mbox{$V = 200$ m$/$min}:
\begin{description}

   \item [080A15 (Figure~\ref{fig:[mode][feed]}b)]
   The value of $I_\mr{mode}$ decreases with $t_1$. However, the rate of decrease is
   higher for lower values of $t_1$.

   \item [080M40 (Figure~\ref{fig:[mode][feed]}d)]
   The value of $I_\mr{mode}$ is observed to decrease with $t_1$. However, the rate of
   decrease is higher for lower $t_1$ values, and above 0.1~mm$/$rev, $I_\mr{mode}$
   does not change.

   \item [304S15 (Figure~\ref{fig:[mode][feed]}f)]
   The value of $I_\mr{mode}$ is observed to decrease with increasing $t_1$.

   \item [6082-T6 (Figure~\ref{fig:[mode][feed]}h)]
   Between 0.01 and 0.06~mm$/$rev, $I_\mr{mode}$ is observed to decrease with $t_1$.
   Above 0.06~mm$/$rev, $I_\mr{mode}$ is observed to remain constant but with a rising
   tendency.

\end{description}
Finally, it must be added that, in all cases, the data is
reasonably scattered.

Figures~\mbox{\ref{fig:[mode][080A15][width]}--\ref{fig:[mode][6082-T6][width]}} show
the variation of $I_\mr{mode}$ with $w$ for four different combinations of $V$ (75 and
200~m$/$min) and $t_1$ (0.02 and 0.1~mm$/$rev). From the analysis of the plots, it can
be concluded that, generally, $I_\mr{mode}$ increases very quickly with increasing $w$
at low $w$ values, and since the rate of increase of $I_\mr{mode}$ decreases as $w$
rises, $I_\mr{mode}$ increases very slowly at higher $w$ values, tending to settle to a
constant $I_\mr{mode}$ value. However, this exact trend was not observed in all cases,
such as: for \mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}, and 080M40
(Figure~\ref{fig:[mode][080M40][width]}d), below widths of 0.6~mm, $I_\mr{mode}$ is
observed to rise with increasing $w$, between 0.6 and 1.2~mm, $I_\mr{mode}$ is observed
to fall, and above 1.2~mm, $I_\mr{mode}$ seems to settle to a constant value; for
\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}, and 304S15
(Figure~\ref{fig:[mode][304S15][width]}d), $I_\mr{mode}$ remains more or less constant
with varying $w$, and it decreases slightly above widths of 1.2~mm; for \mbox{$V = 75$
m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}, and 6082-T6
(Figure~\ref{fig:[mode][6082-T6][width]}a), $I_\mr{mode}$ rises in the \mbox{0.1--0.3
mm} range, it falls in the \mbox{0.3--0.6 mm} range, and it rises again above widths of
cut of 1.2~mm; for \mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}, and 6082-T6
(Figure~\ref{fig:[mode][6082-T6][width]}b), $I_\mr{mode}$ rises abruptly in the
\mbox{0.1--0.3 mm} range, it remains constant in the \mbox{0.3--0.6 mm} range, and it
rises again above 1.2~mm; for \mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev},
and 6082-T6 (Figure~\ref{fig:[mode][6082-T6][width]}c), $I_\mr{mode}$ rises abruptly in
the \mbox{0.1--0.3 mm} range, it decreases between 0.3 and 0.6~mm, and it remains
constant above widths of 0.6~mm.

Figure~\ref{fig:[freq][speed]} shows the variation of $f_\mr{mean}$ with $V$ for
\mbox{$t_1 = 0.02$} and 0.1~mm$/$rev, and \mbox{$w = 1.2$ mm}. By observing the plots,
it can be stated that, as a general trend, the value of $f_\mr{mean}$ decreases with
increasing $V$ in an almost linear relationship. However, some deviations from this
general trend can be perceived: for \mbox{$t_1 = 0.02$ mm$/$rev} and 080A15
(Figure~\ref{fig:[freq][speed]}a), $f_\mr{mean}$ increases with $V$ between 50 and
75~m$/$min, but it decreases above 75~m$/$min; for \mbox{$t_1 = 0.1$ mm$/$rev} and
080A15 (Figure~\ref{fig:[freq][speed]}b), $f_\mr{mean}$ remains relatively constant
below speeds of 150~m$/$min, although very high scatter is observed; for \mbox{$t_1 =
0.02$ mm$/$rev} and 304S15 (Figure~\ref{fig:[freq][speed]}e), the relationship between
$f_\mr{mean}$ and $V$ can be represented by a straight line, excepting at 150~m$/$min,
where $f_\mr{mean}$ falls below the straight line relationship; for \mbox{$t_1 = 0.02$
mm$/$rev}, and 6082-T6 (Figure~\ref{fig:[freq][speed]}g), $f_\mr{mean}$ remains
constant in the \mbox{50--100 m$/$min} speed range, it decreases in the \mbox{100--200
m$/$min} range, and it becomes constant again above 200~m$/$min.

Figure~\ref{fig:[freq][feed]} shows the variation of $f_\mr{mean}$ with $t_1$ for
\mbox{$V = 75$} and 200~m$/$min, and \mbox{$w = 1.2$ mm}. A common feature in all plots
is that, above $t_1$ values of 0.06~mm$/$rev, $f_\mr{mean}$ increases with increasing
$t_1$. Although, for \mbox{$V = 200$ m$/$min} and 6082-T6
(Figure~\ref{fig:[freq][feed]}g), $f_\mr{mean}$ remains relatively constant above
0.04~mm$/$rev. Under 0.06~mm$/$rev, no clear common trend can be established.

Figures~\mbox{\ref{fig:[freq][080A15][width]}--\ref{fig:[freq][6082-T6][width]}} show
the variation of $f_\mr{mean}$ with $w$ for four different combinations of $V$ (75 and
200~m$/$min) and $t_1$ (0.02 and 0.1~mm$/$rev). From the analysis of the plots, it can
be affirmed that generally $f_\mr{mean}$ is not significantly affected by $w$, although
very high scatter is also present in the data.

\clearpage

\begin{figure}[p]
   \center{\includegraphics{[mode][speed].eps}}
   \caption[Variation of AE level with cutting speed.]
   {Variation of AE level with cutting speed.
   (a)~080A15, \mbox{$V = 75$ m$/$min}. (b)~080A15, \mbox{$V = 200$ m$/$min}.
   (c)~080M40, \mbox{$V = 75$ m$/$min}. (d)~080M40, \mbox{$V = 200$ m$/$min}.
   (e)~304S15, \mbox{$V = 75$ m$/$min}. (f)~304S15, \mbox{$V = 200$ m$/$min}.
   (g)~6082-T6, \mbox{$V = 75$ m$/$min}. (h)~6082-T6, \mbox{$V = 200$ m$/$min}.}
   \label{fig:[mode][speed]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[mode][feed].eps}}
   \caption[Variation of AE level with feed rate.]
   {Variation of AE level with feed rate.
   (a)~080A15, \mbox{$V = 75$ m$/$min}. (b)~080A15, \mbox{$V = 200$ m$/$min}.
   (c)~080M40, \mbox{$V = 75$ m$/$min}. (d)~080M40, \mbox{$V = 200$ m$/$min}.
   (e)~304S15, \mbox{$V = 75$ m$/$min}. (f)~304S15, \mbox{$V = 200$ m$/$min}.
   (g)~6082-T6, \mbox{$V = 75$ m$/$min}. (h)~6082-T6, \mbox{$V = 200$ m$/$min}.}
   \label{fig:[mode][feed]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[mode][080A15][width].eps}}
   \caption[Variation of AE level with width of cut; work material 080A15.]
   {Variation of AE level with width of cut; work material 080A15.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[mode][080A15][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[mode][080M40][width].eps}}
   \caption[Variation of AE level with width of cut; work material 080M40.]
   {Variation of AE level with width of cut; work material 080M40.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[mode][080M40][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[mode][stainless][width].eps}}
   \caption[Variation of AE level with width of cut; work material 304S15.]
   {Variation of AE level with width of cut; work material 304S15.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[mode][304S15][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[mode][aluminium][width].eps}}
   \caption[Variation of AE level with width of cut; work material \mbox{6082-T6}.]
   {Variation of AE level with width of cut; work material \mbox{6082-T6}.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[mode][6082-T6][width]}
\end{figure}

\clearpage

\begin{figure}[p]
   \center{\includegraphics{[freq][speed].eps}}
   \caption[Variation of AE mean frequency with cutting speed.]
   {Variation of AE mean frequency with cutting speed.
      (a)~080A15, \mbox{$V = 75$ m$/$min}. (b)~080A15, \mbox{$V = 200$ m$/$min}.
   (c)~080M40, \mbox{$V = 75$ m$/$min}. (d)~080M40, \mbox{$V = 200$ m$/$min}.
   (e)~304S15, \mbox{$V = 75$ m$/$min}. (f)~304S15, \mbox{$V = 200$ m$/$min}.
   (g)~6082-T6, \mbox{$V = 75$ m$/$min}. (h)~6082-T6, \mbox{$V = 200$ m$/$min}.}
   \label{fig:[freq][speed]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[freq][feed].eps}}
   \caption[Variation of AE mean frequency with feed rate.]
   {Variation of AE mean frequency with feed rate.
   (a)~080A15, \mbox{$V = 75$ m$/$min}. (b)~080A15, \mbox{$V = 200$ m$/$min}.
   (c)~080M40, \mbox{$V = 75$ m$/$min}. (d)~080M40, \mbox{$V = 200$ m$/$min}.
   (e)~304S15, \mbox{$V = 75$ m$/$min}. (f)~304S15, \mbox{$V = 200$ m$/$min}.
   (g)~6082-T6, \mbox{$V = 75$ m$/$min}. (h)~6082-T6, \mbox{$V = 200$ m$/$min}.}
   \label{fig:[freq][feed]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[freq][080A15][width].eps}}
   \caption[Variation of AE mean frequency with width of cut; work material 080A15.]
   {Variation of AE mean frequency with width of cut; work material 080A15.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[freq][080A15][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[freq][080M40][width].eps}}
   \caption[Variation of AE mean frequency with width of cut; work material 080M40.]
   {Variation of AE mean frequency with width of cut; work material 080M40.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[freq][080M40][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[freq][stainless][width].eps}}
   \caption[Variation of AE mean frequency with width of cut; work material 304S15.]
   {Variation of AE mean frequency with width of cut; work material 304S15.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[freq][304S15][width]}
\end{figure}

\begin{figure}[p]
   \center{\includegraphics{[freq][aluminium][width].eps}}
   \caption[Variation of AE mean frequency with width of cut; work material \mbox{6082-T6}.]
   {Variation of AE mean frequency with width of cut; work material \mbox{6082-T6}.
   (a)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (b)~\mbox{$V = 75$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.
   (c)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.02$ mm$/$rev}.
   (d)~\mbox{$V = 200$ m$/$min}, \mbox{$t_1 = 0.1$ mm$/$rev}.}
   \label{fig:[freq][6082-T6][width]}
\end{figure}
