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\chapter{Conclusions and Recommendations} \label{chap:conclus_recommen}


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The fundamental objective of the present thesis was the understanding of the generation
mechanisms of acoustic emission (AE) during the course of metal cutting. In
Chapters~\ref{chap:introd} and~\ref{chap:review}, the most relevant theories on the
fields of metal cutting and AE were presented, followed by a review of the
state-of-the-art models of AE generation during metal cutting. In
Chapter~\ref{chap:method}, the experimental procedure was described, and the
corresponding results presented in Chapter~\ref{chap:results}. In
Chapter~\ref{chap:discuss}, a novel qualitative model relating continuous AE from metal
cutting with continuous-type chip formation was developed, revealing that the
opposition of obstacles against moving dislocations is the main mechanism of AE
generation in the typical plastic deformation regimes occurring in metal cutting. The
importance of this model arises from the fact that as an excellent agreement was found
between model predictions and experimental results, a considerable contribution for the
knowledge of AE generation during the course of metal cutting was undoubtedly achieved,
as originally proposed, and, consequently, in the following section, the suggested
mechanisms of AE generation proposed by the model are concisely described. Afterwards,
all the conclusions arrived at during the analyses performed in
Chapter~\ref{chap:discuss} for the development of the proposed AE theory are thoroughly
summarized. Finally, in the last section, some recommendations for further work are
also provided.

\section{Generation of Acoustic Emission during Metal Cutting} \label{sec:main_conclus}

As continuous-type AE is thought to be generated due to plastic deformation during
metal cutting with continuous chip formation, without built-up edge (BUE), and with a
sharp tool (Section~\ref{sec:ae_metal_cut}), and as dislocation motion is the main
mechanism responsible for plastic deformation in metals (Section~\ref{sec:disloc_AE}),
a relationship between AE and dislocation motion was investigated for the typical
plastic deformation regime encountered in metal cutting. At the high temperatures
involved in metal cutting, flow stress decreases with temperature in the so-called
diffusion controlled regime, and at the very high strain rates encountered in metal
cutting, opposing viscous damping forces become the dominant mechanism governing
dislocation movement (Section~\ref{sec:mech_disloc_cut}). Furthermore, as the flow
stress is a combination of the stress needed to overcome dislocation obstacles plus the
stress needed to overcome the damping forces, the total power involved in plastic
deformation ($\dot{U}$) can be expressed as $\dot{U} = \dot{U}_\mr{B} +
\dot{U}_\mr{D}$, where $\dot{U}_\mr{B}$ is the power necessary for the dislocations to
transpose obstacles, and $\dot{U}_\mr{D}$ is the power to overcome the damping forces
(Section~\ref{sec:ae_disloc_model}).

Most published models typically relate the the power of the AE signals ($I_\mr{power}$)
to the total work of deformation $\dot{U}$, but, as shown in
Section~\ref{sec:cut_ae_power}, this assumption is rather incorrect, since it is only
valid for constant values of feed rate ($t_1$) and width of cut ($w$), although the
cutting speed ($V$) is allowed to vary. Furthermore, Rangwala and
Dornfeld~\cite{rangwala91a} suggested that, as viscous damping is the main mechanism
governing plastic deformation in metal cutting, $I_\mr{power}$ should be proportional
to $\dot{U}_\mr{D}$. However, as shown in Section~\ref{sec:ae_theory}, AE is a high
frequency stress wave generated due to the rapid release of strain energy, and,
therefore, a process with rapid energy variation is necessary, which is not the case of
$\dot{U}_\mr{D}$, since, as shown in Section~\ref{sec:eval_disloc_model},
$\dot{U}_\mr{D}$ should remain more or less constant during dislocation movement.

The model proposed in the present thesis (Section~\ref{sec:ae_disloc_model}) assumes
that although the mechanics of plastic deformation from metal cutting is manly
governed by viscous damping, AE is generated due to the rapid release of strain
energy when moving dislocations surpass obstacles, since as a dislocation approaches
an obstacle, strain energy is stored, and as its maximum value is reached, this
strain energy is rapidly released as the dislocation overtakes the obstacle,
resulting in the emission of an AE pulse ($I_\mr{power}$ is a function of
$\dot{U}_\mr{B}$). The detected AE is a result of the combined effect of many AE
pulses, generated at different locations, which are transmitted to a remote sensor.
Furthermore, in Section~\ref{sec:ae_disloc_model}, it was concluded that the energy
level of the detected AE is expected to increase with strain and strain rate, but to
decrease with temperature; the frequency content of AE was predicted to increase with
strain rate, to decrease with temperature, and to remain unaffected by strain.
Moreover, it was also concluded that the characteristics of the transmission path,
sensor, and instrumentation also play an important role in the detected emissions.

In order to assess the validity of the proposed model, two sets of original metal
cutting experiments (Tests~A and~B) were accomplished for four different work materials
(two carbon steels, a stainless steel, and an aluminium alloy), during which AE and
also other signals (cutting forces, vibration, and temperature) were acquired: in
Test~A (Section~\ref{sec:procedure_test_A}), the cutting conditions were varied over a
wide range, and, in Test~B (Section~\ref{sec:procedure_test_B}), the work material was
preheated in order to initiate cutting with different workpiece temperatures
($T_\mr{W}$). Good agreement was obtained between Test~A and published results
(Section~\ref{sec:compar_test_A}).

Both energetic and frequency components of AE were extracted from the experimental
results, according to the most appropriate data processing techniques: since phenomena
that lead to unwanted AE bursts could not be completely unavoidable, a technique that
disregards the influence of these random bursts in the calculation of the power of AE
($I_\mr{power}$), named AE mode ($I_\mr{mode}$)~\cite{blum90}, was utilized as a
representation of the energy content of continuous AE ($I_\mr{power} = I_\mr{mode}^2$);
a technique that indicates the frequency value that divides the AE power spectrum into
two parts of equal energy, called mean frequency ($f_\mr{mean}$)~\cite{rangwala91b},
was utilized as a representation of the frequency content of AE\@. Furthermore, in
order to predict basic metal cutting parameters, such as strain, strain rate, flow
stress, and temperature, a technique developed by Oxley and his
co-workers~\cite{oxley89} was employed, but only predictions for the two carbon steel
work materials were possible.

In Section~\ref{sec:parameters_AE}, it was concluded that AE is manly generated due to
secondary plastic deformation, and, according to the energy analysis performed in
Section~\ref{sec:energy_analysis}, it was concluded that $I_\mr{power}$ increases with
both primary strain and secondary strain rate, but, according to
Section~\ref{sec:ae_temp}, $I_\mr{power}$ decreases with temperature. Moreover, in
Section~\ref{sec:frequency_analysis}, it was concluded that $f_\mr{mean}$ increases
with strain rate, decreases with temperature, but it remains unaffected by variations
of strain. Therefore, as the results provided by the experiments together with Oxley's
predictions are in agreement with the predictions of the afore-mentioned qualitative
model, it substantiates the theory that the main generation mechanism of AE during
metal cutting is provided by the release of strain energy when moving dislocations
interact with obstacles in the material being deformed at the very high strain rates
and temperatures typically encountered in metal cutting processes.


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\section{Summary of Conclusions} \label{sec:summ_conclus}

This section presents a summary of all the conclusions arrived at throughout the
present thesis:
\begin{itemize}

   \item Test~A results showed that $I_\mr{power}$ increases with $V$ and decreases
   with $t_1$, according to the approximate relationship $I_\mr{power} \propto
   V^{n_1}t_1^{n_2}$, where $n_1$ and $n_2$ are work material dependent; index $n_1$
   was found to be between $3.7$ and $4.6$, and $n_2$ between $-0.63$ and $-0.01$.
   Moreover, $I_\mr{power}$ was observed to increase with $w$, but  with decreasing
   rate of increase, so that $I_\mr{power}$ tends to a constant value for high $w$
   values. In the frequency domain, although very scattered, $f_\mr{mean}$ was observed
   to decrease with $V$ and to remain more or less unchanged with $t_1$ and $w$.

   \item Other two sets of experiments were performed in order to test AE generation
   when $t_1$ and $w$ approach very low values: feed rate and width of cut
   variation tests, respectively. However, the AE data from these tests were observed
   to be very scattered, which was attributed to the small length of the acquired data
   sets (approximately 10~ms). In order to remove the unwanted effect of burst-type AE
   in the computation of $I_\mr{mode}$, data sets longer than 100~ms must be acquired.

   \item Results from the width of cut variation tests showed that when high amplitude
   vibrations are present, named as chatter, the resulting AE signal is highly affected
   by these vibrations (the level of $I_\mr{power}$ was observed to increase up to 20
   times on the onset of chatter).

   \item According to Test~B results, $I_\mr{power}$ was observed to decrease with
   increasing workpiece temperature $T_\mr{W}$.

   \item Since most published
   models~\cite{dornfeld80,kannatey-asibu81,schmenk84,blum90,rangwala91a,saini96}
   relate $I_\mr{power}$ to cutting power $\dot{U}$, according to the proportion
   $I_\mr{power} \propto \dot{U}$, this relationship was investigated against Test~A
   results. It was concluded that this relationship was solely observed if $t_1$ and
   $w$ were kept constant, and only $V$ was allowed to vary, which was the case of the
   experimental procedure used to derive most published models. Nevertheless, if only
   $V$ was changed, Test~A AE data seemed to hold a relationship of the type
   $I_\mr{power} \propto \dot{U}^n$, where $n > 1$.

   \item The finite-difference technique was employed in order to determine the
   relationship between the temperature at the tool-chip interface ($T_\mr{int}$) and
   the temperature measured by the two thermocouples ($T_1$ and $T_2$) placed below the
   tool-chip interface. For a given value of $T_\mr{int}$, $T_2$ was predicted to be
   lower than $T_1$, as expected, since $T_2$ was measured further from the tool-chip
   interface, and $T_1$ and $T_2$ were predicted to increase with increasing $w$ and
   $l_\mr{int}$. As expected, $T_1$ and $T_2$ were found to increase with $T_\mr{int}$.
   Moreover, since $T_1$ and $T_2$ are dependent on $l_\mr{int}$, and $l_\mr{int}$ is
   dependent on the cutting process and not known in advance, this makes practical
   predictions of $T_\mr{int}$ from measurements of $T_1$ and $T_2$ rather difficult.

   \item In order to access the accuracy of the semi-empirical model developed by Oxley
   and co-workers~\cite{oxley89} to predict basic metal cutting parameters, the
   experimental force and temperature results from Test~A and also the temperature
   results from Test~B were used to be compared against predictions of cutting forces
   and temperatures from Oxley's model. A fairly good agreement was observed between
   predictive and experimental results, but for the lowest values of $V$ and $t_1$, the
   experimental cutting force results were observed to be below predictions; this was
   attributed to the onset of BUE, since BUE is known to contribute to the reduction of
   the cutting forces.

   \item In order to investigate the typical relationship observed between
   $I_\mr{power}$ and $w$ ($I_\mr{power}$ increases with $w$, but its rate of increase
   decreases with $w$) shown by Test~A results and also by published
   results~\cite{lan85,messaritis86,inasaki81,lan86,blum90}, a very simple model for AE
   generation and propagation was developed. It was concluded that as $w$ increases,
   and AE events are generated further apart, some AE waves travel longer distances
   than others to a remote AE sensor, resulting in a difference in phase delay for the
   different arriving waves. Consequently, due to the effect of phase attenuation, the
   resultant AE signal detected by the sensor does not increase proportionally to the
   increase of AE activity at the generation source that accompanies the increase in
   deformation volume due to increasing $w$.

   \item As it was demonstrated that Oxley's theory can be used to model the cutting
   process rather accurately, it was decided to run Oxley's model with Test~A cutting
   conditions to predict the basic cutting parameters that govern the physics of
   plastic deformation in metal cutting, so that the most important parameters that
   influence the level of AE could be evaluated. Besides, it was also concluded that
   the AE signals measured during Test~A (measured at the tool side) were manly
   generated due to plastic deformation at the tool-chip interface~\cite{uehara84}.
   Moreover, it was realized that $I_\mr{power}$ is mostly influence by the effect of
   primary strain ($\gamma_\mr{AB}$), secondary strain rate ($\dot{\gamma}_\mr{int}$),
   and interface temperature $T_\mr{int}$. However, it was also found out that the
   effect of $T_\mr{int}$ on $I_\mr{power}$, if temperature $T_\mr{W}$ is kept
   constant, are masked by the influence of $\gamma_\mr{AB}$ and
   $\dot{\gamma}_\mr{int}$, and by using Test~A experimental results together with
   Oxley's model predictions, the following empirical relationship was established:
   $I_\mr{power} \propto \gamma_\mr{AB}^{n_1}\dot{\gamma}_\mr{int}^{n_2}$, where $n_1 =
   4.5$ and $n_2 = 2.4$. However, by analysing Test~B results, where $T_\mr{W}$ was
   allowed to vary, $I_\mr{power}$ was clearly seen to decrease with $T_\mr{int}$, and
   the previous empirical relationship can not, therefore, be valid any longer.

   \item As pointed out in the previous section, at the high strain rates and
   temperatures typically found in metal cutting, plastic deformation is governed by
   the motion of dislocations in the so-called viscous damping
   regime~\cite{kumar68,kumar69}. In this regime, the movement of dislocations is
   opposed by damping forces, which are proportional to dislocation speed, and also by
   forces posed by dislocation obstacles. Although theses two types of forces are
   liable for the dynamics of the moving dislocations, and, hence, the dynamics of
   plastic deformation, it was suggested that only the forces posed by the obstacles
   could originate AE, since AE is composed by high frequency waves, and only the rapid
   release of strain energy due to the passage of dislocations across the obstacles
   could originate the high frequency of the detected emissions. According to the
   proposed model, the following trends were predicted: $I_\mr{power}$ increases with
   strain and strain rate, but it decreases with temperature; $f_\mr{mean}$ increases
   with strain rate, decreases with temperature, and it remains unaltered with strain.
   These trends agree with Test~A and Test~B experimental data, indicating that the
   release of strain energy when moving dislocations surmount obstacles may be the most
   relevant source of continuous AE during continuous-type chip generation processes.

\end{itemize}


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\section{Recommendations for Further Work} \label{sec:recommen}

In this section, in order to aid any future research work to be undertaken in the
areas covered by this thesis, some final recommendations and suggestions for possible
alterations are provided:
\begin{itemize}

   \item Since only predictions for the two carbon steel work materials were possible
   with Oxley's theory~\cite{oxley89}, an extension of the theory to use other type of
   work materials must be investigated. Some work has already been undertaken by
   Adibi-Sedeh~\etal~\cite{adibi-sedeh03} to extend Oxley's model for other type of
   steels, for aluminium alloys, and for copper. Moreover, it is also proposed that,
   once an extended Oxley's model is accomplished, metal cutting should be simulated
   for the other two non-carbon steel work materials (stainless steel 304S15 and
   aluminium alloy \mbox{6082-T6}), so that the basic cutting parameters, such as
   strain, strain rate, flow stress, and temperature can be predicted for these two
   materials as well. Subsequently, the relationship defined in
   Section~\ref{sec:energy_analysis} (Equation~\ref{eq:AE_S_AB_SR_int}) should be
   verified for these other two work materials, since when tested for the two carbon
   steels, Equation~\ref{eq:AE_S_AB_SR_int} was observed to be material independent.
   All other analyses, such as the frequency analysis presented in
   Section~\ref{sec:frequency_analysis} and the temperature analysis presented in
   Section~\ref{sec:ae_temp}, should be repeated for the two work materials 304S15 and
   \mbox{6082-T6}. Depending on the results of the analysis of these two non-carbon
   steel work materials, the qualitative model presented in Section~\ref{sec:disloc_AE}
   should be revalidated or modified accordingly.

   \item In order to obtain valuable results from the feed rate and width of cut
   variation tests, these tests should be repeated with longer acquisition lengths
   (more than 100~ms) of the AE data sets, so that the effect of unwanted busts can be
   removed from the computation of $I_\mr{mode}$.

   \item If Test~A were to be repeated, the range of cutting conditions $V$ and $t_1$
   should be raised, since, during the experimental procedure, the occurrence of BUE
   was detected during the course of Test~A for the lowest values of $V$ and $t_1$.
   When BUE is present, Oxley's model predictions do not agree so well with the
   experimental results (Figures~\ref{fig:[Oxley_R][speed]}
   and~\ref{fig:[Oxley_R][feed]}). Another reason to raise $V$ and $t_1$ is due to the
   fact that Oxley's model did not converge for some of the lowest vales of $V$ and
   $t_1$, and results for these conditions were found by extrapolation.

\end{itemize}
