%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Acoustic Emission} \label{sec:ae}

Acoustic emission may be defined as the transient elastic wave generated by the rapid
release of energy within a material~\cite{spanner74}. This elastic wave propagates in
all directions, ultimately reaching the surface of the material, where it may be
detected by a suitable sensor. The detected emissions normally undergo some signal
conditioning process, so that they may be acquired and stored for future signal
processing and analysis. This process is shown schematically in
Figure~\ref{fig:ae_process_diagram} and is discussed in more detail in
Section~\ref{sec:ae_theory}, where the basis of the known AE theory is described.
Subsequently, Section~\ref{sec:ae_metal_cut} deals with the generation of AE during
the course of metal cutting, along with the introduction of the most relevant
published models.
\begin{figure}[h]
   \center{\includegraphics{ae_process_diagram.eps}}
   \caption{Diagram of the different stages of the AE process.}
   \label{fig:ae_process_diagram}
\end{figure}


\subsection{Acoustic Emission Theory} \label{sec:ae_theory}

This section introduces some of the AE theory necessary for the understanding of the AE
signals generated during the process of metal cutting. It goes over the different stages
of the AE process, as introduced in Figure~\ref{fig:ae_process_diagram}, i.e.\ generation,
propagation, detection, signal conditioning, and signal processing.

\subsubsection{Generation}

Basically, AE is a high frequency and low amplitude elastic stress wave generated due
to the rapid release of strain energy from localized sources within a material. Thus,
if a material is loaded, stresses gradually build up, and, as the material deforms
elastically, strain energy is stored. If the stresses at some location of the
material reach its maximum strength, this strain energy is rapidly released,
resulting in a rearrangement of the internal structure of the material. This
localized release of strain energy is called an AE event, and since it is highly
complex and non-uniform, the resulting AE wave will be non-stationary and stochastic
in character. Consequently, Ivanov~\cite{ivanov84} proposed a stochastic pulse
process to be a complete model of an AE event, so that AE is formed due to a series
of discrete pulses, the characteristic and shape of which depend on the physical
mechanisms of each individual event. In metals, the main sources of AE are normally
associated with the dislocation movement accompanying plastic deformation and with
the initiation and extension of cracks in a structure under stress.

\begin{figure}[h]
   \center{\includegraphics{ae_types.eps}}
   \caption{Continuous and burst-type AE.}
   \label{fig:ae_types}
\end{figure}
The rate by which the AE events are generated will qualitatively define the appearance of
the propagating AE wave. Thus, as shown in Figure~\ref{fig:ae_types}, two types of AE
waves are normally distinguished:
\begin{description}

   \item [Bust-type AE]
   Burst-type emissions are short duration pulses and are associated with the discrete
   release of high amplitude strain energy, such as the development of cracks. If AE
   events are sufficiently separated in time, the emission will appear as a train of
   individual busts, and each event can be readily detected.

   \item [Continuous AE] If many events from different sources are generated at the
   same time, individual events can no longer be distinguished, and the emissions will
   appear to be continuous. The waveform of a continuous-type AE signal is similar to a
   Gaussian random noise, but the amplitude varies with acoustic emission activity. In
   metals, this form of emission is generally considered to be associated with the
   motion of dislocations.

\end{description}
However, as shown in Figure~\ref{fig:ae_types}, higher amplitude bust-type AE may be
observed in conjunction with continuous emissions, and it is possible that the two
types of emissions are due to concurrent generating mechanisms. For example, in a
process where plastic deformation and fracture subsist, continuous AE is normally
attributed to plastic deformation, whereas the individual bursts are attributed to
the fracture process.

Moving dislocations are the dominant mechanism of plastic deformation in
metals.\footnote{A description of dislocation theory is out of the scope of this
review. For information on dislocations, literature may be
consulted~\cite{{hull84,honeycombe84}}. Also, there is a short introduction on
dislocation theory in Appendix~\ref{chap:disloc}.}  A description of the basic
mechanisms by which dislocations can cause AE was suggested by Gillis~\cite{gillis72}.
Basically, it is based on the fact that dislocations have periodic positions in the
lattice, which provides a minimum energy configuration. As a dislocation moves from one
minimum energy position to the next, the lattice elastic strain is increased until the
middle position is reached. After this, the elastic strain is suddenly released to
produce a vibrational wave in the lattice, which is believed to be the origin of the
detected AE waves. Gillis also speculated that all dislocation lines move
cooperatively, since each tends to move according to the stress field imposed by its
moving neighbours, and this has important consequences because then the vibration waves
produced by one dislocation tend to be in phase with the others.

Rouby~\etal~\cite{rouby77} proposed that continuous AE from plastic deformation is
due to the effect of a large number of elementary sources, homogeneously distributed
within the specimen, and randomly emitting during time. In order to explain the
spectral characteristics of the emissions, Rouby~\etal\ proposed that if each
dislocation (with length $l_\mr{D}$) moves at speed $V_\mr{D}$ between two obstacles
separated by distance $d_\mr{B}$, far way form the source, an AE signal may be
detected, whose frequency spectrum will display a maximum value that appears at
frequency
\begin{eqnarray}
   f_\mr{max} = \frac{V_\mr{D}}{2d_\mr{B}}
   \label{eq:rouby_ae_model}
\end{eqnarray}
As plastic strain increases, more obstacles are generated, and thus $d_\mr{B}$
decreases, leading to an increase of $f_\mr{max}$.

More generally, in a review paper by Skal's'kyi~\etal~\cite{skalskyi03}, it was
concluded that the accelerated motion of dislocations and their sudden stop are the
generation source of AE elastic waves. However, the exact mechanism by which AE is
generated during plastic deformation is still quite unclear, as it was concluded in a
recent review about the current understanding of the mechanisms of AE~\cite{ono05},
since though the understanding of AE from materials during fracture has advanced
greatly, that due to plastic deformation remains still quite elusive. Besides, these
two publications~\cite{skalskyi03,ono05} showed that no model relating AE to plastic
deformation at the typically high levels of strain rate normally encountered in metal
cutting have evolved so far, and it is unreasonable to assume that the low strain rate
AE source mechanisms are prevalent at high strain rates, since at high strain rates,
the deformation mechanisms and the dynamics of dislocation motion are very different
from the low strain rate case~\cite{rangwala91a}.

\subsubsection{Propagation}

As AE is generated, it propagates as ultrasonic waves, which can be longitudinal
(vibration in direction of motion) or transverse (vibration perpendicular to direction
of motion). Longitudinal and transverse waves travel at different speeds $c_\mr{L}$ and
$c_\mr{T}$, respectively, and, for many materials, $c_\mr{L} \approx 2c_\mr{T}$. As
they travel through different media, the characteristics of the AE waves undergo
considerable distortions. There are two main causes of distortion of acoustic
waves~\cite{blitz71,spanner74}: geometrical losses and attenuation. Since AE is
generally supposed to be generated from a point source, AE is considered to propagate
as spherical waves, whose amplitude ($I$) decreases inversely with distance ($x$) from
the source:
\begin{eqnarray}
   I = I_0\frac{x_0}{x}
   \label{eq:geometrical_lossses}
\end{eqnarray}
where $I_0$ is the amplitude at distance $x_0$. These are called geometrical losses
and are independent of frequency and material properties. Moreover, far from the
generating source, AE can be assumed to propagate as plane waves, so that geometrical
losses can be neglected. The amplitude of AE wave attenuates as it progresses
thorough the medium due to three major causes: diffraction, scattering, and
absorption. The following equation holds for wave amplitude attenuation:
\begin{eqnarray}
   I = I_0e^{-a (x - x_0)}
   \label{eq:attenuation}
\end{eqnarray}
where, $I_0$ is the amplitude at $x_0$, and $a$ is the attenuation coefficient which can
be expressed as
\begin{eqnarray}
   a = Af + Bf^4
   \label{eq:attenuation_coeff}
\end{eqnarray}
where $f$ is the frequency, and $A$ and $B$ are constants which depend on material and
type of wave (longitudinal or transverse).

\begin{figure}[h]
   \center{\includegraphics{reflection_refraction.eps}}
   \caption{Reflection and transmission of waves at the boundary with another material.}
   \label{fig:reflection_refraction}
\end{figure}
Another important phenomenon is the reflection and transmission of waves resulting when
an acoustic wave strikes the boundary with another medium. As shown in
Figure~\ref{fig:reflection_refraction}, if a longitudinal wave travelling through a
solid medium~A meets the boundary with medium~B at an angle $\alpha_\mr{L}$ with the
normal to the boundary, the following waves are reflected at the boundary: a
longitudinal wave reflected at an angle $-\alpha_\mr{L}$ to the normal to the boundary
and a transverse wave reflected at an angle $-\alpha_\mr{T}$ to the normal to the
boundary. In addition, a longitudinal wave transmitted into medium~B is refracted at
the boundary with an angle \mbox{$180^\circ + \beta_\mr{L}$} to the normal to the
boundary, and, if material B is a solid, a transverse wave will also be transmitted and
refracted at the boundary with an angle \mbox{$180^\circ + \beta_\mr{T}$} to the normal
to the boundary. The acoustic velocities for the various waves are related to one
another in the following manner:
\begin{eqnarray}
   \frac{c_\mr{AL}}{\sin\alpha_\mr{L}} = \frac{c_\mr{AT}}{\sin\alpha_\mr{T}} =
   \frac{c_\mr{BL}}{\sin\beta_\mr{L}} = \frac{c_\mr{BT}}{\sin\beta_\mr{T}}
   \label{eq:reflec_transm}
\end{eqnarray}
where $c_\mr{AL}$ and $c_\mr{AT}$ are the longitudinal and the transverse wave speeds in
medium~A, and $c_\mr{BL}$ and $c_\mr{BT}$ are the longitudinal and the transverse wave
speeds in medium~B\@.

When the incident transverse wave strikes the boundary at a right angle ($\alpha_\mr{L} =
0^\circ$), a transverse wave is reflected back into medium~A, and also another transverse
wave is transmitted forward through medium~B, both at $90^\circ$ with the boundary. The
relative amounts of reflected and transmitted energies are dependent on the
dissimilarities of the two materials, and these dissimilarities are represented by the
relative values of the characteristic acoustic impedances of both materials~A and~B
($r_\mr{A}$ and $r_\mr{B}$, respectively). For a given material, the characteristic
acoustic impedance is solely dependent on the physical characteristics of the material and
can be found from
\begin{eqnarray}
   r = \rho c_\mr{L}
   \label{eq:impedance}
\end{eqnarray}
where $\rho$ is the material density. Therefore, if $r_\mr{A} = r_\mr{B}$, no energy is
reflected, but the more $r_\mr{A}$ differs from $r_\mr{B}$, the more energy is reflected
back into medium~B\@.

\subsubsection{Detection}

At the surface of the material, the amplitude of the AE vibrations is very small
(usually a few nanometres), and, therefore, a high sensitivity transducer, which
converts the mechanical surface vibrations into electrical signals, is required for
reliable detection of AE\@. Most commercial AE transducers involve a piezoelectric
ceramic element manufactured from lead zirconate titanate (PZT).
Figure~\ref{fig:pzt_transducer} shows a conventional PZT transducer. However, although
other type of sensors have also been proposed, PZT sensors are the most reliable,
sensitive, and robust and are, therefore, the most widely used~\cite{reuben98}.
\begin{figure}[h]
   \center{\includegraphics{pzt_transducer.eps}}
   \caption{Piezoelectric transducer.}
   \label{fig:pzt_transducer}
\end{figure}

For efficient coupling of ultrasound between the transducer and a solid surface, a
suitable coupling film (e.g.\ oil or grease) must be provided to avoid an air gap
between the solid and the transducer, which would give rise to very small
transmission of AE to the transducer. This is due to the fact that there is a very
large difference between the characteristic acoustic impedances of, for instance, a
solid like steel and air ($r_\mr{steel}/r_\mr{air} \approx 10^5$), and, as shown
previously, nearly no acoustic energy would be transmitted to the transducer. Since
$r_\mr{oil}$ is much closer to the value of $r_\mr{steel}$ ($r_\mr{steel}/r_\mr{oil}
\approx 50$), much more acoustic energy is transmitted to the
transducer.\footnote{The values of the characteristic acoustic impedances were taken
from Blitz~\cite{blitz71}.}

\subsubsection{Signal Conditioning}

Signal condition, which is dependent on each particular system requirement, is purely
electronic and takes the electrical output signal from the AE sensor and provides an
electrical signal for further data acquisition or other processing. The most common
systems include a preamplifier, a band-pass filter, and an amplifier. A typical AE
system operates in the ultrasonic frequency range (e.g.\ 100--1000~kHz). The lower
frequency limit is imposed by the maximum frequency of unwanted background noises that
may be colouring the signal of interest; the upper frequency limit is imposed by
attenuation, which tends to limit the upper range of detection of AE signals; also, in
order to prevent aliasing,\footnote{The sample rate must be greater or equal to two
times the highest frequency content in the input signal. When this rule is violated,
undesired signals appear in the frequency band of interest. This is called aliasing.}
if the AE signal is going to be acquired, the maximum frequency of the signal must be
less than at least half of the sampling rate of the acquisition system. Therefore, the
low-pass frequency of the band-pass filter has to be sufficient to suppress low
frequency noise signals, and its high-pass frequency has to be low enough in order to
prevent aliasing.

\subsubsection{Signal processing}

Due to the stochastic character of the AE signals, the analysis and interpretation of
AE is normally quite complex. Consequently, signal processing techniques are needed
to process the raw AE signals. Next, the most important and common AE signal
processing techniques are reviewed:\footnote{Literature may be consulted for more
complex techniques; for example, Li~\cite{li02} and Diniz~\etal~\cite{diniz92}
reviewed some processing methods utilized to extract features from AE signals in view
of metal cutting monitoring.}

\begin{description}

   \item [Energy representation] The most common way to represent the energy of a
   signal\footnote{When one refers to AE energy, one is actually referring to energy
   per unit time, i.e.\ power. Moreover, since signals are normally obtained in volts
   (V), the power of the signals are presented in square volts (V$^2$), which are also
   the power units commonly found in AE literature.} is by calculating its root mean
   square (RMS). This is done by taking the square root of the mean of the square of
   the signal time series: \begin{eqnarray} I_\mr{RMS} = \sqrt{\frac{1}{n}\sum_{i =
   1}^n{I^2_i}} \label{eq:rms} \end{eqnarray} where $I_i$ is the amplitude of the
   signal at sampling instant $i$, and $n$ is the number of samples in the series.
   However, since the RMS computation does not avoid the influence of undesirable
   outlying values, such as randomly appearing burst-type signals that may be colouring
   a continuous emission, a new technique was developed~\cite{blum90}, where the raw
   signal is first full-wave rectified and additionally low-pass filtered; then, the
   maximum value of the probability density function of the resulting time series is
   found, so that the most common amplitude, the mode, can be obtained. The mode of a
   time series $I_i$ may be designated as $I_\mr{mode}$. Furthermore, the power of AE
   ($I_\mr{power}$) can be calculated either as $I^2_\mr{RMS}$ or $I^2_\mr{mode}$.

   \item [Count techniques] There are two major techniques: total number of counts
   ($N$) and count rate ($\dot N$). The total number of counts is the number of times a
   signal overcomes a given threshold. The number of counts per unit time is the count
   rate. The dependence of the count techniques on a threshold level can lead to
   problems, since if the signal amplitude changes, the count becomes meaningless if the
   threshold is also not changed.

   \item [Frequency analysis] When a signal is sampled, it is represented as a series
   of amplitudes as a function of time (time domain). The signals can also be
   represented as a function of frequency (frequency domain), and normally the fast
   Fourier transform (FFT) algorithm is utilized to compute the transformation from
   the time to the frequency domain. The distribution of the power of the signal in the
   frequency domain is known as the power spectrum. However, the power spectrum is
   still a series of amplitudes containing half of the number of samples of the
   original time series, and, therefore, a simpler parameter is necessary to
   characterize a signal in the frequency domain, and such a parameter is the mean
   frequency ($f_\mr{mean}$), which indicates the frequency value that divides the
   spectrum into two parts of equal energy~\cite{rangwala91b}:
   \begin{eqnarray}
      f_\mr{mean} = \frac{\sum_{i = 1}^n{S_i f_i}}{\sum_{i = 1}^n S_i}
      \label{eq:mean_freq}
   \end{eqnarray}
   where $f_i$ is the frequency at sample $i$, $S_i$ is the signal power at frequency
   $f_i$, and $n$ is the number of frequency samples.
\end{description}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Acoustic Emission from Metal Cutting}
\label{sec:ae_metal_cut}

In metal cutting, there are two major processes normally associated with the generation
of AE: plastic deformation and fracture. It has been
proposed~\cite{kannatey-asibu81,moriwaki83,li02} that the sources that contribute to
the generation of AE during metal cutting are the following
(Figure~\ref{fig:ae_zones}):
\begin{itemize}
   \item Plastic deformation in the primary and secondary zones.
   \item Tool-chip and tool-work sliding friction in the secondary
   and tertiary zones, respectively.
   \item Collision, entangling, and fracture of chips.
   \item Fracture of the cutting tool.
\end{itemize}
\begin{figure}[h]
   \center{\includegraphics{ae_zones.eps}}
   \caption[Sources of AE in metal cutting.]
   {Sources of AE in metal cutting. (a)~Continuous chip formation.
   (b)~Discontinuous chip formation.}
   \label{fig:ae_zones}
\end{figure}
Plastic deformation and friction is known to produce continuous AE, whereas collision,
entangling, and fracture of chips, and  breakage of the cutting tool is known to
produce burst-type emissions. Moreover, AE has been reported to be dependent on many
parameters, such as work and tool materials, tool geometry, cutting speed, feed rate,
width of cut, cutting fluids, etc.

\subsubsection{Energy Analysis of Continuous Acoustic Emission}
\label{sec:ae_cont_energy}

For continuous AE generation, it must be assumed that chip generation is continuous and
without BUE\@. Furthermore, the tool is normally considered to be perfectly sharp, so
that the tertiary zone source of AE can be neglected. In this section, the most
relevant AE generation models from continuous chip operations are reviewed.

One of the first attempts to model continuous AE from metal cutting was achieved by
Dornfeld and Kannatey-Asibu~\cite{dornfeld80}; the energy rate (power) of the AE
signals was stated to be proportional to the plastic work of deformation ($\dot U$).
Generally, $\dot U$ can be defined as:
\begin{eqnarray}
   \dot U = \int_v \sigma_{ij}\dot\epsilon_{ij}\mr{d}v
   \label{eq:plastic_work}
\end{eqnarray}
where $\sigma_{ij}$ and $\dot\epsilon_{ij}$ are the tensor notations for the applied
stresses and strain rates,\footnote{In a three-dimensional coordinate system ($x$,
$y$, and $z$), a small body (dimensions $dx$, $dy$, and $dx$) is subjected to nine
stress components $\sigma_{ij}$ ($i$ and $j$ are iterated over $x$, $y$, and $z$).
This collection of stresses is called the stress tensor. The same principle can be
used for the strain and strain rate tensors. Reference~\cite{hosford83} may be
consulted for more information.} respectively, acting on a volume $v$ of the material
participating into deformation. Moreover, $I_\mr{RMS}$ was used to represent the AE
energy rate. An expression for $\dot U$ was obtained by considering only primary
deformation, so that Equation~\ref{eq:plastic_work} was simplified and equated to
$I^2_\mr{RMS}$ as follows:
\begin{eqnarray}
   I^2_\mr{RMS} = Kk \dot\gamma_\mr{AB} v
   \label{eq:dornfeld_ae_model}
\end{eqnarray}
where $K$ is a constant of proportionality, $k$ is the shear strength of the material
(assumed to be constant), and $\dot \gamma_\mr{AB}$ is the mean shear strain rate at
the primary zone. The volume $v$ was derived from the slip line field for orthogonal
cutting without BUE from Lee and Shaffer~\cite{lee51}. The strain rate $\dot
\gamma_\mr{AB}$ was derived based upon experimental values of shear zone thickness from
Kececioglu~\cite{kececioglu58}. Moreover, it was observed that metal cutting was a good
source of AE and that AE was sensitive to strain rate, as proposed in
Equation~\ref{eq:dornfeld_ae_model}. However, since the model only accounts for
deformation in the primary deformation zone, and since other important sources of AE
were neglected, Dornfeld and Kannatey-Asibu concluded that the level of AE predicted by
the model would be underestimated.

Kannatey-Asibu and Dornfeld~\cite{kannatey-asibu81} developed a more sophisticated
model by considering that AE was generated mainly due to plastic deformation in the
primary and secondary zones and also sliding friction in the secondary zone. The
influence of the tertiary zone was neglected, since cutting with a sharp tool was
assumed. The work rate done in the primary and secondary zones was equated to
$I^2_\mr{RMS}$, and by assuming constant shear strength $k$, and simplified linear
friction conditions at the tool-chip interface, the following relationship was
obtained:
\begin{eqnarray}
   I^2_\mr{RMS} = K \left[ kwV \left(
   \frac{\cos\alpha}{\sin\phi\cos{(\phi -\alpha)}}t_1 +
   \frac{1}{3}(l_\mr{int} + 2l_1)\frac{\sin\phi}{\cos{(\phi - \alpha)}}
   \right) \right]
   \label{eq:kannatey-asibu_ae_model}
\end{eqnarray}
where $K$ is a constant of proportionality, and all the other variables are as
previously defined. In order to evaluate the validity of
Equation~\ref{eq:kannatey-asibu_ae_model}, orthogonal cutting tests were performed
with tubular workpieces of an aluminium alloy and a mild steel. In a first set of
tests, the feed rate was kept constant, and $\alpha$, $V$, and the workpiece material
were allowed to vary. The level of AE was observed to be strongly dependent on $V$,
increasing with increasing $V$. The steel workpiece produced a higher level of AE
than the aluminium alloy, as expected, since the shear strength of the steel is
higher than that of the aluminium. The level of $I_\mr{RMS}$ was also observed to
increase with $\alpha$. Moreover, a plot of predicted against experimental values of
$I_\mr{RMS}$, indicated that Equation~\ref{eq:kannatey-asibu_ae_model} was not
universal since a dependency on $\alpha$ was present (the constant of proportionality
$K$ was rake angle dependent). Equation~\ref{eq:kannatey-asibu_ae_model} was
subsequently modified by replacing constant $K$ by $K\sin\alpha$ to give a better
relationship between predicted and experimental $I_\mr{RMS}$ values. Furthermore, a
second set of tests was performed by employing tools with restricted contact lengths,
so that variations of AE with tool-chip contact length could be estimated. In order
to keep the AE generated from the primary shear zone constant with varying tool-chip
contact length, the shear angle was kept constant by adjusting the feed rate
accordingly. It was observed that $I^2_\mr{RMS}$ increased linearly with contact
length for the lower lengths, and then it started to reduce in slope for the higher
contact lengths. The reduction in slope at the higher contact lengths was attributed
to the onset of sliding friction, suggesting that less AE activity is generated due
to friction than bulk plastic deformation. The point at which the slope starts to
change was used to estimate the boundary between sticking and sliding.

Schmenk~\cite{schmenk84} used the model developed by Kannatey-Asibu and
Dornfeld~\cite{kannatey-asibu81} (Equation~\ref{eq:kannatey-asibu_ae_model}) to derive
an expression for $I^2_\mr{RMS}/v$ (specific AE output). For a tool with $0^\mr{\circ}$
rake angle, and by assuming a shear angle of $30^\mr{\circ}$, and that $l_1 =
l_\mr{int}/2 = t_1$, the specific AE output was simplified to the following expression:
\begin{eqnarray}
   \frac{I^2_\mr{RMS}}{v} = u = K(2 + 0.67)
   \label{eq:schmenk_ae_model}
\end{eqnarray}
where $v = t_1wV$. Within the brackets, the left hand term represents the contribution of
the primary shear zone, while the right hand term represents the contribution of the
tool-chip interface. As a result, Schmenk concluded that deformation in the primary zone
was the dominant source of AE\@. Cutting tests with a ductile aluminium alloy, performed
on a milling machine, showed that there was a significant decrease of specific AE output
with uncut chip thickness, which was attributed to the size effect.

In order to quantify the relative contribution from the primary and secondary zones,
Lan and Dornfeld~\cite{lan86} extracted two terms from
Equation~\ref{eq:kannatey-asibu_ae_model}: $t_1\cos\alpha/[\sin\phi\cos{(\phi -
\alpha)}]$, representing the primary zone contribution to AE, and $(l_\mr{int} +
2l_1)\sin\phi/[3\cos{(\phi - \alpha)}]$, representing the secondary zone contribution
to AE\@. Machining tests with a high speed steel, in which measurements of the shear
angle $\phi$ and total tool-chip contact length $l_\mr{int}$ were included, revealed
that both the primary and secondary shear zones contributed approximately by the same
amount of energy to the total AE signal. These results oppose Schmenk's
conclusions~\cite{schmenk84}, i.e.\ the primary zone is the major AE contributor, which
was attributed to the assumption that $l_\mr{int} = 2t_1$. Furthermore, Lan and
Dornfeld developed a further model considering signal attenuation and tool flank
contact:
\begin{eqnarray}
   I_\mr{RMS} = K \left( kwV \left[
   K_1\frac{\cos\alpha}{\sin\phi\cos{(\phi-\alpha)}}t_1 +
   K_2\frac{1}{3}(l_\mr{int} + 2l_1)\frac{\sin\phi}{\cos{(\phi-\alpha)}} +
   K_3V_\mr{B} \right] \right)^m
   \label{eq:lan_ae_model}
\end{eqnarray}
where $m$ is material dependent, $V_\mr{B}$ is the average length of the flank wear
land, and $K_1$, $K_2$, and $K_3 $ are factors for signal attenuation, corresponding
to signal transmission losses between the primary shear zone, tool-chip interface
zone, flank wear zone, and the transducer, respectively. The magnitude of $K_1$ was
found to be between $0.2$ and $0.25$, while both $K_2$ and $K_3$ were assumed to be
one. Moreover, machining tests performed with a low carbon steel showed that
$I_\mr{RMS}$ was not very sensitive to the variations in feed rate and width of cut,
contradicting Equation~\ref{eq:lan_ae_model} predictions. In order to justify this
contradiction, Lan and Dornfeld pointed out that the analytical derivation of
Equation~\ref{eq:lan_ae_model} was based upon orthogonal machining, whereas the
experiments were conducted with oblique machining conditions. The size effect was
also mentioned as a reason for the high values of AE energy encountered at low values
of uncut chip thickness.

Messaritis and Borthwick~\cite{messaritis86} proposed the use of Oxley's semi-empirical
theory~\cite{oxley98} for the prediction of AE activity during metal cutting, since the
shear plane model used to derive the AE energy models described above was, according to
the authors, an over-simplistic representation of the cutting process. Preliminary
machining tests on a low carbon work material showed that although $I_\mr{RMS}$ was
slightly higher in semi-orthogonal cutting than in orthogonal cutting, semi-orthogonal
conditions could still be used with reasonable accuracy in conjunction with Oxley's
theory. Predictions of $\dot\gamma$ (strain rate), showed that $\dot\gamma$ was
invariable with $w$, decreased with $t_1$ and increased with $V$. The same trends were
observed with experimental results of $I^2_\mr{RMS}$ with $w$, $t_1$, and $V$. The
relative insensitivity of $I_\mr{RMS}$ to varying widths of cut showed that the
dependence of AE on volume was very small, and since $k$ is dependent on $\dot\gamma$,
Messaritis and Borthwick concluded that $\dot\gamma$ was the dominant parameter in AE
generation, and, as a result, the following relationship was suggested:
\begin{eqnarray}
   I^2_\mr{RMS} = A + B\dot\gamma
   \label{eq:messaritis_ae_model}
\end{eqnarray}
where $A$ and $B$ are dimensional constants dependent on the wave
propagation path and transducer installation.

Blum and Inasaki~\cite{blum90} observed that $I_\mr{RMS}$ contains the influence of
randomly appearing bursts caused by unavoidable noise sources, such as chip breakage
and impact. Consequently, a new AE energy parameter, which eliminates the
interference of randomly appearing noises, named $I_\mr{mode}$ (mode of the
previously full-wave rectified and low-pass filtered raw AE signals, as defined in
Section~\ref{sec:ae_theory}), was proposed. Experimental machining tests were
conducted with a medium carbon steel work material, and the primary ($\dot{U}_\mr{AB}
= F_\mr{AB}V_\mr{S}$) and secondary ($\dot{U}_\mr{int} = F_\mr{int}V_\mr{C}$) energy
consumptions were calculated. It was observed that $\dot{U}_\mr{AB}$,
$\dot{U}_\mr{int}$, and $I_\mr{mode}$ increased with increasing $V$. Despite both
energy consumptions increased with increasing $t_1$, $I_\mr{mode}$ showed an opposite
falling tendency. Both $I_\mr{mode}$ and $\dot U_\mr{AB}$ decreased with increasing
$\alpha$, although $\dot U_\mr{int}$ increased with increasing $\alpha$. As in
previous results, $I_\mr{mode}$ exhibited insensitivity to varying $w$, demonstrating
that AE generation is not significantly affected by the volume of deforming material.
However, both energy consumptions showed a strong increase with rising $w$.
Furthermore, the following relationship was suggested:
\begin{eqnarray}
   I^2_\mr{mode} \propto \dot\gamma^m
   \label{eq:blum_ae_model}
\end{eqnarray}
where $m$ is the strain rate sensitivity. Kececioglu's~\cite{kececioglu58} shear zone
thickness results were used to determine $\dot\gamma$.  Experimental results of
$I_\mr{mode}$ were plotted against calculated $\dot\gamma$ values and appeared to be in
agreement with the relationship proposed in Equation~\ref{eq:blum_ae_model}.

Since, at the high strain rates encountered in metal cutting (higher than
1000~s$^{-1}$), the deformation mechanisms and the dynamics of the motion of
dislocation are very different from the low strain rate deformation regimes, Rangwala
and Dornfeld~\cite{rangwala91a}, based on Kumar~\etal~\cite{kumar68} and
Kumar~\cite{kumar69}, proposed a new mechanism of AE generation during metal cutting. A
linear relationship between flow stress and strain rate was considered, suggesting that
the dynamics of dislocation motion was governed by damping mechanisms, i.e.\ $F =
BV_\mr{D}$, where $F$ is the unit force acting on the dislocation per unit length,
$V_\mr{D}$ the velocity of the dislocation between obstacles, and $B$ the damping
coefficient. Moreover, if dislocation damping was responsible for AE generation,
Rangwala and Dornfeld suggested that the power of the AE signal ($I^2_\mr{RMS}$) should
be proportional to the damping power ($\dot U_\mr{D}$):
\begin{eqnarray}
   I^2_\mr{RMS} \propto \dot U_\mr{D} =
   \frac{B}{\rho_\mr{MD}b^2}\dot\epsilon^2v
   \label{eq:damping_power}
\end{eqnarray}
where $\rho_\mr{MD}$ is the mobile dislocation density, $b$ the Burgers vector of the
crystal lattice\footnote{For more information on dislocation theory,
Appendix~\ref{chap:disloc} and relevant literature on the
subject~\cite{hull84,honeycombe84} may be consulted.} and $v$ the volume involved in
plastic deformation. In order to evaluate the viability of dislocation damping as a source
mechanism of AE at high strain rates, orthogonal machining tests were performed with an
aluminium alloy tubular workpiece. A first set of tests used a restricted contact length
tool with variable cutting speeds and feed rates. A linear relationship between
$I_\mr{RMS}$ and calculated shear velocity $V_\mr{S}$ was observed, implying that, at
constant contact length, $I_\mr{RMS}$ was a linear function of the strain rate in the
primary zone. This relationship is also observed in Equation~\ref{eq:damping_power},
corroborating the assumption that dislocation damping may be one of the contributing
mechanisms for AE generation in metal cutting. Assuming that AE is generated only by
dislocation damping associated with plastic deformation in the primary and secondary shear
zones, that the primary zone thickness is equal to the secondary zone thickness, and that
there is no sliding zone at the tool-chip interface, Rangwala and Dornfeld derived the
following relationship:
\begin{eqnarray}
   I^2_\mr{RMS} = KV^2_\mr{S} \left( \frac{t_1}{\sin\phi} + l_\mr{int}\sin^2\phi \right)
   \label{eq:rangwala_ae_model}
\end{eqnarray}
A second set of tests employed tools with varied contact lengths for different
cutting speeds and constant feed rate. With low contact length tools, the
relationship between experimental values and Equation~\ref{eq:rangwala_ae_model}
predictions of $I_\mr{RMS}$ were reasonably linear. However, as the contact length
increased, a decay from linearity was observed. This was attributed to the onset of
sliding friction for higher tool contact lengths, which was neglected in the
development of Equation~\ref{eq:rangwala_ae_model}.

Saini and Park~\cite{saini96} have also developed a model that equates $I^2_\mr{RMS}$ to
the work rate done in the primary and secondary zones of deformation:
\begin{eqnarray}
   I^2_\mr{RMS} = kwVt_1 \left[
   K_1\frac{\cos\alpha}{\sin\phi\cos{(\phi - \alpha)}} +
   K_2\frac{2m\sin{(\phi + \lambda - \alpha)}}{(n + 2)\cos\lambda\cos{(\phi - \alpha)}}
   \right]
   \label{eq:saini_ae_model}
\end{eqnarray}
where $\lambda$ is the friction angle (Equation~\ref{eq:friction_angle}), $m$ is the
coefficient of the chip contact length ($m = 2$ for carbon steel), and $n$ (parabolic
constant) was determined from
\begin{eqnarray}
   n = \frac{2kwl_\mr{int}}{F_\mr{Y}\sin\alpha + F_\mr{X}\cos\alpha} - 2
   \label{eq:parabolic_constant}
\end{eqnarray}
where the cutting forces $F_\mr{X}$ and $F_\mr{Y}$ were determined from experimental
measurements. The signal attenuation constants $K_1$ and $K_2$, for the primary and
secondary deformation zones, respectively, were found by a computational statistical
analysis technique, resulting in \mbox{$K_1 = 0.00098$} and \mbox{$K_2 = 0.00157$}.
Orthogonal turning tests, carried out with a carbon steel, showed that the with of cut
had no influence on $I_\mr{RMS}$. The variation of $I_\mr{RMS}$ with $V$ and $\alpha$
showed that the predictions from Equation~\ref{eq:parabolic_constant} and the
experimental results were in agreement, where $I_\mr{RMS}$ increased with $V$ and
decreased with $\alpha$. Saini and Park argued that one major advantage of this model
was in the determination of $l_1$ and $l_2$, which were based on realistic assumptions
of the frictional stresses in the sticking and sliding zones.

In conclusion, by assuming that the AE energy rate is proportional to the plastic
work of deformation, it can be derived that the AE energy is virtually proportional
to the applied stress, strain rate, and volume of material participating into
deformation. All published experimental results led to the definite conclusion that
the AE power was strongly dependent on strain
rate~\cite{dornfeld80,messaritis86,blum90,rangwala91a}, and since strain rate is
directly dependent on cutting speed, a strong relationship was also observed between
the cutting speed and the AE energy
rate~\cite{dornfeld80,kannatey-asibu81,inasaki81,messaritis86,blum90,saini96}.
Moreover, the AE energy was observed to be essentially unaffected by the width of
cut~\cite{inasaki81,lan86,messaritis86,blum90}, although increasing AE energy with
increasing width of cut has also been reported~\cite{lan85}. The independence of the
AE power from the width of cut implies that the dependence of AE on volume is
insignificant, since the volume of deforming material is proportional to the width of
cut, and, in principle, the width of cut affects neither the shear strength nor the
strain rate. Hence, since the flow stress is a function of strain rate, it was
proposed~\cite{messaritis86,blum90} that the AE energy was essentially only strain
rate dependent. Some experimental results showed that the AE energy decreased with
feed rate~\cite{dornfeld80,messaritis86,blum90}, whereas other
results~\cite{dornfeld80,inasaki81,lan85,lan86,rangwala91a} showed that the AE energy
remained roughly constant with varying feed rate. However, in most cases, it was also
observed that the variation of AE power with feed rate showed a similar trend to the
variation of strain rate with feed rate~\cite{messaritis86,blum90,rangwala91a},
supporting the theory that the AE energy is a function of strain rate and not volume
dependent. With the exception of the results presented by Kannatey-Asibu and
Dornfeld~\cite{kannatey-asibu81}, the AE energy was observed to decrease with
increasing tool rake angle~\cite{lan86,blum90,saini96}. Experimental data on the
variation of AE with different material properties is scarce and insufficiently
systematized. Lan and Dornfeld~\cite{lan86} heat treated workpieces of a medium
carbon steel to different hardness values and observed $I_\mr{RMS}$ to increase
linearly with increasing hardness. In addition, materials with higher shear strength
values were observed to generate higher levels of AE
energy~\cite{kannatey-asibu81,lan85}.

\subsubsection{Frequency Analysis of Continuous Acoustic Emission}
\label{sec:ae_cont_freq}

This section reviews published material about the frequency characteristics of AE during
metal cutting. Unfortunately, not much work has been done on this subject.

Grabec and Leskovar~\cite{grabec77} studied the spectrum of AE in the \mbox{0--100 kHz}
range, generated during the machining of an aluminium alloy, and observed that in the
low frequency range, below 15~kHz, the spectrum was practically discrete, which was
attributed to the several modes of mechanical resonance of the whole cutting system. In
the range above 15~kHz, the spectrum was observed to be continuous, which was
attributed to the deformation and friction from the cutting process. It was also
observed that both feed rate and width of cut did not influence the spectrum
appreciably, so that the cutting speed was the dominant factor affecting the high
frequency content of the spectrum.

Yaohui and Rongbao~\cite{yaohui88} utilized a method called maximum entropy spectrum to
analyse the AE generated during the machining of aluminium. With this method, individual
separate zones were identified in the spectrum, corresponding to different AE generation
mechanisms, such as plastic deformation, friction and BUE\@. It was also observed that AE
generated due to fracture and impact of chips to be a random noise signal with a wide
frequency band.

Rangwala and Dornfeld~\cite{rangwala91b} presented a study of the spectral characteristics
of AE generated during the machining of an aluminium alloy. Two parameters of the signal
power spectrum were used: the mean frequency ($f_\mr{mean}$, as defined in
Section~\ref{sec:ae_theory}) and the standard deviation of the mean frequency
($\sigma_\mr{mean}$). The value of $f_\mr{mean}$ was observed to increase with $V$ up to a
certain value of $V$, after which $f_\mr{mean}$ started to decrease. Rangwala and Dornfeld
explained this trend by noting that at low cutting speeds, as $V$ increases, the strain
rate also increases, and then AE is expected to shift towards higher frequencies; however,
at high strain rates, the tool-chip interface temperature also increases, and, at some
point, it is expected that the temperature effects offset the effects of strain rate,
causing AE to shift towards lower frequencies. Moreover, The value of $\sigma_\mr{mean}$
was observed to increase with $V$, and this was attributed to the widening of the primary
shear zone with increasing $V$, resulting in a larger variation of strain rates;
consequently, the AE sources operate in a wider frequency region, causing a higher spread
of the spectral power distribution. In addition, $f_\mr{mean}$ and  $\sigma_\mr{mean}$ did
not exhibit any clear trend with varying feed rate, and no definite explanation was
provided by Rangwala and Dornfeld. Finally, $f_\mr{mean}$ was observed to increase with
tool-chip contact length, indicating that AE due to chip sliding is concentrated in the
higher frequencies. This is consistent with the fact that the temperatures in the sliding
zone are not very high, causing AE to shift towards higher frequencies.

\subsubsection{Burst-Type Acoustic Emission from Metal Cutting} \label{sec:ae_burst}

The study of bust-type AE can be divided into two major fields:

\begin{description}

   \item [Chip form] The main types of chip formation are shown in
   Figure~\ref{fig:chip_types} as continuous, continuous with BUE, discontinuous, and
   segmented. Another possible application of AE is the detection of chip form
   during metal cutting. It has been suggested that the burst-type AE signals generated
   due to chip breakage can be used to distinguish between continuous and discontinuous
   chip formation, since continuous chips generate continuous type AE\@. In discontinuous
   chip formation processes, each AE burst has been observed to be related to the breaking
   of the chip~\cite{dornfeld83,uehara84,dornfeld85}. Different chip forms were generated
   from the variation in the feed rate \cite{dornfeld83,dornfeld85}, and the average chip
   breaking frequency (number of chips produced per unit time) was calculated and observed
   to be well correlated to the average rate of AE burst events. Uehara and
   Kanda~\cite{uehara84} used four different materials to produce different chip forms
   (continuous with BUE, discontinuous, and segmented) and demonstrated that the different
   types of chip form produce different AE patterns.  Furthermore, during operations with
   continuous chips, the congestion or entanglement of the chip around the tool and
   workpiece is undesirable. It was observed that during chip congestion or entanglement,
   there is a sudden increase of high amplitude AE signals \cite{dornfeld83,dornfeld85}.

   \item [Tool fracture] Another promising use of AE is the detection of tool failure.
   Burst-type AE signals are detected when cracking, chipping, and fracture of the cutting
   tool is observed~\cite{moriwaki80,lan84}. In order to facilitate tool failure, Lan and
   Dornfeld~\cite{lan84} used a hardened work material and pre-slotted inserts. A
   significant burst of acoustic emission was detected at the moment of tool fracture. It
   was observed that $I^2_\mr{RMS}$ increased with increasing fracture area. Moreover,
   chipping was seen to generate a lower burst AE signal because of the smaller fracture
   area. It was also observed that it was difficult to distinguish between a burst AE
   signal related to chipping and noise signals due to chip breakage and impact. Diei and
   Dornfeld~\cite{diei87} proposed a quantitative model, relating the peak of $I_\mr{RMS}$
   to both the fractured area and the resulting cutting force at tool fracture. Good
   agreement was obtained between experimental values and model predictions.

\end{description}

\subsubsection{Tool Wear and Acoustic Emission} \label{sec:ae_tool_wear}

Acoustic emission has been proposed as a suitable method for detecting cutting tool
wear. Li~\cite{li02} presented an updated review of the AE-based methods for tool wear
monitoring during turning. Generally, the level of AE generation has been observed to
increase with flank wear~\cite{inasaki81,lan82,messaritis86,naerheim88,blum90}. Inasaki
and Yonetsu~\cite{inasaki81} observed an approximate linear increase of the level of AE
with flank wear, and the rate of increase was observed to be higher for higher cutting
speeds. However, Messarits and Borthwick~\cite{messaritis86} observed that the rate of
increase of $I_\mr{RMS}$ with flank wear decreased with increasing flank wear. Blum and
Inasaki~\cite{blum90} observed that, when no significant crater was developed, although
both energy consumptions in the primary and secondary zones increased only slightly
with flank wear, $I_\mr{mode}$ exhibited a steep increase with flank wear. Reverse
cutting tests (workpiece rotates backwards and only the flank surface of the tool
touches the workpiece) revealed that the amount of AE generated due to sliding friction
in the tertiary zone was small compared to the amount of AE generated during normal
cutting. Therefore, as the flank surface of the tool wears, $V_\mr{B}$ increases and
the rightmost term of Equation~\ref{eq:lan_ae_model}~\cite{lan86} becomes significant.
Moreover, Uehara and Kanda~\cite{uehara84} observed that the power spectrum of the AE
signals were strongly affected by tool wear.

Most studies have only considered the influence of flank wear on the AE parameters,
but Naerheim and Lan~\cite{naerheim88} concluded that when crater wear occurred along
with flank wear, one influence cancelled the other. The AE level tended to become
constant as cutting time elapsed, since the increase in flank wear increased AE
generation, whereas the increase in crater wear decreased AE generation, owing to the
fact that the increase in crater wear increased the effective rake angle. Lan and
Dornfeld~\cite{lan82} had already observed that the level of AE seemed to decrease
with crater wear. Therefore, when flank and crater wear were present, the level of
wear from the analysis of $I_\mr{RMS}$ was difficult to estimate due to the opposing
effects of the two types of wear.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Summary of Literature} \label{sec:summ_literature}

As stated at the beginning of this chapter, the review of the relevant literature was
divided into two major areas: metal cutting and AE.

The most simplified metal cutting conditions were assumed: metal cutting is orthogonal,
the chip does not spread to either side, the tool is perfectly sharp, the chips are
continuous and without BUE, no chatter is present, and there is no externally applied
coolant or lubricant. With these conditions, two important zones of deformation can be
identified: primary zone and secondary zone. The chip is formed in the primary zone,
which is a narrow zone of intense shear that extends from the tool edge to the work
surface. This zone has been modelled as a plane~\cite{ernst41}, called the shear plane,
and a very important angle can be defined between this plane and the direction of the
cutting speed, the shear angle $\phi$; a parallel-sided shear zone has also been used
to model the primary zone of deformation~\cite{oxley89}. The secondary zone of
deformation is defined by the contact between the tool rake face and the chip as it
flows over the tool. The earliest analysis treated the tool-chip interface as a sliding
friction situation~\cite{ernst41}; however, it has been found that the tool-chip
interface is formed by a region of sliding friction (nearest to the point where the
chip leaves the tool) and a region involving plastic shear of the chip (nearest to the
cutting edge)~\cite{zorev63}; the tool-chip interface has also been modelled as a zone
of constant plastic shear with no sliding~\cite{oxley89}.

Metal cutting modelling deals mainly with the prediction of $\phi$, since this angle
defines the geometry of the cutting process. No estimation of forces, stresses, and
temperatures can be made without first evaluating $\phi$. Two types of models have
emerged: the fist type considers that deformation is performed with constant material
properties~\cite{ernst41,lee51,kobayashi59}, and, in the second type, material
properties are allowed to vary due to the effects of strain, strain rate, and
temperature~\cite{oxley89}. Modelling with constant material properties is an
oversimplification, and, although contributing to the understanding of the cutting
process, predictions of $\phi$ are quite inaccurate when compared with experimental
results from different work materials. A semi-empirical model that allows material
properties to vary, developed by Oxley and co-workers~\cite{oxley89}, has proven to
give excellent predictions of $\phi$, cutting forces, and temperatures when compared
with experimental results; however, at present, this model can only provide predictions
for carbon steel work materials.

Acoustic emission may be defined as the transient elastic wave generated by the rapid
release of strain energy within a material, which propagates in all directions,
ultimately reaching the surface of the material, where it can be detected by an
appropriate sensor. In metals, the main sources of AE are normally associated with the
dislocation movement accompanying plastic deformation and with the initiation and
extension of cracks in a structure under stress; dislocation movement is normally
associated with a continuous type of AE, whereas high amplitude and short duration
pulses, called burst-type AE, are associated with cracking processes.

In metal cutting processes with continuous chip formation, without BUE, and with a
perfectly sharp tool, AE generation is normally attributed to the plastic work of
deformation occurring in the primary and secondary deformation zones, and,
consequently, AE is expected to be of continuous type. A number of more or less
sophisticated models that relate AE from metal cutting have emerged; basically, most of
theses models are based on the same principle: the power of the AE signals is
proportional to the plastic work of
deformation~\cite{dornfeld80,kannatey-asibu81,schmenk84,blum90,rangwala91a,saini96}.
Theses models seem to be in agreement with experimental data when only $V$ is allowed
to vary, and $t_1$ and $w$ are kept constant. According to some of the above-mentioned
models, the power of AE should increase with $t_1$ and
$w$~\cite{kannatey-asibu81,schmenk84,saini96}; however, experimental results showed
that AE is essentially unaffected by $w$~\cite{inasaki81,lan86,messaritis86,blum90},
although AE has also been reported to increase with $w$~\cite{lan85}; some experimental
results showed that AE power decreases with
$t_1$~\cite{dornfeld80,messaritis86,blum90}, whereas other results showed that AE power
remains relatively unaffected by
$t_1$~\cite{dornfeld80,inasaki81,lan85,lan86,rangwala91a}. A preliminary analysis of
the published results shows that AE should be strain rate dependent and volume
independent.

In conclusion, none of the AE models developed so far appear to give a satisfactory
solution for the problem, since they only agree with the experimental results when only
$V$ is allowed to change, and all the other variables are maintained constant, and,
consequently, a different approach to the problem is necessary. Therefore, as stated in
Section~\ref{sec:obj_struct}, it is the objective of the present thesis to investigate
the generation mechanisms of AE during metal cutting, and as dislocation motion is
considered to be the main mechanism responsible for plastic deformation, a relationship
between AE and the motion of dislocations accompanying plastic deformation at the
typical strain rates and temperatures encountered in metal cutting is going to be
examined. Since most published experiments were performed for quite limited cutting
conditions and work materials, a series of cutting tests is going to be performed for a
wide range of cutting conditions and work materials. For the prediction of important
parameters that define the physics of metal cutting, the semi-empirical model developed
by Oxley and co-workers~\cite{oxley89} is going to be employed. A signal processing
technique~\cite{blum90}, named AE mode, which minimizes the influence of undesirable
outlying values from the AE data, is going to be used to compute the power of AE\@.
Finally, a technique~\cite{rangwala91b}, called mean frequency, is going to be employed
to calculate the average frequency content of AE\@.
