Analysis of tool chatter in turning operation on lathe machine

Analysis of tool chatter in turning operation on lathe
machine
Submitted in partial fulfilment for the award of the degree of
BACHELOR OF TECHNOLOGY
In
Mechanical Engineering
(28 May 2014- 14 July 2014)
Submitted by: -
Aakash Gautam(111601)
Abhay Rai(111603)
Aditya Kr. Singh(111610)
Devanshu Yadav(111628)
Vijay Pratap Singh(111689)
DEPARTMENT OF MECHANICAL ENGINEERING
JAYPEE UNIVERSITY OF ENGEENERING AND TECHNOLOGY
A-B ROAD, RAGHOGARH, DT. GUNA-473226, MP., INDIA

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JAYPEE UNIVERSITY OF ENGINEERING & TECHNOLOGY
MECHANICAL ENGINEERING DEPARTMENT
A.B.ROAD,P.B.No.1, RAGHOGARH, DIST: GUNA (M.P) INDIA
PHONE : 07544 267051, 267310-14 FAX : 07544 267011
Website : www.juet.ac.in
CERTIFICATE
This is to certify that the work titled “Analysis of tool chatter in turning operation on lathe
machine” submitted by “ Aakash Gautam (111601), Abhay Rai (111603), Aditya Kr. Singh
(111610), Devanshu Yadav (111628), Vijay Pratap Singh (111689)” in partial fulfilment for the
award of degree of Bachelor of Technology of Jaypee University of Engineering & Technology;
Guna has been carried out under my supervision at JUET Guna campus. This work has not been
partially or wholly to any other University or Institute for the award of this or any other degree or
diploma.
Dr. Bhagat Singh
Lecturer
Mechanical Engineering Department
JUET, GUNA
Place…………………
Date………………….

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ACKNOWLEDGEMENT
Successful completion of work will never be one man’s task. It requires hard work in right
direction. There are many who have helped to make our experience as a student a rewarding one.
In particular, we express our gratitude and deep regards to our thesis guide Dr. Bhagat Singh for
kindly providing us to work under his supervision and guidance. We extend our deep sense of
indebtedness and gratitude to him first for his valuable guidance, constant encouragement & kind
co-operation throughout period of work which has been instrumental in the success of thesis.
We also express our sincere gratitude to Mr. Arun Kumar Pandey, Mechanical Engineering
Department, for providing valuable departmental facilities. We are greatly indebted to our family
members for extending their loving support throughout.
Name of Students Signature
Aakash Gautam (111601) ………………………..
Abhay Rai (111603) ………………………..
Aditya Kr. Singh (111610) ……………………......
Devanshu Yadav (111628) ………………………...
Vijay Pratap Singh (111689) ………………………...

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Abstract
Chatter vibrations are present in almost all cutting operations and they are major obstacles in
achieving desired productivity. Regenerative chatter is the most detrimental to any process as it
creates excessive vibration between the tool and the workpiece, resulting in a poor surface finish,
high-pitch noise and accelerated tool wear which in turn reduces machine tool life, reliability and
safety of the machining operation. There are various techniques proposed by several researchers
to predict and detect chatter where the objective is to avoid chatter occurrence in the cutting
process in order to obtain better surface finish of the product, higher productivity and tool life. In
this paper, some of the chatter stability prediction, chatter detection and chatter control techniques
for the turning process are reviewed to summarize the status of current research in this field. The
objective of this review work is to compare different chatter stability prediction, chatter detection
and chatter control techniques to find out most suitable technique/s and to identify a research scope
in this area. One scope of research has been identified as establishing a theoretical relationship
between chatter vibration and tool wear in order to predict tool wear and tool life in the presence
of chatter vibration.

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Table of contents
Certificate ....................................................................................................................................... II
Acknowledgement.........................................................................................................................III
Abstract..........................................................................................................................................IV
Chapter 1 .........................................................................................................................................1
Introduction .....................................................................................................................................1
1.1 Background................................................................................................................................1
1.2 Tool chatter in machine tools ....................................................................................................1
1.3 Chatter suppression techniques .................................................................................................2
1.4 Problem definition.....................................................................................................................4
1.5 Methodology adopted................................................................................................................5
1.6 Organization of the thesis..........................................................................................................5
Chapter 2 .........................................................................................................................................7
Literature survey..............................................................................................................................7
2.1 Analytical techniques for chatter stability prediction................................................................7
2.1.1Stability lobes diagram (sld)...............................................................................................7
2.1.1.1Analytical models based on the number of dof..........................................................8
2.1.1.2.Analytical models based on compliance/flexibility of tool – workpiece system....10
2.1.2 Nyquist plots....................................................................................................................12
2.1.3 Finite element method/analysis (fem/fea) .......................................................................13
2.2 Experimental techniques .........................................................................................................14
2.2.1 Signal acquisition and processing techniques .................................................................15
2.2.1.1 Force and vibration measurements..........................................................................15
2.2.1.2 Chip analysis technique...........................................................................................20
2.2.2 Artificial intelligence techniques.....................................................................................21
2.2.2.1 Ann technique..........................................................................................................21
2.2.2.2 Fuzzy logic technique..............................................................................................23
Chapter 3 .......................................................................................................................................25
Theoretical analysis of tool chatter................................................................................................25
3.1 Dynamics of orthogonal turning during chatter ......................................................................25
3.2 Simulink model .......................................................................................................................29
Chapter 4 .......................................................................................................................................37
Wavelet packets and hilbert–huang transform ..............................................................................37
4.1 Wavelet transform ...................................................................................................................37
4.2 Wavelet packet transform........................................................................................................40
4.3 Hilbert–Huang transform.........................................................................................................41
4.4 Proposed chatter detection methodology.................................................................................42
4.5 Simulation................................................................................................................................43
Chapter 5 .......................................................................................................................................48
Chatter quantification using response surface methodolgy (rsm) .................................................48
5.1 Introduction .............................................................................................................................48
5.2 Response surface methodology (rsm) .....................................................................................48
5.2.1 Test for significance of the regression model..................................................................50
5.2.2 Test for significance on individual model coefficients ...................................................51
5.2.3 Test for lack-of-fit ...........................................................................................................51

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5.3 Response surface regression for chatter amplitude .................................................................52
5.3.1 Analysis of variance (anova) ...........................................................................................53
5.3.2 Plots of main effects of interaction parameters on chatter amplitude .............................57
5.3.3 Residual plots for chatter vibration .................................................................................57
5.3.4 Checking adequacy of mathematical models ..................................................................59
Chapter 6 .......................................................................................................................................60
Summary and scope for further research.......................................................................................60
6.1 Summary and conclusions.......................................................................................................60
6.2 Scope for further research .......................................................................................................61
References .....................................................................................................................................62
List of Figures
Figure 3.1(Various Experiments of bitumen)……………………………………………...….....18
Figure 4.1(Washing of aggregates) ............................................... Error! Bookmark not defined.
Figure 4.2(Heating of aggregates and shredded plastic) ............... Error! Bookmark not defined.
Figure 4.3(Plastic coated aggregates)............................................ Error! Bookmark not defined.

vii
Figure 4.4(Impact value, Crushing value and Los angles apparatus)............................................23
Figure 4.5(Marshall Test)………………………………………………………………………..23
Figure 5.1(Phase diagram of Marshall Specimen)….……………………………………...33
Figure 5.2(Grading requirement of fresh aggregate)……………...………………………..…....34
Figure 5.3(TABLE-8OF IRC: 111-2009)…………………………………………………….….34
Figure 5.4(Interaction model for the Plastics waste coated aggregate bitumen mix).....……..….46
List of Tables and Graphs

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CHAPTER 1
INTRODUCTION
1.1 Background
Vibration is an undesirable phenomenon in machining processes. It results in the reduction of
material removal rate (MRR), poor surface finish and increased tool wear. Tool chatter is a primary
component of machine vibration and affects the process directly. It causes instability to machining
process leading to loss of control over the process. Hence, many researchers have attempted to
study and suppress the tool chatter problems. The techniques used for chatter suppression can be
broadly classified as active damping and passive damping. Both techniques have their own pros
and cons. Hence it becomes necessary to study both techniques and compare the performance of
them to know the best chatter suppression method. This forms the basic motivation for choosing
chatter suppression problem and taking up this study.
In recent years, many works have been reported for turning operation. The dynamics and
governing phenomenon may vary from operation to operation. Hence, one has to study the
individual process characteristics in order to handle the tool chatter problem in an effective way.
Turning is an operation that is widely used in industries. Studying the chatter suppression of
turning operation will add value to the literature and useful to many industries. Hence, chatter
detection and suppression of turning tool was chosen for this research work. In active damping
techniques, the tool chatter has to be predicted in advance and the control signal is to be given to
damper in order to suppress the chatter in on-line basis. Prediction and identification of chatter
frequencies is a challenge. This study proposes three such predictive algorithms to be used for
chatter identification. This chapter gives a brief introduction to the problem under investigation,
possible solutions and outlines the organization of the thesis.
1.2 Tool chatter in machine tools
Two major types of vibrations occurring in machining are forced vibration and self-excited
vibration. The unbalance of rotating members, servo instability, or force on a multi-tooth cutter
may result in forced vibration. The cutting tool oscillates at the frequency of the cutting force.
When this frequency is close to a natural frequency of the tool, large amplitude vibrations due to
resonance occur. Self-excited vibration or chatter is the most important type of vibration in

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machining process. Two mechanisms known as regeneration and mode coupling are the major
reasons for machine–tool chatter. The former is due to the interaction of the cutting force and the
workpiece surface undulations produced by preceding tool passes. Regenerative chatter occurs
when cuts overlap and the cut produced at time‘t’ leaves small waves in the material that are
regenerated during each subsequent pass of the tool. The regenerative type is found to be the most
detrimental to the production rate in most machining processes. If regenerative vibrations become
large enough that the tool does not contact the workpiece as a result multiple-regenerative chatter
occurs.
Mode coupling is produced by relative vibration between the tool and the workpiece that occurs
simultaneously in two different directions in the plane of cut. In fact, mode coupling usually occurs
when there is no interaction between the vibration of the system and undulated surface of the
workpiece. In this case, the tool traces out an elliptic path that varies the depth of cut in such a way
as to bolster the coupled modes of vibrations. The amplitude of self-excited vibration increases
until some non-linearities in the machining process limit this amplitude. Self-excited frequency is
usually close to a natural frequency of the cutting system.
1.3 Chatter suppression techniques
Regenerative chatter is due to a closed loop interaction between two independent entities: the
machine tool structural dynamics and the dynamics of the cutting process. Any method of chatter
suppression tries to influence one of the two entities, so that the ultimate goal of higher stability is
achieved. Prominent among the methods of influencing the cutting process is online control of
spindle speed. This is affected in two ways, either by the "spindle speed selection" method or by
"spindle speed modulation". Changing the spindle speed to the stable part of the stability lobe
diagram can stabilize an unstable machining operation.
The control unit monitors the frequency content of the vibrations of the cutting tool and identifies
if a self-excited chatter vibration component exists in the sensor signal. If a chatter frequency is
identified, the chatter control program is invoked, which searches for the closest spindle speed
where the stability is the highest. If such a speed is found, a speed change command is sent to the
driving motor of the spindle. If no such favorable speed is found, the program commands the
reduction of the axial width of cut. The method uses a simplified calculation of the stability lobe
diagram from the identified chatter frequency. Since turning operations are associated with

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changes in the structural resonant properties, due to changing of machine configurations and
dimensions of the workpiece, stability lobe diagrams are not unique and are dependent on the
machining condition. In that respect, for proper functioning of the algorithm, a thorough
knowledge of all possible stability limits is necessary.
In order to handle such a situation, an adaptive control strategy for changing the feed and the axial
depth of cut in the turning operation was proposed with an aim of maximum utilization of the
capacity of the machine. The method involves detection of the dominant chatter frequency by
sensing the sound, emanated in the cutting process by a microphone and analyzing its frequency
content. The cutting force signal, sensed with dynamometers, is usually used for chatter
monitoring. In that case identification of the chatter frequency may be difficult.
Another approach is to use audio signals since generation of a loud noise is typical of an unstable
turning process. The sensed audio signal should normally contain a distinct peak, corresponding
to the chatter frequency. This makes chatter detection more efficient than using a dynamometer.
The method does not require the knowledge of the stability lobe diagram for stabilization of
chatter. However, there are some limitations. The technique performs well if there is a single
dominant natural frequency of the structure. In reality, more than one structural mode may be
involved in chatter. The control strategy works well in the high spindle speed regions, where there
are well separated lobes. Convergence may be poor in the low spindle speed regions, where the
stability lobes overlap each other and in situations where multiple structural modes contribute to
chatter. The method also requires stoppage of machine feed every time the spindle speed is
changed. The procedure also requires the chatter instability to be triggered in order to identify it
and then take a corrective action. This may be detrimental to the life of the machine tool.
Another popular on-line method for chatter avoidance is the spindle speed modulation technique.
This involves a continuous periodic modulation of the spindle speed with a very low frequency.
The technique is however costly and limited by the inertia of the rotating parts of the machine.
Online control of the tool geometry is also used to suppress chatter. It is well known that an
adjustment of the tool clearance and rake angles to cause more rubbing between the tool and the
metal surface, results in dissipation of energy and stabilization of chatter.
Vibration control during machining process is an important strategy to suppress chatter vibration.
The aim of this strategy is to reduce the relative displacements between the tool and the workpiece
and thus suppress chatter.

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However, in order to regulate speed and frequency of chatter vibration it is very essential to
identify the onset of chatter and also the chatter frequency. Chatter identification and suppression
is adopted in the present study. The motivation behind this choice arises from many studies, which
emphasize on the chatter frequencies and their identification.
1.4 Problem definition
In the last few decades a lot of works have been done on chatter in turning operations. Literature
is rich in the methods of tool chatter, parameters affecting tool chatter. Various types of techniques
have also been adopted to extract the features of tool chatter. Although a lot of work has been done
on chatter in turning, still there are certain aspects that have to be explored within the domain of
this study. These are:
(a) A lot of work have been done to study the effect of tool chatter on tool wear experimentally,
but no concrete theoretical relationship has been developed. So, one scope of research has been
identified as establishing a theoretical relationship between chatter vibration and tool wear in order
to predict tool wear and tool life in the presence of chatter vibration.
(b) There are very few research works which considered compliance of tool–workpiece system.
Tool–workpiece compliance should always be considered to constitute a more realistic model.
(c) In the previous research effect of process damping has not been considered in the prediction of
tool chatter.
(d) Develop a suitable simulink model to envisage a suitable simulink model to envisage
(e) In the previous works, analysis of tool chatter has been done in either time-domain or
frequency-domain. A suitable signal processing technique has to be adopted in order extract the
features of tool chatter in both the above mentioned domains simultaneously. Wavelet
transformation of signal is such technique.
(f) Vibration signals are contaminated with noisy signal as such it is very difficult to extract the
frequencies pertaining to the tool chatter. So, in this respect, a suitable signal processing technique
has to be developed in order to de-noise the vibration signals and thereby extract the tool chatter
frequencies.

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1.5 Methodology adopted
The problem dealt in the present work has been studied in three phases: Mathematical model has
been developed to dynamic equilibrium equation for tool chatter considering process damping.
This mathematical relation has been utilized to develop a suitable simulink model in MATLAB in
order to simulate the tool chatter signals contaminated with noise. Further, these simulated signals
have been validated by comparing with the bench mark problems.
A new hybrid approach, considering wavelet packet transformation (WPT) and Hilbert-Huang
transformation (HHT) is developed in order to detect the chatter frequencies in the noisy
environment.
Finally, response surface methodology approach has been adopted in order to quantify the effect
of cutting parameters (speed, feed and depth of cut) on tool chatter.
1.6 Organization of the thesis
The research presented in this thesis provides a framework to study the tool chatter phenomenon,
its identification and severity prediction in turning operations. The investigation as outlined in this
thesis is broadly divided into seven chapters. The thesis is organized as follows:
Chapter 1: This chapter serves as a brief introduction to the thesis work and summarizes the
importance, motivation, aims and objectives of the present investigation.
Chapter 2: This chapter contains a detailed survey of relevant literature on various aspects of tool
chatter in turning operation. Most of the past and present important researches carried out by
various investigators have been presented in details. This chapter is divided into different sections
emphasizing types of tool chatter, mechanisms of tool chatter, various tool chatter terminologies
and techniques used for identifying suppressing tool chatter in turning on lathe.
Chapter 3: This chapter presents a detailed description of the theoretical analysis for tool chatter
in turning considering process damping. Further, this mathematical model is utilized to develop a
simulink model in MATLAB.
Chapter 4: In this chapter, a new hybrid approach, considering wavelet packet transformation
(WPT) and Hilbert-Huang transformation (HHT) is developed in order to detect the chatter
frequencies in the noisy environment.
Chapter 5: In this chapter, response surface methodology approach has been adopted in order to
quantify the effect of cutting parameters (speed, feed and depth of cut) on tool chatter.

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Chapter 6: This chapter summarizes the important conclusions drawn from the observations
discussed in the previous chapters along with some suggestions for continuing the future research
in this field.

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CHAPTER 2
LITERATURE SURVEY
Chatter is a problem of instability in the metal cutting process. The phenomenon is characterized
by violent vibrations, loud sound and poor quality of surface finish. Chatter causes a reduction of
the life of the tool and affects the productivity by interfering with the normal functioning of the
machining process. The problem has affected the manufacturing community for quite some time
and has been a popular topic for academic and industrial research. Since then many researchers
investigated to identify, characterize and suppress the tool chatter in turning operation. This
chapter presents a review of some of the significant contributions in the field of tool chatter
analysis with a focus on turning operation. Generally, the complete review is categorized in two
methods of chatter stability prediction: Analytical and Experimental Techniques.
2.1 Analytical techniques for chatter stability prediction
Various techniques are available in the literature for the analytical prediction of chatter stability
conditions. Among them, construction of stability lobes diagram (SLD), Nyquist plots and finite
element method are most frequently utilized techniques in the literature are reviewed critically
here. The construction of SLD is the most popular technique among researchers because of its
simplicity and clarity in defining stable and unstable cutting states. The SLD can be produced for
mathematical models containing any number of DoF (degrees of freedom) cutting processes.
2.1.1 Stability lobes diagram (SLD)
The most significant cutting parameter, which is decisive for the generation of chatter in a turning
process, is the depth of cut (chip width) b. The cutting process is more stable when the chip width
is smaller. By increasing chip width, chatter starts to occur at a certain chip-width blim. (limiting
depth of cut) and becomes more energetic for all values of b> blim. Therefore, blim is the most
important parameter for the stability of cutting. The value of blim depends on the dynamic
characteristics of the structure, on the work-piece material, cutting speed and feed, and on the
geometry of the tool [1]. SLD can be used for the prediction of chatter stability in a turning process.
The limiting depth of cut blim is plotted against spindle speed (N) on the SLD as shown in a typical
plot in Fig. 2.1. Vibrations between the tool and work-piece appear as different lobes (n = 1, 2, 3

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...) and any depth of cut and spindle speed combination which falls below these lobes results in a
stable (chatter-free) operation and above these lobes in an unstable (chatter) operation. With the
help of SLDs it is very easy to choose ideal spindle speed and depth of cut combinations for
maximum metal removal rate (MRR) in a turning process.
Fig. 2.1 Stability lobe diagram
Meritt [2] presented stability conditions through stability charts, in which it was possible to predict
chatter in terms of process parameters, such as depth of cut and spindle speed. This was an
important contribution since it allowed an improvement in material removal rate without chatter
by selecting appropriate process parameters. Linear chatter stability models presented by Das and
Tobias [3] and Tlusty [4] have considered the effects of instantaneous, regenerative chip thickness
on the dynamic force. The stability models presented here did not include the complete chip
formation process. However, the CIRP group formed and led by Tlusty found that the chatter in
turning and other operations does not result from the negative damping of the chip formation
process but from self-excited vibrations due to force– displacement interaction between the
machine tool and the cutting process. To generate SLDs, analytical modeling can be done by
considering different parameters in the model, which are reviewed in the following subsections.
2.1.1.1 Analytical models based on the number of DoF
A turning process can be modeled by considering an SDoF orthogonal process, 2DoF or 3DoF
systems. To obtain critical chatter free cutting parameters, analytical prediction of chatter stability

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limits for orthogonal cutting is necessary which is well documented by Tobias and Fishwick [5],
Merritt [2], Tobias [6], Tlusty [7] and Altintas and Weck [8]. In most of these research works, the
turning tool is represented by an SDoF spring–mass system which is cutting a rigid work-piece
where the cutting force is linear with the process parameters. The research carried out with such
assumptions is referred to as linear stability analysis/ theory. Cutting tool parameters like tool
angles and wear have been accounted for in the models to understand their effects on chatter
stability. Hanna and Tobias [9] presented an SDoF time delay-differential equation with square
and cubic polynomial terms; these nonlinear terms were related to structural stiffness and cutting
force. The model has predicted the chatter stability, which is affected by the width of cut in three
ranges like an unconditionally stable range, a conditionally stable range and an unstable range. But
it is quite clear from the work that even if the cutting process is considered stable, there is an
existence of unstable periodic motions, which limits the application of linear stability theory for
manufacturing industries.
Chandiramani and Pothala [10] depicted the dynamics of chatter with a 2DoF model of the cutting
tool which is quite oversimplified. It was found that an increase in the width of cut causes frequent
tool-leaving-cut events and increased chatter amplitudes. The frequency of tool disengagement
was increased with cutting velocity, despite the cutting force in the shank direction remaining
constant over a certain velocity range. The chatter amplitude increases and then decreases when
the cutting velocity or the uncut chip thickness is increased. Since chatter vibration is between the
tool and work-piece, models for both are considered generally. The shooting technique used to
calculate periodic solutions is not efficient enough and some structural nonlinearities should have
been included in the model to make it more accurate too. Budak and Ozlu [11, 12] compared an
SDoF and multi-dimensional stability models by several simulations and chatter experiments. The
effects of three cutting angles, the insert nose radius and the dynamics of the components were
included in the cutting system in all directions in their 3DoF model. As these parameters cannot
be included in an SDoF model, it can give erroneous results. It was also shown that when
inclination angle or nose radius exists on the tool, a multi-dimensional solution is needed since the
SDoF stability formulation fails to represent the dynamics of the process accurately. Dassanayake
[13] studied tool chatter with turning dynamics using a 3DoF model and also compared it with an
SDoF model. In a 3DoF model the work-piece is modeled as a system of three rotors namely,
machined, being machined, and unmachined regions connected by a flexible shaft. It was found

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that neglecting work-piece vibrations in modeling fine turning operation would misinterpret
machining dynamics and inevitably impact the surface finish and geometrical tolerance of the final
product. It means that the workpiece vibrations should also be considered along with tool
vibrations for more accurate modeling of the turning process.
Suzuki et al. [14] presented an SDoF and a 2DoF analytical model by defining equivalent transfer
function to understand the effects of the cross transfer function and the cutting force ratio on chatter
stability. It was found that critical widths of cut in the CW (clockwise) and CCW (counter
clockwise) rotation processes were significantly different from each other in the experiment, even
when the other conditions were the same. Both analytical models based on SDoF and 2DoF
systems give the same solutions. SDoF system analysis gives the solutions easily and clarifies the
effects of the cross transfer function and the cutting force ratio on chatter stability. Stability limits
have been estimated from the vector diagram of the equivalent transfer function. It was also found
that the 2DoF model is redundant and not useful in understanding the plunge cutting process.
Dombovari et al. [15] presented an SDoF model of orthogonal cutting to analyze large-amplitude
motions. The model was formulated as a delay differential algebraic equation (DDAE) and
included the regenerative effect of the turning process and the non smoothness when contact
between the cutting tool and the work-piece is lost. The simple SDoF model has been employed
to derive a smoothed version of the orthogonal cutting system without algebraic effects and it
displays complex dynamics including chaotic oscillation in the process. After reviewing these
analytical models based on the number of DoF, the authors observe that there is no point of creating
a model with two or higher degree of freedom if it does not provide much better prediction than
the SDoF model. Even a simple SDoF model provides quite accurate prediction of chatter stability
for the turning process. However, it would be a challenge to create a more realistic multi-
dimensional chatter model of the process by incorporating all the geometrical and dynamic
parameters along with the nonlinear relationships associated among these parameters.
2.1.1.2.Analytical models based on compliance/flexibility of tool – workpiece system
Only a few researchers have considered tool and workpiece flexibilities in the analysis of chatter
vibration and chatter stability prediction. Shanker [16] proposed a general method for the
analytical evaluation of the stability limit in oblique turning of a slender workpiece, held between
the centers. The method considered the effects of the workpiece dimensions and its compliance.

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The compliance of the head and tailstock centres, system damping and other important cutting
parameters were also considered to predict the chatter stability accurately. Benardos et al. [17]
considered a rigid tool and a flexible workpiece for analytical modelling of a turning process.
The flexible workpiece which is supported only at one end undergoes elastic deformation reducing
allowable depth of cut in the process. The results also show the impact of not having a tailstock
on cylindricity of the workpieces due to the effects of numerous forces generated by the cutting
tool. Although there is a qualitative agreement between analytical and experimental results which
supports the cutting mechanism of the work, the quantitative performance in terms of measured
deflections of the workpiece was not satisfactory due to the fact that the boundary conditions of
the analytical model assumed zero elastic deflection of the workpiece which is not true in reality.
Chen and Tsao [18, 19] presented 2DoF dynamic models of a cutting tool with and without the
tailstock supported workpiece using beam theory. The effects of workpiece parameters are studied
on the dynamic stability of the turning process by treating the workpiece as a continuous system.
The effect of the critical chip width under different spindle speed was investigated. By considering
the deformation of the workpiece under different conditions, the results showed that the critical
chip width of the deformed case was always larger than the rigid body case especially at lower
natural frequencies. Although these 2DoF models are very good at predicting the stability and
evaluating the influence of the elastic deformation and the workpiece natural frequency on the
critical chip width for two different workpiece end conditions, they are very complex for studying
the three- dimensional model and nonstationary cutting conditions, particularly in the case of the
vibratory situations.
Vela-Martınez et al. [20] developed a multiple degrees of freedom model based on the compliance
between the cutting tool and the workpiece, which was compared with an SDoF model. This
compliant model predicts a larger stability area when compared with the SDoF model, but this
result is not yet experimentally validated. This model can be used to predict stability limits more
accurately when the dynamics of both the cutting tool and the workpiece are similar or when
slender cutting tools must be used.
Sekar et al. [21] considered the effects of deflections of a tailstock-supported workpiece and
presented a compliant 2DoF dynamic cutting force model by considering the relative motion of
the workpiece with the cutting tool. It was found that when a slender and flexible workpiece is
being cut, the critical chip width at higher speeds is considerably larger than a rigid workpiece.

12
The effect of cutting position, workpiece dimensions, cutter flexibility and cutter damping on the
dynamic stability is very well presented in this dynamic model. Urbikain et al. [22] presented an
algorithm to predict stability in straight turning of a flexible workpiece by Chebyshev collocation
method. This SDoF compliant model incorporates variables like round inserts, tool lead angle,
cutting speed and depth of cut. The finite element (FE) model of concentrated mass workpiece
was analyzed using ANSYS to find dynamic parameters. The compliant model is useful for low
order lobes and provides accuracy in stability prediction for up to 87.5% but inaccuracies arises
from modeling and the input parameters of the model like cutting coefficients and modal
parameters. There are very few research works which considered compliance of tool–workpiece
system and the authors believe that the tool–workpiece compliance should always be considered
to constitute a more realistic model.
2.1.2 Nyquist plots
Some researchers used control theory to predict chatter vibrations. It includes the use of Nyquist
plots. Nigm [23] proposed a method based on the feedback control theory which was conceptually
similar to that of Merritt [2], but it has the advantage of accounting for the dynamics of the cutting
process. The analysis method was strong enough for implementing it either graphically or
analytically and it could account for the full range of regeneration. The author used Nyquist
criterion to predict the stability. The method only requires plotting the operative receptance instead
of plotting the open-loop frequency response locus as required by the Nyquist criterion. Plotting
the operative receptance is even less time consuming than plotting the open-loop frequency
response locus. Minis et al. [24] used the Nyquist criterion as an alternative approach to derive the
critical stability parameter by finding the left-most intersection of the Nyquist plot with the
negative real axis. But this approach could be applied to only two-dimensional orthogonal
machining. Wang and Cleghorn [25] also performed stability analysis using the Nyquist criterion.
The chatter stability of the dynamic cutting process is solved using the Nyquist criterion by
Altintas et al. [26] to identify the dynamic cutting force coefficients for analyzing the effect of
cutting speed, tool wear, vibration frequency and wavelength on the chatter stability. It was
proposed that the amount of removed material is dependent on the uncut chip area.
Eynian and Altintas [27] presented an SDoF and 3DoF turning model for stability prediction by
modeling the transfer matrix between the displacements and cutting forces. The process damping

13
force is also included in the model and finally stability prediction is analytically carried out using
the Nyquist criterion.
The problem with the Nyquist technique is that it can only be applied to determine if the cutting
conditions are stable. So the TDS technique is clearly superior to the Nyquist technique because it
provides stable and unstable regions on SLDs by comparing width of cut and cutting speed. The
TDS technique involves some outstanding aspects such as nonlinear characteristics of the cutting
operation and it is a more effective technique for analysis.
2.1.3 Finite element method/analysis (FEM/FEA)
There are different other techniques presented in the literature for the development of analytical
stability analysis. One of them is FEM/FEA. Wang and Cleghorn [25] presented a finite-element
beam model of a spinning stepped shaft workpiece to perform stability analysis using the Nyquist
criterion. Baker and Rouch [28] analysed the instability of a machining process using the FEM
technique and created a structural model of the machine tool system using the commercial ANSYS
software but the integrity of the results is not validated by experimental results. The effect of
structural parameters was investigated on machine instability without assessing the dynamics of
the cutting process models. However the method presented allows for inclusion of both cutting
tool and workpiece flexibility in the analysis. Mahdavinejad [29] predicted the stability of a turning
operation by finite element analysis using ANSYS software. The flexibility of the machine’s
structure, workpiece and tool has been considered in this FEA model. Brecher et al. [30] proposed
a FEA-based 3-dimensional turning model. This 3D-FEA model has the potential to determine the
resulting cutting forces for even complex- shaped tool geometries. An approach was used to reduce
the calculation time by using characteristic diagrams for the calculated process forces in the FEA-
model by focusing on the thrust and feed forces. FEM/FEA technique is quite useful in predicting
the stability at the design stage of any process, which saves heaps of time and money in any
production environment. Urbikain et al. [31] performed a FE model in ANSYS using 3D 10-node
tetrahedral solid elements type SOLID92 for the workpiece. Different geometries were designed
and analyzed giving as a result a final workpiece of 35,516 elements. Afterwards a FE analysis
was carried out to produce a workpiece and the modal parameters were periodically updated to
consider workpiece evolution during machining within the stability algorithm.

14
A limitation with any FEM model is that it cannot take into account the properties of the joint
between the mating parts of the machine tool as these properties are difficult to describe
mathematically. With the advancements in computing capabilities and technology, the futuristic
analytical models are more likely to be studied using FEM/FEA techniques.
2.2 Experimental techniques
Due to increasing demand of cutting down the production costs under market pressure, unattended
machining is the key feature in most of the manufacturing industries. So, in unmanned turning
operation, automatic detection of regenerative chatter is very important in order to avoid
detrimental effects on surface integrity and damage to the workpiece or machine tools caused by
catastrophic tool failure resulting from large amplitude vibrations. Experimental techniques are
useful in predicting the stability condition in offline mode and detecting chatter onset in online
mode. These experimental techniques have potential to establish an unmanned machining
environment. Some experimental techniques are employed offline for the chatter stability
prediction by producing the SLD of the system with the help of modal parameters of the tool–
workpiece system obtained through modal testing. However, this SLD would be a semi-analytical
one. A true/realistic SLD would rather be obtained with the help of actual cutting tests, however
the task involved in obtaining SLD by direct cutting test is very tedious and time consuming. The
experimental validation is imperative to know whether a specific process is stable based on the
comparisons with the theoretical chatter onset conditions obtained from the chatter stability
prediction model and by identifying chatter onset in the cutting process. This identification is
possible using tool condition monitoring (TCM) techniques. Experimental techniques are
classified and reviewed here based on techniques used for chatter stability prediction and chatter
detection.
The condition monitoring system for any machine tool is necessarily custom built and thus
depends upon the type of the machine tool as described by Siddhpura et al. [32]. Tool condition
monitoring can be carried out using force, vibration and acoustic signals which are very useful for
the monitoring of the process. Armarego et al. [33,] repeated orthogonal cutting tests for a range
of cutting speed, rake angle and uncut chip thickness to generate an orthogonal cutting database
for a certain tool and work material pair. Knight [34] presented experimental stability charts for

15
turning with a simplified machine–tool structure model for various cutting conditions and these
show considerable variations in the level of stability with speed, feed and rake angle.
2.2.1 Signal acquisition and processing techniques
Verification and detection of predicted chatter stability is possible with various sensors which can
measure force, displacement, velocity, acceleration, acoustic signals generated from a machining
process. Various sensors are used to acquire the above signals and become part of the signal
acquisition system. Signal processing is then carried out to obtain useful information from the
signals received through the sensors. Traditional signal processing techniques like time-domain,
frequency domain and time–frequency domain analysis are generally explored.
Tlusty and Andrews [35] reviewed several sensors and their capabilities for chatter detection, tool
breakage detection in machining processes in order to develop an unmanned machining centre.
Force, vibration and acoustic sensors were tested for turning and milling. It was found that the
force signals were the best signals for chatter detection in comparison to vibration signals. Because
chatter is a relative vibration between the tool and the workpiece and, as such, is difficult to
measure with a vibration transducer whereas the cutting force is a direct indicator of the relative
vibration between tool and workpiece and very characteristic patterns of force variation make it
possible to clearly distinguish chatter.
Heyns [36] reviewed these signal processing techniques and found that the time domain and
frequency domain methods are used extensively for tool wear and chatter estimation. But time–
frequency domain methods like Wavelet transform have higher capabilities which have not yet
been completely exploited. Zhu et al. [37] argued that time domain methods are most commonly
used in TCM, but these methods lose some signal information in the time domain. Fast Fourier
Transform (FFT) and Wavelet Transform (WT) were compared and it was found that WT is far
more effective than FFT, because of its scarcity and localization properties. WT yields frequency
information in a time-localized fashion. WT has great potential in detecting abrupt changes in tool
conditions in TCM. It is robust and insensitive to changing working conditions.
2.2.1.1 Force and vibration measurements
Force and vibration signals are preferred by most of the researchers because they provide thorough
insight into the dynamics of the cutting process and they are very useful in the condition

16
monitoring of machining processes. The force and vibration measurement technique is one of the
most commonly used techniques in detecting regenerative chatter, due to the complex relationship
between cutting forces, vibrations and mechanisms causing chatter. Different signal processing
techniques are used to obtain the required signals from force and vibration measurements.
Shanker [16] verified his 2DoF chatter stability prediction model with a flexible workpiece for
oblique turning by impact testing and vibration measurements. The natural frequency and the
system damping of the workpiece were determined by exciting it at several points along their
length and obtaining a resonance curve. The chatter frequency was recorded by a vibration pick-
up mounted on the tool shank. It was proposed that tool geometry has little effect on the limit of
stability, but the stability is significantly affected by dimensions and compliance of the workpiece.
Rahman and Ito [38] presented a method to determine the onset of chatter by online measurement
of the horizontal deflection of the workpiece using eddy current type displacement pick- ups. A
piezoelectric type three-component dynamometer was also used for in-process measurement of
cutting forces. This technique of measuring workpiece deflection would be quite useful to verify
the compliant tool–workpiece models as discussed in Section 3.1.2.
Bao et al. [39] distinguished the basic difference between the distributions of the probability
density function of the vibration signals before and after chatter and that is utilized to detect chatter
in turning. They selected the interval frequency difference ‘H’ in the amplitude domain of the
dynamic cutting force as a parameter for early chatter stability prediction. This prediction
parameter was obtained from the probability density function of the dynamic signal. It was also
not influenced by the cutting conditions because it was a relative value and it had greater prediction
accuracy. The transition state defined by the process between stable state and chatter state is
assumed to be the complex combination of random signal and sine signal. Although it was a novel
technique with feature extraction in a chatter recognition system, a pattern classifier is required
for cutting state identification.
Yeh and Lai [40] developed a chatter monitoring and signal processing system for turning a slender
workpiece. In monitoring, the dynamic component of the cutting force was detected and its
standard deviation value was computed through signal processing. Chatter occurrence was judged
using the steep increment of this value. Instead of selecting a simple threshold like Lin and Hu
[41], a double-standard concept was proposed for the threshold selection to avoid misjudgements
in chatter detection. It was also mentioned that the tool nose run-off will affect the cutting force

17
and performance of the machining process. Therefore, the tool nose run-off was also selected as
one of the control factors in this study.
Thomas and Beauchamp [42] carried out statistical investigation of modal parameters of cutting
tools in dry turning. Cutting forces were measured using strain gauges in the tangential and radial
directions. A tri-axial accelerometer was mounted on the tool to measure accelerations in the feed,
cutting or tangential directions, and also in the thrust or radial directions. Acceleration signals were
analyzed in the frequency domain using an FFT Analyzer. It was also found that increasing the
tool nose radius reduces the tangential cutting force. This allows a larger feed rate to be used which
decreases the machining time and hence reduces the unit production cost.
Chiou et al. [43] experimentally validated an analytical stability model including process damping.
The characteristic parameters like cutting stiffness, structural stiffness and natural frequency,
damping ratio and specific contact force were determined experimentally. For this, a dynamometer
was mounted to the tool post to measure cutting forces in the feed and cutting directions. The
impact testing was carried out to identify the structural response of the machine–tool system. The
displacement of the tool and velocity ratios were obtained from acceleration signals detected from
a pair of accelerometers mounted to the tail stock, one horizontally and the other vertically, during
machining at different surface velocities. It was demonstrated that the effect of tool wear flat is to
enlarge the range of stable cutting while the effect of the Coriolis force associated with the spinning
of the workpiece is the reverse, especially at high cutting speeds, through their effects on the
system damping.
Chiou and Liang [44] measured the vibration of the turning tool by an accelerometer attached to
the back of the shank. The acceleration signals were amplified by a charge-amplifier prior to being
digitized with an emulated digital oscilloscope. The acceleration signals were used to observe the
sudden change of the vibration amplitude to detect chatter conditions. Impact testing was carried
out to identify natural frequency and damping ratio associated with the cutting tool. Forces were
measured by a dynamometer and displacement by a dial gauge to determine characterist ic
parameters. It was found that the region of stability enlarges when the contact damping effect on
the tool flank is considered in comparison to that with a sharp tool. It means that the stability
against chatter improves as flank wear increases.
Rao and Shin [45] collected force, acceleration and surface texture data to verify the chatter
stability predictions of their dynamic force model. All the experiments were performed on a 7 HP

18
engine lathe with a fixed spindle speed drive. Machining tests were carried out by cutting AISI
4140 steel workpieces with uncoated carbide inserts of nose radius 0.8 mm (Kennametal SPG
422). Force and acceleration data were recorded by a Fourier analyzer, which was followed by
frequency response measurements. The roughness profile for the machined surface was recorded
for the unstable–stable cases using a Profilometer. The dynamic force model could predict the
stability limit for turning at large depths of cut as well as finish turning where chatter occurs. The
dynamic force model was implemented on a computer to generate time-saving chatter stability
predictions. Although the effect of workpiece vibration on cutting dynamics was neglected in the
model, this technique is still an effective tool for planning and selecting cutting parameters.
Grabec et al. [46] developed a new method for the detection of chatter onset based on
characterization of changes in process dynamics. Model performance was demonstrated by
experiments with turning in which the transition to chatter is caused by the variation of cutting
depth. The signal from the cutting force was characterized by the normalized coarse-grained
entropy rate whose value exhibits a drastic drop at the onset of chatter. The characteristic value of
coarse-grained entropy rate was determined which is insensitive to variation of cutting conditions,
to automatic online detection of chatter.
Dimla and Lister [47] have used tool-post dynamometer as a force sensor to measure all three
cutting force components to find the static and dynamic components of the cutting force and
reviewed research work for the force sensors. The authors suggested that the use of the force sensor
is vital in the development of a TCM system. A 3-axis accelerometer was investigated to monitor
vibration signals of a turning operation and the conclusion was drawn that the vibration signals are
most sensitive to tool wear. Time domain analysis established the nature and level of static force
magnitude change while frequency analysis demonstrated the dynamic force signatures’ response
to cutting conditions as well as accrued wear levels. This research has found ubiquitous industrial
use compared to other research which have been carried out concerning the development of a
reliable TCM system.
Clancy et al. [48] successfully validated a chatter stability prediction model for a face turning
operation using an accelerometer by attaching it to the tool shank. A large spike in the acceleration
spectrum close to the natural frequency was an indicator of chatter. Ozlu and Budak [49] used a
modal setup to measure the transfer functions of the workpiece and the tool on a conventional
manual lathe machine. The modal test setup consisted of an impact hammer, an accelerometer and

19
a data acquisition system. The collected data was analyzed by CurPro software. This technique is
not only useful in studying the influence of the variation of the modal parameters along the tool
axis but it can be applied to varying tool geometries.
Kebdani et al. [50] found natural frequency and the damping ratio of the tool system by impact
testing. Frequency responses were obtained by attaching an accelerometer on one side of the tool.
Structural stiffness was obtained by simultaneous measurements of displacement and static force
applied at the end of the workpiece through the tool. The displacement of the tool system was
measured by a dial gauge. The cutting stiffness was found by measuring thrust force for given
cutting conditions. The static force and the thrust force were measured by a dynamometer
connected to the tool system.
Kotaiah and Srinivas [51] carried out cutting experiments on an engine lathe to verify the tool
overhang effects on cutting dynamics when a flexible workpiece is considered. A tri-axial tool
post-strain gauge dynamometer was used to measure cutting forces in three directions. Kayhan
and Budak [52] used a TCM method for the experimental investigation of chatter effects on tool
life. A laser displacement sensor was used to collect vibration data during the turning tests.
Calibration tests were performed using a force dynamometer to determine the cutting constant.
Cutting force and displacement data were collected continuously during the tests. The tool
dynamics was obtained using impact testing and modal analysis. Impact tests and modal analysis
were also used to determine chatter limits and modal frequencies for each tool holder length case.
Taylor et al. [53] investigated the process damping stability of turning difficult-to-cut materials
with a custom-built flexible tool holder. The tool displacement was measured using an inductive
sensor focused on an aluminium target. Accelerometers were also used to measure vibrations in
the feed and cutting directions. Modal parameters were measured using a modal hammer and the
inductive probe. The cutting stiffness was determined by performing calibration tests using a rigid
tool holder and a dynamometer. Storch and Zawada-Tomkiewicz [54] presented distribution of
unit forces on the nose of a tool insert to reveal conditions for the chip formation on the rake face
and to find the machined surface quality on the flank face. Unit force distribution and values were
established based on force measurements in the orthogonal direction for free and non-free turning.
But the calculated and measured unit forces are only useful for single point cutting with a sharp
cutting tool having fixed tool geometry and with uniform temperature assumption, which is

20
contrasting to the industrial conditions. The tool wear will actually change the tool geometry soon
after the cutting begins which causes a change in the distribution of unit forces.
Apart from chatter, the cutting forces are also sensitive to other parameters and can vary with
cutting speed, depth of cut and work hardness, making correlation with chatter more complicated.
Vibration measurement is easy to implement but the recorded signals depend highly on cutting
conditions, workpiece material and machine structure. Although force and vibration measurements
require very expensive instruments like dynamometers and accelerometers which are sometimes
very difficult to mount on a turning machine due to their configurations, they will still be pursued
as TCM techniques in future to detect chatter as they portray the true nature of the dynamics of
the cutting process.
2.2.1.2 Chip analysis technique
Some researchers have analyzed the chips generated in a turning process to determine stability
conditions and to detect chatter occurrence. However, the authors of the current paper believe that
analysis of chip formation could only provide information about chatter after it has actually
occurred. So, this method is unable to predict chatter onset in advance.
Nurulamin [55] studied the mechanism of instability of chip formation on micro section
metallographic specimens of chip roots, received by instantly stopping the cutting process at
different phases of the full cycle of instability as well as on micro-section metallographic
specimens of the chip. On such specimens, with the help of a metallographic microscope and
micro-hardness measuring instruments, the grain orientation, borders of different zones and micro
hardness were measured and on their basis, the shear angle, length of different zones and contact
areas and also the time of each phase of the cycle were determined. It was discovered that physical
cause of chatter is the instability of chip formation and by self excitation between tool and
workpiece at the resonant frequency.
Tangjitsitcharoen [56] presented a method for in-process monitoring and identification of cutting
states for a CNC turning machine. The method utilizes the power spectrum density (PSD) of the
dynamic cutting force. Experimental results discovered that there are three types of patterns of
PSD when the cutting states are continuous chip formation, broken chip formation and chatter.
The broken chip formation was desirable for a stable and reliable operation. During continuous
chip formation, the dynamic feed force was small and PSD was large when the frequency was less

21
than 50 Hz. During broken chip formation, a large varying dynamic feed force was observed with
large PSD at chip breaking frequency. And when chatter occurs, the PSD obtained was larger than
continuous and broken chip formations.
Patwari et al. [57] observed the top and sectional views of chips using SEM (scanning electron
microscope) and discovered that chips produced during turning and thread cutting exhibit identical
regularly spaced serrated teeth along the free edge of the chip. After analyzing chatter amplitudes
it was also found that chatter appears in the system when the chip serration frequency is equal to
or an integer multiple of the prominent natural frequency of the system components.
Nurulamin et al. [58] identified that the chips formed in turning, thread-cutting and milling
operations show a common type of discreteness in the form of secondary saw teeth. The primary
saw teeth were identified apart from secondary saw teeth and their frequencies. Chips were studied
using SEM, optical microscope and a digital camera. It was found that chip formation is unstable
due to the formation of secondary saw teeth, primary saw teeth and cracks at the boundary between
two adjacent secondary saw teeth. Chatter appeared in the system when the frequency of the chip
formation instability becomes approximately equal to or an integer multiple of the prominent
natural frequencies of the system components in a turning process. The tool holder was the
prominent system component responsible for chatter in the turning process. Some researchers still
associate chip formation with the dynamics of the turning process and to decide chatter conditions.
However chip analysis would merely remain the post mortem of the process/behaviour as it could
not predict the stability of the process in advance.
2.2.2 Artificial intelligence techniques
Several researchers have presented artificial intelligence techniques like Artificial Neural network
(ANN) and Fuzzy logic to predict and detect the occurrence of chatter by classifying signal
features obtained through sensory signals. These artificial intelligence techniques are reviewed in
this section.
2.2.2.1 ANN technique
ANN is an information processing paradigm that is inspired by the way biological nervous
systems, such as the brain process information. The key element of this paradigm is the novel
structure of the information processing system. It is composed of a large number of highly

22
interconnected processing elements (neurons) working in unison to solve specific problems. ANN
can be used for applications like pattern recognition or data classification of signal features,
through a learning process.
Tansel et al. [59] used a single-sensor input to predict chatter development using neural network.
The proposed method successfully identified 98% of the harmonic signals with only 5% error.
Chatter signals were presented to two MLP-based neural network architectures. One identified the
system harmonics and another was used to estimate the frequency to analyze the acceleration
signals to predict chatter. For combining these two separate procedures, an algorithm was
developed to identify chatter and its frequency. Testing was carried out using a function generator
and by online testing in turning operation, where it could detect unstable vibrations and as a result
save substantial tool life.
Tansel [60] demonstrated the use of neural network to identify the dynamics of a 3DoF turning
process over a large cutting speed range (50–105 m/min) and to simulate the turning process.
The model estimates the discrete transfer functions used for simulation and/or calculation of
frequency domain characteristics of the system. Also, the neural network can represent nonlinear
structures better than the conventional time series models and the stability conditions could be
more accurately evaluated by using the neural network cutting dynamics simulator. The accuracy
of the predictions was found to be much greater at higher cutting speeds. The neural network model
also represents the nonlinear characteristics of cutting dynamics, while the time series methods
use only the linear models.
Dimla Jr et al. [61] reviewed tool condition monitoring techniques which are mostly developed
through the application of neural network and by observing variations in one or more of the process
responses (outputs) related to tool deformation and, consequently, exploited to investigate the
aspect of tool wear monitoring and control. But there is only a brief mention of chatter detection
using neural networks and most of the neural network based tool condition monitoring systems
presented in the literature should be considered offline since they have not been tested or
implemented online.
Lange and Abu-Zahra [62] used wavelet packet analysis to filter the ultrasound wave signals
generated from the turning process. A multi-layer perceptron ANN was employed to correlate the
response of the ultrasound sensor to the accelerometer measurement of tool chatter. The system

23
response to various frequency levels of tool chatter could then be investigated but the chatter
frequency could not be measured.
Kotaiah et al. [63] studied effects of cutting parameters in orthogonal turning on the critical chatter
lengths over the workpiece and the static cutting forces on the tool by a series of experiments.
After measuring the dynamic cutting forces, surface roughness and critical chatter lengths, the
relations between the input and output parameters were established using radial- basis function
(RBF) neural network model and it was further employed to genetic algorithms (GA) to optimize
the machining data. Use of neural network technique in micro-cutting operations by several
researchers is very well summarized by Chae et al. [64] and the estimation of tool condition in
micro- machining of steel and aluminium has been explained. However, chatter detection was not
carried out using ANN techniques in this work. The neural network technique requires extensive
experimental data for a specific process and material condition, which can be inconsistent for
different processes, cutting conditions and material conditions.
The neural network is becoming the most powerful simulation tool for cutting dynamics with
respect to accuracy, flexibility, and computational speed when synthesized with sophisticated
algorithms and multi-processor neural network hardware.
2.2.2.2 Fuzzy logic technique
Fuzzy logic can process information like our brain. Fuzzy logic systems base their decision on
inputs in the form of linguistic variables derived from membership functions which are formulae
used to determine the fuzzy set to which a value belongs and the degree of membership in that set
as explained by Bojja [65]. These variables are then matched with the preconditions of linguistic
IF–THEN rules, which are called fuzzy logic rules, and the response of each rule is obtained
through fuzzy implication.
Du et al. [66] presented a study on tool condition monitoring in turning using the fuzzy set theory.
Tool conditions like tool chatter, breakage, tool wear were considered. Force, vibration and power
sensors were monitored and signature features were selected to describe the signature
characteristics of various tool conditions. The linear fuzzy methodology was compared with
several classification schemes, including the K-mean, the Fisher’s pattern recognition methods
and fuzzy C-mean method and it was found that results from the proposed fuzzy method indicate
an overall 90% reliability for detecting tool conditions.

24
Tansel et al. [67] proposed S-transformation to prepare 3D plots to display variation of the
amplitude of acceleration signals from a turning operation in the time and frequency domain. A
frequency–time–damping index plot was obtained from the S-transformation result. The
frequency–time–amplitude characteristics of the acceleration were calculated from S-
transformation and it was better than Wavelet transformations methods like Dubechies 3, Morlet
and short time Fourier transformation (STFT). The variance of the damping index in a small band
around the natural frequency of the workpiece was found as the best indicator of chatter. Fuzzy
logic controllers were used for automatic chatter detection. The use of a local area network (LAN)
was proposed to integrate the data collection, computation and dissemination processes to store
the vibration history of machining for critical parts and reporting the results to the operators with
wireless devices.
The decision making in a fuzzy system is fast due to its simplicity but it suffers from the difficulties
in selecting suitable membership functions for the target system. Overall ANN technique was
found to be better and more popular than HMM and Fuzzy techniques due to its trainability,
massively parallel structure, higher accuracy of prediction/classification of signal features, quick
implementation and commercially available ANN hardware and software. ANN dramatically
reduces computational time in decision making, pattern recognition and simulation studies.

25
CHAPTER 3
THEORETICALANALYSIS OFTOOLCHATTER
Machine tool dynamics have been an important issue of interest amongst the machining
community due to its significant role in the stability and other outcomes of the processes. The
dynamics of the machine tool have great impact on chatter stability of the process. Whatever
method is used for predicting instability, reliable results are only obtained when the dynamics of
the structure and the cutting process are correctly incorporated in the method. Earlier chatter
research done before focused mainly on cutting process parameters like speed, feed and depth of
cut to be included in the dynamic models of the turning process. These models were unable to
represent the true nature of machine–tool dynamics and as a result the prediction accuracy was
low. In the present work, new parameters like process damping, tool wear, tool geometry, stiffness
of machine components, compliance between tool and workpiece have been incorporated in the
dynamic models of machine tool. These new dynamic models are very close to the real dynamic
nature of the machine–tool system and proved to be more accurate in predicting the
stability/instability of the turning process. These new dynamic models are discussed in subsequent
sections.
3.1 Dynamics of orthogonal turning during chatter
Regenerative chatter vibration arises due to the interaction between the metal cutting process and
the machine tool structure as shown in Fig. 3.1 and it is a major obstacle in achieving maximum
material removal rate (MRR). Self excited chatter vibrations are much more detrimental to finished
surfaces and cutting tools due to their unstable behaviour which results in large relative
displacements between the tool and workpiece.
Fig. 3.1 Machine tool and cutting process interaction

26
Regenerative chatter occurs at the frequency of the most dominant mode of the machine tool
structure. Excitation of this mode causes a relative motion between the machine tool and the
workpiece due to the tool cutting over a previously machined undulated or wavy surface. Fig. 3.2
displays the relative motion between the tool and the workpiece in turning.
Fig. 3.2 Mechanism of regeneration
The tool parameters m, k and c are the mass, stiffness and damping coefficient, respectively, and
V is the cutting velocity of the workpiece. Here, x(t) is the wave generated during the current
revolution and x(t-T) is the wave generated during the previous revolution of the workpiece. The
phase delay/shift (θ) between the waves in the previous revolution x(t-T) and in the current
revolution x(t) is the key factor governing the occurrence of chatter in the turning process. If the
two waves are in phase (θ=0), the undulations on the workpiece will not grow and the process will
remain stable because the chip thickness variation is negligible resulting in a relatively constant
force on the tool. From the point of view of energy transfer in the turning system, the onset of
chatter can be regarded as the stability threshold of the system in which the energy supplied to the
system is equal to the energy dissipated by the system. So, when there is no phase delay/shift
(ϴ=0), there is no surplus energy in the system resulting in a stable cutting process. However,
when the waves are not in phase, the undulations on the workpiece grow due to energy being
supplied to the cutting tool and the dissipated energy is less than the supplied energy. This finally
results in an unstable cutting process. Under these vibrations, the chip thickness varies
continuously which in turn creates dynamic cutting forces at a frequency close to one of the natural
modes, and further excites the system.
A mathematical model considering a Single Degree of Freedom (SDoF) orthogonal turning
process with a flexible tool and relatively rigid workpiece is shown in Fig. 3.3. The model

27
incorporates various forces acting on the physical system like the inertia force, damping force,
spring force and the cutting force. The model is presented by considering a sharp tool with only
the cutting force in feed direction acting in the system.
Fig. 3.3 SDoF orthogonal turning model
When this SDoF flexible tool is cutting a rigid workpiece, the equation of motion of the dynamic
system can be modeled in the radial (feed) direction as:
       fmx t cx t kx t F t   (3.1)
where,
 fF t = cutting force in feed (x) direction=      f fF t K b x t T x t       (3.2)
Kf is the cutting coefficient in feed direction, b is the chip width (width of cut), mm, T is the time
delay between current time and previous time, [x(t-T)-x(t)] is the dynamic chip thickness due to
tool vibration.
Substituting Eq. (3.2) in Eq. (1) and dividing by m gives;
         fK bc k k
x t x t x t x t T x t
m m k m
       (3.3)
Applying Laplace transform and using relations,
2 n
c
m
 , 2
n
k
m
  and assuming
fK b
k
 
 2 2 2
2 1sT
n n ns s e   
    (3.4)
From Eq. (3.4), the transfer function of the system with a sharp tool can be obtained by direct
derivation from differential equation as;
  2 2
1
2 n n
s
s s 
 
 
(3.5)

28
Substituting s j in Eq. (3.5), where  is the chatter vibration frequency, the real and
imaginary parts of the transfer function are found as;
 
 
2 2
nG
R
 



 (Real part) (3.6a)
 
 
 
2 n
H
R
 



 (Imaginary part) (3.6b)
where,
     
2 22 2 2
2n nR        (Denominator)
n is the natural frequency of the system,  is the frequency of chatter vibration.
The limiting width of cut at which the turning process switches from stable to unstable can be
found by the relation;
 lim
1
2 f
b
K G 
  (3.7)
The stability equation leads to a positive real depth of cut only when the real part  G  of the
transfer function between the tool and workpiece is negative. So, Eq. (3.7) gives only an absolute
depth of cut when the minimum (most negative) value of  G  is considered. Defining the phase
angle;
 
 
1
tan
H
G



  
   
 
and with some mathematical manipulation, the spindle period (T) and phase shift (θ) can be
obtained as;
 
1
2T n 

  , 3 2    (3.8)
The spindle speed can be obtained by;
60N
T
 (3.9)
Eqs. (7)–(9) can be used to produce the so-called stability lobes diagram (SLD) showing the
relationship between the limiting width of cut (blim) and spindle speed (N) for the turning operation
as shown in Fig. 2.1. The chatter SLDs are constructed by scanning the possible chatter frequencies

29
from the transfer function where the real part is negative, e.g.,   0G   . The SLD distinguishes
regions of stable (chatter-free) and unstable cutting operation for different combinations of width
of cut and spindle speed. When the width of cut and spindle speed are selected under the stability
lobes, the process would be stable leading to a smooth surface finish and less dynamic loads on
the machine tool system. By selecting specific combinations of width of cut and spindle speed,
chatter vibrations can be avoided to achieve a stable turning process throughout.
3.2 Simulink model
Simulink, developed by The MathWorks, is a commercial tool for modeling, simulating and
analyzing dynamic systems. Its primary interface is a graphical block diagramming tool and a
customizable set of block libraries. It offers tight integration with the rest of the MATLAB
environment and can either drive MATLAB or be scripted from it. Simulink is widely used in
control theory and digital signal processing for simulation and design. The advantages of simulink
are:
A quick way to develop the model in contrast to text based-programming language such as e.g.,
C.
Simulink has integrated solvers. In text based-programming language such as e.g., C we need to
write our own solver.
In the present work, simulink model has been developed to generate chatter signals at different
cutting conditions (speed, feed and depth of cut) in a noisy environment. The effectiveness of the
chaos spindle speed, feed and depth of cut variation technique is tested via numerical simulation
of the turning process of a cylindrical workpiece. The simulink toolbox is used to simulate the
orthogonal turning considering the dynamic equation developed in the previous section. Both
linear and nonlinear problems can be easily handled using this software tool. The simulink
simulation model is shown in Fig. 3.4. The simulation parameters used are as follows: m =100 kg,
c=5321 Ns/m, k=4×107 N/m, kc=2000 N/mm2, S0=1200rpm, f0=1mm/ rev, b=2 mm, and the input
gain kp=1000.

30
Fig. 3.4 Simulink model
To ensure that simulation results are comparable, all simulations on chatter suppression using
different cutting parameters variation are conducted on this model. Simulations start with constant
spindle speeds of S0=1200rpm. After the chatter fully develops, sinusoidal spindle speed variation
is activated at t=1.0 s. This simulation result showed the ability of the technique to augment
stability. At the same time, the trace of a self-excited periodic vibration at 0.5 s can be found after
spindle speed, feed and depth of cut variation is activated. In order to investigate which kind of
chaotic time series is more effective for chatter suppression using chaotic spindle speed variation,
several types of chaotic motion equations, such as DUFFING, LORENZ-1, LORENZ-2,
ROSSLER, and MACKEY-GLASS, are tested during the simulations.
During the simulation, function ode45 in the simulink tool box was used to generate chaotic
signals, e.g.,      , :,2 45@ _1, 0100 , 1;0;1t y ode Lorenz    as input after it was amplified and
step functioned (the initial input is 0 and the operation time is 1 s). Other simulation conditions
are the same as the sinusoidal input. It is found that with sufficient variation magnitude to cover
stable and unstable regions, positive results for chatter suppression can be reached by using either
DUFFING, LORENZ-1, LORENZ-2, ROSSLER, or MACKEY-GLASS, though LORENZ-1 and
DUFFING codes result in the best performance. The simulation study above showed that the
results of using either sinusoidal or chaotic signals for cutting parameters variation all lead to
significant improvement of chatter suppression at the same simulation conditions. However, beats

31
happen after sinusoidal variation is activated at t=1.0 s. The effectiveness of LORENZ-1 chaotic
code for chatter suppression is better than that by using sinusoidal and DUFFING signals. These
simulation results verified the ability of the chaotic spindle speed, feed and depth of cut variation
technique to augment machining stability. Signals are simulated at various speed, feed and depth
of cut at different simulation time. These signals are stored in workspace of the MATLAB with
.mdl extension files. Some of the plots of chatter vibration in time domain at different cutting
parameters is shown in Figs. 3.5-3.12.
Fig. 3.5 Simulated; case 1: depth of cut = 1 mm, feed = 0.6 mm/rev and speed = 1200 rpm
2.xls
0 0.2 0.4 0.6 0.8 1
Time (s)
-10
-5
0
5
10
15
Amplitude(m)
-10
-5
0
5
10
15
0.xls
0 0.2 0.4 0.6 0.8 1
Time (s)
-30
-20
-10
0
10
20
30
Amplitude(m)
-30
-20
-10
0
10
20
30

32
Fig. 3.9 Simulated; case 5: depth of cut = 1 mm, feed = 1 mm/rev and speed = 1200 rpm
1.xls
c:documents and settingsb.singhdesktoptc4amplitude1.xls
0 0.2 0.4 0.6 0.8 1
Time (s)
-30
-20
-10
0
10
20
30
40
Amplitude(m)
-30
-20
-10
0
10
20
30
40
5.xls
0 0.2 0.4 0.6 0.8 1
Time (s)
-1
-0.5
0
0.5
1
1.5
Amplitude(m)
-1
-0.5
0
0.5
1
1.5
3.xls
0 0.2 0.4 0.6 0.8 1
Time (s)
-3
-2
-1
0
1
2
3
4
Amplitude(m)
-3
-2
-1
0
1
2
3
4

33
Fig. 3.10 Simulated; case 6: depth of cut = 3 mm, feed = 1 mm/rev and speed = 1600 rpm
2.xls
0 0.2 0.4 0.6 0.8 1
Time (s)
-10
-5
0
5
10
15
Amplitude(m)
-10
-5
0
5
10
15
8.xls
0 0.2 0.4 0.6 0.8 1
Time (s)
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
Amplitude(m)
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
11.xls
0 0.2 0.4 0.6 0.8 1
Time (s)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Amplitude(m)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3

34
From these time domain spectrum following inferences are drawn;
 It is quite evident that the depth of cut is the most influential parameter.
 With the increase in depth of cut chatter increases.
 Feed is the second important parameter governing chatter.
 With the increase in feed chatter increases.
 Speed is the third important parameter controlling chatter.
 With the increase in feed chatter increases.
However, in time domain only amplitude of chatter vibration with respect to the time is
evident, but the information regarding the chatter frequency and location is missing. So, in this
respect, Fast Fourier Transformation (FFT) is done on these signals in order to extract the
frequency features of the respective signals. Some of the FFT plots are shown in Figs. 3.13-
3.17.
Fig. 3.13 FFT; case 1: depth of cut = 1 mm, feed = 0.6 mm/rev and speed = 1600 rpm

35

36
Fourier transform identifies all spectral components present in the signal; however it does not
provide any information regarding the temporal (time) localization of the components
Following are the FT shortcomings:
They analyze the signal globally, not locally
FT can only tell what frequencies exist in the entire signal, but cannot tell, at what time instances
these frequencies occur
Not able to reveal inherent information of non stationary signal
Chatter frequencies contain very little energy and difficult to obtain in noisy environment
To overcome the shortcomings, Envelope detector (ED) or high frequency resonance technique
(HFRT) is often used with fast Fourier transform (FFT) to identify faults
Computation of ED is complicated and requires expensive equipment and experienced operator in
process
In order to obtain time localization of the spectral components, the signals need to be analyzed
locally, so wavelet transformation has been adopted in the present work.

37
CHAPTER 4
WAVELET PACKETS AND HILBERT–HUANG TRANSFORM
Chatter detection is an important task to improve productivity and part quality in the machining
process. Since measured signals from sensors are usually contaminated by background noise and
other disturbances, it is necessary to find efficient signal processing algorithms to identify the
chatter as soon as possible. This chapter is presents an effective chatter identification method for
turning process based on the study of two advanced signal processing techniques, i.e., wavelet
package transforms (WPT) and Hilbert–Huang transform (HHT). The WPT works as a
preprocessor to denoise the measured signals and hence the performance of the HHT is enhanced.
The proposed method consists of four steps. First, the measured signals are decomposed by the
WPT, so that the chatter signals are allocated in a certain frequency band. Secondly, wavelet
packets with rich chatter information are selected and are used to reconstruct new signals. Thirdly,
the reconstructed signals are analyzed with HHT to obtain a Hilbert–Huang spectrum, which is a
full time–frequency–energy distribution of the signals. Finally, the mean value and standard
deviation of the Hilbert–Huang spectrum are calculated to detect the chatter and identify its levels
as well. The proposed method is applied to turning process and the comparison with the bench
mark experimental results prove that the method can identify the chatter effectively.
4.1 Wavelet transform
Wavelet analysis is a windowing technique with variable sized regions. It allows use of long time
intervals where we need more precise low-frequency information and use of shorter regions where
we want high-frequency information. Advantages of wavelet transform are:
Signals with sharp sudden changes could be better analyzed with an irregular wavelet than with a
smooth sinusoid.
In other words, local features can be better captured with wavelets which have local extent
Wavelet transform (WT) of the simulated signal is done by selecting the morlet wavelets as the
mother wavelets. Some of the result is depicted in the Figs. 4.1-4.3. From the 2-D and 3-D time -
frequency spectrum it is inferred that WT transformation is not suitable to indentify chatter in the
presence of noisy environment.

38
Fig. 4.1(a) 3-D plot; case 1: d = 1mm, f = 1 mm and N = 2000 rpm
Fig. 4.1(b) 2-D plot; case 1: d = 1mm, f = 1 mm and N = 2000 rpm
Fig. 4.2(a) 3-D plot; case 2: d = 1mm, f = 0.8 and N = 1600 rpm

39
Fig. 4.2(b) 2-D plot; case 2: d = 1mm, f = 0.8 and N = 1600 rpm
Fig. 4.3(a) 3-D plot; case 3: d = 1mm, f = 0.6 and N = 1200 rpm
Fig. 4.3(b) 2-D plot; case 3: d = 1mm, f = 0.6 and N = 1200 rpm

40
From the wavelet transform plots, it is quite evident that only wavelet transform is not suitable to
detect chatter when the signals are contaminated with noise. In the figures we can see many peaks
at various frequencies. Thus it is not possible to properly denoise the signal and extract the chatter
frequency by employing only wavelet transform. So, in order to eliminate this drawback a new
hybrid approach combining wavelet packet transform and Hilbert – Huang transform is proposed.
4.2 Wavelet packet transform
WPT is a generalization of CWT. Instead of just decomposing the low frequency components,
WPT splits both the low-pass band and high-pass band at all stages so that a more precise
frequency-band partition over the whole frequency range is generated. Thus, the frequency
resolution is enhanced.
Although HHT is a powerful time–frequency analysis method, it is still not a perfect tool to extract
signal features in practical applications, especially when the signal-to-noise ratio (SNR) of the
measured data is low. A preprocessor to denoise the measured signal may enhance the performance
of the HHT remarkably. The noises are often background disturbances whose frequency band
overlaps with the interested signals. Thus, it is difficult to eliminate the noise effectively with
general filters. An orthogonal discrete wavelet transform (DWT) can compress the ‘‘energy’’ of
the signal in a relatively small number of big coefficients, while the energy of the white noise will
be dispersed throughout the transform with relatively small coefficients. However, DWT provides
poor frequency resolution for the high frequency components of a signal. Therefore, the wavelet
transform is not a suitable method for analyzing the signal with great quantity of middle- and high-
frequency information. Alternatively, the wavelet packet transform (WPT) provides the same
frequency resolution in the full frequency range, which may be a good choice of the preprocessor
for the HHT. In this study, HHT with WPT as a preprocessor is introduced to detect the chatter in
the turning process. The vibration signals are first decomposed by WPT, and then the wavelet
packets with rich chatter information are selected for HHT. The mean value and standard deviation
of the Hilbert–Huang spectrum are calculated to identify the chatter.
A vibration signal x(t) is decomposed by the WPT, and the decomposed frequency-band signal x
i,j
is produced, where x
i,j
denotes the jth frequency-band signal at level i (j=1, 2, .., J) where J is the
number of decomposed frequency-band signals. Where i is the number of decomposition levels.
As an illustration, the three-level WPT decomposition process of x(t) is displayed in Fig. 4.4.

41
Fig. 4.4 Three-level WPT decomposition process of x(t)
4.3 Hilbert–Huang transform
HHT essentially consists of two steps: empirical mode decomposition (EMD) and Hilbert
transform. By EMD, a complicated signal is decomposed into a series of simple oscillatory modes,
designated as intrinsic mode function (IMF), and a residue. Hilbert transform is then invoked for
each IMF to obtain the instantaneous frequencies and the instantaneous magnitudes, which
comprise the Hilbert–Huang spectrum of the signal.
Given an arbitrary signal x(t), following the EMD method, finally a decomposition of the signal
into N IMFs and a residue rN can be achieved and shown as;
 
1
N
n N
n
x t c r

  (4.1)
The IMFs, c1, c2,... cN, are nearly mono component signals and include different frequency bands
ranging from high to low. The frequency components contained in each frequency band are
different and they change with the variation of signal x(t), while rN represents the central tendency
of signal x(t).
Hilbert transform can be thought of as the convolution of signal x(t) with the function;
 1
( )
x
H t d
t


 



 (4.2)
Combining x(t) and H(t), we can obtain the analytic signal z(t) of x(t).

42
         ij t
z t x t iH t a t e   (4.3)
where,
     2 2
a t x t H t  is the instantaneous amplitude of x(t)
 
 
 
arctan
H t
t
x t
  is the instantaneous phase of x(t)
If the signal x(t) is mono component, then the instantaneous frequency is given by;
 
 d t
t
dt

  (4.4)
As discussed before, the EMD can generate almost mono component IMFs. Applying the Hilbert
transform to each IMF, and calculating the instantaneous frequency and amplitude, we can express
signal x(t) in the following form;
      
1
exp
N
n n
n
x t a t i t dt

   (4.5)
Using Eq. (4.5), the signal x(t) can be mapped to a two dimensional time–frequency plane. The
time–frequency distribution of the amplitude is the so called Hilbert–Huang spectrum.
4.4 Proposed chatter detection methodology
The task for the chatter detection is to find out the chatter frequencies from the measured signals.
In the machining process, the measured data are usually contaminated by the background noise.
The suppression or elimination of noise is critical for the feature extraction of the chatter. Since
the noises are broadband, a natural and intuitive idea is to decompose the measured data to some
narrow band components so that the energy of the noise is dispersed in these narrow bands. The
chatter signal may be allocated in a frequency band and then the SNR will be enhanced. It is well
known that WPT is orthogonal, complete, local and computing efficient, which may be a perfect
tool to solve this problem. Then, EMD operation is used on those narrow band signals, and thus
the obtained IMFs will also have narrow frequency bands and their instantaneous frequencies will
be more close to the chatter frequency pattern.
The framework of the proposed chatter detection scheme is illustrated in Fig. 4.5. At the very
beginning, simulink model is used to simulate the signals (e.g., vibration) generated in the
machining process. Then the proposed chatter identification procedure starts, which consists of

43
four steps. First, the measured signals are decomposed by the WPT, so that the chatter signals are
allocated in a certain frequency band. Second, wavelet packets with rich chatter information are
selected as feature packets and then reconstructed. Third, HHT is used to analyze the reconstructed
signals, and the Hilbert–Huang spectrum, which is a full time– frequency–energy distribution of
the signal, is obtained. Finally, the mean value and standard deviation of the Hilbert–Huang
spectrum are calculated to identify the chatter.
Fig. 4.5 Flowchart of the proposed methodology
4.5 Simulation
The simulated chatter signal consists of three components.
The first two components are two sinusoidal waves with low and high frequencies, respectively.
Considering modulation is a typical mode appearing in the chatter vibration signals, amplitude and
phase modulation component with relatively small amplitudes is added as the third component.
The simulated chatter signal and its three components are shown in Figs. 4.6 (a)-(d), respectively.
The spectrum of the simulated chatter signal is shown in Fig. 4.7. It can be seen that the modulation
component is very weak compared with the sinusoidal waves.

44
Fig. 4.6 Three components and simulated chatter signals: (a) modulation component, (b) high-
frequency sinusoidal wave, (c) low-frequency sinusoidal wave and (d) simulated chatter signal
Fig. 4.7 Spectrum of the simulated chatter signal
The simulated chatter signal is pre-processed with WPT first. The decomposition level is 3, and
eight wavelet packets (x3,j, j= 1,2,3,...,8) are obtained accordingly. The second wavelet packet x3,2
with frequency-bandwidth of 50–250Hz is selected and reconstructed ,as shown in Fig. 4.8.

45
Fig. 4.8 Reconstructed wavelet packets x3,2 of the simulated chatter signals
Initially the signal is decomposed using empirical mode decomposition, known as intrinsic mode
functions (IMFs) as shown in Fig. 4.9 for a sample cutting conditions.
Fig. 4.9 Intrinsic mode function up to five levels

46
HHT is performed on the reconstructed wavelet packet to obtain the Hilbert–Huang spectrum. The
modulation component that indicates the chatter is extracted clearly. In order to demonstrate the
efficiency of the WPT preprocessor, the time–frequency spectrum of the simulated chatter signal
using the HHT is presented in both 2 and 3-D time frequency spectrum as shown in Fig. 4.10.
From these plots it is quite evident that by adopting the proposed methodology, noise frequency
is eliminated. Peaks are only for the chatter frequency. Moreover, it is also clear that without the
WPT pre-processor, the Hilbert–Huang spectrum cannot reveal the chatter phenomenon.
Fig. 4.10 (a) 3-D spectrum of the simulated signal using HHT with WPT pre-processor
Fig. 4.10 (b) 2-D HHT spectrum using WPT pre-processor
Although there is obvious dissimilarity between Hilbert– Huang spectra under different working
conditions, other numerical parameters are still needed to more easily identify the cutting state.
The mean value and standard deviation of the Hilbert–Huang spectra are calculated to find proper
indices for chatter identification, as listed in Table 4.1. The mean value of the Hilbert–Huang
1
0.8
0.6
0.4
0.2
0 50
100
150
200
250
Tim
e
(s)
Frequency (Hz)
0
4
8
12
16
20
Amplitude(

m)
3.xls
Continuous Wavelet Time-Frequency Spectrum
1.xls
Continuous Wavelet Time-Frequency Spectrum
0 0.2 0.4 0.6 0.8 1
Time (s)
0
50
100
150
200
250
300
Frequency(Hz)

47
spectrum represents the vibration amplitude in the machining process. When chatter happens, the
vibration is strengthened and the vibration amplitude will increase. The standard deviation of the
Hilbert–Huang spectrum reveals the uneven degree of vibration amplitude in the given frequency
range. When chatter occurs, the vibration energy centralizes around the chatter frequencies and
hence the uneven degree increases, which lead to increase of the standard deviation. In the stable
cutting process, the mean value and standard deviation are 1.43 and 0.08. For the slight chatter
case, the mean value and standard deviation increase to 2.6 and 0.14, and for the severe chatter
case, these values increase to 9.39 and 0.44. Therefore, the mean value and standard deviation of
the Hilbert–Huang spectra can be used as indices to simply identify the chatter.
Table 4.1 Mean and standard deviation of the three cases of chatter
Chatter Indices Case1:Stable
cutting
Case2:Slight
chatter
Case3:Severe
Chatter
Mean value 1.43 2.60 9.39
Standard
deviation
0.08 0.14 0.44

Analysis of tool chatter in turning operation on lathe machine

Analysis of tool chatter in turning operation on lathe machine

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