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 ENGINEERINGJAYPEE UNIVERSITY OF ENGEENERING AND TECHNOLOGY
A-B ROAD, RAGHOGARH, DT. GUNA-473226, MP., INDIA
JAYPEE UNIVERSITY OF ENGINEERING & TECHNOLOGYMECHANICAL ENGINEERING DEPARTMENT
A.B.ROAD,P.B.No.1, RAGHOGARH, DIST: GUNA (M.P) INDIAPHONE : 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 SinghLecturerMechanical Engineering DepartmentJUET, 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........................................................................................................................................iiAcknowledgement..........................................................................................................................iiiAbstract..........................................................................................................................................ivChapter 1.........................................................................................................................................1Introduction.....................................................................................................................................11.1 Background................................................................................................................................11.2 Tool chatter in machine tools....................................................................................................11.3 Chatter suppression techniques.................................................................................................21.4 Problem definition.....................................................................................................................41.5 Methodology adopted................................................................................................................51.6 Organization of the thesis..........................................................................................................5Chapter 2.........................................................................................................................................7Literature survey..............................................................................................................................72.1 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).......................................................................132.2 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..............................................................................................23Chapter 3.......................................................................................................................................25Theoretical analysis of tool chatter................................................................................................253.1 Dynamics of orthogonal turning during chatter......................................................................253.2 Simulink model.......................................................................................................................29Chapter 4.......................................................................................................................................37Wavelet packets and hilbert–huang transform..............................................................................374.1 Wavelet transform...................................................................................................................374.2 Wavelet packet transform........................................................................................................404.3 Hilbert–Huang transform.........................................................................................................414.4 Proposed chatter detection methodology.................................................................................424.5 Simulation................................................................................................................................43Chapter 5.......................................................................................................................................48Chatter quantification using response surface methodolgy (rsm).................................................485.1 Introduction.............................................................................................................................485.2 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..................................................................59Chapter 6.......................................................................................................................................60Summary and scope for further research.......................................................................................606.1 Summary and conclusions.......................................................................................................606.2 Scope for further research.......................................................................................................61References.....................................................................................................................................62
List of Figures
Figure 3.1(Various Experiments of bitumen)……………………………………………...….....18Figure 4.1(Washing of aggregates)...............................................................................................21
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Figure 4.2(Heating of aggregates and shredded plastic)...............................................................22Figure 4.3(Plastic coated aggregates)............................................................................................22Figure 4.4(Impact value, Crushing value and Los angles apparatus)............................................23Figure 4.5(Marshall Test)………………………………………………………………………..23Figure 5.1(Phase diagram of Marshall Specimen)….……………………………………...33Figure 5.2(Grading requirement of fresh aggregate)……………...………………………..…....34Figure 5.3(TABLE-8OF IRC: 111-2009)…………………………………………………….….34Figure 5.4(Interaction model for the Plastics waste coated aggregate bitumen mix).....……..….46
List of Tables and Graph s
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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
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operations are associated with 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.
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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.
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> b lim. Therefore, blim is
the most important parameter for the stability of cutting. The value of b lim 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
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different lobes (n = 1, 2, 3 ...) 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.
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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 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
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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 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.
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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. 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 work- piece 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
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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.
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
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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
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
13
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 work- piece. 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.
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.
14
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 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
15
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 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
16
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 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
17
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
characteristic 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 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
18
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 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
19
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 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
20
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 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.
21
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
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 turn- ing 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.
22
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 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 work- piece 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
23
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.
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.
24
CHAPTER 3 THEORETICAL ANALYSIS OF TOOL CHATTER
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
25
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
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
26
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
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:
(3.1)
where,
= cutting force in feed (x) direction= (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;
27
(3.3)
Applying Laplace transform and using relations,
, and assuming
(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;
(3.5)
Substituting in Eq. (3.5), where is the chatter vibration frequency, the real and
imaginary parts of the transfer function are found as;
(Real part) (3.6a)
(Imaginary part) (3.6b)
where,
(Denominator)
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;
(3.7)
The stability equation leads to a positive real depth of cut only when the real part 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 is considered. Defining the
phase angle;
28
and with some mathematical manipulation, the spindle period (T) and phase shift (θ) can be
obtained as;
, (3.8)
The spindle speed can be obtained by;
(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 from the transfer function where the real part is negative, e.g., .
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.
29
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=1200 rpm, f0=1 mm/ rev, b=2 mm, and the
input gain kp=1000.
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=1200 rpm. 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.
30
During the simulation, function ode45 in the simulink tool box was used to generate chaotic
signals, e.g., 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 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.
2.xls
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31
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Fig. 3.7 Simulated; case 3: depth of cut = 3 mm, feed = 0.6 mm/rev and speed = 1200 rpm5.xls
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Fig. 3.8 Simulated; case 4: depth of cut = 1 mm, feed = 0.8 mm/rev and speed = 1200 rpm
32
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Fig. 3.11 Simulated; case 7: depth of cut = 2 mm, feed = 0.8 mm/rev and speed = 1200 rpm
33
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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.
34
Fig. 3.13 FFT; case 1: depth of cut = 1 mm, feed = 0.6 mm/rev and speed = 1600 rpm
Fig. 3.14 FFT; case 2: depth of cut = 1 mm, feed = 0.6 mm/rev and speed = 2000 rpm
Fig. 3.15 FFT; case 3: depth of cut = 2 mm, feed = 0.8 mm/rev and speed = 1200 rpm
35
Fig. 3.16 FFT; case 4: depth of cut = 2 mm, feed = 0.6 mm/rev and speed = 1600 rpm
Fig. 3.17 FFT; case 5: depth of cut = 1 mm, feed = 0.6 mm/rev and speed = 1200 rpm
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.
36
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
37
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.
Fig. 4.1(a) 3-D plot; case 1: d = 1mm, f = 1 mm and N = 2000 rpm
38
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
Fig. 4.2(b) 2-D plot; case 2: d = 1mm, f = 0.8 and N = 1600 rpm
39
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
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
40
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
xi,j
is produced, where xi,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;
(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;
(4.2)
42
Combining x(t) and H(t), we can obtain the analytic signal z(t) of x(t).
(4.3)
where,
is the instantaneous amplitude of x(t)
is the instantaneous phase of x(t)
If the signal x(t) is mono component, then the instantaneous frequency is given by;
(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;
(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.
43
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
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.
44
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.
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
45
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.
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.
46
Fig. 4.9 Intrinsic mode function up to five levels
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 pre- processor, 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.
47
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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 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
48
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 Case 1: Stable cutting
Case 2: Slight chatter
Case 3: Severe Chatter
Mean value 1.43 2.60 9.39
Standard deviation
0.08 0.14 0.44
49
CHAPTER 5 CHATTER QUANTIFICATION USING RESPONSE SURFACE
METHODOLGY (RSM)
5.1 Introduction
Chatter in turning is a non linear phenomenon and dependent on a number of cutting parameters.
Correct assessment of these parameters is essential to quantify the severity of chatter in turning.
There are a number of parameters such as; speed, feed and depth of cut, affecting chatter which
cannot be assessed correctly using the classical theory. Alternatively, experiments are performed
to ascertain the effectiveness of these parameters on chatter. Turning operation is extensively
performed in many modern industries to fabricate the structures. The main problem faced in the
manufacture of these structures is the selection of optimum combination of input variables for
achieving the required chatter free turning. This problem can be solved by developing the
mathematical models through effective and strategic planning and executing experiments by
RSM. Response surface methodology (RSM) is a technique used to determine and represent the
cause and effect of relationship between true mean responses and input control variables
influencing the responses as a n-dimensional hyper surface. The present investigation highlights
the use of RSM by designing a three-factor three-level Full Factorial design matrix with full
replication of planning, conducting, executing and developing the mathematical models. This is
useful for predicting the severity of chatter during turning.
5.2 Response surface methodology (RSM)
RSM is a collection of mathematical and statistical data that are useful for the modeling and
analysis of problems in which a response of interest is influenced by several variables with an
objective to optimize the response. RSM also quantifies the relationships among one or more
measured responses and the input factors. Response surface methodology (RSM) explores the
relationships between several control variables to develop a mathematical model for the
response. However, an experimental design involves choosing the appropriate combination of
various factors and the levels of each factor for developing a model. Since experimental runs
cost both time and money, it is pertinent to minimize the number of runs without compromising
50
the desired goals. In order to achieve this, some strategies such as; Full Factorial (FF), Box–
Benhken (BB), Central Composite Designs (CCD) etc. are frequently used.
The CCD design of experiment (DOE) allows the designer to utilize 3 levels for each factor
(with each factor placed at one of each equally spaced value to ensure orthogonality and near
rotatability) to adequately quantify second-order response models in 15 runs, inclusive of 3-
replicated center points of a cubical design region. However, Full Factorial (FF) designs use
different levels of various factors with every level of each factor combining with those of other
factors. They are good for first-order response models, enabling the estimation of main and
interaction effects. However, as the number of factors and levels increase, the number of
requisite runs becomes cost and time prohibitive, and therefore the Taguchi designs, and
fractional factorial design are utilized for product improvement and cost reduction. However, the
Taguchi designs suffer a major inadequacy of handling interaction and confounding effects.
Weaknesses of the Taguchi designs such as;
Unnecessary complication using inner and outer arrays.
Non-recognition of randomized experiments to save the cost of changing level settings.
Non- applicability of orthogonal arrays to processes involving factors that vary with time and
cannot be quantified exactly, and noise factors may not always be independent of one another.
The techniques require the designer to be aware of all control and noise factors affecting a
product or process.
Minitab-14 software are used to develop the experimental plan for RSM. The same software was
also used to analyze the data collected by following the steps as follows:
Choose a transformation if desired. Otherwise, leave the option at “None”.
Select the appropriate model to be used. The Fit Summary button displays the sequential F-tests,
lack-of-fit tests and other adequacy measures that could be used to assist in selecting the
appropriate model.
Perform the analysis of variance (ANOVA), post-ANOVA analysis of individual model
coefficients and case statistics for analysis of residuals and outlier detection.
Inspect various diagnostic plots to statistically validate the model.
If the model looks good, generate model graphs, i.e., the Contour and 3D graphs, for
interpretation. The analysis and inspection performed in steps (3) and (4) above will show
whether the model is good or otherwise. Very briefly, a good model must be significant and the
51
lack-of-fit must be insignificant. The various coefficient of determination, R2 values should be
close to 1. The diagnostic plots should also exhibit trends associated with a good model and
these have been elaborated subsequently.
Multiple response optimizations are performed either by inspecting each response on the
interpretation plots or using the graphical and numerical tools. Moreover, RSM designs also help
to quantify the relationships between one or more measured responses and the input factors. The
data collected is analyzed statistically using regression analysis to establish a relationship
between the input factors and response variables. Regression is performed in order to develop a
functional relationship between the estimated variables. The performance of the model depends
on a large number of factors which interact in a complex manner. A second order response
surface model is usually expressed as:
(5.1)
where, , (i = 1, 2 . . . z), (i = 1, 2 . . . z) and (i = 1, 2 . . . z-1, j = 2,3 . . . z) are the
unknown regression coefficients to be estimated by using the method of least squares. In this
expression; x1, x2. . . xz are the input variables that influence the response (R), z is the number of
input factors. The response surface analysis is then done in terms of the fitted surface. The
method of least squares is used to estimate the coefficients of the second order model. The
response surface analysis is then carried out in terms of the fitted surface. The least square
technique is used to fit a model equation containing the input variables by minimizing the
residual errors measured by the sum of square deviations between the actual and the estimated
responses. This involves the calculation of estimates for the regression coefficients, i.e., the
coefficients of the model variables including the intercept or constant term. The calculated
coefficients or the model equation is to be tested for statistical significance. In this respect, the
following tests are performed.
5.2.1 Test for significance of the regression model
This test is performed as an ANOVA procedure by calculating the F-ratio, which is the ratio
between the regression mean square and the mean square error. The F-ratio, also called the
variance ratio, is the ratio of variance due to the effect of a factor (in this case the model) and
52
variance due to the error term. The F-ratio representing the test statistics for multiple
independent variables is mathematically expressed by;
(5.2)
where and are the mean square of the model and residual, respectively.
Mean square (MS) is mathematically defined as the difference between the individual
experimental values and the mean of all the experimental values in the set of experimental data.
The mean square of the model is used to estimate the model variance given by the model sum of
squares divided by the model degrees of freedom. The mean square of the residual is used to
estimate the process variance.
The significance level “β” for a given hypothesis test is a value for which a P-value less than or
equal to “β” is considered to be statistically significant. Typical value for “β” considered in the
present study is 0.05. This value corresponds to the probability of observing an extreme value by
chance.
5.2.2 Test for significance on individual model coefficients
This test forms the basis for model optimization by adding or deleting coefficients through
backward elimination, forward addition or stepwise elimination/addition/exchange. It involves
the determination of the P-value or probability value relating the risk of falsely rejecting a given
hypothesis. The P-value is the probability of rejecting the hypothesis. In statistics, a given
hypothesis is rejected if the P- value is more than 0.05. “Prob. > F” value on an F-test indicates
the proportion of time expected to get the stated F-value if no factor effects are significant. In
general, the lowest order polynomial is considered for adequately describing the system.
5.2.3 Test for lack-of-fit
As replicate measurements are available, a test indicating the significance of the replicate error
compared to the model dependent error can be performed. This test splits the residual or error
sum of squares into two portions; one is due to pure error based on the replicate measurements
and the other due to lack-of-fit because of model performance. The test statistic for lack-of-fit is
the ratio between the lack-of-fit mean square and the pure error mean square. As established, this
53
F-test statistic can be used to determine whether the lack-of-fit error is significant or not at the
desired significance level, β. Insignificant lack-of-fit is desired as significant lack-of-fit indicates
that there might be contributions in the input variables–response relationship that are not
accounted for in the model. Additional checks are required to determine whether the model
actually describes the experimental data or not. The checks performed include determining the
variance coefficient of determination, R2. These R2 coefficients have values between 0 and 1.
R2 is the variation between the mean of the residuals and the individual parameters. It is
mathematically expressed by;
(5.3)
where is the summation of the squares of the individual experimental values that are
included in the model. is the summation of the squares of the individual experimental
values which are not included in the model.
In addition to the above, the adequacy of the model is also investigated by examining the
residuals. The residuals represent the differences between the observed and predicted responses.
It is examined using the normal probability plots and the plots of the residuals versus the
predicted response. If the model is adequate, the points on the normal probability plot should
form a straight line. On the other hand, the plots of the residuals versus the predicted response
normally do not follow any definite pattern.
In the present study RSM has been adopted to ascertain the influence of various parameters on
the chatter mechanism in turning. The input variables are depth of cut (d), feed (f) and speed (N)
and the output response is the chatter amplitude (A).
5.3 Response surface regression for chatter amplitude
A polynomial model of second order type has been proposed to represent the relationship
between the amplitude and independent input variables. The performance of the model depends
on a large number of factors that can interact in a complex manner. In the present work, the input
variables are depth of cut (d), feed (f) and speed (N) and the output response is the chatter
amplitude (A). A full factorial design is used with three design factors for each of three levels to
describe responses, to estimate the parameters in the second-order model. Overall 33 = 27 free
54
chatter vibration simulation runs have been conducted to evaluate the responses. The important
factors and their levels are shown in Table 5.1.
Table 5.1 Design of simulation runs
Sl. No. d (mm) f (mm/rev) N (rpm) A (um)1 0.6 1 1200 5.552 0.6 1 1600 6.223 0.6 1 2000 7.454 0.6 2 1200 9.115 0.6 2 1600 11.116 0.6 2 2000 12.997 0.6 3 1200 16.228 0.6 3 1600 18.989 0.6 3 2000 21.8210 0.8 1 1200 11.6511 0.8 1 1600 13.4212 0.8 1 2000 16.1813 0.8 2 1200 19.2214 0.8 2 1600 22.615 0.8 2 2000 26.5316 0.8 3 1200 27.8717 0.8 3 1600 32.8818 0.8 3 2000 37.1619 1 1 1200 27.1120 1 1 1600 31.1721 1 1 2000 34.9222 1 2 1200 45.523 1 2 1600 51.2124 1 2 2000 62.725 1 3 1200 84.2226 1 3 1600 111.1727 1 3 2000 123.36
The full quadratic model for chatter amplitude is expressed in term of the uncoded values of the
independent variables as;
(5.4)
55
5.3.1 Analysis of variance (ANOVA)
Analysis of variance (ANOVA) has been performed to determine the significant and non-
significant parameters as well as to validate the full model as given in expression (5.4). The
ANOVA has been carried out on the model for a confidence level of 95%. The results of
ANOVA performed on the full model have been listed in Tables 5.2 - 5.4.
Table 5.2 Estimated regression coefficient for the full quadratic model
Term Coef SE Coef T P Constant 334.424 86.552 3.864 0.001 d (mm) -706.744 142.501 -4.960 0.000 f (mm/rev) -81.493 18.797 -4.336 0.000 N (rpm) -0.038 0.071 -0.537 0.598 d (mm)*d (mm) 369.153 82.641 4.467 0.000 f (mm/rev)*f (mm/rev) 5.856 3.306 1.772 0.094 N (rpm)*N (rpm) -0.000 0.000 -0.134 0.895 d (mm)*f (mm/rev) 78.229 11.687 6.694 0.000 d (mm)*N (rpm) 0.055 0.029 1.881 0.077 f (mm/rev)*N (rpm) 0.008 0.006 1.419 0.174 S = 8.097 R-Sq = 95.4% R-Sq(adj) = 92.9%
From the table the parameters and their interaction terms for which the value of “P” is greater
and equal to 0.05 are eliminated by using back propagation elimination approach. Finally we get
the reduced quadratic model given by;
(5.5)
Table 5.3 Estimated regression coefficient for the reduced quadratic model
Term Coef SE Coef T P Constant 246.28 67.65 3.641 0.001 d (mm) -618.79 166.42 -3.718 0.001 f (mm/rev) -44.80 11.80 -3.798 0.001 d (mm)*d (mm) 369.15 102.17 3.613 0.002 d (mm)*f (mm/rev) 78.23 14.45 5.414 0.000
Table 5.4 Analysis of Variance
56
Source DF Seq SS Adj SS Adj MS F P Regression 4 21788 21788 5447.09 54.36 0.000 Linear 2 17543 2419 1209.66 12.07 0.000 Square 1 1308 1308 1308.23 13.06 0.002 Interaction 1 2938 2938 2937.51 29.31 0.000 Residual Error 22 2205 2205 100.21 Lack-of-Fit 4 1113 1113 278.20 4.59 0.010 Pure Error 18 1092 1092 60.65 Total 26 23993
5.3.2 Surface and contour plots
The effects of the parameter interactions in the form of response surfaces and contour plots on
chatter vibration are shown in Figs. 5.1–5.3.
0
A (um)
15
30
2f (mm/ rev)
1 2
30
45
120033
1600
1200
2000
N (rpm)
Hold Valuesd (mm) 0.8
Surface Plot of A (um) vs N (rpm), f (mm/ rev)
Fig. 5.1(a) Surface plot: Effect of feed and speed on the chatter vibration
f (mm/ rev)
N (
rpm
)
3.02.52.01.51.0
2000
1900
1800
1700
1600
1500
1400
1300
1200
Hold Valuesd (mm) 0.8
A (um)
20 - 3030 - 4040 - 50
> 50
< 1010 - 20
Contour Plot of A (um) vs N (rpm), f (mm/ rev)
Fig. 5.1(b) Contour plot: Effect of feed and speed on the chatter vibration
57
0
A (um)
20
40
0.8d (mm)
20
0.6
20
40
0.8
60
1.01.0
1600
2000
1200
2000
1600 N (rpm)
Hold Valuesf (mm/rev) 2
Surface Plot of A (um) vs N (rpm), d (mm)
Fig. 5.2 (a) Surface plot: Effect of depth of cut and speed on the chatter vibration
d (mm)
N (
rpm
)
1.00.90.80.70.6
2000
1900
1800
1700
1600
1500
1400
1300
1200
Hold Valuesf (mm/rev) 2
A (um)
20 - 3030 - 4040 - 5050 - 60
> 60
< 1010 - 20
Contour Plot of A (um) vs N (rpm), d (mm)
Fig. 5.2 (b) Contour plot: Effect of depth of cut and speeds on the chatter vibration
A (um)
0
50
0.60.8
d (mm)
0.60.8
A (um)
100
11.01.0
2 f (mm/ rev)1
3
f (mm/ rev)
Hold ValuesN (rpm) 1600
Surface Plot of A (um) vs f (mm/ rev), d (mm)
Fig. 5.3 (a) Surface plot: Effect of depth of cut and feed on the chatter vibration
58
Fig. 5.3 (b) Contour plot: Effect of depth of cut and feed on the chatter vibration
From these plots it is evident that with the increase in depth of cut, feed and speed the chatter
vibration increases.
5.3.2 Plots of main effects of interaction parameters on chatter amplitude
The plot of main effects for chatter amplitude is shown in Fig. 5.4. These plots are used to
compare the changes in the mean levels to know the factors which influence the response the
most. The inclination of speed effect line with respect to the X-axis is least among the three
parameters, which indicates that the effect of speed is least. Further, the slope of depth of cut is
more than the feed line, with respect to the X-axis which shows that the effect of depth of cut is
more pronounced than feed on chatters amplitude as evident from Fig. 5.4.
59
Me
an
of
A (
um
)
1.00.80.6
60
40
20
321
200016001200
60
40
20
d (mm) f (mm/rev)
N (rpm)
Main Effects Plot (data means) for A (um)
Fig. 5.4 Main effects plot: (a) Response is chatter amplitude
5.3.3 Residual plots for chatter vibration
The regression model is used for determining the residuals of each individual experimental run.
The difference between the measured values and predicted values are called residuals. The
residuals are calculated and ranked in ascending order. The normal probabilities of residuals for
chatter vibration is shown in Fig. 5.5. The normal probability plot is used to vary the normality
assumptions. The data are spread roughly along the straight line for chatter amplitude, indicating that
the data are normally distributed.
Residual
Perc
ent
3020100-10-20
99
95
90
80
70
605040
30
20
10
5
1
Normal Probability Plot of the Residuals(response is A (um))
Fig. 5.5 Normal probability plot of the residuals
60
Fig. 5.6 shows the residuals against the observation order. This plot is used to show the
correlation between the residuals. From this plot, it is emphasized that a tendency to have runs of
positive and negative residuals indicates the existence of a certain correlation. Also the plots
show that the residuals are distributed evenly in both positive and negative directions along the
run. Hence, the data is said to be independent.
Observation Order
Re
sid
ua
l
2624222018161412108642
30
20
10
0
-10
-20
Residuals Versus the Order of the Data(response is A (um))
Fig. 5.6 Residual versus order of the data
Fig. 5.7 indicates the residuals versus fitted values, showing the maximum variation of -20 to 30
between the measured and the fitted values. These plots do not reveal any obvious pattern and
therefore the fitted models are ample. A low value 0.010 of lack of fit establishes that the
developed model is statistically significant.
Fitted Value
Resi
dual
100806040200
30
20
10
0
-10
-20
Residuals Versus the Fitted Values(response is A (um))
61
Fig. 5.7 Residuals versus the fitted values
5.3.4 Checking adequacy of mathematical models
The goodness of fit for the mathematical models has also been tested by coefficient of
determination (R2) and adjusted coefficient of determination (R2adj). The R2 is the proportion of
the variation in the dependent variable explained by the regression model. On the other hand,
R2adj is the coefficient of determination adjusted for the number of independent variables in the
regression model. Unlike R2, the R2adj may decrease if the variables considered in the model do
not add significantly to the model fit. The R2 and R2adj values of mathematical model for chatter
amplitude are found to be 95.4% and 92.9%, respectively which clearly establish the excellent
correlation between the experimental and the predicted values of the responses.
In the present chapter, response surface methodology has been adopted to quantify the
dependence of chatter vibration amplitude on cutting parameters such as; depth of cut, feed and
speed. A statistical full quadratic model is developed, using the ANOVA interaction parameters
having less influence on the response is determined considering 95% confidence level. Further,
back elimination propagation technique is used to eliminate these non influential parameters
from full quadratic model and finally reduced quadratic model is developed as given by
expression 5.5. Moreover, statistical analysis is done to check the significance of this reduced
model.
62
CHAPTER 6 SUMMARY AND SCOPE FOR FURTHER RESEARCH
The aim of this thesis is to explore the mechanism of tool chatter in turning operation.
Motivation for this study stems from the need to suppress tool chatter during turning in order to
improve its dynamic performance and tool life. Keeping these objectives in view, theoretical and
signal processing analyses have been carried out in chapters 3-4. Quantification of chatter
amplitude and its dependence on various cutting parameters have been presented in chapter 5.
This chapter summarizes the important conclusions drawn from the observations discussed in the
previous chapter along with some suggestions for continuing future research in this field.
6.1 Summary and conclusions
In this study, a chatter identification method for the turning process was presented. Theoretical
analysis has been done to develop the mathematical model of dynamic equilibrium equation
considering process damping. This mathematical model was utilized to develop a simulink
model in order to simulate the chatter signal in noisy environment. Further, a new hybrid signal
processing technique (combination of WPT and HHT) has been proposed to predict and detect
the chatter in turning operation. To enhance the performance of HHT, WPT was used as
preprocessor to decompose the measured signal into a set of narrow band at first. Then, wavelet
packets with rich chatter information were selected as feature packets and then reconstructed.
HHT was utilized to analyze the reconstructed signals, and the Hilbert–Huang spectrum was
obtained. To extract the chatter characteristics, the mean value and standard deviation of the
Hilbert–Huang spectrum are calculated as chatter indices. The proposed method was verified
through case studies (i.e., stable, slight chatter and severe chatter), and the results have shown
that:
a) HHT with the WPT preprocessor works more efficiently than individual HHT for chatter
detection. Without preprocessing, the Hilbert–Huang spectrum of the measured vibration signal
cannot reveal the chatter phenomenon.
b) Both the mean value and the standard deviation of the Hilbert– Huang spectrum can reveal
chatter. The standard deviation is independent of cutting conditions and hence can be used in
different turning processes. The mean value can be used as an additional chatter index.
63
Moreover, response surface methodology has been invoked to develop the relation between the
chatter vibration amplitude and various cutting parameters such as; depth of cut, feed and speed.
Analysis of variance (AMOVA) has been done to check the statistical significance of the
developed model. Surface and main effects plot has been generated and from the response
surface analysis following conclusions has been developed;
(a) It was observed, depth of cut, feed and speed governs the phenomenon of tool chatter.
(b) With the increase in the values of these cutting parameters tool chatter amplitude drastically
increases.
(c) Depth of cut is the predominant governing factor among these three parameters.
6.2 Scope for further research
In the present investigation, the mechanism of tool chatter, its identification and the various
parameters affecting chatter amplitude have been presented in details to enable the engineers for
chatter free turning in real applications. However, the present study can be extended for further
research as enumerated below:
Tool chatter/wear state estimation can be accomplished by analyzing cutting forces and
vibration signals obtained from various sensors.
Establish a theoretical relationship between chatter vibration and tool wear which shows
effects of chatter vibrations on tool wear analytically.
Effects of self-excited chatter vibrations on tool wear can be ascertained.
Effect of other parameters such as; tool nose radius, chip thickness and cutting forces on
the severity of tool chatter can be considered.
64
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